How To Place Risk Pooling In Business Logistics

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2 Methods of Risk Pooling in Business Logistics and Their Application I n a u g u r a l d i s s e r t a t i o n zur Erlangung des akademischen Grades Doktor der Wirtschaftswissenschaften (Dr. rer. pol.) eingereicht an der Wirtschaftswissenschaftlichen Fakultät der Europa-Universität Viadrina in Frankfurt (Oder) im September 2010 von Gerald Oeser Frankfurt (Oder)

3 Uncertainty is the only certainty there is, and knowing how to live with insecurity is the only security. John Allen Paulos, Professor of Mathematics at Temple University in Philadelphia

4 To my brother, who never failed to support me

5 Acknowledgements First and foremost I would like to express my gratitude to my Ph.D. advisor Prof. Dr. Dr. h.c. Knut Richter, Chair of General Business Administration, especially Industrial Management, European University Viadrina Frankfurt (Oder), Germany for his extensive mentoring. He also kindly gave me the opportunity of gaining experience in teaching graduate courses in addition to my research. For willingly delivering his expert opinion on my thesis as the second referee I thank Prof. Dr. Joachim Käschel, Professorship of Production and Industrial Management, Technical University Chemnitz, Germany very much. I would also like to gratefully acknowledge the support of all employees of Prof. Richter's chair, especially Dr. Grigory Pishchulov: Among other things, he helped me carry out the Subadditivity Proof for the Order Quantity Function (5.1) in Appendix E mathematically formally correctly. Furthermore, I thank Prof. Dr. Dr. h.c. Werner Delfmann, Director of the Department of Business Policy and Logistics, University of Cologne, Germany for the opportunity offered and for showing me that the world cannot be explained by mathematics alone. Moreover, I appreciate the diverse support of the following professors during my Master's and doctoral studies: Ravi M. Anupindi (University of Michigan), Ronald H. Ballou (Case Western Reserve University), Gérard Cachon (University of Pennsylvania), Ian Caddy (University of Western Sydney, Australia), Sunil Chopra (Northwestern University), Chandrasekhar Das (emeritus, University of Northern Iowa), David Dilts (Oregon Health and Science University), Bruno Durand (University of Nantes, France), Philip T. Evers (University of Maryland), Amit Eynan (University of Richmond), Dieter Feige (emeritus, University of Nuremberg, Germany), Jaime Alonso Gomez (EGADE - Tec de Monterrey, Mexico City and University of San Diego), Drummond Kahn (University of Oregon), Peter Köchel (emeritus, Technical University Chemnitz, Germany), David H. Maister (formerly Harvard Business School), Alan C. McKinnon (Heriot-Watt University, UK), Esmail Mohebbi (University of West Florida), Steven Nahmias (Santa Clara University), Teofilo Ozuna, Jr. (The University of Texas-Pan American), David F. Pyke (University of San Diego), Pietro Romano (University of Udine, Italy), Wolfgang Schmid (European University Viadrina Frankfurt (Oder), Germany), Yossi Sheffi (Massachusetts Institute of Technology), Edward Silver (emeritus, University of Calgary, Canada), Jacky Yuk- Chow So (University of Macau, China), Jayashankar M. Swaminathan (University of

6 North Carolina), Christian Terwiesch (University of Pennsylvania), Ulrich Thonemann (University of Cologne, Germany), Biao Yang (University of York, UK), and Walter Zinn (The Ohio State University). I express gratitude to the paper merchant wholesaler Papierco for the insight into its operations, the opportunity of optimizing its logistics, and the financial support. I am also thankful to my friends: Without them writing this dissertation would have been a lonesome experience. Finally, I thank my father for constantly pushing and financially supporting me and proofreading my thesis.

7 Geleitwort Die vorgelegte Dissertation widmet sich dem großen Thema Risk Pooling in der Business- Logistik. Die Aggregation von Risiken der Logistikprozesse ist ein derart universelles Problem, so dass Autoren verschiedenster Wissenschafts- und Anwendungsgebiete dazu ihre Positionen, Lösungsansätze und Modelle dargestellt haben. Bisher hatte noch niemand den Mut aufgebracht, diese kaum überblickbare Menge an Literaturquellen zu sichten und nach wissenschaftlichen Kriterien zu ordnen. Herr Oeser hat sich dieser Aufgabe gestellt und hat sie mit Bravour gemeistert. Bei aller Bedeutung dieser aufwendigen akademischen Aktivitäten darf jedoch nicht vergessen werden, dass Risk Pooling ein Problem der Praxis ist, und dass die entsprechenden theoretischen Untersuchungen letztendlich der Praxis dienen sollen. Die Vielfältigkeit des Problems kann dabei kaum durch ein relevantes Basismodell erfasst werden. Es ist das Verdienst des Autors, mit der Entwicklung einer Grundkonzeption für ein Entscheidungsunterstützungssystem zur Auswahl der geeigneten Risk Pooling Strategien Unternehmen und besonders Unternehmensberatungen ein Instrument in die Hand zu geben, mit dem sich die vielfältigen Situationen der Unternehmen analysieren lassen. Er belässt es jedoch nicht beim Entwurf der Konzeption, sondern demonstriert auch überzeugend dessen Anwendung anhand eines Unternehmens. Es ließen sich viele weitere Vorzüge des hier veröffentlichten Werkes nennen. Es soll an dieser Stelle jedoch dem Leser überlassen bleiben sich ein Urteil zu bilden. Herr Oeser bietet dem Leser mit seiner Dissertation auf jeden Fall keine leichte Kost, denn der behandelte Gegenstand lässt eine oberflächliche Betrachtung nicht zu. Wer sollte dieses Werk lesen? Wissenschaftler und Studenten aus den Gebieten Operations Management, Logistik, Operations Research werden hier viel Neues und Interessantes, auch viele Probleme für die weitere Forschung finden. Unternehmensberatungen werden viele angeführte Lösungen zur Komplexitätsbewältigung in ihren Projekten anwenden können. Ich bin überzeugt, dass die vorgelegte Dissertation neue Forschungen und Projekte anregen wird. Das ist das Schönste, was sich ein Autor wohl wünschen kann. Prof. Dr. Dr. h.c. Knut Richter

8 Table of Contents List of Figures... X List of Tables... XI List of Abbreviations, Signs, and Symbols... XII Abstract... XIV 1 Introduction Problem: Growing Uncertainty in Business Logistics and Need for a Tool to Choose Among Risk Pooling Countermeasures Objective Object and Method Structure and Contents Risk Pooling in Business Logistics Business Logistics Risk Pooling Research Placing Risk Pooling in the Supply Chain, Business Logistics, and a Value Chain Defining Risk Pooling Explaining Risk Pooling Characteristics of Risk Pooling Methods of Risk Pooling Storage: Inventory Pooling Transportation Virtual Pooling Transshipments Procurement Centralized Ordering Order Splitting Production Component Commonality Postponement Capacity Pooling VII

9 Table of Contents 3.5 Sales and Distribution Product Pooling Product Substitution Choosing Suitable Risk Pooling Methods Contingency Theory Conditions Favoring the Individual Risk Pooling Methods The Risk Pooling Methods' Advantages, Disadvantages, Performance, and Trade-Offs A Risk Pooling Decision Support Tool Applying Risk Pooling at Papierco Papierco Problems Papierco Faces Fierce Competition in German Paper Wholesale Supplier Lead Time Uncertainty Customer Demand Uncertainty Distribution Requirements Planning (DRP) Demand Forecasting Methods Solving Papierco's Problems Determining Suitable Risk Pooling Methods for Papierco Emergency Transshipments between Papierco's German Locations Optimizing Catchment Areas Increase in Transshipments and Its Causes Transshipments Are Worthwhile for Papierco Centralized Ordering Papierco's Current Order Policy Stock-to-Demand Order Policy with Centralized Ordering and Minimum Order and Saltus Quantities Benefits of Centralized Ordering for Papierco Product Pooling Inventory Pooling Challenges in IT and Organization Summary Conclusion VIII

10 Table of Contents Appendix A: A Survey on Risk Pooling Knowledge and Application in 102 German Manufacturing and Trading Companies Introduction Motivation: Scarce Survey Research on Risk Pooling Objective The Survey Research Design Data Analysis and Findings Risk Pooling Knowledge and Utilization in the German Sample Companies Association between the Knowledge of Different Risk Pooling Concepts Association between Knowledge and Utilization of Risk Pooling Concepts Association of the Utilization of Different Risk Pooling Concepts Risk Pooling Knowledge and Utilization in the Responding Manufacturing and Trading Companies Knowledge and Utilization of the Different Risk Pooling Concepts in Small and Large Responding Companies Critical Appraisal Questionnaire Answers Appendix B: Proof of the Square Root Law for Regular, Safety, and Total Stock Appendix C: What Causes the Savings in Regular Stock through Centralization Measured by the SRL? Appendix D: Tables Appendix E: Subadditivity Proof for the Order Quantity Function (5.1) Bibliography IX

11 List of Figures Figure 2.1: Number of Publications on Risk Pooling in Business Logistics... 7 Figure 2.2: Placing Risk Pooling in Business Logistics... 9 Figure 2.3: Important Value Activities Using Risk Pooling Methods Figure 4.1: Risk Pooling Decision Support Tool Figure 5.1: Total Fine Paper Sales in Tons per Month in Germany (BVdDP 2010a: 8) Figure 5.2: Papierco's Total Fine Paper Sales to Customers in Germany in Tons per Month Figure 5.3: Papierco's 2007 Warehouse Sales to Customers per Week of Seven Standard Paper Products from the Hemmingen Warehouse Figure 5.4: 2007 Incoming Goods, Warehouse Sales, and Inventory at Warehouse Hemmingen Figure 5.5: 2007 Incoming Goods, Warehouse Sales, and Inventory at Warehouse Reinbek Figure 5.6: Comparison of Current and Optimal Catchment Areas of Papierco's Warehouses Figure 5.7: Inventory Turnover Curves for Papierco Figure 5.8a: Product Purchase Planning at Papierco's Member Companies Figure 5.8b: Product Purchase Planning at Papierco's Member Companies Figure 5.9: Stockkeeping at Papierco's Warehouses in February Figure A.1: Risk Pooling Knowledge and Utilization in the German Sample Companies Figure A.2: Risk Pooling Knowledge and Utilization in the Sample Manufacturing and Trading Companies Figure A.3: Knowledge and Utilization of the Different Risk Pooling Concepts in Small and Large Responding Companies Figure A.4: Questionnaire X

12 List of Tables Table 3.1: Risk Pooling Methods' Building Blocks Table 5.1: The Extent of Transshipments at Papierco Table 5.2: Effects of Centralized Ordering at Papierco Table A.1: Comparing Respondents with the Total Population of Manufacturing and Trading Companies in Germany Table A.2: Significant Correlations at the 5 % Level of the Knowledge of Risk Pooling Concepts Table A.3: Significant Correlations at the 5 % Level (except in the case Product Substitution/Demand Reshape) between Knowledge and Utilization of Risk Pooling Concepts Table A.4: Significant Correlations at the 5 % Level between the Utilization of Risk Pooling Concepts Table A.5: Survey Participants' Answers to the Questionnaire Table D.1: Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies Table D.2: Comparison of Important Inventory Consolidation Effect, Portfolio Effect, and Square Root Law Models Table D.3: Conditions Favoring the Various Risk Pooling Methods Table D.4 The Risk Pooling Methods' Advantages, Disadvantages, Performance, and Trade-Offs XI

13 List of Abbreviations, Signs, and Symbols Common general, business, logistics, supply chain management (SCM), operations research (OR), mathematical, and statistical abbreviations, signs, and symbols apply 1 and are not listed here. CC component commonality CE consolidation effect CO centralized ordering COE centralized ordering effect COV coefficient of variation of demand CP capacity pooling CS cycle stock Dipl.-Kfm. Diplomkaufmann (MBA equivalent) DP demand pooling DUR demand uncertainty reduction EFR effective fill rate for the customer ELT emergency lateral transshipment EOS economies of scale FR item fill rate IC inventory holding cost i. i. d. independent and identically distributed IP inventory pooling ITO in terms of LP lead time pooling LT lead time LTUR lead time or lead time uncertainty reduction n. e. c. not elsewhere classified NLT endogenous lead times OP order policy OS order splitting 1 Cf. e. g. Soanes and Hawker (2008), Friedman (2007), Lowe (2002), Obal (2006), Silver et al. (1998) and Slack (1999), Clapham and Nicholson (2009), and Dodge (2006). XII

14 List of Abbreviations, Signs, and Symbols PCE PE PM PoD PP PQE PRE PS RMSE RPDST RS SL SLA sqrt SRL SS TC TS TSC VP vs. XLT portfolio cost effect portfolio effect postponement point of (product) differentiation product pooling portfolio quantity effect proportional reduction of error product substitution root mean square error risk pooling decision support tool regular stock transshipment sending location service level adjustment square root square root law safety stock transportation cost transshipments transshipment cost virtual pooling versus, here: is traded off against exogenous lead times is approximately equal to is preferred to XIII

15 Abstract Purpose/topicality: Demand and lead time uncertainty in business logistics increase, but can be mitigated by risk pooling. Risk pooling can reduce costs for a given service level, which is especially valuable in the current economic downturn. The extensive, but fragmented and inconsistent risk pooling literature has grown particularly in the last years. It mostly deals with specific mathematical models and does not compare the various risk pooling methods in terms of their suitability for specific conditions. Approach: Therefore this treatise provides an integrated review of research on risk pooling, notably on inventory pooling and the square root law, according to a value-chain structure. It identifies ten major risk pooling methods and develops tools to compare and choose between them for different economic conditions following a contingency approach. These tools are applied to a German paper merchant wholesaler, which suffers from customer demand and supplier lead time uncertainty. Finally, a survey explores the knowledge and usage of the various risk pooling concepts and their associations in 102 German manufacturing and trading companies. Triangulation (combining literature, example, modeling, and survey research) enhances our investigation. Originality/value: For the first time this research presents (1) a comprehensive and concise definition of risk pooling distinguishing between variability, uncertainty, and risk, (2) a classification, characterization, and juxtaposition of risk pooling methods in business logistics on the basis of value activities and their uncertainty reduction abilities, (3) a decision support tool to choose between risk pooling methods based on a contingency approach, (4) an application of risk pooling methods at a German paper wholesaler, and (5) a survey on the knowledge and utilization of risk pooling concepts and their associations in 102 German manufacturing and trading companies. XIV

16 1 Introduction 1.1 Problem: Growing Uncertainty in Business Logistics and Need for a Tool to Choose Among Risk Pooling Countermeasures Product variety has increased dramatically in almost every industry 2 particularly due to increased customization 3. Product life cycles have become shorter, demand fluctuations more rapid, and products can be found and compared easily on the internet. 4 This causes difficulties in forecasting for an increased number of products, demand and lead time uncertainty, intensified pressure for product availability, and higher inventory levels 5 to provide the same service 6. This trend is expected to continue and likely grow worse. 7 Supply chains 8 are more susceptible to disturbances today because of their globalization, increased dependence on outsourcing and partnerships, single sourcing, little leeway in the supply chain, and increasing global competition. 9 Disruptions, such as production or shipment delays, affect profitability (growth in operating income, sales, costs, assets, and inventory). 10 Risk pooling is [o]ne of the most powerful tools used to address [demand and/or lead time] variability in the supply chain 11 particularly in a period of economic downturn 12, as it allows to reduce costs and to increase competitiveness Cox and Alm (1998), Van Hoek (1998a: 95), Aviv und Federgruen (2001a), Ihde (2001: 36), Piontek (2007: 86), Ganesh et al. (2008: 1124f.). Ihde (2001: 36), Chopra and Meindl (2007: 305), Piontek (2007: 86). Rabinovich and Evers (2003a: 226), Chopra and Meindl (2007: 305, 333). Dubelaar et al. (2001: 96). Ihde (2001: 36), Swaminathan (2001: 125ff.), Chopra and Meindl (2007: 305, 333), Rumyantsev and Netessine (2007: 1) Cecere and Keltz (2008). A supply chain consists of all parties involved, directly or indirectly, in fulfilling a customer request. The supply chain includes not only the manufacturer and suppliers, but also transporters, warehouses, retailers, and even customers themselves (Chopra and Meindl 2007: 3). Dilts (2005: 21). These ideas of Professor David M. Dilts, Owen Graduate School of Management, Vanderbilt University, have not appeared in a formal publication yet. He granted us permission to cite them as personal correspondence on July 23, Hendricks and Singhal (2002, 2003, 2005a, 2005b, 2005c), Hoffman (2005). Simchi-Levi et al. (2008: 48). We will differentiate between the often confused terms variability, uncertainty, and risk in section 2.3. Cf. Hoffman (2008), Chain Drug Review (2009a), Hamstra (2009), Orgel (2009), Pinto (2009b), Ryan (2009). 1

17 1 Introduction Although risk pooling is often central to many recent operational innovations and strategies 13, an important concept in business logistics and supply chain management (SCM) 14, and was already described in logistics in , it is mentioned in few German text books 16 mostly limited to the square root law (SRL). Most other publications also only consider inventory pooling 17 or a single other type 18 of risk pooling 19. Exceptions are Neale et al. (2003: 44f., 50, 55), Fleischmann et al. (2004: 70, 93), Taylor (2004: 301ff.), Muckstadt (2005: 150ff.), Reiner (2005: 434), Anupindi et al. (2006), Heil (2006), Brandimarte and Zotteri (2007: 30, 36, 38, 39, 57, 58, 70), Sheffi (2007), Simchi-Levi et al. (2008), Sobel (2008: 172), Van Mieghem (2008), Cachon and Terwiesch (2009), and Bidgoli (2010). Our survey of 102 German manufacturing and trading companies of various sizes and industries (see appendix A 20 ) showed that the different risk pooling concepts are known fairly well, but not widely applied despite their potential benefits. Choosing risk pooling methods is difficult for companies, as the literature does not compare the various methods in terms of their suitability for certain conditions holistically. 21 Most of the work in risk Cachon and Terwiesch (2009: 350). Romano (2006: 320). Flaks (1967: 266). For example Pfohl (2004a: 115ff.), Tempelmeier (2006: 41f., 153f.), Bretzke (2008: 147, 152, 154). For example Bramel and Simchi-Levi (1997: 219f.), Martinez et al. (2002: 14), Christopher and Peck (2003: 132), Dekker et al. (2004: 32), Ghiani et al. (2004: 9), Daskin et al. (2005: 53f.), Li (2007: 210), Taylor (2008: 13-3), Mathaisel (2009: 19), Shah (2009: 89f.), Wisner et al. (2009: 513). A type is a category of [ ] things having common characteristics (Soanes and Hawker 2008). We distinguish ten main types of risk pooling that have in common that they may reduce total demand and/or lead time variability and thus uncertainty and risk by pooling individual demand and/or lead time variabilities. We call them methods (e. g. in the title of this treatise), whenever we focus on the ways of risk pooling, as a method is a way of doing something (Soanes and Hawker 2008). If the focus is on choosing and implementing one or several risk pooling methods for a specific company under specific conditions, we refer to this as risk pooling strategy. A strategy is a plan designed to achieve a particular longterm aim (Soanes and Hawker 2008). In the case of risk pooling this plan can comprise one or more risk pooling methods combined in order to reduce demand and/or lead time uncertainty. We use the term concept, if we aim at the abstract idea (Soanes and Hawker 2008) or would like to include the SRL, PE, and inventory turnover curve, which are rather tools to measure the risk pooling effect on inventories than risk pooling methods. Pfohl (2004b: 126, 355), Enarsson (2006: 178). For the sake of readability and content unity we placed the survey in the appendix. However, Evers (1999) compares inventory centralization, transshipments, and order splitting. Swaminathan (2001) designs a framework for deciding between part and procurement standardization (component commonality), process standardization (postponement), and product standardization (substitution) according to product and process modularity, Wanke and Saliby (2009: 690) one for choosing between inventory centralization (demand pooling) and regular transshipments ( serving [ ] demands from all centralized facilities and enabling demand and lead time pooling). Benjaafar et al. (2004a, 2005) find in systems with endogenous supply lead times, multisourcing (Benjaafar et al. 2004a: 1441f., 1446) and capacity pooling (Benjaafar et al. 2005: 550, 563) perform better than inventory pooling, if utilization (arrival rate divided by service rate) is high. Eynan and Fouque (2005) show that demand reshape is more efficient than component commonality. 2

18 1 Introduction pooling is rather focused on one aspect and holistic treatments are rare. 22 There is little empirical and to our knowledge no survey research on the various methods of risk pooling combined. Most publications develop mathematical models for a specific risk pooling method under certain assumptions and (optimal inventory) policies that minimize inventory for a given service level or maximize service level for a given inventory. They do not explore whether this risk pooling method is the best for the given situation or whether it can be combined with other ones. 1.2 Objective Thus the objective of this treatise is to advance research on and aid practice in selecting and applying risk pooling methods in business logistics. More specifically, the aims of this research can be formulated as follows: 1. Develop the first comprehensive and concise definition of risk pooling. 2. Critically review and structure the research on risk pooling within a value-chain framework according to this definition. 3. Develop tools to compare and choose appropriate risk pooling methods and models for different economic conditions with a contingency approach. 4. Apply these tools to a German paper merchant wholesaler, which faces customer demand and supplier lead time uncertainty. 5. Examine the knowledge and usage of the various risk pooling concepts and their associations in 102 German trading and manufacturing companies by means of a survey. 1.3 Object and Method The research object (German: Erfahrungsgegenstand) is an empirical phenomenon (a part of reality) that is to be described. The scientific object or selection principle (German: Erkenntnisgegenstand) is the perspective and specific question used to examine the research object. 23 Our research object comprises business logistics in a company that experiences demand and/or lead time uncertainty. Our scientific object is risk pooling that can decrease this uncertainty of the company, which is perceived as a collection of value activities (val Personal correspondence with Professor Christian Terwiesch, The Wharton School, University of Pennsylvania on July 2, Schneider (1987: 34f.), Chmielewicz (1994: 19ff.), Söllner (2008: 5), Neus (2009: 2). 3

19 1 Introduction ue chain approach). Business logistics plans, organizes, handles, and controls all material, product, and information flows across these value activities 24 in an efficient, effective, and customer-oriented manner (logistics perspective). Our main specific research questions are: What risk pooling methods are available? What economic conditions make the individual methods worthwhile? How can a company choose adequate risk pooling methods? We derive the adequacy of the identified risk pooling methods from contingency factors (contingency approach). In order to enhance the quality of our research we use triangulation 25 to gather various types of information 26 on risk pooling by literature, example, modeling, and survey research. This integrated approach also accounts for our holistic ambition and leads to results not attainable by the individual research methods separately 27. Weaknesses of some methods can be balanced by the strengths of others. 28 Van Hoek (2001: 182f.) already proposed triangulation to improve research on postponement, one type of risk pooling. For problems of triangulation, such as coping with conflicting results, epistemological problems, and the debatable higher validity of findings, please refer to e. g. Bryman (1992: 63f.), Denzin and Lincoln (2005: 912), Blaikie (1991: 122f.), and Fielding and Fielding (1986: 33). A holistic approach may not be as profound as an atomistic one. However, as noted before such a holistic approach is novel to risk pooling research. 1.4 Structure and Contents This treatise is divided into six chapters and an appendix. After this introduction (chapter 1), we outline previous risk pooling research in business logistics, identify ten main types of risk pooling, and place them in the supply chain, business logistics, and a value chain. This results in the five logistics value activities storage, transportation, procurement, production, and sales and distribution, where risk pooling is important. Completing outlining our research framework, we define, explain, and characterize risk pooling in business logistics (chapter 2). Chapter 3 defines, classifies, and characterizes the ten identified risk pooling methods within the five logistics value activities and according to their uncertainty reduction abilities To Porter (2008: 75) inbound and outbound logistics are primary value activities themselves besides operations, marketing and sales, and service. We adopt a cross-functional view of logistics. Denzin (1978: 291) defines triangulation as the combination of methodologies in the study of the same phenomenon. Graman and Magazine (2006: 1070). Jick (1979: 603f.), Fielding and Fielding (1986: 33), Graman and Magazine (2006: 1070). Blaikie (1991: 115). 4

20 1 Introduction Research on inventory pooling is reviewed in more detail 29, as it is the earliest and most extensive and prominent one. In particular, we attempt to remedy inconsistencies regarding the SRL, a tool to estimate the inventory savings from risk pooling by inventory pooling: Under what assumptions can the SRL be applied to regular, safety, and total stock, as researchers do not agree on them? What causes the inventory savings measured by the SRL? Are its results confirmed in practice? Is the SRL questioned justifiedly? After examining the portfolio effect (PE), a generalization of the SRL, and the inventory turnover curve, we compare the various SRL and PE models in a synopsis (table D.2) based on their assumptions and assign them to groups. This facilitates choosing an appropriate model to determine stock savings from inventory pooling for specific conditions or adapt the existing models by adding or dropping assumptions. Chapter 4 merges the results of our literature review in a synopsis about conditions making the various risk pooling methods favorable, their advantages, disadvantages, and basic trade-offs. Based on this synopsis and contingency theory, a Risk Pooling Decision Support Tool is developed for choosing an appropriate risk pooling strategy for a specific company and specific conditions. This tool is applied to a German paper wholesaler in chapter 5 to choose suitable risk pooling methods to cope with demand and lead time uncertainty. In this context we also show that in contrast to Maister (1976: 132) and Evers (1995: 2, 14f.) centralization or centralized ordering can reduce cycle stocks, if the replacement principle or stock-to-demand replenishment policy is followed in case minimum order and saltus quantities have to be observed (section ). If risk pooling is shown to be beneficial in theory and in practice also for this German paper wholesaler, to what extent are its different methods known, applied, and associated in 102 German manufacturing and trading companies? To answer this question we present a survey in appendix A for the above reasons. Such a survey has not been conducted before and is demanded by some authors 30. The conclusion (chapter 6) summarizes our findings and identifies avenues for further research Professor Walter Zinn, Fisher College of Business, The Ohio State University, believes this is sorely needed (personal correspondence on July 4, 2008). For example by Thomas and Tyworth (2006: 254f.) for order splitting and by Huang and Li (2008b: 19) for postponement. 5

21 2 Risk Pooling in Business Logistics This chapter outlines our research framework: It gives an overview of previous risk pooling research (section 2.1), identifies ten main types of risk pooling and embeds them in the supply chain, business logistics, and a value chain (section 2.2), which sets the structure for chapter 3, defines risk pooling in business logistics (section 2.3), explains its mathematical and statistical foundations (section 2.4) and examines five general features of risk pooling (section 2.5). 2.1 Business Logistics Risk Pooling Research Risk pooling in business logistics is an active field of research with well over 600 publications so far. The number of publications in this area has steadily increased since its scarce beginnings in the 1960s, gained momentum especially in the 80s and 90s and reached its peak in 2003 as figure 2.1 shows. Perhaps driven by the economic downturn, research activity in 2009 was the highest after Most research focused on inventory pooling (centralization, the square root law, portfolio effect, and inventory turnover curve), postponement and delayed (product) differentiation, and transshipments and inventory sharing. Figure 2.1 is based on the literature databases Business Source Complete, Business Source Premier, EconLit, and Regional Business News accessed via EBSCOhost January 11, After the concept borrowed from modern portfolio and insurance theory has been mainly applied to inventory centralization, meanwhile research focuses on other forms of risk pooling, especially postponement and transshipments, and the coordination of risk pooling arrangements and cost and profit allocation through contracts 31 and fair allocation rules, schemes, or methods 32 with game theory. The academics dealing with risk pooling in business logistics are of different backgrounds (mathematics, operations research (OR), operations management (OM), management science, decision sciences, statistics, computer sciences, engineering, business administration, management, economics, game theory, production, marketing, logistics/supply chain management, physical distribution, and transportation), orientation (quantitative, analytical, modeling, simulation, empirical, and qualitative research), and Dana and Spier (2001), Cheng et al. (2002), Cachon (2003), Wang et al. (2004), Bartholdi and Kemahloğlu-Ziya (2005), Cachon and Lariviere (2005), Özen et al. (2008, 2010). Gerchak and Gupta (1991), Robinson (1993), Hartman and Dror (1996), Anupindi et al. (2001), Lehrer (2002), Granot and Sošić (2003), Ben-Zvi and Gerchak (2007), Dror and Hartman (2007), Wong et al. (2007a), Dror et al. (2008). Robinson (1993), Raghunathan (2003), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), and Sošić (2006) consider allocations based on the Shapley (1953) value. 6

22 2 Risk Pooling in Business Logistics prominence. Therefore they use inconsistent terms 33, frameworks, and structures and made our thorough literature review and definitions necessary. One might argue that due to these differences this research must not be compared and only major research should be cited. However, in contrast to previous research we would like to pursue a more holistic approach to convey an integrated overview of business logistics risk pooling. Even less prominent research can draw attention to important details and show directions for further research. Some often cited risk pooling research has not been published in highly ranked journals. 34 Nevertheless most of the cited references are from the latter. Most risk pooling research is quantitative and designs mathematical models of problems, develops solution methods (exact methods, algorithms, simulation methods, and heuristics), and determines solutions (optimal inventory control and risk pooling, e. g. transshipment, policies) Number of Publications Inventory Pooling (150) Postponement (105) Transshipments (95) Component Commonality (55) Virtual Pooling (51) Capacity Pooling (41) Product Substitution (40) Order Splitting (37) Centralized Ordering (27) Product Pooling (21) Year of Publication Figure 2.1: Number of Publications on Risk Pooling in Business Logistics Bender et al. (2004: 233) made similar observations for location theory. For example Eppen and Schrage (1981). 7

23 2 Risk Pooling in Business Logistics 2.2 Placing Risk Pooling in the Supply Chain, Business Logistics, and a Value Chain Business logistics 35 comprises the holistic, market-conform, and efficient planning, organization, handling, and control of all material, product, and information flows from the supplier to the company, within the company, and from the company to the customer 36 and back (reverse logistics 37 ). As figure 2.2 shows, the efficient and effective material, product, and information flow is impaired by inter alia demand and lead time uncertainty. Risk pooling methods can mitigate these uncertainties. They can be implemented at or between the various supply chain members (suppliers, manufacturers, wholesalers, distribution centers, central warehouses, delivery or regional warehouses, retailers, stores, and customers). Thoroughly reviewing the literature referred to in section 2.1, we identified ten risk pooling methods: capacity pooling, central ordering, component commonality, inventory pooling, order splitting, postponement, product pooling, product substitution, transshipments, and virtual pooling. We will define and characterize them in detail in chapter 3. They can be implemented everywhere along the supply chain. Component commonality rather concerns production. In general capacity and inventory pooling and postponement may pool inventories or capacities of or for different locations. Component commonality, postponement, product pooling, and product substitution may refer to products or their components. Transshipments and virtual pooling deal with product, material, and information flows between supply chain members within an echelon or across echelons, and central ordering and order splitting with procurement between supply chain members. In our opinion, all mentioned risk pooling methods but order splitting can reduce demand uncertainty, order splitting only lead time uncertainty, component commonality, capacity pooling, inventory pooling, product pooling, and product substitution only de Business logistics (management) is difficult to distinguish from supply chain management (SCM). The terms are often used synonymously, although logistics is majorly seen as a part of SCM and not vice versa as in earlier literature (Ballou 2004b: 4, 6f., Larson and Halldórsson 2004, CSCMP 2010). According to Kotzab (2000) the German business logistics conception already comprised a holistic management along the whole value creation chain before it adopted the English term SCM. Gabler's business enzyclopedia defines SCM as building and administrating integrated logistics chains (material and information flows) from raw materials production via processing to end consumers (Alisch et al. 2004: 2870). Wegner (1996: 8f.). See e. g. Richter (1996a, 1996b, 1997), Richter and Dobos (1999, 2003a, 2003b), Dobos and Richter (2000), Richter and Sombrutzki (2000), Richter and Weber (2001), Richter and Gobsch (2005), Gobsch (2007). 8

24 2 Risk Pooling in Business Logistics mand uncertainty. Transshipments and virtual pooling, postponement, and central ordering may dampen both uncertainties. Concerning order splitting and component commonality there are dissenting individual opinions, which we will elaborate on in section 4.4. Various economic conditions have been found to favor the different risk pooling methods. We will focus on these favorable conditions in chapter 4. They flow into a Risk Pooling Decision Support Tool that helps to determine suitable risk pooling methods for specific conditions (section 4.4). This tool is applied to determine adequate risk pooling methods for a German paper merchant wholesaler for coping with its demand and lead time uncertainty in chapter 5. Demand Uncertainty Suppliers Manufacturers Distributors Retailers Customers Lead Time Uncertainty Economic Conditions Material, product, and information flow Risk pooling methods Figure 2.2: Placing Risk Pooling in Business Logistics Supply chain member names based on Chopra and Meindl (2007: 5). Logistics may be considered as a cross-organizational (figure 2.2) and at every member of the above supply chain a cross-departmental coordination function across all divisions, especially storage, transportation, procurement, production of goods and services (including R&D, recycling, and remanufacturing), and sales and distribution (including order processing, recovery, return, and disposal) 38 in the value chain in figure Delfmann (2000: 323f.), Ballou (2004b: 9ff., 27, 29), Kuhlang and Matyas (2005: 659f.), Grün et al. (2009: 15, 305), Wannenwetsch (2009: 21f.). 9

25 2 Risk Pooling in Business Logistics The value chain is a management concept that was developed by Porter (1985: 33ff.) and describes a company as a collection of activities. These activities create value, use resources, and are linked in processes. In our value chain, the main value activities are procurement, production, and sales and distribution, which are supported by the value activities transportation and storage. Value activities are technologically and economically distinct activities [ a company] performs to do business 39. Inventory pooling (IP) mainly pertains to storage, virtual pooling (VP) via dropshipping and cross-filling and transshipments (TS) to transportation, centralized ordering (CO) and order splitting (OS) to procurement, capacity pooling (CP), component commonality (CC), and (form) postponement (PM) to production, and product pooling (PP) and product substitution (PS) to sales. However, VP, extending a location's inventories to other locations' ones, is also related to storage and sales, transportation and sales or service capacities may be pooled, any logistics decision may be postponed, and PP and PS may be applied in production as well. This not mutually exclusive and exhaustive classification is reflected in figure 2.3 and the next chapter's structure. We structured our review according to the value chain approach, because we focus on the impact of risk pooling on the five mentioned logistics value activities. Risk pooling helps a company to cope with demand and/or lead time uncertainty and thus to carry out these value activities at a lower cost for a given service level, a higher service level for a given cost, or a combination of both 40. Thus it may increase expected profit 41 by reducing expected costs and/or increasing expected revenue. It may allow a company to win a competitive advantage over its competitors by effectively combining Porter's (2008: 75) competition strategies of differentiation and cost leadership, e. g. in mass customization enabled by postponement Porter (2008: 75) Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350). Porter's (1985: 38) value chain considers margin instead of profit. Margin is the difference between total value and the collective cost of performing the value activities. For example Feitzinger and Lee (1997). 10

26 2 Risk Pooling in Business Logistics Transportation CP, PM, TS, VP Procurement CO, OS, PM Production CC, CP, PM, PP, PS Sales & Distribution CP, PM, PP, PS, VP Profit Storage IP, PM, VP Figure 2.3: Important Value Activities Using Risk Pooling Methods 2.3 Defining Risk Pooling The literature offers various definitions of and confusion about the terms variability, variance, or volatility 43, uncertainty 44, and risk 45. Lead time and demand uncertainty may arise from lead time and demand variability or incomplete knowledge 46. Uncertainty is the inability to determine the true state of affairs of a system 47. Uncertainty caused by variability is a result of inherent fluctuations or differences in the quantity of concern. More precisely, variability occurs when the quantity of concern is not a specific value but rather a population of values 48. Lead time and demand uncertainty may lead to economic risk 49, the possibility 50 of a negative deviation from expected values or desired targets 51. The corporate target is expected profit (figure 2.3), the difference of expected revenue and expected cost. 52 The possibility of a positive deviation from an expected value constitutes a chance. 53 Despite the costs risk pooling entails 54, it may reduce variability and thus uncertainty and expected (ordering, inventory holding, stockout, and backorder) costs 55 and/or increase expected revenue (product availability, fill rate, service level) 56 and thus expected profit Hubbard (2009: 84f.). Outside of finance, volatility may not necessarily entail risk this excludes considering volatility alone as synonymous with risk (Hubbard 2009: 91). Knight (2005: 19ff.), Haimes (2009: 265ff.), Hubbard (2010: 49f.). Wagner (1997: 51), Knight (2005: 19ff.), Hubbard (2009: 79ff., 2010: 49f.). Cf. Haimes (2009: 265). For a detailed treatment of the confusion about the terms uncertainty and variability please refer to Haimes (2009: 265ff.). Haimes (2009: 265). Haimes (2009: 266). Bowersox et al. (1986: 58), Delfmann (1999: 195), Pishchulov (2008: 17). Wagner (1997: 51). Cf. e. g. Wagner (1997: 51), Köhne (2007: 321). Wagner (1997: 52). Wagner (1997: 51). Kim and Benjaafar (2002: 16), Cachon and Terwiesch (2009: 328). 11

27 2 Risk Pooling in Business Logistics We define risk pooling in business logistics as consolidating individual variabilities (measured with the standard deviation 58 ) of demand and/or lead time in order to reduce the total variability 59 they form and thus uncertainty and risk 60 (the possibility of not achieving business objectives 61 ). The individual variabilities are consolidated by aggregating 62 demands 63 (demand pooling 64 ) and/or lead times 65 (lead time pooling 66 ). Consolidating and aggregating mean combining several different elements [ ] into a whole 67. As individual variabilities 68 and not individual risks 69 are pooled, the term risk pooling is misleading. Nonetheless, we use it, because it is conventional Eppen (1979), Chen and Lin (1989), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996: 114, 1997: 71f.), Cherikh (2000: 755), Eynan and Fouque (2003: 704), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Wong (2005), Jiang et al. (2006: 25), Thomas and Tyworth (2006: 253), Chopra and Meindl (2007: 324ff.), Pishchulov (2008: 8, 17f.), Schmitt et al. (2008a: 14, 20), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331, 344, 350). Krishnan and Rao (1965), Tagaras (1989), Tagaras and Cohen (1992: 1080f.), Evers (1996: 111, 114, 1997: 71f., 1999: 122), Eynan (1999), Cherikh (2000: 755), Ballou and Burnetas (2000, 2003), Xu et al. (2003), Ballou (2004b: ), Wong (2005), Kroll (2006), Reyes and Meade (2006), Chopra and Meindl (2007: 324ff.), Cachon and Terwiesch (2009: 325, 329, 344, 350). Anupindi and Bassok (1999), Cherikh (2000: 755), Lin et al. (2001a), Eynan and Fouque (2003: 704, 707, 2005: 98), Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Özen et al. (2005), Chopra and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: ), Cachon and Terwiesch (2009: 331), Yang and Schrage (2009: 837). Sussams (1986: 8), Romano (2006: 320). The standard deviation is the most commonly used and the most important measure of variability (Gravetter and Wallnau 2008: 109). Zinn et al. (1989: 2) and Chopra and Meindl (2007: 307) consider the standard deviation a measure of uncertainty. Cachon and Terwiesch (2009: 331f., 282f.) and Chopra and Meindl (2007: 307) use the derived coefficient of variation (standard deviation divided by mean) as a measure for demand variability or uncertainty. Pooling independent random variables does not change total variability measured with the variance. Of course, one could argue that the measuring unit of the variance is squared and therefore difficult to interpret and that the standard deviation and not the variance is used to calculate safety stock. Pooling variabilities measured with the range may even increase total variability. Cf. e. g. Chopra and Meindl (2007: 336). Cf. e. g. Pishchulov (2008: 18). Wagner (1997: 51). Cf. e. g. Anupindi et al. (2006: 167), Chopra and Meindl (2007: 336). Gerchak and Mossman (1992: 804), Swaminathan (2001: 131), Hillier (2002b: 570), Randall et al. (2002: 56), Gerchak and He (2003: 1027), Özer (2003: 269), Chopra and Sodhi (2004: 55, 60), Nahmias (2005: 334), Anupindi et al. (2006: 167, 187), Çömez et al. (2006), Romano (2006: 320), Chopra and Meindl (2007: 177), Pishchulov (2008: 8, 18, 26), Simchi-Levi et al. (2008: 48, 196, 281, 348), Yu et al. (2008: 1), Yang and Schrage (2009: 837), Bidgoli (2010: 209). Evers (1997: 55, 57, 1999: 121f.), Benjaafar and Kim (2001), Benjaafar et al. (2004a: 1442, 2004b: 91), Chopra and Sodhi (2004: 59ff.), Tomlin and Wang (2005: 37), Gürbüz et al. (2007: 302), Van Mieghem (2007: 1270f.), Ganesh et al. (2008: 1134), Cachon and Terwiesch (2009: 332), Wanke and Saliby (2009: 690), Yang and Schrage (2009: 837). Thomas and Tyworth (2006: 254). Evers (1999: 121f.), Cachon and Terwiesch (2009: 336). Soanes and Hawker (2008). Gerchak and He (2003: 1028). The business logistics risk pooling literature finds the risk related to the uncertainty of individual demands (Zinn 1990: 12), risk over uncertainty in customer demand (Anupindi and Bassok 1999: 187), standard deviations (Zinn 1990: 13) or variances of individual demands (Zinn 1990: 16), risk over demand uncertainty (Weng 1999: 75) or risk over random supply lead time (Weng 1999: 82), inventory 12

28 2 Risk Pooling in Business Logistics Among others Hempel (1970: 654), Wacker (2004: 630), and the references they give make requirements for a good 70 definition. To our knowledge previous attempts to define risk pooling do not satisfy them. They merely describe its causes 71, effects 72, or aim 73, only target demand pooling 74, and equate risk pooling with inventory pooling 75 and the square root law 76. Moreover they do neither define nor differentiate between variability 77, uncertainty, and risk. The business logistics risk pooling literature states risk pooling reduces variability 78, lead-time variability 79, lead time demand variability 80, demand variability 81, demand variation 82, variation 83, demand variance 84, variance of delivery time 85, the variance of the retailers' net inventory processes 86, the mean and variance of cycle stock 87, uncertainty 88, demand uncertainty 89, the uncertainty the firm faces 90, the effect of uncertainty 91, risks (Van Hoek 2001: 174, Pishchulov 2008: 27), inventory risk (Kemahlioğlu-Ziya 2004: 76), forecast risk (Chopra and Sodhi 2004: 58, 60), risk (Schwarz 1989: 830, 832, McGavin et al. 1993: 1093, Chopra and Sodhi 2004: 58, 60f., Simchi-Levi et al. 2008: 357, Yang and Schrage 2009: 837), risks (Aviv and Federgruen 2001a: 514, Gerchak and He 2003: 1027), risk over the outside-supplier leadtime (Schwarz 1989: 828, McGavin et al. 1993: 1093), lead-time risk (Thomas and Tyworth 2006: 245f., 2007: 169), lead-time uncertainty (Evers 1997: 70, Thomas and Tyworth 2006: 245), lead-time fluctuations (Evers 1997: 70), demand uncertainty (Evers 1997: 70), uncertainty (Evers 1994: 51, Rabinovich and Evers 2003a: 206), or quantity and timing uncertainty (Collier 1982: 1303) is or are pooled. A good [formal conceptual] definition [ ] is a concise, clear verbal expression of a unique concept that can be used for strict empirical testing (Wacker 2004: 631). Hempel (1970: 654) requires inclusivity, exclusivity, differentiability, clarity, communicability, consistency, and parsimony. Nahmias (2005: 334), Anupindi et al. (2006: 168), Romano (2006: 320), Simchi-Levi et al. (2008: 48), Wisner et al. (2009: 513), Bidgoli (2010: 209). Gerchak and He (2003: 1027), Özer (2003: 269), Romano (2006: 320), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 350), Bidgoli (2010: 209). Chopra and Meindl (2007: 212), Cachon and Terwiesch (2009: 321). Flaks (1967: 266), Gerchak and Mossman (1992: 804), Gerchak and He (2003: 1027), Özer (2003: 269), Nahmias (2005: 334), Anupindi et al. (2006: 187), Chopra and Meindl (2007: 212). Anupindi et al. (2006: 168). Wisner et al. (2009: 513). Tallon (1993: 192, 199f.) equates variability with uncertainty. Eynan and Fouque (2005: 91), Anupindi et al. (2006: 167). Thomas and Tyworth (2007: 171). Benjaafar and Kim (2001). Flaks (1967: 266), Zinn (1990: 11), Randall et al. (2002: 56), Eynan and Fouque (2003: 705, 2005: 91), Romano (2006: 320), Thomas and Tyworth (2006: 255, 2007: 188), Chopra and Meindl (2007: 212), Pishchulov (2008: 18), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 331), Wisner et al. (2009: 513), Bidgoli (2010: 209). Eynan and Fouque (2005: 91), Nahmias (2005: 334). Evers (1999: 133). Kemahlioğlu-Ziya (2004: 71). Masters (1980: 71), Ihde (2001: 33). Schwarz (1989: 830). Thomas and Tyworth (2006: 247f.) Pishchulov (2008: 22), Simchi-Levi et al. (2008: 281). Eynan and Fouque (2003: 714), Pishchulov (2008: 17). 13

29 2 Risk Pooling in Business Logistics the risk associated to the variability 92, the impact of individual risks 93, risks associated with forecasting errors and inventory mismanagement 94, and inventory risk 95. Risk pooling is described to hedge uncertainty so that the firm is in a better position to mitigate the consequence of uncertainty 96, enables one to avoid [ ] uncertainty 97, or removes some of the uncertainty involved in planning stock levels 98. It is also referred to as statistical economies of scale 99, portfolio efficiencies 100, Pooling Efficiency trough Aggregation or Principle of Aggregation 101, and IMPACT OF AGGREGATION ON SAFETY INVENTORY 102. Risk pooling is also considered a form of operational hedging. Hedging is the action of a decision maker to mitigate a particular risk exposure. Operational hedging is risk mitigation using operational instruments 103, e. g. pure diversification or demand pooling 104. For more on operational hedging please refer to Boyabatli and Toktay (2004) and Van Mieghem (2008: ). 2.4 Explaining Risk Pooling Risk pooling can be shown e. g. for inventory or location pooling: Let a single product be stocked at n separate locations. Demand for this product is a normal random variable 105 x i with known mean µ i and standard deviation 106 σ i for each location i = 1,, n. The standard devia- 90 Cachon and Terwiesch (2009: 321). 91 Özer (2003: 269). 92 Risk pooling is applied to portfolio theory in finance here [sic!] the risk associated to the variability in the return from individual stocks is diluted when an investor keeps a portfolio of stocks (Zinn 1990: 12). 93 Dilts (2005: 23). 94 Yang and Schrage (2009: 837). 95 Chopra and Sodhi (2004: 59). 96 Cachon and Terwiesch (2009: 321). 97 Pishchulov (2008: 26) remarks this for risk pooling through delayed differentiation. 98 Jackson and Muckstadt (1989: 2). 99 Eppen (1979: 498), Eppen and Schrage (1981: 52), Evers (1994: 51), Özer (2003: 269), Rabinovich and Evers (2003a: 206). 100 Eppen and Schrage (1981: 52). 101 Anupindi et al. (2006: 187, 189). 102 Chopra and Meindl (2007: 318). 103 Van Mieghem (2007: 1270). 104 Van Mieghem (2007: 1270f.). 105 A random variable is a variable that takes its values (realizations) with certain probabilities respectively whose values are assigned to certain probability densities (Alisch et al. 2004: 3454). 106 If (the empirical distribution of) demand is forecast (Thonemann 2005: 255f.), σ i is the standard deviation of the distribution of the forecast error in formula (2.1) for calculating safety stock (Caron and Marchet 1996: 239, Pfohl 2004a: 114, Thonemann 2005: 255f., Chopra and Meindl 2007: 306). An estimate of expected demand (forecast value) is ordered to satisfy the expected value of demand and safety stock is 14

30 2 Risk Pooling in Business Logistics tion σ i is a measure of dispersion of individual values of the random variable x i around the mean µ i for every entity i and therefore a measure of x i 's variability 107. If each location just satisfies its own demand, location i needs to hold an amount of safety stock that allows it to hedge against the demand uncertainty associated with x i. Let the optimal safety stock at location i in accordance with the newsboy model 108 be, (2.1) where z is the safety factor that corresponds to a certain target service level. Therefore, the total safety stock across all locations is. (2.2) If all inventory holding is centralized at one location, this location needs to serve the total demand. (2.3) The individual demands are aggregated across all locations. Safety stock in the centralized system is, (2.4) where (2.5) is the standard deviation of x and ρ ij is the correlation coefficient of the value of the random variable for locations i and j. It can be formally shown that the aggregated variability (standard deviation of total demand σ a ) is less than or equal to the sum of the individual variabilities built up as protection against the forecast error, which is at least as high as the demand uncertainty or standard deviation of demand (personal correspondence with Professor Ulrich W. Thonemann, University of Cologne, in 2008), and not against uncertainty in demand (Thonemann 2005: 255f.). A high safety stock is needed, if the (standard deviation of the) forecast error is high. The size of demand fluctuations is irrelevant (Thonemann 2005: 257). If the distribution of demand is known, σ i is the standard deviation of demand (Zinn et al. 1989: 4) and safety stock is held to hedge against uncertainty in demand. The higher the uncertainty in demand, the higher is the safety stock. The standard deviation of demand is zero and no safety stock is needed, if there is no demand uncertainty (Thonemann 2005: 238) and no lead time uncertainty either. Nonetheless, some companies forecast demand, but wrongly use the standard deviation of demand instead of the standard deviation of the forecast error in calculating safety stock (Korovessi and Linninger 2006: 489f.). 107 Gravetter and Wallnau (2008: 109). 108 See e. g. Thonemann (2005: 220), Cachon and Terwiesch (2009: 235). 109 Cf. Mood et al. (1974: 178), Zinn et al. (1989: 5), Jorion (2009: 43). This expression is also written 2 (Eppen 1979: 500) or 2 (cf. Weisstein 2010). The double summation sign indicates that all possible combinations of i and j should be included in calculating the total value (Moyer et al. 1992: 222), where j is larger than i. 15

31 2 Risk Pooling in Business Logistics (sum of standard deviations of demand at the n locations σ) because of the subadditivity property of the square root of non-negative real numbers 110 : 2. (2.6) Therefore the safety stock in the centralized system is less than or equal to the one in the decentralized one 2. (2.7) Inequality (2.6) is a special case of the known Minkowski inequality for p = 2. It is always correct, if the variances exist, therefore also for the Poisson and Binomial distribution. 111 Hence, the standard deviation of the aggregate demand is lower than or equal to the sum of the standard deviations of the individual demands. Consequently, inventory pooling or centralization at a single location can reduce the amount of safety stock necessary to ensure a given service level. The reduction in safety stock depends on the correlations between x i, i = 1,, n. Inventory pooling does not always reduce safety stock due to the less-than-or-equal sign. Yet, the sum of the individual variabilities (standard deviations) only equals the total aggregated variability (the square root of the sum of the individual variances plus two times the covariance of the random variable's value for two entities i and j) in two cases: (1) The random variables x i are perfectly positively correlated (the coefficient of correlation ρ ij equals 1, i, j): (2.8) (2) Random variables x i cannot mutually balance their fluctuations, if at least n-1 σ i equal zero: If n-1 σ i equal zero, (2.6) becomes (2.9) for this single non-zero σ i. If all σ i are zero, (2.6) becomes 110 Gaukler (2007). 111 Minkowski (1896), Abramowitz and Stegun (1972: 11), Bauer (1974: 72), Gradshteyn and Ryzhik (2007: 1061). 112 Cf. Moyer et al. (1992: 222). This expression is also written, (cf. Jorion 2009: 43). 16

32 2 Risk Pooling in Business Logistics 0. (2.10) Apart from this, for independent (the correlation coefficient ρ ij is equal to 0, i, j) normally distributed random variables risk pooling leads to variability reduction:. (2.11) The highest possible variability reduction is achieved, if there are negative correlations which make the second term under the square root equal to minus the first term 113 in (2.6). Some authors 114 give the impression that risk pooling always reduces total variability or enables to reduce inventory, although this must not be the case as shown above. Likewise industry and academia often assume that inventory pooling, a type of risk pooling, always is beneficial, i. e. it either reduces costs or increases profits, and that the value of inventory pooling increases with increasing variability of demand. 115 Kemahlioğlu-Ziya (2004: 40) states this was only always correct for normally distributed demand such as in Eppen (1979) or Eppen and Schrage (1981). She neglects though that this is not correct for perfectly positively correlated demands and if at least n-1 σ i equal zero. Furthermore, for uncertain demand and certain conditions more willingness to substitute may not lead to higher expected profits or lower optimal total inventory 116 for full 117 and partial substitution or risk pooling Cf. Eppen (1979: 500). 114 Tallon (1993: 186) imprecisely remarks, Mathematically, the square root of the sum of the variances is less than the sum of the individual standard deviations. Likewise, Anupindi et al. (2006: 191) inaccurately state the inventory benefits from physical centralization result from the statistical principle called the principle of aggregation, which states that the standard deviation of the sum of random variables is less than the sum of the individual standard deviations. Gaukler (2007) uses the less-than-orequal sign, but inconsistently says the standard deviation of the aggregate demand was lower than (not lower than or equal to) the sum of the standard deviations of the individual demands. Although Gaukler (2007) states his remarks were not intended to be a rigorous derivation of this concept, they should be consistent. It is well known that the pooled demand has a lower standard deviation than the sum of standard deviations of individual demands. Thus, the safety stock as well as inventory holding and shortage costs are lower when products are more substitutable (Ganesh et al. 2008: 1134). Inventory pooling represents a strategy of consolidating inventories and aggregating stochastic demands, enabling reductions in inventory holding and shortage costs (Pishchulov 2008: 8). Risk pooling suggests that demand variability is reduced if one aggregates demand across locations (Romano 2006: 320, Simchi-Levi et al. 2008: 48). The aggregation of demand stemming from risk pooling leads to reduction in demand variability, and thus a decrease in safety stock and average inventory (Simchi-Levi et al. 2008: 50). Centralizing inventory reduces both safety stock and average inventory in the system (Simchi-Levi et al. 2008: 51). Finally, inventory pooling does not automatically reduce inventory, but it may allow to reduce the inventory necessary to provide a given service level. 115 Kemahlioğlu-Ziya (2004: 40). 116 Yang and Schrage (2009: 837). 117 Baker et al. (1986), Pasternack and Drezner (1991), Gerchak and Mossman (1992). 118 McGillivary and Silver (1978), Parlar and Goyal (1984), Anupindi and Bassok (1999), Ernst and Kouvelis (1999), Rajaram and Tang (2001), Netessine and Rudi (2003). 17

33 2 Risk Pooling in Business Logistics Yang and Schrage (2009) show this inventory anomaly (after demand substitution or risk pooling the company ought to hold more stock rather than less) for full substitution with any right skewed demand distribution 119 if the shortage is somewhat higher than the holding cost per unit, for partial substitution with exponential, Normal, Poisson, and uniform demands even if they are negatively correlated, as well as for more than one period, with backlogging, lost sales, more than two products, and with setup costs. The inventory anomaly is increasing as the underage is close to the overage cost per unit and as the correlation between demands decreases. 120 The relative difference of the shortage to holding cost for which the anomaly arises increases with increasing right skewedness. A company will not face the inventory anomaly, if it uses a shortage penalty, but minimizes inventory carrying costs subject to a fixed target service level. However, it may not seize the chance to increase sales and profits, if it augments demand pooling without raising inventory. The likelihood of the inventory anomaly is higher with short lead times and lower with less frequent but larger orders, e. g. with high setup costs. 121 Inventory pooling may reduce costs and increase profits for the supply chain party holding inventory 122, but may reduce the total supply chain profits. In a two-echelon supply chain, where the upper echelon (the supplier) carries inventory, the lower echelon (the retailers), whose revenues depend only on sales, may lose profits due to pooling. 123 The supplier and the retailers are likely to benefit from risk pooling inventory, if the stockout penalty cost is high. 124 The normal random variable x i in our derivation of risk pooling can also be the demands for i unique components, product versions, substitute products, customized products, or (replenishment) lead times to i locations. They are aggregated to the demand for a common component in component commonality 125, universal product in product pooling, all substitutes in product substitution or demand reshape, the undifferentiated generic product in postponement or delayed product differentiation, or to an aggregated lead time across all locations, suppliers, or deliveries in lead time pooling (emergency transshipments and order splitting). The aggregated demand and/or lead time x may fluctuate less, as the stochas- 119 Actual demand distributions tend to be right skewed (Yang and Schrage 2009: 847). 120 Yang and Schrage (2003: 1). 121 Yang and Schrage (2009: 847). 122 Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005). 123 Anupindi and Bassok (1999). 124 Dai et al. (2008: 411). 125 Dogramaci (1979: 130) shows that the standard deviation of demand for the common component (σ c ) would be less than or equal to the sum of the standard deviation[s] of lead time demand of the components it replaces. 18

34 2 Risk Pooling in Business Logistics tic fluctuations (σ i ) of the individual demands and/or lead times usually balance each other to a certain extent (equation 2.6). Risk pooling by demand pooling in transshipments, virtual pooling, centralized ordering, and capacity pooling can be derived in the same manner as shown for inventory pooling: Demands are pooled across locations. 2.5 Characteristics of Risk Pooling We now turn to describing five important characteristics common to most risk pooling methods: (1) increasing returns, but (2) diminishing marginal returns with increasing application as well as increasing benefit with (3) increasing demand variability, (4) decreasing demand correlation, and (5) decreasing concentration of uncertainty. (1) The benefit of or return on risk pooling is variability reduction and thus enabled inventory reduction for a given service level or increase in service level for a given inventory. The risk pooling return generally (in the following cases) increases with increasing application or the number of participants: It augments with the number of participating stock-keeping locations in inventory pooling 126, time and logistics postponement 127, transshipments 128, and cross-filling 129, (substitutable) products and degree of substitution in product substitution, demand reshape 130, and resource flexibility 131, products in the product line 132 or products being postponed 133 in manufacturing postponement, products sharing components (increasing commonality) in component commonality 134, as well as 126 Lin et al. (2001a), Heil (2006: 170), Netessine and Rudi (2006), Milner and Kouvelis (2007), Cachon and Terwiesch (2009: 282f.). 127 Zinn and Bowersox (1988: 133), Heil (2006: 170). 128 Jönsson and Silver (1987a: 224), Robinson (1990), Diks and de Kok (1996: 378), Tagaras (1999), Evers (2001: 313), Herer et al. (2002), Tagaras and Vlachos (2002), Dong and Rudi (2004), Burton and Banerjee (2005), Hu et al. (2005), Heil (2006: 170). 129 Ballou and Burnetas (2000, 2003), Ballou (2004b: ). 130 Eynan and Fouque (2003, 2005), Ganesh et al. (2008: 1124). 131 Tomlin and Wang (2005: 51). 132 Zinn (1990: 14), Swaminathan and Tayur (1998). 133 Graman and Magazine (2006: 1075). 134 Collier (1982: 1303), Srinivasan et al. (1992: 26), Grotzinger et al. (1993: 532f.), Eynan and Fouque (2005), Chew et al. (2006: 247). 19

35 2 Risk Pooling in Business Logistics retailers in pooling over the outside-supplier lead time or centralized ordering 135 and risk pooling by drop-shipping or virtual pooling 136. (2) However, the marginal benefit of risk pooling commonly decreases with each additional increase in risk pooling or participant. There appear to be diminishing marginal returns to risk pooling 137, e. g. to cross-filling 138 and transshipments with increasing number of locations transshipping 139 or increasingly even allocation of demand across locations 140, to virtual pooling by drop-shipping with increasing number of retailers 141, to component commonality 142, postponement 143, product substitution 144, capacity pooling, and location pooling 145. The marginal benefit of location pooling decreases with increasing number of pooled locations 146, so that the main benefit is gained by consolidating a few locations and it might not be necessary to pool all locations 147. The same applies to transshipments. 148 Capacity pooling with a little bit of flexibility 149 as long as it is designed with long chains 150 almost has the same benefit as full flexibility. Companies can benefit from any 135 Jackson and Muckstadt (1989: 14), Kumar and Schwarz (1995), Gürbüz et al. (2007). 136 Netessine and Rudi (2006: 845). 137 Similarly, in corporate finance we can observe diminishing marginal risk reduction with increasing number of securities: At first diversification reduces portfolio risk (standard deviation or volatility) rapidly, then more slowly with increasing number of randomly chosen stocks (Statman 1987: 353, 355). In recent years stocks have become individually more volatile but are increasingly less than perfectly correlated. Therefore an investor needs to hold more stocks to capture the majority of benefits from diversification than before (Campbell et al. 2001: 40). 138 Ballou and Burnetas (2000, 2003), Ballou (2004b: ). Based on Ballou's (2003b: 81) numerical example, we devise the general formula for the effective fill rate EFR for the customer in dependence of the for all locations equal item fill rate FR (0 1) and the number n of locations that cross-fill as 1 1. The first derivative of EFR with respect to n shows that the more locations crossfill the higher is the EFR: 1 ln 1 0. However, the incremental increase in EFR diminishes with increasing number of locations taking part in cross-filling: 1 ln 1 ln Evers (1997: 70). 140 Evers (1996: 128). 141 Netessine and Rudi (2006: 852). 142 Chopra and Meindl (2007: 327f.) find by a numerical example that the marginal benefit [ marginal reduction in safety stock] decreases with increasing commonality for independent and normally distributed end-product demand, but formulate this result as if generally valid. Bagchi and Gutierrez (1992) show by two numerical examples (817) that increasing component commonality results in increasing marginal returns when the criteria are aggregate service level and aggregate stock requirement (815) for two end-products that face independent, identically exponentially, geometrically, or Poisson distributed demands and share up to three components (815, 817f., 824). They do not give an intuitive explanation (829). 143 Zinn (1990: 14), Graman and Magazine (2006: 1075, 1080). 144 Eynan and Fouque (2003: 707, 2005: 96). 145 Cachon and Terwiesch (2009: 323, 349). 146 Cachon and Terwiesch (2009: 323, 349). 147 Cachon and Terwiesch (2009: 323f.). 148 Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: ), Kranenburg and Van Houtum (2009). 20

36 2 Risk Pooling in Business Logistics amount of risk pooling as long as they implement it appropriately 151 and demand is not perfectly positively correlated. Graman and Magazine (2006: 1075) similarly observe pertaining to postponement that it is only necessary to postpone a portion of a product to realize most of the benefits of such a strategy. The mathematical inventory model shows that almost all of the positive benefits of postponement (such as lower inventories) can be achieved with a partial (low-capacity) postponement scenario 152. Cachon and Terwiesch (2009: 324) show diminishing marginal returns of location pooling with increasing mean for independent Poisson demands. 153 This must not necessarily hold for other distributions such as the normal one. 154 (3) The (demand) risk pooling effect decreases with increasing demand correlation 155 and any Magnitude (relative sizes of the standard deviations of demand), and increases 149 Flexibility means that a plant is capable of producing more than one product. With no flexibility each plant can only produce one product; with total flexibility every plant can produce every product (as in manufacturing postponement). Graphically lines called links indicate which plant is capable of producing which product. Flexibility allows production shifts to high selling products to avoid lost sales (Cachon and Terwiesch 2009: 344f.). 150 A chain is a group of plants and [ products] that are connected via links (Cachon and Terwiesch 2009: 346). 151 Cachon and Terwiesch (2009: 349). 152 Graman and Magazine (2006: 1080). 153 [T]he standard deviation of a Poisson distribution equals the square root of its mean. Therefore, Coefficient of variation of a Poisson distribution [ ]. As the mean of a Poisson distribution increases, its coefficient of variation decreases, that is, the Poisson distribution becomes less variable. Less variable demand leads to less inventory for any given service level. Hence, combining locations with Poisson demand reduces the required inventory investment because a higher demand rate implies less variable demand. However, because the coefficient of variation decreases with the square root of the mean, it decreases at a decreasing rate. In other words, each incremental increase in the mean has a proportionally smaller impact on the coefficient of variation, and hence on the expected inventory investment (Cachon and Terwiesch 2006: 324). This can also be derived formally: The first derivative of the coefficient of variation with respect to the mean λ is smaller than zero, the second one larger than zero: 0, For the normal distribution it depends on how the coefficient of variation changes with respect to the mean. With the Poisson distribution it decreases as the mean increases, but this is not necessarily the case with the normal distribution. However, we find that there are at least diminishing marginal returns to pooling of normally distributed independent demands with the same standard deviation and mean. For normally distributed independent demand the coefficient of variation of pooled demand is. If the standard deviation and mean is the same at each pooled location i, this expression simplifies to. The first and second derivative of COV with respect to the number n of pooled locations shows that as n increases COV decreases at a decreasing rate: 0, Eppen (1979), Zinn et al. (1989: 12), Inderfurth (1991: 109, 111), Netessine and Rudi (2003: 329), Alfaro and Corbett (2003), Corbett and Rajaram (2004, 2006), Heil (2006: 170), Chopra and Meindl (2007: 319), Cachon and Terwiesch (2009: 349). In serial or divergent multi-stage base-stock production/distribution systems the lower the demand correlation, the further upstream safety stocks should be held and vice versa and the lower the worth of safety stocks because of product-dependent risk diversification (risk pool- 21

37 2 Risk Pooling in Business Logistics with decreasing correlation and Magnitude 156. Likewise the value of lead time risk pooling (order splitting 157 and transshipments) increases with decreasing correlation of replenishment lead times. Therefore, many companies attempt to reduce inventory and manufacturing costs by manipulating correlated demand sources, or inducing demand patterns that balance each other in an average sense 158, i. e. by risk pooling, while maintaining sales. 159 The bullwhip effect 160 can be reduced by risk pooling (effects) 161, production smoothing, and seasonality 162, so that it may be overestimated 163. Evers and Beier (1993) and Evers (1995) debatably show that there are no further savings in safety stock after a first consolidation because of the arising perfectly positive correlation. Tyagi and Das (1999: 211) show that if demands are correlated and one appropriately takes advantage of their characteristics, a partial may be more cost-efficient than complete pooling of customers. On the other hand, Xu and Evers (2003) claim that partial can never outperform complete pooling only based on demand correlation. Examples suggesting that one should prefer partial to complete aggregation were based on inconsistent correlation matrices. (4) The benefits of risk pooling generally increase with a structured ( a common linear transformation 164 ) increase in demand variability 165, if lead times are exogenous (for inventory pooling, product consolidation, and delayed differentiation 166 ). Gerchak and He ing) (Inderfurth 1991: 109, 111). Nonetheless, the total safety stock size may increase with decreasing correlation due to the impact of time-dependent risk diversification on carrying safety stocks at the still more costly final stage level because of long replenishment lead times (Inderfurth 1991: 111). 156 Zinn et al. (1989: 3, 12), cf. Tallon (1993: 201), Tyagi and Das (1998: 201), Wanke (2009: 122). 157 Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188). 158 Burer and Dror (2006: 1). 159 Gerchak and Gupta (1991), Ruusunen et al. (1991), Hartman and Dror (2003: 243f.), Tyagi and Das (1999). 160 The bullwhip effect describes that demand (order) variabilities are amplified as they move upstream the supply chain (Lee et al. 1997a: 93, 1997b: 546, 2004: 1875, Sucky 2009: 311). It is caused by demand forecast updating or demand signaling, order batching, price fluctuation, as well as rationing and shortage gaming (Lee et al. 1997a: 95, 1997b: 546, 2004: 1883) and can be counteracted by avoiding multiple demand forecast updates, breaking order batches, stabilizing prices, and eliminating gaming in shortage situations (Lee et al. 1997a: 98ff., 1997b: 555ff., 2004: 1883ff.). 161 Hartman and Dror (2003: 244), Lee et al. (2004: 1882), Cachon et al. (2007: 475), Chen and Lee (2009: 781), Sucky (2009: 311). 162 Cachon et al. (2007). 163 Cachon et al. (2007), Sucky (2009). 164 Gerchak and He (2003: 1027). 165 Kemahlioğlu-Ziya (2004: 22), Zinn et al. (1989), Alfaro and Corbett (2003), Eppen (1979). 166 Benjaafar and Kim (2001: 19f.), Benjaafar et al. (2004b: 90f., 2005). 22

38 2 Risk Pooling in Business Logistics (2003) provide a newsvendor counterexample with convex ordering where increased variability of two individual demands reduces the benefits of risk pooling. If supply lead times are endogenous in multi-item finite capacity production-inventory systems, both higher demand variability 167 and capacity utilization (arrival rate divided by service rate) 168 or asymmetric backordering or holding costs make risk (inventory) pooling 169 less valuable 170. (5) Assuming a multivariate normal distribution and uncorrelated demands, the value of pooling is lower when uncertainty is more concentrated, i. e. the less uniform or more dispersed the values of the standard deviations of the demands are. 171 Correspondingly, the PE will be larger when variances are of similar rather than highly varying magnitude Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1446). 168 Benjaafar and Kim (2001: 19), Kim and Benjaafar (2002: 15), Benjaafar et al. (2004a: 1438, 2004b: 71, 2005: 550). 169 While the relative benefit of inventory pooling tends to diminish with utilization, the relative benefit of capacity pooling tends to increase with utilization (Benjaafar et al. 2005: 550). 170 Kim and Benjaafar (2002: 15). 171 Alfaro and Corbett (2003: 24). 172 Tyagi and Das (1998: 201), cf. Zinn et al. (1989). 23

39 3 Methods of Risk Pooling After clarifying the prerequisites in the previous chapter, we will now enumerate the ten identified risk pooling methods and their synonyms, present a classification according to their ability to pool demands and/or lead times, and define, classify, and characterize them correspondingly within the structure of the aforementioned five logistics value activities. First, under the heading storage we deal with inventory pooling and centralization, the SRL, PE, and inventory turnover curve, as this area shows the earliest and most extensive research in risk pooling (cf. figure 2.1) and requires a review 173. The various SRL and PE models are compared in a synopsis (table D.2) based on their assumptions. This facilitates choosing an appropriate model to determine stock savings from inventory pooling for specific conditions or adapt the existing models by adding or dropping assumptions and relates our centralized ordering considerations in section to these models. Afterwards, virtual pooling, which is related to inventory pooling, and transshipments are examined (transportation). Upon considering risk pooling in these two original (traditional) logistics duties that refer to the transfer of objects (above all of goods) 174, we survey it in the derivative logistics areas 175 procurement (centralized ordering and order splitting), production (component commonality, postponement, and capacity pooling), and sales and distribution (product pooling and substitution) downstream the value chain. Perhaps since risk pooling and centralization of inventories (distribution or warehouse networks) are closely related, the terms inventory pooling 176 or just pooling 177 are often used interchangeably and ambiguously for risk pooling (methods), although inventory pooling literally merely refers to the consolidation or centralization of inventory, is a type 178 or manifestation 179 of risk pooling, and takes advantage of the possible benefits of risk pooling. 173 Personal correspondence with Professor Walter Zinn, Fisher College of Business, The Ohio State University on July 4, Delfmann (2000: 323). 175 Delfmann (2000: 323). 176 Benjaafar and Kim (2001: 13), Kemahlioğlu-Ziya (2004: 11), Gaur and Ravindran (2006: 482), Pishchulov (2008: iii, 23f., 26, 28ff., 133), Simchi-Levi et al. (2008: 239). 177 Evers (1999: 121), Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Kemahlioğlu-Ziya (2004: 11), Pishchulov (2008: iv, vi, vii, 8, 17f.). 178 A finite set of outlets with randomly fluctuating demands bands together to reduce costs by buying, storing and distributing their inventory jointly. This is termed inventory centralization and is a type of risk pooling (Burer and Dror 2006: 1). Cachon and Terwiesch (2009: 321). 179 Gerchak and He (2003: 1027). 24

40 3 Methods of Risk Pooling After a thorough literature review we conclude that apart from (1) inventory pooling 180, location pooling 181, or (physical) inventory or warehouse centralization 182 (SRL, PE, selective stock keeping, inventory turnover curve), risk pooling in business logistics can also be achieved by (2) virtual pooling 183, virtual inventory or inventories 184, electronic inventory 185, virtual centralization 186, virtual warehouse 187 or warehousing 188, virtually aggregating inventories 189, or information centralization 190, (3) transshipments (stock sharing between inventory locations) 191 or location substitution 192, (4) centralized ordering 193, consolidated distribution 194, risk pooling over the outside-supplier lead time 195, or warehouse risk-pooling 196, (5) order splitting or multiple suppliers 197, (6) component commonality 198, component sharing 199, part standardization 200, or procurement standardization 201, 180 Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 13), Anupindi et al. (2006: 189, 273), Heil (2006), Yang and Schrage (2009: 837). Cf. also references in section Cachon and Terwiesch (2009: 321ff.). 182 Eppen (1979), Zinn (1990: 12), Benjaafar and Kim (2001: 13), Martinez et al. (2002: 14), Ghiani et al. (2004: 9), Reiner (2005: 434), Anupindi et al. (2006: ), Sheffi (2006: 117f., 2007), Brandimarte and Zotteri (2007: 57f.), Chopra and Meindl (2007: 336), Pishchulov (2008: iii, 17, 133). 183 Cachon and Terwiesch (2009: 321, 350, 469), Mahar et al. (2009: 561). 184 Snyder (1995), Christopher (1998: 135), Hutchings (1999), Caddy and Helou (2000: 1715), Planning & Reporting (2001), Randall et al. (2002: 56), Sawyers (2003), Ballou (2004b: 335, ), Kroll (2006). 185 Christopher (1998: 135). 186 Anupindi et al. (2006: 194f., 314, 335). 187 Electrical Wholesaling (1997), Faloon (1999), Franse (1999), Duvall (2000), Purchasing (2000), AFSAC (2001), Gourmet Retailer (2002). 188 Verkoeijen and dehaas (1998). 189 Chopra and Meindl (2007: 336). 190 Chopra and Meindl (2007: 321f.). 191 Benjaafar and Kim (2001: 13), Taylor (2004: 301ff.), Diruf (2005, 2007), Nonås and Jörnsten (2005: 521), Muckstadt (2005: 150ff.), Heil (2006), Sheffi (2006: 248, 2007), Yang and Schrage (2009: 837). 192 Yang and Schrage (2009: 838). 193 Diruf (2005, 2007), Nonås and Jörnsten (2005: 521), Heil (2006). 194 Cachon and Terwiesch (2009: 336ff.). 195 Schwarz (1989: 828), Pishchulov (2008: iii, 133). 196 Schwarz (1989: 828). 197 Sheffi (2007: 99f., ). 198 Alfaro and Corbett (2003: 15), Neale et al. (2003), Reiner (2005: 434), Anupindi et al. (2006: 192, 194, 273), Sheffi (2006, 2007: ), Brandimarte and Zotteri (2007: 30, 36, 38f.), Chopra and Meindl (2007: 326ff.), Yang and Schrage (2009: 837), Bidgoli (2010: 21). 199 Benjaafar and Kim (2001: 13). 200 Zinn (1990: 12), Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 201 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 25

41 3 Methods of Risk Pooling (7) postponement, delayed (product) differentiation, 202 process standardization 203, or modularization strategies 204, (8) capacity pooling and flexible manufacturing 205, (9) product pooling 206, stock keeping unit (SKU) rationalization 207, universal or generic design 208, or product standardization 209, as well as (10) product substitution 210, item substitution 211, interchangeability 212, demand reshape 213, or product commonalities 214. Risk Pooling Methods Building Blocks IP VP TS CO OS CC PM CP PP PS DP LP Table 3.1: Risk Pooling Methods' Building Blocks As highlighted in our definition in section 2.3, risk pooling (methods) may take advantage of demand pooling (DP) and/or lead time pooling (LP). DP aggregates stochastic demands, so that higher-than-average demands may balance lower-than-average ones. 215 LP balances higher-than-average and lower-than-average lead times: A late-arriving order may be compensated by an early-arriving one 216, so that safety stock can be reduced, inventory availability in- 202 Benjaafar and Kim (2001: 13), Alfaro and Corbett (2003: 12), Neale et al. (2003), Fleischmann et al. (2004: 93), Taylor (2004: 301ff.), Sheffi (2004: 95f., 100, 2006: 297, 2007), Hwarng et al. (2005: 2841, 2842), Reiner (2005: 434), Anupindi et al. (2006: 167, 169, 193), Enarsson (2006: 178), Heil (2006), Brandimarte and Zotteri (2007: 39, 70), Chopra and Meindl (2007: 328f.), Pishchulov (2008: iii, 27, 133), Sobel (2008: 172), Cachon and Terwiesch (2009: 341ff.), Yang and Schrage (2009: 837). Many authors consider postponement and delayed (product) differentiation synonyms (e. g. Lee and Tang 1997, Johnson and Anderson 2000, Aviv and Federgruen 2001a: 512, 2001b: 578, Swaminathan and Lee 2003, Matthews and Syed 2004, Anupindi et al. 2006: 193, Caux et al. 2006: 3244, Anand and Girotra 2007, Li et al. 2007, Simchi-Levi et al. 2008: 190, 346, Graman and Sanders 2009, LeBlanc et al. 2009). At least form postponement can be equated with delayed (product) differentiation and therefore the latter be considered a subform of postponement. For a distinction of these terms, which is not relevant for our further considerations, please refer to Pishchulov (2008: 24-29). 203 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 204 Reiner (2005: 434). 205 Anupindi et al. (2006: 224), Graves (2008: 36), Cachon and Terwiesch (2009: 344ff.). 206 Cachon and Terwiesch (2009: 321, 330ff.). 207 Alfaro and Corbett (2003: 12), Neale et al. (2003), Sheffi (2006: 119, 2007), Sobel (2008: 172). 208 Pishchulov (2008: 17), Cachon and Terwiesch (2009: 330). 209 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 345ff.). 210 Anupindi et al. (2006: 192), Chopra and Meindl (2007: 324ff.), Yang and Schrage (2009: 837). 211 Benjaafar and Kim (2001: 13). 212 Sheffi (2006: 210, 2007). 213 Eynan and Fouque (2003, 2005). 214 Reiner (2005: 434). 215 Evers (1997: 55), Chen and Chen (2003). 216 Evers (1999: 122). 26

42 3 Methods of Risk Pooling creased, or both 217. Transshipments pool both lead times and demands, order splitting only the former. 218 Cachon and Terwiesch (2009: 336) consider consolidated distribution and delayed differentiation types of LP: Lead times between the supplier and the retail stores in the directdelivery model are combined to a single lead time between the supplier and the distribution center (DC) in the consolidated-distribution model. 219 Actually (forecast) demands are pooled over or during the outside-supplier lead time 220. Thus it is likely that higher-thanaverage and lower-than-average demands balance each other and inventory can be reduced for a given service level (DP). All risk pooling building blocks can reduce variability and thus inventory 221 for a given service level, increase the service level for a given inventory, or a combination of both 222. Table 3.1 can result in a classification according to the notation DP/LP that indicates which risk pooling properties the risk pooling method of concern relies upon. A 1 indicates that the respective property applies, a 0 the contrary. IP would be classified as a 1/0 risk pooling method. 3.1 Storage: Inventory Pooling Inventory pooling is the combination of inventories and satisfying various demands from it in order to reduce inventory holding and shortage costs through risk pooling. 223 It is also called vendor pooling 224, product consolidation 225, demand pooling 226, pooling 227, distributor integration 228, location pooling 229, or inventory centralization 230. It can e. g. be achieved by inventory 231 or warehouse (system) centralization 232 or selective stock keeping respectively specializa- 217 Evers (1997: 71, 1999: 122). 218 Evers (1997, 1999: 121). 219 Cachon and Terwiesch (2009: 339). 220 Eppen and Schrage (1981), Schwarz (1989), Schoenmeyr (2005: 4), Gürbüz et al. (2007: 293). 221 Cf. Romano (2006: 320), Simchi-Levi et al. (2008: 48), Cachon and Terwiesch (2009: 325, 350), Bidgoli (2010: 209). 222 Cf. Chopra and Meindl (2007: 336), Cachon and Terwiesch (2009: 325, 350). 223 Benjaafar and Kim (2001: 13), Kim and Benjaafar (2002: 12), Gerchak and He (2003: 1027), Benjaafar et al. (2005), Anupindi et al. (2006: 191), Pishchulov (2008: 8, 17), Cachon and Terwiesch (2009: 322). 224 Monezka and Carter (1976: 207). 225 Benjaafar et al. (2004b: 73). 226 Benjaafar et al. (2004a: 1442, 2004b: 91). 227 Kemahloğlu-Ziya (2004), Bartholdi and Kemahloğlu-Ziya (2005), Benjaafar et al. (2005). 228 Simchi-Levi et al. (2008: 261, 263). 229 Cachon and Terwiesch (2009: 322). 230 Monezka and Carter (1976: 207). 231 Benjaafar et al. (2004a: 1438). 232 Eppen (1979), Benjaafar and Kim (2001: 13), Taylor (2004: 304f.), Reiner (2005: 434), Heil (2006). 27

43 3 Methods of Risk Pooling tion 233. The latter strives to reduce inventory carrying cost treating products differently without reducing the service level substantially. For example, products with a low turnover might be stocked only at few locations due to cost considerations. 234 Inventory pooling is e. g. considered in location and allocation decisions 235, satisfying both on-line and store demand 236, speculative online exchanges 237, airline revenue management 238, for spare parts of airlines 239 and of U.S. manufacturing companies 240, and for Saturn 241, General Motors 242, Intel 243, and Airbus 244. Inventory pooling is a 1/0 risk pooling method: Inventories are consolidated and stochastic demands aggregated, as they are satisfied from the consolidated inventory 245. Thus demand variabilities may balance each other (demand pooling). The lead times to the separate inventories are pooled to the lead time to the consolidated stock according to Cachon and Terwiesch's (2009: 336, 339) notion of lead time pooling, but this actually is demand pooling during the replenishment lead time. Inventory pooling does not pool lead times, so that their variabilities may balance each other according to Evers (1997: 69ff., 1999: 121) and Wanke and Saliby (2009: 678f.). Inventory centralization can reduce expected costs in a cost minimization model 246 or increase profits and service level 247 in a profit maximization model 248 or in incentivecompatible laboratory experiments in behavioral operations management (OM) 249, even if 233 Anupindi et al. (2006: 191f.), Chopra and Meindl (2007: 322ff.) 234 Pfohl (2004a: 122f.). 235 Nozick and Turnquist (2001), Teo et al. (2001), Shen et al. (2003), Miranda and Garrido (2004), Hall (2004), Croxton and Zinn (2005), Klijn and Slikker (2005), Shu et al. (2005), Snyder et al. (2007), Vidyarthi et al. (2007), Naseraldin and Herer (2008), Ozsen et al. (2008), Taaffe et al. (2008), Lee and Jeong (2009). 236 Bendoly (2004), Bendoly et al. (2007: 426). 237 Milner and Kouvelis (2007). 238 Airline revenue management involves dynamically controlling the availability and prices of many different classes of tickets to maximize revenues (Zhang and Cooper 2005: 415). 239 Hearn (2007), Burchell (2009), Cattrysse et al. (2009). 240 Carter and Monczka (1978). 241 Treece (1996). 242 Kisiel (2000). 243 Johnson (2005). 244 Aviation Week & Space Technology (2006). 245 Pishchulov (2008: 8, 17). 246 For example Eppen (1979), Chen and Lin (1989). 247 Eynan (1999). 248 For example Cherikh (2000), Lin et al. (2001a). 249 Ho et al. (2009). 28

44 3 Methods of Risk Pooling locations differ in profitability (selling price and stockout costs) 250, because of risk pooling over uncertainty in customer demand 251 and economies of scale 252 and scope 253. Centralization (decreasing the number of warehouses) generally reduces inbound transportation costs from the supplier to the warehouses because of a higher utilization of transportation means (economies of density 254 ), possibly the distances between the production facility and the central warehouse(s) 255, and the unit costs 256 in the warehouse system due to higher utilization (economies of scale). The systemwide total throughput is distributed over a smaller number of warehouses and thus the average throughput per warehouse increases. 257 The warehouse costs per item (unit costs for space, product handling, and personnel) decrease through economies of scale. 258 The fixed costs per order and per unit holding costs usually diminish with centralization. 259 Fixed warehouse costs, especially personnel costs, are distributed over a larger warehouse throughput so that the unit costs decrease with increasing utilization 260 and the return on rationalization investments in more productive low-cost methods increases (economies of scale) 261. Variable warehouse costs, particularly handling costs, diminish by mechanization or automation. 262 However, increasing mechanization or automation reduces flexibility Eynan (1999: 38ff.) considers a central warehouse for a single product that supplies retailers from different markets, which differ in product prices and stockout costs, according to the first come, first served principle. Surprisingly the centralized system usually performs better than the decentralized one: Considering the whole system, possible cannibalization effects of low-price-market demands at the expense of high-price-market ones are overcompensated. 251 Anupindi and Bassok (1999: 187), cf. Teo et al. (2001), Lim et al. (2002: 668), Snyder and Shen (2006), Schmitt et al. (2008a, 2008b), Ho et al. (2009). 252 Lim et al. (2002: 668), Rabinovich and Evers (2003a). Economies of scale are decreasing unit costs with increasing output (Adam 1979: 950, Gutenberg 1983, Busse von Colbe and Laßmann 1986: 197, Monopolkommision 1986: 231, Chandler 1990: 17, Bohr 1996: 375, Samuelson and Nordhaus 1998, Alisch et al. 2004: 771). 253 Rabinovich and Evers (2003a). Economies of scope arise as cost synergy effects, if the combined production of goods is cheaper than the separate one (Alisch et al. 2004: 771). In the literature among others the portfolio effect is given as an economic reasoning for them: Diversification in different projects reduces the total investment risk. Fritsch et al. (2001: 96) observe this effect with research and development in a multi-product company, Bohr (1996: 382f.) with the general use of financial means. 254 Economies of density are cost advantages due to increasing utilization in a transportation system (Harris 1977, Caves et al. 1984: 472). 255 Fawcett et al. (1992: 37), Pfohl (1994: 141), Delfmann (1999: 193). 256 Unit costs are the costs that are defined by the distribution of total costs to the output to be produced (Kistner and Steven 2002: 88). 257 Vahrenkamp (2000: 32). 258 Williams (1975), McKinnon (1989: 104). 259 Maister (1976: 132), McKinnon (1989: 102f.), Lim et al. (2002: 668). 260 Schulte (1999: 377), Vahrenkamp (2000: 34). 261 Paraschis (1989: 16), Pfohl (1994: 142), Vahrenkamp (2000: 34), Ihde (2001: 316). 262 Beuthe and Kreutzberger (2001: 249). 263 Stein (2000: 486), Ackerman and Brewer (2001: 231). 29

45 3 Methods of Risk Pooling Centralization can lead to economies of massed reserves, if it is used to lower systemwide safety stock through risk pooling and thus unit holding costs. 264 The latter are further reduced by less inventory loss and thus lower risk costs in the centralized system. 265 Economies of massed reserves are cost savings due to centralized reserve holding with increasing firm size. 266 Among others Bowersox et al. (1986: 283ff.), Fawcett et al. (1992: 5), Pfohl (1994: 141), and Delfmann (1999: 193) argue that in spite of constant basic inventory and increasing in transit inventory total inventory is lowered by reducing safety stock in the centralized system. Higher utilization of inbound transportation means with centralization decreases the number of stock placements and removals. 267 Therefore setups are reduced and larger loading and unloading equipment can be used saving time in the transportation system. Reducing idle time leads to a higher utilization in time and therefore to economies of density using larger means of transportation. 268 On the other hand, in a centralized logistics system outbound transportation costs may be higher because of lower utilization 269 and longer distances from the central warehouse(s) to customers 270 and thus perhaps the service level might be lower 271. Centralization may entail diseconomies of scale mostly in organization. 272 With increasing size there are no gains from rationalization anymore, but increasing transaction and coordination costs and thus increasing warehouse unit costs in big warehouse systems. 273 Das and Tyagi (1997) develop an optimization model for determining the optimal degree of centralization as a tradeoff between inventory and transportation costs. Inventory centralization games optimize and allocate the savings from a centralized inventory, so that the participants' cooperation is maintained Bowersox et al. (1986: 286), Paraschis (1989: 16), Vahrenkamp (2000: 34f.), Ihde (1976: 39f., 2001: 316). 265 Vahrenkamp (2000: 32). 266 Scherer and Ross (1990: 100). 267 Schulte (1999: 377). 268 Pfohl (1994: 142), Vahrenkamp (2000: 35). 269 In the medium term smaller transportation vehicles might be used to increase utilization (Fawcett et al. 1992: 5, Delfmann 1999: 193, Vahrenkamp 2000: 31). 270 Delfmann (1999: 193), Ballou (2004b: 573f.). 271 Schulte (1999: 377), Vahrenkamp (2000: 31), Lee and Jeong (2009: 1169), Wanke (2009: 122). 272 Chandler (1990: 25), Scherer and Ross (1990: 103f.), Bohr (1996: 385f.). 273 Pfohl (1994: 143), Delfmann (1999: 194). 274 Hartman et al. (2000), Anupindi et al. (2001), Slikker et al. (2001, 2005), Müller et al. (2002: 118f.), Granot and Sošić (2003), Hartman and Dror (2005: 93), Özen and Sošić (2006), Ben-Zvi and Gerchak (2007), Chen and Zhang (2007, 2009), Drechsel and Kimms (2007), Dror et al. (2008), Özen et al. (2008), Chen (2009), Zhang (2009). 30

46 3 Methods of Risk Pooling The risk pooling effect on (safety) stock levels evoked by inventory pooling or centralization can be quantified with the square root law (SRL), portfolio effect (PE), and inventory turnover curve. Maister's (1976) SRL states that the total system wide stock of n decentralized warehouses is equal to that of a single centralized one multiplied with the square root of the number of warehouses n. There is some confusion about which part of inventory 275 it can be applied to and about its underlying assumptions 276. Nevertheless, it applies to regular stock 277, if an economic order quantity (EOQ) order policy is followed, the fixed cost per order and the per unit stock holding cost, demand at every location, and total system demand is the same both before and after centralization. 278 It holds for safety stock, if demands at the decentralized locations are uncorrelated 279, the variability (standard deviation) of demand at each decentralized location 280, the safety factor (safety stock multiple) 281 and average lead time are the same at all locations both before and after consolidation, average total system demand remains the same after consolidation 282, no transshipments occur 283, lead times and demands are independent and identically distributed random variables and independent of each other 284, the variances of lead time are zero 285, and the safety-factor (kσ) approach is used to set safety stock for all facilities both before and after consolidation 286. It applies to total inventory, the sum of regular and safety stock 287, if the aforementioned assumptions of the SRL as applied to regular and safety stock hold collectively. A formal proof is given in appendix B. The savings in regular stock measured by the SRL stem from the assumption of constant 275 Heskett et al. (1974: 462), Ballou (2004b: 380). Professor emeritus Ronald H. Ballou, Weatherhead School of Management, Case Western Reserve University, agreed with us in a personal correspondence on May 15, Sussams (1986: 9), Bowersox et al. (2002: 469), Coyle et al. (2003: 259f.), Ballou (2004b: 380), Chopra and Meindl (2007: 320). 277 Regular or cycle stock is the inventory necessary to meet the average demand during the time between successive replenishments. The amount of cycle stock is highly dependent on production lot sizes, economical shipment quantities, storage space limitations, replenishment lead times, price quantity discount schedules, and inventory carrying costs (Ballou 2004b: 331), and affected by inventory policy (Ballou 2004b: 379). 278 Maister (1976: 125, 127, 131). 279 Maister (1976: 132). 280 Maister (1976: 130). 281 Maister (1976: 132). 282 Evers and Beier (1993: 110), Evers (1995: 4). 283 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 284 Evers and Beier (1993: 110), Evers (1995: 4). 285 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 286 Maister (1976: 129). 287 Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou 2004b: 330f.), which is neglected here. 31

47 3 Methods of Risk Pooling fixed costs per order, holding costs, and total demand for all locations before and after centralization. Thus, if an EOQ policy is followed, the total order fixed cost usually is lower because of less orders and the inventory holding cost is lower due to a smaller total EOQ in the centralized than in the decentralized system. For the proof please refer to appendix C. This is called EOQ cost effect by Schwarz (1981: 147) and order quantity effect by Evers (1995: 5). Savings in safety stock stem from the subadditivity of the square root (the square root of the sum of the individual demand variances of the decentralized locations is usually less than the sum of the standard deviations of demand of the decentralized locations), i. e. from balancing demand variabilities (demand risk pooling). Schwarz (1981: 147), Zinn et al. (1989: 3), and Evers (1995: 5) identify this as the portfolio effect. Total cost savings from centralizing safety stock are probably larger than the ones from cycle stock centralization 288, because centralized cycle stocks have to be transported to the customer eventually, so that extra transportation costs are probably high. Centralized safety stocks only have to be transported to the customer in the less frequent case of a stockout, so that additional expenses for premium transportation are relatively small. If both cycle and safety stocks are centralized some warehouses might be closed and fixed costs saved. 289 Although some researchers 290 claim the SRL estimated real savings well, in of practical cases we reviewed it overestimated actual inventory savings often sig- 288 Maister (1976: 134), Evers (1995: 17). 289 Maister (1976: 134), Evers (1995: 17). 290 Pfohl (1994: 141). Sussams (1986: 10) gives an example where a company's savings in safety stock (calculated with the standard deviation of demand of the decentralized and centralized depots) from reducing the number of depots from five to one would only be 2.76 % higher than the ones predicted by the SRL, although the variability (standard deviation) of demand at the decentralized depots is not the same, demands are not uncorrelated as the correlation coefficients we calculated show, but all locations use the same safety stock multiple (two times the standard deviation of demand). The SRL assuming uncorrelated demands coincidentally predicts similar savings to the ones calculated on the basis of the actual standard deviations in this case. Here the correlations of sales between the different depots balance each other when demands are consolidated, so that Zinn et al.'s (1989: 3) portfolio effect (percent reduction of safety stock due to centralization of correlated demands) of % resembles the savings of the SRL of %. However, as Zinn et al. (1989: 6, 10) show this need not be the case at all. Note that Sussams (1986: 10) compares two theoretical savings calculated with the SRL and on the basis of calculated standard deviations and not the theoretical savings estimated by the SRL with the actual savings realized by the company and his table contains mistakes. He concludes that the SRL has been tested against 24 different situations, and in all cases there was close agreement between the theoretical and the practical results. It was concluded that, subject to the reservations concerning the normality of the demand pattern, the square root law may be used with confidence to estimate differences in buffer stock requirements for different configurations of depots. However, it is not clear whether the savings theoretically predicted with the SRL were compared to actually realized or calculated savings and whether the assumptions of the SRL as applied to safety stock were fulfilled in the practical cases. Therefore Sussams' (1986: 10) conclusion is not intersubjectively verifiable. 291 Newson (1978), Voorhees and Sharp (1978: 75f.). Ballou (1981: 148ff.) shows for several real companies from different industries that the inventory savings predicted by the SRL are higher than the actual savings. This might be caused by joint ordering (to benefit from volume buying and shipping, which increases inventory levels), forward buying, diversion from the EOQ pull policy for some products, use of 32

48 3 Methods of Risk Pooling nificantly. This means its assumptions are not fulfilled 293 in these cases or there were other inventory- 294 or service-related changes. It is difficult to isolate the effect of inventory centralization. 295 The SRL shows the inventory necessary for a given service level in dependence of the number of stocking locations, if its underlying assumptions are fulfilled. This does not mean that reducing the number of warehouses automatically reduces inventory. None of the aforementioned sources states whether the assumptions to the SRL were fulfilled. Therefore actually no statements can be made about the accuracy of the SRL's results. However, it seems that the SRL tends to over-predict 296 actual inventory savings, as its assumptions are not fulfilled: In a survey that we conducted in the winter of 2008 none of the eleven participating companies from different countries and industries fulfilled all assumptions of the SRL when applied to safety stock (table D.1). They fulfilled at least two (respondents 1, 4, and 5) and at the most seven (respondent 10) of these eleven assumptions. Only one company (respondent 3) fulfilled all five assumptions necessary for applying the SRL to regular stock. Two companies (respondents 4 and 11) did not fulfill any of the assumptions of the SRL when applied to regular stock. Evers (1995: 17) already remarked that the SRL is based on numerous limiting assumptions which collectively are not likely to be found in practice, although Coyle et al. (2003: 259) call them reasonable. push distribution (where production considerations are more important than inventory replenishment ones) or a stock-to-demand order policy (relates inventory levels directly to demand), multiple product types with different service policies in the aggregated product group, no equal product service levels and costs, and poor inventory management. According to Ashford (1997: 20), Nike Europe intended to reduce its footwear storage locations from 20 to 2 and was predicted by the consultancy Touche Ross to save 11 % of inventory costs (calculated by us with the given data) instead of 68 % as predicted by the SRL. Nike planned to reduce its apparel storage locations from 20 to 1 with predicted savings of 12 % (calculated by us) as opposed to 78 %. Close-outs were estimated to decrease by 33 % for footwear and 50 % for apparel. It is not stated how the inventory savings were predicted and whether they were actually realized. McKinnon (1997: 81), Watson and Morton (2000), Hammel et al. (2002). McKinnon (2003: 24) considers two companies. Lovell et al. (2005), Progress Software Corporation (2007), clearpepper supply chain consulting & education (2009). We interviewed the Supply Chain Manager of a U.S. wireless telecommunication device production company with 6,000 employees. This manufacturer reduced the number of warehouses from 80 to 15 and thus reduced regular stock by 50, safety stock by 75, and total average inventory by 50 %. The SRL predicts inventory savings of % and thus estimates the savings in regular and total stock fairly well in this case. Table D.1 shows which assumptions of the SRL this respondent 10 fulfilled. 292 A U.S. chemical company went from 100 to 89 warehouses. Inventory costs (including order processing and warehousing costs) were reduced (projected by DISPLAN and later verified from accounting records) by 76 % (compared to 6 % predicted by the SRL). These savings resulted not only from closing 11 warehouses, but also from reallocating demand among the remaining warehouses while maintaining the company's high level of customer service (Ballou 1979: 68). 293 Cf. Ballou (1981: 148ff.). 294 Ballou (1979: 68), McKinnon (1997: 81). 295 McKinnon (1997: 81). 296 McKinnon (1997: 81). 33

49 3 Methods of Risk Pooling Researchers questioning Maister's (1976) SRL challenge its assumptions illogically 297, do make other assumptions and therefore arrive at different results 298, or give no clear reason 299. Nonetheless, the other SRL- and PE-models compared in table D.2 might be applied as their assumptions are fulfilled. Eppen (1979) showed for the assumptions listed in table D.2 that the expected total system inventory holding and penalty costs increase with the square root of the number of warehouses. 300 His research was extended to Poisson demand 301, any (non-negative) demand distributions with concave holding and penalty cost functions 302, and to include costs for the transportation of goods between locations with overage and underage in the centralized system 303. Zinn et al.'s (1989) portfolio effect (PE) is a generalization of the SRL and shows the reduction in aggregate safety stock by centralizing several warehouses' inventories in one warehouse in percent for the assumptions listed in table D.2. The PE was used to estimate the effect of postponement on safety stock 304 and extended to include holding, transportation, facility investment, and procurement costs 305, multiple consolidation points 306, variable lead times 307, both safety and cycle stocks ( consolidation effect ) as well as various assumptions 308, the effect of non-emergency 309 and emergency transshipments 310, and unequal demand variances and possibly unequal capacities of centralized locations Durand (2007). 298 Das (1978), Evers and Beier (1993), Evers (1995). 299 Durand and Paché (2006). 300 Kemahlioğlu-Ziya (2004: 9) wrongly states that Eppen (1979) is the first to model and analyze the benefits of inventory centralization. 301 Stulman (1987). 302 Chen and Lin (1989). 303 Chang and Lin (1991). They are extended by Chang et al. (1996), who consider delay supply product cost. 304 Zinn (1990). 305 Mahmoud (1992: 203ff.). 306 Evers and Beier (1993). 307 Tallon (1993). 308 Evers (1995). 309 Evers (1996). In nonemergency transshipments a certain proportion of demand is always filled from other locations' inventory (Evers 1996: 129). The PE model of Evers and Beier (1993) can be utilized to determine the percentage reduction in safety stocks from nonemergency transshipments without considering the effect on cycle stocks and transportation costs (Evers 1996: 111). 310 Evers (1997). The PE model of Evers (1996) underestimates the benefits of an emergency transshipment policy, as it does not adequately consider the number of locations, lead times, and desired fill rates (Evers 1997: 68ff.). 311 Tyagi and Das (1998: 197). Savings in aggregate safety stocks are maximal, if every centralized location delivers the same portion of each decentralized location's demand. Centralization can be beneficial, even if customers have unequal demand variances and more centralized locations are established than there are customer ones (Tyagi and Das 1998: 201f.). 34

50 3 Methods of Risk Pooling The inventory turnover curve shows average inventory in dependence of the inventory throughput for a specific company. It can be constructed from a company's stock status reports and be used to estimate the average inventory (not only safety stock as with the PE) for any (planned) warehouse throughput (shipments from the warehouse or sales) without the limitations of the SRL. Thus one can assess the effect of centralization, decentralization (changing the number and/or size of warehouses), or combining warehouses on average inventory as well as the performance of inventory management and control policies for a specific company Transportation Virtual Pooling Virtual pooling extends a company's warehouse or warehouses beyond its or their physical inventory to the inventory of other own or other companies' locations 313 by means of information and communication technologies (ICT) 314, drop-shipping 315, and cross-filling 316. [D]emand across [these locations] is pooled, which smoothes demand fluctuations 317. Therefore inventory availability is improved for a given inventory investment or maintained with less inventory. 318 If virtual pooling entails cross-filling, it may pool lead times. However, this corresponds to transshipments and is considered in the next section. Therefore virtual pooling is a 1/0 risk pooling method Transshipments Lateral transshipments are monitored company internal or external product shipments on the same level or echelon of the value or supply chain, e. g. among retailers. 319 They are also called intra-echelon transshipments 320, stock transfer 321, lateral (re)supply 322, inventory sharing 323, stock redistribution 324, virtual pooling 325, or information pooling Ballou (1981, 2000, 2004a, 2004b: 381f., 2005). 313 Caddy and Helou (2000: 1715), Planning & Reporting (2001), Kroll (2006). 314 Memon (1997), Christopher (1998: 135), Planning & Reporting (2001), SDM (2001), Frontline Solutions Europe (2002), Electrical Wholesaling (2003), Mason et al. (2003), Fung et al. (2005), Kroll (2006), Cioletti (2007), Cachon and Terwiesch (2009: 350, 469). 315 Planning & Reporting (2001), Randall et al. (2002, 2006), Netessine and Rudi (2006). 316 Ballou (2004b: 335, ). 317 Randall et al. (2002: 56). 318 Cachon and Terwiesch (2009: 350). 319 Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Simchi-Levi et al. (2008: 239), Yang and Schrage (2009: 838). 320 Burton and Banerjee (2005), Chiou (2008: 439). 321 Archibald et al. (1997). 35

51 3 Methods of Risk Pooling Emergency or reactive 327 lateral transshipments (ELT) transfer products from a location with a surplus to a location that faces a stockout 328. Yang and Schrage (2009: 838) regard ELT as location substitution. Preventive or proactive 329 lateral transshipments are conducted, if a retailer anticipates a stockout before demands are realized 330. Lee et al. (2007) combine emergency and preventive lateral transshipments in their transshipment policy service level adjustment (SLA). In virtual lateral transshipments a capacitated manufacturing plant designates arriving demands to be served by another, more remote one. This can help capacitated plants to work together to better deal with random demands and save costs. In contrast to the source plant of real lateral transshipments the one of the virtual lateral transshipment may have negative inventory levels throughout the transshipment process. 331 All of the above lateral transshipments must not be confused with cross-docking (reloading of goods at transfer points or hubs) 332 or shipping goods from a warehouse to a demand-satisfying location 333, which is also called transshipments sometimes. If locations from the same echelon cannot transship inventory to prevent a stockout, an upper-level supplier can fill the demand via a cross-level, inter-echelon, or vertical transshipment 334. This might resemble virtual pooling carried out by drop-shipping 335. Emergency transshipments pool both demands across locations or retailers 336 (by permitting alternative locations to satisfy customer demands) and lead times (by providing the whole system with the possibility of partial stock replenishments) and allow a company 322 Sherbrooke (1992), Yanagi and Sasaki (1992). 323 Anupindi et al. (2001), Grahovac and Chakravarty (2001), Zhao et al. (2005), Herer et al. (2006), Sošić (2006), Chiou (2008: 427), Kutanoglu (2008). 324 Das (1975), Jönsson and Silver (1987a, 1987b), Bertrand and Bookbinder (1998), Tagaras and Vlachos (2002), Hu et al. (2005). 325 Çömez et al. (2006). 326 Herer et al. (2006: 185), Özdemir et al. (2006a). 327 Herer et al. (2006: 185f.). 328 Lee (1987), Çömez et al. (2006), Herer et al. (2006: 185), Yang and Schrage (2009: 838). 329 Herer et al. (2006: 185f.). 330 Tagaras (1999), Lee et al. (2007). Preventive lateral transshipments are not useful in two-location periodic review inventory systems with nonzero replenishment lead times and uncertain future material requirements and availability (Tagaras and Cohen 1992). 331 Yang and Qin (2007). 332 Campbell (1993), Hoppe and Tardos (2000), Petering and Murty (2009). 333 Köchel (2007). 334 Chiou (2008: 427, 439, 443). 335 Netessine and Rudi (2006). 336 Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Çömez et al. (2006), Wanke and Saliby (2009), Yang and Schrage (2009: 837). 36

52 3 Methods of Risk Pooling to remain close to customers 337. They enable a company to exploit risk pooling 338 or statistical economies of scale 339, i. e. advantages that result from the pooling of uncertainty 340. As a result (safety) stock 341 and (inventory holding, shortage, backorder, or total system) costs 342 can be reduced for a given service level, which leads to leanness 343, customer service level (fill rates, product availability, or delivery time) can be improved without raising inventory levels 344, which enables agility or flexibility 345, or a combination of both (increasing service while decreasing inventory levels) 346, which is called leagility 347. Transshipments may decrease lost sales, the rejection rate of returns 348, and replenishment lead times 349 and improve revenues 350 and performance 351. In a static stochastic demand system, transshipments balance stock levels at different locations through emergency stock transfers from one location with overage to another one with underage. In a dynamic deterministic demand system, transshipments may save fixed and variable replenishment costs 352, if e. g. one location makes a larger replenishment order to transship some of it to other locations 353 (cf. section on centralized ordering). Inventory consolidations do not pool lead times, may close stock keeping installations near markets 354, restructure the logistics network fundamentally, which is difficult to change or undo at least in the short term 355, and increase order cycle times and/or transpor- 337 Evers (1997, 1999), Wanke and Saliby (2009). 338 Tagaras and Vlachos (2002), Tagaras (1999), Dong and Rudi (2002, 2004), Çömez et al. (2006), Zhao and Atkins (2009: 667). 339 Evers (1997, 1999). 340 Evers (1994: 51). 341 Jönsson and Silver (1987a: 224), Tagaras (1989), Diks and de Kok (1996: 378), Evers (1996), Mercer and Tao (1996), Evers (1997: 71f.), Köchel (1998a: 190), Evers (1999), Kukreja et al. (2001), Herer et al. (2002), Minner et al. (2003), Minner and Silver (2005). 342 Das (1975), Lee (1987), Robinson (1990), Evers (1996: 114), Köchel (1998a: 190), Alfredsson and Verrijdt (1999), Evers (2001: 313), Grahovac and Chakravarty (2001), Kukreja et al. (2001), Herer et al. (2002), Tagaras and Vlachos (2002), Daskin (2003), Minner et al. (2003), Kukreja and Schmidt (2005), Minner and Silver (2005), Wong (2005), Çömez et al. (2006), Yang and Qin (2007), Chiou (2008: 428), Kutanoglu and Mahajan (2009: 728). 343 Herer et al. (2002). 344 Krishnan and Rao (1965), Tagaras (1989), Chang and Lin (1991), Sherbrooke (1992), Evers (1996, 1997: 71f., 1999), Hong-Minh et al. (2000), Herer et al. (2002), Minner et al. (2003), Xu et al. (2003), Minner and Silver (2005), Zhao et al. (2005), Chiou (2008: 427), Kutanoglu (2008: 356). 345 Herer et al. (2002), Zhao et al. (2008). 346 Evers (1997), Needham and Evers (1998), Evers (1999), Minner et al. (2003), Minner and Silver (2005), Zhao et al. (2008: 400). 347 Herer et al. (2002). 348 Ching et al. (2003). 349 Herer et al. (2002). 350 Reyes and Meade (2006). 351 Wong (2005), Wong et al. (2007b: 1045), Chiou (2008: 429). 352 Herer and Rashit (1999: 525), Herer and Tzur (2003: 419). 353 Herer and Tzur (2003: 419). 354 Evers (1999: 122). 355 Domschke and Drexl (1996: 1), Klose and Stähly (2000: 434), Klose (2001: 3). 37

53 3 Methods of Risk Pooling tation costs to customers 356. The stockout probability for a given system inventory level is lower in a decentralized system with emergency transshipments than in a centralized one. 357 Therefore these two systems are not generally equal as in Chang and Lin (1991) with no replenishment times and no transshipment transportation costs. 358 Transshipments are similar to order splitting 359, but orders from facilities employing transshipments are not necessarily placed at the same time, while split orders are 360 and order splitting only pools lead times 361. Transshipments may decrease customer service (increase the number of receipts per order and/or order cycle times) and increase transportation or rebalancing 362, transaction (shipment documentation, receiving, handling and administration) costs 363, the sending location's cost of reordering the transshipped product from the supplier and its probability of a stockout 364, and daily average inventories 365, and require willingness to share stock 366. Not all supply chain members may benefit from transshipments: they can increase overall or retailer inventories and harm the distributor or individual retailers in a supply chain, in which a manufacturer supplies integrated or autonomous retailers with a one-forone inventory policy via a central depot. 367 Dong and Rudi (2002, 2004) find that if the wholesale price is endogenous, a single manufacturer benefits from its retailers' transshipments, the more, the larger the risk pooling effect. The identical (except in their normal demands) retailers in many situations are worse off under transshipment due to a higher wholesale price, especially if the risk pooling effect is large. Zhang (2005) extends Dong and Rudi's (2004) results under normal demand to general demand distributions. Shao et al. (2009) also conclude that a manufacturer and the decentralized retailers via which he sells may be hurt by transshipments. If the manufacturer controls the transshipment price, he prefers selling through decentralized retailers. If the latter control the trans- 356 Evers (1999: 122). 357 Evers (1997: 69ff., 1999: 121). 358 Evers (1997: 69ff.). 359 Sculli and Wu (1981), Hayya et al. (1987), Sculli and Shum (1990). 360 Evers (1997: 75). 361 Evers (1999: 122, 132). 362 Jönsson and Silver (1987a: 224), Diks and de Kok (1996: 378), Evers (1997: 56), Evers (1999: 122), Burton and Banerjee (2005: 169). 363 Evers (1999: 122, 2001: 312f.). 364 Evers (2001: 312f.). 365 Reyes and Meade (2006). 366 Evers (1999: 122). 367 Grahovac and Chakravarty (2001). 38

54 3 Methods of Risk Pooling shipment price, they realize higher profits than a chain store and the manufacturer may prefer selling via a chain store. Most research deals with transshipments of goods or commodities between warehouses, retailers, or production locations. Cohen et al. (1980) consider transfers of patients between hospitals and capacity decisions. Lue (2006) introduces transshipments to chemical manufacturing systems with continuous material flows to maintain non-stop operations, since it is costly to shut down and restart the production process. Transshipments affect the ordering policy and should be considered in it. 368 The majority of publications model transshipments and determine (optimal) replenishment order and transshipment 369, ordering 370, stocking, or inventory control 371, stocking or inventory control and transshipment 372, production and transshipment 373, and transshipment 374 policies, rules, heuristics, or algorithms under different assumptions. Similarly to the inventory centralization games in section 3.1, Anupindi et al. (2001), Granot and Sošić (2003), Sošić (2006), and Zhao et al. (2005) study the conditions (profit allocations) that make retailers jointly share their residual supply/demand with the other retailers in a manner that maximizes the additional profit in inventory sharing games. Small incentives for transshipments can achieve the benefits of a full-inventory sharing policy. 375 Köchel (1998a) provides a survey on multi-location inventory models with lateral transshipments, foremost on research conducted at the Technical University Chemnitz, Germany concerning the coordination of ordering decisions of all locations. Chiou (2008) and Paterson et al. (2009) present more general reviews of transshipment problems in supply chain systems and inventory models with lateral transshipments. In summary, transshipments are a 1/1 risk pooling method. 368 Robinson (1990), Hu et al. (2005), Kukreja and Schmidt (2005). 369 For example Köchel (1975, 1977, 1982, 1988), Tagaras (1989), Arnold and Köchel (1996), Arnold et al. (1997), Köchel (1998b), Herer and Rashit (1999), Bhaumik and Kataria (2006). 370 For example Robinson (1990), Tagaras and Vlachos (2002), Hu et al. (2005), Herer et al. (2006), Olsson (2009). 371 For example Das (1975), Lee (1987), Tagaras and Cohen (1992), Kukreja et al. (2001), Jung et al. (2003), Kukreja and Schmidt (2005), Wong (2005), Wong et al. (2005a, 2005b, 2007b), Gong and Yucesan (2006), Lue (2006), Yang and Qin (2007), Kranenburg and Van Houtum (2009). 372 Diks and de Kok (1996), Archibald et al. (1997), Hu et al. (2008). 373 Zhao et al. (2008). 374 Tagaras (1999), Evers (2001), Axsäter (2003a), Minner et al. (2003), Burton and Banerjee (2005: 169), Minner and Silver (2005), Wee and Dada (2005), Çömez et al. (2006), Zhao et al. (2006), Archibald (2007), Lee et al. (2007), Archibald et al. (2009). 375 Zhao et al. (2005). 39

55 3 Methods of Risk Pooling 3.3 Procurement Centralized Ordering Centralized ordering 376 places joint orders for several locations and later allocates the orders (perhaps by a depot) to the requisitioners or distribution points in consolidated distribution according to current demand information. 377 This is also called pooling risk over (the) outsidesupplier lead time(s) 378, lead time pooling [ ] achieved by consolidated distribution 379, coordinated replenishment 380, central ordering 381, or centralized purchasing 382. The allocation decision is postponed and stochastic demands can be treated in an aggregate form until it is made. This reduces uncertainty and system stock because of a portfolio effect over the lead time from the supplier 383, portfolio efficiencies 384, or statistical economies of scale 385. As explained at the beginning of this chapter, centralized ordering does not entail lead time pooling, so that lower-than-average supplier lead times may not balance higher-than-average ones. Consequently, centralized ordering is a 1/0 risk pooling method. Compared to independent and individual or local 386 ordering centralized ordering can lead to economies of scale, i. e. it can take advantage of quantity discounts ( joint ordering effect 387 ) and save ordering 388 and shipping costs 389. It can make more frequent shipments economical in comparison to direct delivery from the suppliers and thus reduce inventory even further or increase the service level 390. If a warehouse, depot, or distribution center (DC) is introduced to allocate the stock 391, DC operating and extra transportation costs from the DC to the requisitioners or retailers are incurred. 392 A unit must travel a longer distance from the supplier to the retailer. However, 376 Eppen and Schrage (1981: 51), Erkip et al. (1990: 381), Ganeshan et al. (2007: 341), Gürbüz et al. (2007: 293). 377 Eppen and Schrage (1981), Cachon and Terwiesch (2009: ). 378 Eppen and Schrage (1981), Schwarz (1989: 828), Schoenmeyr (2005: 4). 379 Cachon and Terwiesch (2009: 336). 380 Gürbüz et al. (2007: 293). 381 Ganeshan et al. (2007: 341). 382 Anupindi et al. (2006: 149f.). 383 Eppen and Schrage (1981: 67). 384 Eppen and Schrage (1981: 52). 385 Eppen (1979: 498), Eppen and Schrage (1981: 52). 386 Ganeshan et al. (2007: 341). 387 Eppen and Schrage (1981: 67). 388 Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293). 389 Gürbüz et al. (2007: 293), Cachon and Terwiesch (2009: 341). 390 Cachon and Terwiesch (2009: 341). 391 Eppen and Schrage (1981), Schwarz (1989: 828), Cachon and Terwiesch (2009: 336ff.). 392 McGavin et al. (1993: 1094), Cachon and Terwiesch (2009: 341). 40

56 3 Methods of Risk Pooling the holding cost for each unit of inventory at the DC is probably lower than at the retail stores. 393 The value of risk pooling through holding inventory at the warehouse, depot, or DC ( depot effect 394 ) and using this inventory between system replenishments to rebalance retailer inventories which have become unbalanced due to variations in individual retailer demands (between replenishment risk pooling) 395 can be substantial 396 (cf. inventory pooling). Schwarz et al. (1985) and Badinelli and Schwarz (1988) find it is not significant, perhaps because the model of Deuermeyer and Schwarz (1981) that they use does not allow the warehouse to balance retailer inventory levels, if system stocks are low Order Splitting Order splitting is simultaneously partitioning a replenishment order into multiple orders with multiple suppliers 398 or into multiple deliveries (scheduled-release) 399. The single order and thus its lead time are split into multiple orders or deliveries and their lead times, so that the variabilities of these lead times may balance each other 400. Thus safety stock needed for a given service level (inventory availability, expected number of backorders or shortage cost) can be reduced, service level increased for a given safety stock level, or both. 401 It can also reduce cycle stock due to successive deliveries of smaller split orders. 402 Consequently, order splitting only pools lead times, not demands 403 and constitutes a 0/1 risk pooling method. Disadvantages of order splitting might include no quantity and transportation discounts because of smaller orders, a higher administrative effort, which electronic data interchange might mitigate, and no long-term partnership with a single supplier, but multiple suppliers may ensure competitive pricing and other favorable terms. 404 Thomas and Tyworth (2006: 246f., 2007: 170f.) critically review the literature on order splitting: On the one hand, the literature assesses the effect of order splitting on the distri- 393 Cachon and Terwiesch (2009: 341). 394 Eppen and Schrage (1981: 67). 395 McGavin et al. (1993: 1093), cf. Schwarz (1989: 830). 396 Jackson and Muckstadt (1984a, 1984b, 1989), Jönsson and Silver (1987a, 1987b), Jackson (1988), McGavin et al. (1993: 1104). 397 McGavin et al. (1993: 1093). 398 Evers (1999: 123), Thomas and Tyworth (2006: 245), Qi (2007). 399 Hill (1996), Chiang (2001), Mishra and Tadikamalla (2006), Thomas and Tyworth (2007: 188). 400 Evers (1999: 122). 401 Evers (1997: 71), Evers (1999: 123), Thomas and Tyworth (2006: 245f.). 402 Thomas and Tyworth (2006: 245). 403 Evers (1999: 123f.). 404 Evers (1999: 123). 41

57 3 Methods of Risk Pooling bution of effective lead times 405 and safety stock carrying and shortage costs with statistics. 406 On the other hand, it compares the average total cost (inventory holding, ordering, shortage, and purchase cost) of order splitting with the one of not order splitting 407 and finds that it reduces cycle stock 408. Order splitting and the just-in-time inventory strategy are analyzed by Pan and Liao (1989), Ramasesh (1990), Hong and Hayya (1992), Hong et al. (1992), Kelle and Miller (2001), and Ryu and Lee (2003). Simultaneously splitting an order among suppliers does not decrease the sum of in-transit and cycle stock, but only total safety stock in the system 409 and increases ordering 410 and shipping costs 411. Most researchers neglect transportation economies of scale, the size of transportation costs compared to inventory costs, in-transit inventory 412, the probability of lead time correlation 413, order dependent supply lead times and unit purchasing prices, and the derived disadvantages and advantages of order splitting 414. Options other than simultaneously splitting replenishment orders among several suppliers might be more promising: 415 Delivering an order in sequential shipments can reduce demand and production variability because of advance demand and delivery information. 416 Orders can also be split between a fast, reliable and a cheaper, less reliable mode or supplier in order to take advantage of cost-performance differences in transportation modes 417 or between capacitated suppliers 418. Lead time variability and freight rates could be 405 The effective lead time in this case will be that of the minimum of the set of random variables representing the lead time of each supplier (Sculli and Wu 1981: 1003). 406 Sculli and Wu (1981), Hayya et al. (1987), Kelle and Silver (1990a, 1990b), Sculli and Shum (1990), Pan et al. (1991), Ramasesh (1991), Fong (1992), Fong and Ord (1993), Guo and Ganeshan (1995), Fong and Gempeshaw (1996), Fong et al. (2000), Geetha and Achary (2000), Kelle and Miller (2001), Mishra and Tadikamalla (2006). 407 Ramasesh (1990), Ramasesh et al. (1991), Hong and Hayya (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Lau (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Mohebbi and Posner (1998), Ganeshan et al. (1999), Sedarage et al. (1999), Tyworth and Ruiz-Torres (2000), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003). 408 Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Hong et al. (1992), Zhou and Lau (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003). 409 Thomas and Tyworth (2006: 254). 410 Sajadieh and Eshghi (2009). 411 Thomas and Tyworth (2006: 246). 412 Thomas and Tyworth (2006: 254, 2007: 188). 413 Minner (2003: 273), Thomas and Tyworth (2006: 254, 2007: 188). 414 Sajadieh and Eshghi (2009: 3272). 415 Thomas and Tyworth (2006: 255). 416 Hill (1996), Janssen et al. (2000), Minner (2003: 276), Thomas and Tyworth (2006: 255). 417 Ganeshan et al. (1999), Minner (2003). 418 Qi (2007). 42

58 3 Methods of Risk Pooling reduced by stable, periodic, long-term transportation commitments. 419 Using emergency transshipments instead of order splitting to reduce variation is attractive in many situations, not only because order splitting is contrary to current theory and practice of vendor relations and lean production Production Component Commonality Component commonality or part standardization 421 designs products that share parts or components 422. These common components can be used for several products. 423 Component commonality is a 1/0 risk pooling method: Demand for the individual components is aggregated (pooled 424 ) to the demand for the (fewer) generic common component(s). 425 This may 426 reduce the variability of demand (quantity and timing uncertainty) and the required (safety) stock for any constant service level 427, increase the service level for a given inventory, or lead to a combination of both, inventory reduction and service increase 428 due to risk pooling 429. Furthermore, component commonality can lower setup, ordering, inventory holding 430, manufacturing 431, logistics 432, and part costs 433 due to econ- 419 Thomas and Hackman (2003), Henig et al. (1997). 420 Evers (1999: 133). 421 Wacker and Treleven (1986: 219), Swaminathan (2001: 129), Simchi-Levi et al. (2008: 345). 422 Srinivasan et al. (1992), Jönsson et al. (1993), Meyer and Lehnerd (1997), Ma et al. (2002), Mirchandani and Mishra (2002), Kim and Chhajed (2001), Labro (2004), Van Mieghem (2004), Ashayeri and Selen (2005), Chew et al. (2006), Humair and Willems (2006). Swaminathan (2001: 131) and Simchi-Levi et al. (2008: 348) also consider commonality in procurement standardization, which exploits commonality in part and equipment purchasing. Demand can be pooled across a large variety of end products, if they are produced on similar machines and/or use common components. Procurement standardization is most effective, if the product is nonmodular and the process modular. 423 Grotzinger et al. (1993: 524). 424 Yang and Schrage (2009: 837). 425 Dogramaci (1979: 129), Guerrero (1985: 409), Vakharia et al. (1996: 15), Kreng and Lee (2004), Labro (2004: 363), Kulkarni et al. (2005: 247), Graman and Magazine (2006: 1074), Bidgoli (2010: 21). 426 Component commonality does not always reduce inventory in a dynamic inventory system with lead times under some common allocation rules (Song and Zhao 2009: 493). 427 Roque (1977), Collier (1981: 95, 1982: 1303), McClain et al. (1984), Baker et al. (1986), Gerchak and Henig (1986, 1989), Wacker and Treleven (1986: 219), Gerchak et al. (1988). 428 Bagchi and Gutierrez (1992: 824f., 829), Srinivasan et al. (1992), Grotzinger et al. (1993: 525f.), McDermott and Stock (1994: 65), Eynan (1996), Eynan and Rosenblatt (1996), Thonemann and Brandeau (2000), Hillier (2002a, 2002b), Thomas et al. (2003), Labro (2004: 363), Mohebbi and Choobineh (2005: 481), Chopra and Meindl (2007: 326ff.). 429 Srinivasan et al. (1992: 26f.), Grotzinger et al. (1993: 524), Swaminathan (2001: 129), Labro (2004: 363), Chew et al. (2006), Simchi-Levi et al. (2008: 345). 430 Dogramaci (1979: 129), Collier (1981: 95, 1982: 1303), Guerrero (1985: 402), Thonemann and Brandeau (2000), Swaminathan (2001: 129, 131), Hillier (2002b: 570), Ma et al. (2002: 524), Mirchandani and Mishra (2002), Mohebbi and Choobineh (2005: 473), Simchi-Levi et al. (2008: 345, 348). 43

59 3 Methods of Risk Pooling omies of scale 434 or order pooling 435, as well as product design costs 436 and design and manufacturing time 437. The order-pooling benefit may be more important than the riskpooling one. 438 Component commonality increases the survival probability of start-up companies 439 and possibly revenue 440. Total stock of product-specific components may increase though 441 depending on the used service-level measure 442. Although component commonality may reduce the average work load, it may increase workload variability and work-in-process inventory variability. 443 Excessive part commonality can reduce product differentiation, so that less expensive customization options might cannibalize sales of more expensive parts. 444 While customer valuation for the high-value product and the chargeable price may be reduced, the ones for the low-value one may be increased by using commonality in vertical product line extensions. 445 Sometimes, it is necessary to redesign products and/or processes to achieve commonality. 446 This may result in a smaller and more economical set of components though. 447 The 431 Collier (1981: 95), Hayes and Wheelwright (1984: ), Walleigh (1989), Kim and Chhajed (2001: 219). 432 Kim and Chhajed (2001: 219). 433 Collier (1982: 1303). 434 Collier (1982: 1303), Kim and Chhajed (2001: 219), Swaminathan (2001: 129, 131), Simchi-Levi et al. (2008: 345, 348). 435 Hillier (2002b: 570). 436 Desai et al. (2001). 437 Maskell (1991: 184f.), Berry et al. (1992), McDermott and Stock (1994: 65), Sheu and Wacker (1997), Mirchandani and Mishra (2002). 438 Hillier (2002b: 570). 439 Thomas et al. (2003). 440 Component commonality allows to produce more of a higher-margin product instead of a low-margin one, if demand exceeds capacity. Therefore it may be optimal even for perfectly positively correlated demands (no risk-pooling benefit), if products have sufficiently different margins ( revenue-maximization option ) (Van Mieghem 2004: 422). 441 Baker et al. (1986), Gerchak and Henig (1986: 157), Gerchak et al. (1988), Gerchak and Henig (1989: 61), Van Mieghem (2004: 423). 442 Gerchak et al. (1988). 443 Guerrero (1985: 409), Vakharia et al. (1996: 3), Ma et al. (2002). 444 Ulrich and Ellison (1999), Kim and Chhajed (2000, 2001: 219), Desai et al. (2001), Krishnan and Gupta (2001), Ramdas and Sawhney (2001), Simpson et al. (2001), Swaminathan (2001: 131), Heese and Swaminathan (2006), Simchi-Levi et al. (2008: 348). 445 Kim and Chhajed (2001: 219). 446 Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129), Ma et al. (2002: 536), Simchi-Levi et al. (2008: 345). 447 Whybark (1989). 44

60 3 Methods of Risk Pooling common component may be more expensive than the unique components it replaces. 448 Still component commonality may reduce total cost. 449 Using commonality as backup safety stock, if unique parts are not available, is better than no commonality or pure commonality, where only common parts are used. 450 Pure commonality is not optimal unless it is free or there are high fixed product and process redesign or complexity costs for procuring and handling two inputs. 451 A component-mismatch problem due to demand uncertainty for end products may arise. 452 The equal-fractile allocation policy 453 that allocates the components so that all products have an equal probability of being out of stock at the end of the period can help to reduce the required safety stock for a given target service level. However, it may keep amply available components at the component level for the product with the highest demand variability ( worst-case product ), although they may be employed to manufacture other end products. This can be avoided by modifying the policy accordingly. 454 Although some publications assert that cost decreases with commonality in general, there are contradictory claims on the effect of commonality on various cost elements and commonality's impact on total cost cannot be determined in general yet. 455 Wazed et al. (2008) review the literature on component commonality. For a review of advantages and disadvantages of component commonality in manufacturing and degree of commonality indices in designing new or assessing existing product families please refer to Wazed et al. (2009). Boysen and Scholl (2009) develop a general solution framework for component-commonality problems Postponement Postponement in general means delaying a decision in production, logistics, or distribution in order to be able to use more accurate information because of a shorter forecast period and an aggregate forecast 456, especially in industries with high demand uncertainty, 457 and commit- 448 Hillier (2002a, 2002b), Van Mieghem (2004: 419), Zhou and Grubbström (2004), Mohebbi and Choobineh (2005: 473). 449 Van Mieghem (2004: 419), Hillier (2002a, 2002b). 450 Hillier (2002a). 451 Van Mieghem (2004: 423). 452 Baker (1985), Chew et al. (2006: 240). 453 Cf. Eppen and Schrage (1981), Bollapragada et al. (1998). 454 Chew et al. (2006: 239f., 248). 455 Labro (2004: 358, 366). 456 Aggregate forecasts usually are more accurate than disaggregate ones (Lawrence and Zanakis 1984: 25, Neumann 1996: 9f., Swaminathan 2001: 126f., Sheffi 2004: 93f., Alicke 2005: 44, Nahmias 2005: 55, Anupindi et al. 2006: 168, 187, Donnellan et al. 2006: x, Chopra and Meindl 2007: 188f., Simchi-Levi et al. 2008: 190, 194, 345, Shah 2009: 166, Bretzke 2010: 77f., Schnuckel 2010: 152) because of statistical 45

61 3 Methods of Risk Pooling ting resources rather to demand than to a forecast 458. The opposite strategy of holding finished goods at locations close to customers in anticipation of sales is called speculation. 459 Postponement strategies can be applied to form, time, and place. 460 This can include product development 461, purchasing 462, order(ing) 463, fulfillment assignment 464, production 465, manufacturing 466, assembly 467, packaging 468, labeling 469, delivery 470, and pricing postponement 471. Form postponement delays product finalization or differentiation until after customer orders have been received. 472 Time postponement delays the forward movement of stock. 473 Rabinovich and Evers (2003b: 36, 41f.) consider emergency transshipments and inventory centralization forms of time postponement. Place postponement keeps inventories in centralized locations until customer orders are received. 474 Logistics or geographic postponement combines time and place postponement. 475 It delays the transportation to individual market areas. 476 Pull postponement moves the decoupling point 477 upbalancing effects, statistical economies of scale, or risk pooling (Bretzke 2010: 77f.). For further explanations please refer to e. g. Neumann (1996: 9f.), Sheffi (2004: 93), Alicke (2005: 44), Nahmias (2005: 55), Donnellan et al. (2006: x), Simchi-Levi et al. (2008: 60), and Schnuckel (2010: 152). 457 Pfohl (1994: 143), Swaminathan and Tayur (1998), Swaminathan (2001: 129f.), Sheffi (2004: 95f., 100), Anupindi et al. (2006: 192f.), Chopra and Meindl (2007: 362), García-Dastugue and Lambert (2007: 57f.), Piontek (2007: 86f.), Simchi-Levi et al. (2008: 346), LeBlanc et al. (2009: 19). 458 Bucklin (1965), Van Hoek (2001: 161). 459 Bucklin (1965). 460 Van Hoek et al. (1998: 33). 461 Yang et al. (2004: 1052), Piontek (2007: 86). 462 Yang et al. (2004: 1052). 463 Granot and Yin (2008), Chen and Lee (2009), Li et al. (2009). 464 Allowing online sales to accumulate and postponing assigning them to fulfillment sites can reduce holding, backorder, and transportation costs (Mahar et al. 2009: 561). 465 Yang et al. (2004: 1052), Anupindi and Jiang (2008: 1876). 466 Zinn and Bowersox (1988), Huang and Lo (2003). 467 Zinn and Bowersox (1988). 468 Zinn and Bowersox (1988), Howard (1994), Graman and Magazine (1998), Cholette (2009), Graman (2010). 469 Zinn and Bowersox (1988), Cholette (2009). 470 Anupindi and Jiang (2008: 1876). 471 Van Mieghem and Dada (1999), Boone et al. (2007: 597), Granot and Yin (2008). 472 Bowersox and Closs (1996), Lee (1998), Van Hoek (2001: 167), Rabinovich and Evers (2003b: 33), Li et al. (2007: 31), Harrison and Skipworth (2008), Wong et al. (2009). 473 Zinn and Bowersox (1988), Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and Evers (2003b: 33), Nair (2005: 449). 474 Bowersox and Closs (1996), Van Hoek et al. (1998: 33), Rabinovich and Evers (2003b: 33), Nair (2005: 449). 475 Pfohl (1994: 145), Bowersox and Closs (1996: 473), Lee (1998), Van Hoek (1998a), Van Hoek et al. (1998: 33), Özer and Xiong (2008). 476 Pfohl (1994: 145). 477 Up to the decoupling point, order-penetration-point, variant determination point, freeze point (Piontek 2007: 86f.), or point of (product) differentiation (PoD) (Lee 1996, Lee and Tang 1997, Meyr 2003) standardized products are made to stock customer-anonymously based on sales forecasts (push strategy). After an order has been received, the standardized products are transformed into various variants customerindividually (make-to-order pull strategy) (Piontek 2007: 86f., Harrison and Skipworth 2008). 46

62 3 Methods of Risk Pooling stream to assemble to order 478. Waller et al. (2000: 138) consider upstream postponement, e. g. delaying ordering of raw materials, and downstream postponement, e. g. distribution or place postponement. Postponement allows to ship a single common generic product longer down the supply chain and change it to individual products (differentiate it) more responsively according to more recent demand information later. 479 On the preceding levels of the supply chain the demands for the individual products are aggregated to the demand for the generic product (demand pooling 480 ), which fluctuates less, since the stochastic fluctuations of the individual demands balance each other to a certain extent because of the risk pooling effect. 481 Postponement constitutes a 1/0 risk pooling method. Furthermore, inventories of the common intermediate product can function as a common buffer. 482 A learning effect may arise, if forecasts can be improved on the basis of observed sales data. 483 Thus the total inventory holding costs and stockouts can be reduced and customer service level 484 and profits increased 485 by better matching supply and demand 486. Besides this risk and cost reduction, postponement can lead to economies of scale, synergistic effects, delayed increase in costs in the value chain and thus decreased capital commitment, and higher flexibility or leagility. 487 However, it is usually necessary to redesign 488 the product specifically for delayed differentiation and to modify the order of manufacturing steps (resequence or operations reversal) 489. This may decrease production volume variability though. 490 Time-based postponement at the company level can increase 478 Lee (1998). 479 Lee (1996), Aviv and Federgruen (2001b: 579). 480 Yang and Schrage (2009: 837). 481 Lee and Tang (1997: 52), Aviv and Federgruen (2001a: 514, 2001b: 579), Alfaro and Corbett (2003: 12, 15), Piontek (2007: 87), Dominguez and Lashkari (2004: 2113), Anupindi et al. (2006: 192f.), Caux et al. (2006), Jiang et al. (2006), Cholette (2009). 482 Weng (1999), Aviv and Federgruen (2001b: 579). 483 Aviv and Federgruen (2001b: 579). 484 Lee (1996), Lee and Tang (1997), Jiang et al. (2006), Davila and Wouters (2007), Li et al. (2008, 2009), LeBlanc et al. (2009: 19), Mahar and Wright (2009), Wong et al. (2009). 485 Jiang et al. (2006), Chopra and Meindl (2007: 364), Cholette (2009). 486 Chopra and Meindl (2007: 364). 487 Aviv and Federgruen (2001b: 579), Herer et al. (2002), Piontek (2007: 86f.). 488 Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994), Davila and Wouters (2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 346). 489 Lee and Tang (1997: 40, 1998), Kapuscinski and Tayur (1999), Jain and Paul (2001), Swaminathan (2001: 129f.), Shao and Ji (2008), Simchi-Levi et al. (2008: 346). 490 Jain and Paul (2001). 47

63 3 Methods of Risk Pooling supply chain inventory, as other members of the supply chain may be forced to use more speculation, i. e. hold more inventories. 491 Postponement reduces risk associated with order mix and order quantity, but may increase stockouts or lost sales due to longer lead, delivery, or order cycle times. 492 Speculation provides a high availability and flexibility because of short lead times and few stockouts. 493 Decreasing (increasing) speculation and increasing (decreasing) postponement increases (decreases) transportation costs and decreases (increases) inventory holding costs. 494 Postponement and speculation can be combined installing an intermediary stage between the suppliers and the buyers close to the buyers and holding uncommitted, anticipatory inventory of the suppliers ready to be shipped on request 495 or postponing only the uncertain part of the demand and producing the predictable part at a lower cost without postponement in tailored postponement 496. The combined principle of postponementspeculation 497 may lower both inventory risk by centralization and order fulfillment times and lost sales. 498 Internet retailers, for instance, depend more on both inventory location speculation (in-stock inventory) and postponement (drop-shipping) to fulfill their orders as their market share and product popularity increase. 499 As products are only delivered after a customer order is received, in general postponement leads to a centralized logistics system. 500 Speculation rather has a decentralizing effect on the logistics system 501 and finished products inventory is stored as close as possible to customers. At the same time speculative processes lead to consolidated flows of goods because of higher order quantities. 502 Consolidated flows of goods support the tendency towards centralized logistics systems. 503 These opposite movements are no contra- 491 García-Dastugue and Lambert (2007). 492 Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al. (2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13). 493 Bucklin (1965: 27), Delfmann (1999: 195). 494 Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Graman and Magazine (1998), Delfmann (1999: 195), Van Hoek (2001: 161). 495 Bucklin (1965: 31). 496 Chopra and Meindl (2007: 366). 497 Bucklin (1965: 28). 498 Bucklin (1965: 31), Pishchulov (2008: 27). 499 Bailey and Rabinovich (2005). 500 Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper (1998: 14), Van Hoek (1998a: 95), Van Hoek et al. (1999b: 506), Nair (2005: 458). 501 Shapiro and Heskett (1985: 53), Klaas (2002: 154). 502 Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157). 503 Pfohl et al. (1992: 95), Kloster (2002: 122). 48

64 3 Methods of Risk Pooling diction, but rather proof of the complex interdependencies between process and structure variables in logistics systems. 504 In practice there is a trend towards customer order oriented logistics systems 505 or postponement as a logical consequence to centralization 506, increasing uncertainty in buyer markets, increasing product variety, individualization of demands, and regional expansion of supply in a globalized economy 507. Postponement is analyzed by Eppen and Schrage (1981) in the steel industry, Heskett and Signorelli (1984) at Benetton, Fisher and Raman (1996) at Sport Obermeyer, Feitzinger and Lee (1997) at HewlettPackard, Magretta (1998), Van Hoek (1998b), and Kumar and Craig (2007) at Dell, Inc., Van Hoek (1998b) with the SMART car, Battezzati and Magnani (2000) for industrial and fast moving consumer goods in Italy, Brown et al. (2000) at a semiconductor firm, Chiou et al. (2002) in the Taiwanese IT industry, Huang and Lo (2003) in the Taiwanese desktop personal computer industry, Dominguez and Lashkari (2004) at a major household appliance manufacturer in Mexico, Caux et al. (2006) in the aluminum-conversion industry, Davila and Wouters (2007) at a disk drive manufacturer, Cholette (2009) in wine distribution, ElMaraghy and Mahmoudi (2009) in the optimal location of nodes of a global automobile wiper supply chain considering currency exchange rates and the optimal modular product structure, Kumar et al. (2009) at 3M Company, Kumar and Wilson (2009) in off-shored manufacturing, and Wong et al. (2009) in terms of the optimal differentiation point positioning and stocking levels. Van Hoek (2001) reviews the literature on postponement dating back to 1965 and puts it in a systematic framework. Boone et al. (2007) review postponement literature published from 1999 to 2006 and conclude research should be extended to non-manufacturing postponement, investigate the slow rate of postponement adoption among practitioners, and continue assessing the relationship between postponement and uncertainty Capacity Pooling Capacity pooling is the consolidation of production 508, service 509, transportation 510, or inventory capacities of several facilities. 511 Without pooling every facility fulfills demand just with its 504 Klaas (2002: 157f.). 505 Van Hoek et al. (1999b: 506). 506 Van Hoek (1998a: 95). 507 Ihde (2001: 36). 508 Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281). 509 Cachon and Terwiesch (2009: 149ff., 325, 349, 467). 510 Masters (1980: 71), Evers (1994), Ihde (2001: 33), Chen and Chen (2003), Chen and Ren (2007). 49

65 3 Methods of Risk Pooling own capacity. With pooling demand is aggregated and fulfilled by a single (perhaps virtually) joint facility. 512 If demand is stochastic, a higher service level can be attained with the same capacity or the same service level can be offered with less capacity. 513 It is also advantageous, if there are economies of scale in obtaining capacity or satisfying demand. 514 Capacity pooling may pool supplier lead times, if the capacities receive separate deliveries from the suppliers and provide the whole system with the possibility of partial stock replenishments 515. However, this is considered under stock sharing (transshipments). Consequently, capacity pooling is regarded as a 1/0 risk pooling method. It is predominantly associated with combining manufacturing capacity 516 and thus creating manufacturing flexibility 517. We adopt this view in the following and subsume pooling of inventory capacity under inventory pooling. Manufacturing flexibility means that a plant is capable of producing more than one product. With no flexibility each plant can only produce one product, with total flexibility every plant can produce every product (as in manufacturing postponement). Flexibility allows production shifts to high selling products to avoid lost sales. 518 Capacity pooling can increase effective capacity to serve more demand, which leads to higher expected sales, profits, and capacity utilization 519 or lower manufacturing flow time. 520 Aggregating demands which were served by individual capacities before and are now served with pooled capacity can reduce demand variability and thus the demandcapacity mismatch cost. However, installing flexibility is expensive 521. If demands are of different variability, pooling production capacities may increase inventory costs for the low-demand-variability facility 522 or total cost Anupindi et al. (2006: 223), Yu et al. (2008: 1), Cachon and Terwiesch (2009: 463). 512 Yu et al. (2008: 1). 513 Anupindi et al. (2006: 224), Yu et al. (2008: 1). 514 Yu et al. (2008: 1). 515 Cf. Evers (1997, 1999), Wanke and Saliby (2009). 516 Plambeck and Taylor (2003), Iyer and Jain (2004), Jain (2007), Simchi-Levi et al. (2008: 281). 517 Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Pringle (2003), Chopra and Sodhi (2004: 59), Goyal et al. (2006), Van Mieghem (2007), Mayne et al. (2008), Cachon and Terwiesch (2009: ). 518 Cachon and Terwiesch (2009: 344f.). 519 Pooling server capacity in a queuing system does not affect utilization, as demand is never lost, but might have to wait longer than desired. The amount of demand fulfilled is independent of the capacity structure (Cachon and Terwiesch 2009: 346). 520 Weng (1998: 587), Chen and Chen (2003), Plambeck and Taylor (2003), Chen and Ren (2007), Van Mieghem (2007: 1251), Cachon and Terwiesch (2009: 344). 521 Cachon and Terwiesch (2009: 151, 348). 522 Iyer and Jain (2004). 523 Jain (2007). 50

66 3 Methods of Risk Pooling 3.5 Sales and Distribution Product Pooling Product pooling is the unification of several product designs to a single generic or universal design 524 or reducing the number of products or stock-keeping units ( SKU rationalization 525 ) thereby serving demands that were served by their own product variant before with fewer products. 526 The demands for the different products are aggregated to the demand for the universal design or the reduced number of SKUs, which fluctuates less thanks to risk pooling. Thus product pooling can reduce demand variability, improve matching of supply and demand, reduce the demand-supply mismatch cost 527, and increase sales and profit or lower inventory for a given target service level. 528 Thus, product pooling constitutes a 1/0 risk pooling method. However, a universal design might not provide the desired functionality to consumers and therefore might not achieve the same total demand as a set of focused designs. It does not permit price discrimination and may be more expensive than focused designs, because the components or quality of components of the universal design targeted to many different uses might not be necessary to some consumers. There might be economies of scale in production and procurement of a single universal component relative to small quantities of several components and lower labor costs though. 529 The risk pooling benefits of selling a universal product may compensate its higher cost. 530 Product pooling is closely related to postponement, where the differentiation of a universal product to individual ones is delayed 531, standardization, and component commonality. It may prohibit risk pooling benefits from product substitution. 524 Cachon and Terwiesch (2009: 330). 525 Jabbonsky (1994), Lahey (1997), Kulpa (2001), Pamplin (2002), Alfaro and Corbett (2003: 12), Neale et al. (2003), HTT (2005), Sheffi (2006: 119, 2007), Covino (2008), Harper (2008), Sobel (2008: 172), Chain Drug Review (2009a, 2009b), Hamstra (2009), MMR (2009), Orgel (2009), Pinto (2009a, 2009b), Ryan (2009), Thayer (2009). 526 Alfaro and Corbett (2003: 12), Cachon and Terwiesch (2009: , 467). 527 The demand-supply mismatch cost is the cost of left over inventory (overage cost) and the opportunity cost of lost sales (underage cost) (Cachon and Terwiesch 2009: , 433f.). 528 Cachon and Terwiesch (2009: 331), Hamstra (2009), Ryan (2009), Thayer (2009: 23). 529 Cachon and Terwiesch (2009: 335), Hamstra (2009), Ryan (2009), Thayer (2009: 23). 530 Cattani (2000). 531 Alfaro and Corbett (2003: 25). 51

67 3 Methods of Risk Pooling Product Substitution In product substitution one tries to make customers buy another alternative product, because the original customer wish is out of stock 532 or although it is available ( demand reshape 533 ). In manufacturer-driven substitution the manufacturer or supplier makes the decision to substitute. Typically the manufacturer or supplier substitutes a higher-value or functionality product, component, or service for a lower-value or functionality one that is not available (downward substitution). 534 Axsäter (2003b: 438) compares this to unidirectional transshipments, where transshipments are only allowed in one direction, perhaps because warehouses differ in their shortage costs. Swaminathan (2001: 130) and Simchi-Levi et al. (2008: 348) relate substitution to product standardization: With risk pooling through product standardization a large variety of products may be offered, but only a few kept in inventory. If a product not kept in stock is ordered, either the product is made or procured or the order filled by downward substitution. In customer-driven substitution, a customer makes the decision to substitute, because his original wish is not available. 535 If only one of two products is a substitute for the other one, this is called one-way substitution. In two-way substitution either product substitutes for the other one. 536 Substitution allows the manufacturer or retailer to aggregate demand across substitutable components or products 537 (demand pooling 538 ). Demand reshape increases the demand mean and variability of one product while reducing them for the other product. Substitution and demand reshape reduce total demand variance 539 ( demand-pooling effect of substitution 540 ) and thus allow to reduce the safety stock for a given customer service level (product availability, fill rate, or average backlogged demand) 541, increase service level without increasing inventory, or a combination of both 542 or increase total profit and raise the customer service level simultaneously by risk pooling 543. Product substitution is a 1/0 risk pooling method. 532 Swaminathan (2001: 130), Chopra and Meindl (2007: 324ff.), Simchi-Levi et al. (2008: 348). 533 Eynan and Fouque (2003, 2005). 534 Gerchak et al. (1996), Hsu and Bassok (1999), Bassok et al. (1999), Swaminathan (2001: 130), Chopra and Meindl (2007: 324), Simchi-Levi et al. (2008: 348). 535 Netessine and Rudi (2003), Chopra and Meindl (2007: 324). 536 Chopra and Meindl (2007: 325). 537 Chopra and Meindl (2007: 324ff.). 538 Yang and Schrage (2009: 837). 539 Eynan and Fouque (2003, 2005). 540 Ganesh et al. (2008: 1124). 541 Chopra and Meindl (2007: 326). 542 Liu and Lee (2007). 543 Weng (1999), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348). 52

68 4 Choosing Suitable Risk Pooling Methods Findings from our thorough literature review are now merged in a synoptic comparison about conditions favoring the ten identified risk pooling methods, their advantages, disadvantages, and basic trade-offs. Based on this synopsis a decision support tool is developed for choosing appropriate risk pooling methods for a specific situation. Therefore a situational approach is used. 4.1 Contingency Theory We adopt a situational approach similar to contingency theory. It claims that there is no one best way as e. g. in Weberian bureaucracy 544 to manage a company or make decisions. 545 It depends (is contingent) on internal and external conditions (contingency factors). 546 The best way to organize depends on the nature of the environment to which the organization must relate 547. Contingency theory is mainly criticized for its positivist 548, deterministic, unidirectional, linear relationships and reduction of complex situations to a limited number of contingency factors. 549 Different from the usual contingency approach we not only use quantitative, empirical 550, but mainly qualitative analysis based on reviewed quantitative analyses, which Donaldson (1999) rejects. Kieser and Kubicek (1992: 220ff.), on the other hand, propose to use empirical correlations not as causalities, but for further interpretations, hypotheses, and empirical analyses. Höhne (2009: 89) and the references she gives support that contingency factors are based on both empirical analyses and plausibility assumptions. We cannot confirm that there is [o]ne best way for each given situation 551 as our contingency factors are not exhaustive and mutually exclusive and thus several risk pooling methods may be adequate. However, Donaldson (1996: 118ff.) remarks there are as many 544 Weber (1980: 124ff., 551ff.). 545 Scherer and Beyer (1998: 333f.). 546 Drazin and van de Ven (1985), Miller and Friesen (1980: 268), Scherer and Beyer (1998: 334). 547 Scott (1981: 114). 548 Positivism is a system recognizing only that which can be scientifically verified or logically proved (Soanes and Hawker 2008). 549 Miller and Friesen (1978: 921), Miller (1981: 2f.), Meyer (1993: 1176), Staehle (1994: 49f., 54), Schreyögg (1995: 159ff., 217f., 219), Frese (1992: 193), Scherer and Beyer (1998: 334ff.), Klaas (2002: 99f.), Höhne (2009: 92f.). 550 Scherer and Beyer (1998: 334), Höhne (2009: 89, 91, 94). 551 Scherer and Beyer (1998: 334). 53

69 4 Choosing Suitable Risk Pooling Methods combinations of environment, strategy, and structure ( fits ) as there are different environmental situations. Thus, for every situation (combination of contingency factors) there may be one best risk pooling strategy, i. e. combination and implementation of risk pooling methods. Starbuck (1981, 1982: 3), Frese (2000: 488f.), and Schreyögg (2008: 54) consider the contingency approach obsolete. Others, however, deem it important 552, popular, often used, and useful 553, as it is open and flexible 554, allows to be combined with other approaches to advance research 555, to make action and design recommendations 556, to systematize contingency factors 557, and to conduct a practice-oriented analysis 558. Therefore it seems adequate for our research. 4.2 Conditions Favoring the Individual Risk Pooling Methods Table D.3 is based on our thorough literature review and shows which conditions render which risk pooling methods favorable. The favorable conditions are demand-, lead-time-, transportation-, service-level-, order-policy-, storage-, product-, process-, company-, and competitionrelated. The risk pooling methods (columns) are arranged according to the previous chapter's structure. Further research is needed to complete this table and confirm the favorable conditions for the different risk pooling methods, especially for product pooling, central ordering, (particularly non-manufacturing) capacity pooling, virtual pooling, and product substitution/demand reshape. We could only speculate and hypothesize about which risk pooling methods the stated favorable conditions also apply to. Therefore, we only check marked them for methods where there is confirmation in the literature and the table is not exhaustive. References and explanations are given in footnotes. 552 Pugh (1981), Donaldson (2001), Daft (2009: 26). 553 For example in management (Hiddemann 2007: 16, Schröder 2008: 68, Müller-Nedebock 2009: 22, Sommerrock 2009: 88, 93f., Segal-Horn and Faulkner 2010: 157f.), organization (Dzimbiri 2009: 86, Güttler 2009: 73f., Höhne 2009: 83, 91, 93f., March 2009: 25, Nobre et al. 2009: 31), finance (Pfeifer 2010: 253), information systems (Andres and Zmud 2001, Sugumaran and Arogyaswamy 2003, Khazanchi 2005), supply management (Staudinger 2007), business logistics and SCM (Hult et al. 2007, Huang et al. 2008, Doch 2009: 39ff.), and supply chain risk management (Wagner and Bode 2008) research. The literature database Business Source Complete accessed via EBSCOhost showed 1,139 results for the search term contingency theory on June 18, Staudinger (2007: 41), Güttler (2009: 73f.). 555 Sommerrock (2009: 144), Güttler (2009: 73f.). 556 Hiddemann (2007: 16), Schröder (2008: 69), Doch (2009: 39ff.), Pfeifer (2010: 262). 557 Doch (2009: 41). 558 Staudinger (2007: 41), Sommerrock (2009: 94). 54

70 4 Choosing Suitable Risk Pooling Methods 4.3 The Risk Pooling Methods' Advantages, Disadvantages, Performance, and Trade-Offs Table D.4 presents the considered risk pooling methods' possible advantages, disadvantages, and basic trade-offs in choosing or rejecting them and compares their performance vis-à-vis other ones. In summary, the risk pooling methods may, on the one hand, reduce demand and/or lead time variability, (safety) stock, lead time, as well as procurement, production, transportation, personnel, and warehouse cost and increase service level (product availability and fill-rate), utilization, sales, profit, and competitiveness. On the other hand, they may increase R&D, redesign, component, product, procurement, production, transportation, transaction, and warehousing cost, as well as cycle stock and cycle time, and decrease customer service, sales, profit, and product functionality. We only check marked the respective risk pooling method's most important effects that are confirmed in the studied literature. References are given in footnotes. Explanations are only given where essential, as we already dealt with the individual risk pooling methods in detail earlier. These three choices maintain the readability of the table. Tables D.3 and D.4 can be used to choose suitable risk pooling methods for a specific company under specific conditions. Scoring methods could be applied or the risk pooling method with the highest net present value or profit (advantages minus disadvantages expressed in monetary units) could be chosen. However, the following decision support tool condenses the most definite distinguishing factors and helps to make a first decision on possible risk pooling methods elegantly, before carrying out a more thorough cost-benefit analysis. 55

71 4 Choosing Suitable Risk Pooling Methods 4.4 A Risk Pooling Decision Support Tool Figure 4.1: Risk Pooling Decision Support Tool 56

72 4 Choosing Suitable Risk Pooling Methods The Risk Pooling Decision Support Tool (RPDST) depicted by a flow chart in figure 4.1 helps in choosing a risk pooling strategy to cope with demand and/or lead time uncertainty (1), if it cannot be reduced more efficiently by other means 559. To facilitate the reader's orientation we introduced numbers in round brackets in this explanation and the flow chart. We will guide you through the flow chart step by step and critically revisit it at the end. (2) If product variety is important, inventory pooling (IP) 560, capacity pooling (CP) 561, component commonality (CC) 562, postponement (PM) 563, product substitution (PS) 564, transshipments (TS) 565, virtual pooling (VP) 566, centralized ordering (CO), and order splitting (OS) are a possibility. IP, CP, TS, VP, CO, and OS may also be applied, if product variety is not important. The first four methods might make more sense, if product variety is important. CC, PM, and PS are not expedient without product variety. If product variety is not important, product pooling (PP), IP, CP, TS, VP, CO, and OS are considered. PP is only meaningful, if product variety is not important. The other methods may also be applied, if product variety is important. (3) If product variety is important and the stockout penalty cost high compared to inventory carrying cost (savings), PS 567, TS 568, VP, CP, CC, PM 569, CO 570, and OS 571 may be 559 In addition to risk pooling it may be reduced by e. g. adding inventory or capacity, having redundant suppliers, which resembles order splitting, increasing responsiveness (Chopra and Sodhi 2004: 55, 60) (quick response (Heil 2006)), flexibility, and capability (Chopra and Sodhi 2004: 55, 60), and improving forecasting (Heil 2006). In LeBlanc et al.'s (2009: 29) model, for instance, PM is favorable unless the forecast is completely accurate. 560 Pfohl (1994: 142), Schulte (1999: 378), Weng (1999: 80), Vahrenkamp (2000: 221), Alfaro and Corbett (2003: 28). 561 Jordan and Graves (1995: 577), Cachon and Terwiesch (2009: 344). 562 Srinivasan et al. (1992: 27), Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348), Song and Zhao (2009: 493). 563 Zinn (1990: 14), Lee and Tang (1997: 52), Pagh and Cooper (1998: 24), Swaminathan and Tayur (1998), Van Hoek (1998b, 2001: 161, 173), Van Hoek et al. (1998), Aviv and Federgruen (2001a: 514), Ihde (2001: 36), Matthews and Syed (2004: 34), Graman and Magazine (2006: 1072), Chopra and Meindl (2007: 363f.), Cachon and Terwiesch (2009: 342, 363). The potential benefits of postponement in the presence of product variety are reduced inventory levels and/or improved service levels (Graman and Magazine 2006: 1072). In general, delayed differentiation is an ideal strategy when [ ] Customers demand many versions, that is, variety is important (Cachon and Terwiesch 2009: 342). 564 Weng (1999: 80), Swaminathan (2001: 130), Eynan and Fouque (2003), Simchi-Levi et al. (2008: 348). 565 Grahovac and Chakravarty (2001), Wong (2005), Simchi-Levi et al. (2008: 231). 566 Guglielmo (1999), Randall et al. (2002: 56f., 2006: 567), Kroll (2006). 567 Liu and Lee (2007: 1, 41). Only the risk pooling effect is considered, the financial aspect of different product margins neglected. 568 TS reduce demand and lead time variability by pooling demand and lead times, decrease stockouts, and thus are sensible, if stockout costs are high (Evers 1997, Needham and Evers 1998, Evers 1999: 133, 2001: 313, Jung et al. 2003, Hu et al. 2005, Wee and Dada 2005: 1519, 1529, Zhao et al. 2005: 545, Lue 2006, Chiou 2008: 428). However, in Jung et al. (2003) the savings from lateral TS decrease with increasing shortage cost from a certain value upwards. 57

73 4 Choosing Suitable Risk Pooling Methods applied. PS (costs of persuading a customer to buy a substitute in case of a stockout and possible customer dissatisfaction because he did not obtain the desired product 572 ), TS (transshipping costs), VP (drop-shipping or cross-filling costs), CP (large costs to have flexibility), and CC (common component costs) may only be worthwhile, if stockout costs are high. PS 573, PM 574, CO 575, and OS 576 may also be considered, if the stockout penalty cost is low. IP is suitable, if the stockout cost is low compared to the inventory (carrying cost) savings from combining inventories, as it increases the distance between the inventory and the buyer and thus delivery time and therefore might increase stockouts 577. As noted earlier in section 2.4 and table D.3, Dai et al. (2008: 407, 410f.) show when IP by a supplier for two retailers may increase the supplier's and retailers' total profits. We consider IP for low stockout costs only, as the decision for or against inventory pooling vis-à-vis the other risk pooling methods is considered. (4) If (2) is answered in the affirmative, (3) with High, and the supplier lead time is highly variable/uncertain or long, TS 578, VP, PM 579, CO, and OS 580 are considered. TS 569 PM may increase flexibility and responsiveness to customer demand (Zinn and Bowersox 1988: 133, Herer et al. 2002, Davila and Wouters 2007), increase customer service, decrease stockout costs, and thus may be sensible, if stockout costs are high. 570 Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5). CO may increase responsiveness to customer demand, if the allocation of the central order to the delivery warehouses, retailers, or stores can be postponed and made more responsively according to more recent demand information (Cachon and Terwiesch 2009: 341), decrease stockout costs, and thus may be sensible, if stockout costs are high. 571 OS can reduce lead time (variability) through lead time pooling and increase inventory availability. Therefore it can be reasonable, if stockout costs are high (Evers 1999: 122, 132). 572 Swaminathan (2001: 131). 573 PS may be worthwhile in case of low stockout costs, if the sold substitute's profit margin is higher than that of the original product wish. Besides, even if the original customer wish is available, PS or demand reshape lowers the total variability of demand and thus inventory costs (Eynan and Fouque 2003, 2005). 574 Besides the risk and stockout cost reduction, PM can lead to economies of scale, synergistic effects, delayed increase in costs in the value chain and thus decreased capital commitment, and higher flexibility (Lee and Tang 1997: 52, Van Hoek 2001: 162, Aviv and Federgruen 2001b: 579, Herer et al. 2002, Kim and Benjaafar 2002: 16, Ma et al. 2002: 534, Graman and Magazine 2006: 1078, Piontek 2007: 86f.). Therefore it may be worthwhile, even if stockout costs are not particularly high. 575 PM (Zinn and Bowersox 1988: 125f., Van Hoek 2001: 161, Rabinovich and Evers 2003b: 35, Yang et al. 2005b: 994, Graman and Magazine 2006: 1078, Pishchulov 2008: 13, Mahar and Wright 2009: 3061) and CO (McGavin et al. 1993: 1094, Cachon and Terwiesch 2009: 341) may lead to a longer delivery time (from the supplier to the retailer) and more stockouts, and therefore stockout costs should be low. Bucklin (1965: 27) remarks that speculation, the opposite strategy to postponement, limits the loss of consumer goodwill due to stockouts. CO may also increase stockouts, if it decreases local knowledge (Ganeshan et al. 2007: 341). 576 Although OS may reduce lead time variability, the split orders are delivered sequentially and thus may lead to more stockouts than a single order or delivery and stockout costs should be low (Chiang 2001: 73, cf. Chiang and Chiang 1996). 577 McKinnon (1989: 104), Fawcett et al. (1992: 36ff.), Schulte (1999: 80, 377), Vahrenkamp (2000: 31f.), Bowersox et al. (1986: 278f.), Evers (1999: 122f.), Ballou (2004b: 573f.), Schmitt et al. (2008a: 14), Cachon and Terwiesch (2009: 336). 578 Evers (1999: 132), Herer et al. (2002), Hu et al. (2005), Wanke and Saliby (2009). However, Evers (1996) finds the percentage reduction in safety stocks obtained by using non-emergency transshipments decreases with increasing coefficient of variation of lead time (lead time variability) and average lead 58

74 4 Choosing Suitable Risk Pooling Methods and VP by cross-filling may pool demands and lead times, i. e. reduce demand and lead time variability. 581 Long order cycles 582 and inflexible production processes 583 favor TS. Long supplier/production lead times support CO. 584 For CO the lead time before the distribution center (DC) should be longer than the one after it. 585 PM and CO may also reduce lead time (variability/uncertainty): Postponement permits firms to be more responsive and other advantages that are often mentioned are risk-pooling and lead-time uncertainty reduction 586. If, for instance, in CO or consolidated distribution product differentiation is delayed (PM) in the DC, total lead time may be reduced 587. Since larger common orders for multiple locations make more frequent shipments economically possible between the suppliers and the DC and the DC and the retailers 588, consolidated distribution might decrease lead time (uncertainty) despite the additional lead time from the DC to the various retailers. If there is no DC and the retailers merely place joint orders with the suppliers which are then allocated according to more recent demand information to the retailers just before the delivery means leave the suppliers, there is no additional lead time between the DC and the retailers. The retailers' higher demand power through CO and closer collaboration between the retailers and the suppliers might further reduce average lead times and lead time fluctuations. OS only pools lead times 589 and is only worthwhile, if lead time time at each market (Evers 1996: 126ff.). It increases at a decreasing rate as the proportion of demand at market i retained at facility i approaches the point where demand at i is spread evenly among all locations (Evers 1996: 128). By spreading the demands, and therefore the variability, more evenly across locations, the opportunity to smooth demand fluctuations increases at a decreasing rate (Evers 1996: 128). 579 Transhipments may be seen as a type of time postponement (Rabinovich and Evers 2003b). 580 Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1997, 1999: 122, 132), Kelle and Miller (2001), Thomas and Tyworth (2006, 2007: 178, 188). According to Thomas and Tyworth (2007: 188), sequentially releasing a split order according to more recent demand information may reduce demand variability. Chiang and Chiang (1996) and Chiang (2001: 67, 73), however, recommend splitting an order into multiple deliveries for low demand variability or service level only. The number of stockout possibilities is proportional to the number of deliveries. Thus OS increases stockouts, the more, the more variable demand is. Kelle and Miller (2001: 407) find dual sourcing may decrease stockouts, if there is no single, reliable supplier [ and] the variability of the lead-time demand is considerable, but is only suitable, if lead time uncertainty cannot be reduced. According to Evers (1999: 123) and Wanke and Saliby (2009: 679) splitting a replenishment order into multiple orders only pools lead times, not demand. Consequently, we recommend OS only for high lead time variability and its lead time pooling, but not its debatable demand variability reduction effect. 581 Evers (1997, 1999: 121), Zhao et al. (2008). 582 Jönsson and Silver (1987a: 224). 583 Grahovac and Chakravarty (2001: 580). 584 Eppen and Schrage (1981: 51), Schoenmeyr (2005: 5). 585 Cachon and Terwiesch (2009: 341), cf. Kumar and Schwarz (1995). 586 Caux et al. (2006: 3243). 587 Dilts (2005: 43). Personal correspondence with Professor David M. Dilts on July 7, Cachon and Terwiesch (2009: 341). 589 Evers (1999: 122, 132). 59

75 4 Choosing Suitable Risk Pooling Methods variability 590 and unit values are (unusually) high (in relation to industry standards) 591. For high stockout costs per unit (3), high lead time variability (4), low order quantity and/or safety stock levels emergency TS perform particularly well compared to OS. 592 In case (4) lead times are neither highly variable/uncertain nor long, but rather demand is variable/uncertain and thus demand pooling important, PS 593, CP 594, CC 595, PM 596 and CO 597 may be appropriate. 590 Kelle and Silver (1990a, 1990b), Pan et al. (1991: 4), Evers (1999: 132), Thomas and Tyworth (2007: 178, 188). 591 Thomas and Tyworth (2007: 178, 188). 592 Evers (1999: 132). 593 Eynan and Fouque (2003, 2005), Chopra and Meindl (2007: 324ff.), Ganesh et al. (2008: 1124). 594 Yu et al. (2008: 1). 595 We will now examine whether CC reduces (the effects of) lead time variability/uncertainty and therefore should be considered, if it is high: Benton and Krajewski (1990: 407) show in a computer simulation experiment with 320 observations that manufacturing environments with intermediate stocking points and commonality significantly dampen the effects of lead time uncertainty (410), tend[ ] to reduce the level of backlogs as well as dampen their sensitivity to lead time uncertainty (412), because commonality causes intermediate inventories to increase (413, cf. 410). However, they are more sensitive to vendor quality ( the ability to supply the requested quantity of nondefective parts or raw materials (404)) and therefore might increase backlogs (413). Yet, the ambition of risk pooling is to decrease inventory for a given service level or vice versa or a combination of both. If there are no intermediate stocking points, they are more sensitive to lead time uncertainty (410). Hence, CC by itself does not reduce the effects of lead time uncertainty. Benton and Krajewski (1990) give no intuitive explanation for the increasing total inventory. Usually common components reduce safety and thus total stock, because they are used in several products (Labro 2004: 362). Eynan and Rosenblatt (1996), Chandra and Kamrani (2004: 175), and Mohebbi and Choobineh (2005: 473) cite Benton and Krajewski (1990) in a truncated manner, aiming at the reduction of lead time uncertainty through CC. Labro (2004) deals with Benton and Krajewski (1990) more accurately. Although Ma et al. (2002) assume deterministic replenishment leadtimes (Ma et al. 2002: 526), they find the major benefits of commonality are risk-pooling and lead time uncertainty reduction. These lead to a safety stock reduction and have been studied extensively by many researchers, including, but not limited to, Baker et al. (1986), Collier (1982), Guerrero (1985), Gerchak et al. (1988), Eynan and Rosenblatt (1996), and Grotzinger et al. (1993) (Ma et al. 2002: 524). Like most CC research (e. g. McClain et al. 1984, Eynan 1996, Thonemann and Brandeau 2000, Hillier 2002a, 2002b, Thomas et al. 2003, Labro 2004: 359), all these researchers mention demand uncertainty reduction as a benefit of CC (Baker et al. 1986: 983, Collier 1982: 1300, 1303, Guerrero 1985: 396, Gerchak et al. 1988: 755), only Eynan and Rosenblatt (1996) lead time uncertainty reduction in the inadequate manner described above. Under restrictive assumptions, Mohebbi and Choobineh (2005: 476, 481) conclude CC tends to be more beneficial with both random component procurement order delays and demand uncertainty than with only one of these uncertainties. They assume, for instance, that the component procurement lead time can only be longer not shorter than the planned one. Actual uniformly distributed demand for finished products, however, can be higher or lower than the forecast (476). Costs (481), safety stock and safety lead times are neglected. Backorders are filled after current demand (475). These researchers do not explain the causes for their observations. Lead time delays mostly reduce average total inventory per component per period (477f.), as they perhaps reduce the time a component remains in storage. This effect increases with increasing demand uncertainty (477), perhaps because a longer-than-planned delivery time may be offset by lower-than-forecast actual demand. This may be amplified by CC and lead to a higher service level than without commonality. However, the product with the lowest number of (three) components and without commonality shows the lowest inventory per component and the highest service levels (478f.). Song and Zhao (2009: 22) even find that in dynamic assemble-to-order systems commonality may not decrease inventories under the first-in-first-out (FIFO) with identical and under the FIFO and modified FIFO (MFIFO) rule for dynamically allocating common components to demand with non-identical com- 60

76 4 Choosing Suitable Risk Pooling Methods (5) If (2) is Yes, (3) High, (4) Yes, and the fixed cost per order high, TS 598, VP, PM, and CO 599 are favorable. If the replenishment order cost is high, one rather resorts to other cheaper and/or faster possibilities (TS, VP, and PM) than placing a replenishment order or tries to combine orders by CO to reduce the number of orders and exploit economies of scale (EOS) and thus lower ordering costs. If it is low 600 and there are no transportation EOS 601, OS may be considered. Due to smaller orders OS cannot take advantage of quantity and transportation discounts and a long-term partnership with a single supplier, but several suppliers may guarantee competitive pricing and other advantageous terms. 602 TS 603, VP, and PM may also be applied, if the fixed order cost is low. (6) In case (2) is Yes, (3) High, (4) Yes, (5) High, and the transshipment or transportation cost is high and there are EOS in ordering, CO 604 or PM 605 can be worthwhile. If the transshipment or transportation cost is low and there are no EOS in ordering, TS 606, VP 607 or likewise PM 608 can be applied. PM may forego EOS: 609 Zinn and ponent replenishment lead times. The value of commonality tends to decrease as [ the common component replenishment lead time] increases under either FIFO or MFIFO. If the common component replenishment lead time fluctuates strongly and the common component is not available, all the products using this component cannot be built. Thus lead time variability/uncertainty of the common component supplier might be more severe than of a specific component supplier (cf. Benton and Krajewski 1990: 413, Labro 2004: 363). All these findings led us to not recommend CC by itself for coping with high lead time variability/uncertainty and to only consider it for the low lead time variability/uncertainty case. 596 Jain and Paul (2001: 595ff.), Anupindi et al. (2006: 193), Chopra and Meindl (2007: 365), Pishchulov (2008: 24). 597 If we follow Cachon and Terwiesch (2009: 336, 339, 341f., 349), CO may only pool demands and may also be applied if lead time (variability) is low. PM or delayed differentiation and CO may increase lead time and only pool demands during lead time. 598 Herer and Rashit (1999: 525), Daskin (2003), Herer and Tzur (2003: 419). 599 Schwarz (1981: 147), Evers (1995: 5, 1999: 133), Gürbüz et al. (2007: 294). 600 Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188). 601 Evers (1999: 122f.), Thomas and Tyworth (2006, 2007), Sajadieh and Eshghi (2009). 602 Evers (1999: 122f.). 603 For TS the fixed order cost is irrelevant (Evers 1999: 132). 604 Eppen and Schrage (1981: 67), Hu et al. (1997, 2005: 34), Gürbüz et al. (2007: 293), Cachon and Terwiesch (2009: 341). 605 Allowing online sales to accumulate and postponing assigning them to a fulfillment site can lead to lower inventory costs (Mahar and Wright 2009), higher utilization of transportation means, and EOS in ordering. PM does not necessarily increase transportation distance, so that transportation costs may be irrelevant. Customers may be willing to wait, so that no premium transportation cost is incurred. The product and process are usually designed, so that the delayed differentiation can be conducted fast (Lee and Tang 1997), the delivery delay is insignificant, and no premium transportation cost is incurred. PM can exploit EOS (Piontek 2007: 87). 606 Jönsson and Silver (1987a: 224), Robinson (1990), Evers (1999: 132f.), Grahovac and Chakravarty (2001), Jung et al. (2003), Hu et al. (2005), Anupindi et al. (2006: 191), Kutanoglu (2008: 356f.). Still TS may save fixed and variable replenishment costs (Herer and Rashit 1999: 525, Herer and Tzur 2003: 419), if e. g. one location makes a larger replenishment order to transship some of it to other locations especially in a dynamic deterministic demand environment (Herer and Tzur 2003: 419). Herer and Rashit (1999) consider a single period random demand environment. 607 Anupindi et al. (2006: 191). In VP small-orders may be drop-shipped more expensively than full truck loads (Randall et al. 2002, Cachon and Terwiesch 2009: 328f.). 61

77 4 Choosing Suitable Risk Pooling Methods Bowersox (1988: 124f.) find that labeling, packaging, and manufacturing PM can lead to lost EOS. In case of large EOS in the manufacturing and/or logistics processes some speculation should be applied instead of manufacturing and full PM. Speculation, the opposite strategy to PM, rather leads to EOS: Speculation permits goods to be ordered in large quantities rather than in small frequent orders. This reduces the costs of sorting and transportation 610. (7) If (2) is Yes, (3) High, (4) Yes, (5) High, and (6) Yes, do you prefer redesigning your products and/or processes 611 to achieve leagility, both agility (responsiveness) and leanness (cost minimization), (PM) 612 to a less expensive, fast implementable and changeable solution that keeps inventory closer to customers (CO) 613? If yes, you may implement PM (8), otherwise CO (9). Time and form PM are appropriate, if welltimed product delivery to and differentiation for the customer are more important than company-internal cost issues. 614 On the one hand, CO may decrease responsiveness because of a lack of local knowledge about sales 615 when ordering. On the other hand, it may increase responsiveness because of allocating the joint order to the delivery warehouses, retailers, or stores according to more recent demand information and because aggregate forecasts usually are more accurate than disaggregate ones 616. It is more likely that CO leads to EOS in ordering than PM. While CO and speculation lead to consolidation of goods in jointly used transfer and transformation processes and EOS 617, PM tends to singularize batches of goods in separate transfer and transformation processes 618. To determine which PM strategy might be most appropriate, you may turn to Zinn and Bowersox (1988), Cooper (1993), Pagh and Cooper (1998), Yang et al. (2004), and Yeung et al. (2007). (10) In case (6) is answered in the negative, and the less expensive, fast implementable and changeable, less cross-functional solution is preferred to redesigning products 608 Bucklin (1965: 27), Zinn and Bowersox (1988: 126), Christopher (1992), Feitzinger and Lee (1997), Delfmann (1999: 195), Van Hoek (2001: 161). 609 Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994). 610 Bucklin (1965: 27). 611 Products and/or processes may have to be redesigned for PM (Lee and Tang 1997, Van Hoek 1998a, Kim and Benjaafar 2002, Yang et al. 2005b: 994, Davila and Wouters 2007, Piontek 2007). PM might lead to higher manufacturing costs (Chopra and Meindl 2007: 365). 612 Feitzinger and Lee (1997), Fliedner and Vokurka (1997), Van Hoek et al. (1999a), Christopher (2000), Van Hoek (2000a), Christopher and Towill (2001), Herer et al. (2002), Graman and Sanders (2009: 206). 613 Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349). 614 Alderson (1957), Rabinovich and Evers (2003b: 34). 615 Ganeshan et al. (2007). 616 Cf. footnote Bucklin (1965: 27), Pagh and Cooper (1998: 14), Delfmann (1999: 195), Klaas (2002: 157). 618 Cooper (1983: 71), Bowersox and Closs (1996: 475), Klaas (2002: 157). 62

78 4 Choosing Suitable Risk Pooling Methods and/or processes 619 and there is no or no significant lead time (uncertainty) reduction benefit in PM after all, TS and VP are considered. If in addition your supplier, wholesaler, or warehouse locations have small-order drop-shipping or cross-filling capabilities 620 (11), VP (12) may be appropriate. If not, TS (13) may do, especially if the TS cost is lower than the VP cost. VP may reduce investment in inventory and fulfillment capabilities as well as overall handling and warehousing costs 621 more than TS. However, VP is only recommendable, if your company possesses the necessary IS capabilities and is powerful within the supply chain, because it might lose product margin and control to the dropshipping party, which could negatively affect service quality. The drop-shipping party might bypass the company and directly sell to customers as it possesses all the information transparency it needs. 622 Virtual inventories provide little benefit in product categories, such as grocery, where consolidation of orders is necessary but impossible to accomplish from a few consolidated wholesalers 623. TS and PM might be used in combination, as emergency TS, an important type of time PM, support implementing form PM 624. If you do not mind redesigning products and/or processes and a more expensive midto long-term cross-functional implementation and your PM strategy may reduce lead time uncertainty (10), PM (14) might be the right method to reduce both demand and lead time uncertainty. TS can increase leagility like PM 625, but perhaps more inexpensively and faster. Returning to (5), if the fixed order cost is low, and (15) both demand uncertainty reduction and lead time (uncertainty) reduction and fewer order placements are preferred to only lead time uncertainty reduction, but avoiding premium transportation and in-transit inventory costs, TS 626, VP 627, and PM 628 come into question and the al- 619 Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001), Swaminathan (2001: 129f.), Herer et al. (2002), Kim and Benjaafar (2002: 12), Yang et al. (2005b: 994), Davila and Wouters (2007: 2245), Shao and Ji (2008), Simchi-Levi et al. (2008: 345f.). 620 Randall et al. (2002: 56), Cachon and Terwiesch (2009: 328f.). 621 Randall et al. (2002: 55). 622 Randall et al. (2002: 56). 623 Randall et al. (2002: 57). 624 Rabinovich and Evers (2003b: 41f.). 625 Herer et al. (2002: 201), Zhao et al. (2008). 626 Tagaras (1989), Tagaras and Cohen (1992), Evers (1997, 1999), Hong-Minh et al. (2000), Herer et al. (2002), Çömez et al. (2006). 627 Randall et al. (2002: 56). 628 Jain and Paul (2001: 595ff.), Yang et al. (2004: 1054), Dilts (2005: 43), Anupindi et al. (2006: 193), Caux et al. (2006: 3243), Chopra and Meindl (2007: 365), Pishchulov (2008: 24). 63

79 4 Choosing Suitable Risk Pooling Methods ready explained decision process (10) through (14) starts. If (15) is negated, OS 629 (16) may be implemented. Moving upwards again, in case (3) is low and (17) inventory reduction is more important than agility (customer responsiveness), IP 630 and PS 631 are considered. If (17) is negated, PM, PS, CO, and OS come into consideration. PM improves agility 632 and flexibility 633 and enables product variety 634, but may not decrease inventory as much as IP or PS. PS performs better than IP in terms of location accessibility and lost sales (customer responsiveness) 635, but may not decrease inventory as much as IP. With PS the customer may get a product right away, but not the originally desired one. CO performs worse than IP in terms of inventory reduction, but keeps inventory near customers 636. The allocation of the central order to the delivery warehouses, retailers, or stores can be postponed and made more responsively according to more recent demand information. Reducing lead time uncertainty OS may lower (safety) stock for a given service level 637, but not as much as IP, as the former only pools lead times, not demands 638. Simultaneously splitting an order among suppliers can reduce cycle stock due to successive deliveries of smaller split orders 639, but not the sum of in-transit and cycle stock in the system 640. OS may be more responsive than IP, because it reduces lead time variability and keeps inventory close to customers. However, OS may increase stockouts, if demand variability is high due to successive deliveries. 641 In case (17) is confirmed, and (18) the fast implementable, changeable, less expensive (especially in terms of transportation cost) solution with higher location accessibility and 629 Evers (1999: 132), Thomas and Tyworth (2007: 172, 178, 188). 630 IP may reduce inventory more than PS, but creates distance between inventory and customers and therefore may reduce product availability and profits (Bowersox et al. 1986: 278f., McKinnon 1989: 104, Fawcett et al. 1992: 36ff., Evers 1999: 122f., Schulte 1999: 80, 377, Vahrenkamp 2000: 31f., Ballou 2004b: 573f., Schmitt et al. 2008a: 14, Cachon and Terwiesch 2009: 336). 631 PS might be seen as not as responsive as PM because the customer does not receive his original wish and is persuaded to buy a substitute, which may cause some customer dissatisfaction, but might reduce inventory more than PM. 632 Zinn and Bowersox (1988), Herer et al. (2002), Davila and Wouters (2007). 633 Lee and Tang (1997: 52), Feitzinger and Lee (1997: 117ff.), Van Hoek (2001: 162), Ma et al. (2002: 534), Graman and Magazine (2006: 1078), Piontek (2007: 86f.). 634 Cachon and Terwiesch (2009: 341). 635 Eynan and Fouque (2003, 2005). 636 Eppen and Schrage (1981), Cachon and Terwiesch (2009: 349), Pishchulov (2008: 22). 637 Evers (1999: 122, 132), Thomas and Tyworth (2006: 245). 638 Evers (1999: 122, 132). 639 Moinzadeh and Nahmias (1988), Pan and Liao (1989), Ramasesh (1990), Sculli and Shum (1990), Pan et al. (1991), Ramasesh et al. (1991), Hong and Hayya (1992), Zhou and Lau (1992), Lau and Zhao (1993), Ramasesh et al. (1993), Chiang and Benton (1994), Lau and Zhao (1994), Gupta and Kini (1995), Chiang and Chiang (1996), Hill (1996), Ganeshan et al. (1999), Chiang (2001), Ghodsypour and O'Brien (2001), Ryu and Lee (2003), Thomas and Tyworth (2006: 245). 640 Thomas and Tyworth (2006: 254). 641 Chiang and Chiang (1996) and Chiang (2001: 67, 73). 64

80 4 Choosing Suitable Risk Pooling Methods fewer lost sales is preferred to product functionality and inventory reduction, PS (19) may be suitable. If (18) is negated, IP (20) might be the right method. In contrast to PS, IP entails aggregate and thus more accurate forecasts 642. Individual demand forecasts for controlling the previously separate inventories are replaced by a more accurate aggregate forecast for managing the consolidated inventory. Of course, PS can only be applied, if products or parts are substitutable, which the preceding affirmation of question (2) suggested. If (17) is negated and (21) lead times are highly variable/uncertain or long, PM, CO, and OS are considered (cf. (4)). If then (22) the fixed order cost is high (CO and PM may be appropriate (cf. (5))) and (23) a perhaps cheaper solution, that keeps inventory closer to customers, is preferred to redesigning products and/or processes to offer customized products more responsively and there are EOS in ordering 643, CO (24) may be chosen. If (23) is negated, PM (25) might be appropriate. If (22) is low (OS and PM may be appropriate (cf. (5))) and product and/or process redesign to reduce demand uncertainty and perhaps lead time (uncertainty) (cf. (4)) is preferred to only lead time pooling and keeping inventory close to customers, but incurring higher ordering costs (26), then PM (25) might be suitable. Otherwise, OS (27) may be worthwhile. If (21) is negated and rather demand pooling is important, PM, PS, and CO are scrutinized (cf. (4)). If then (28) the less expensive, fast implementable, and changeable solution is preferred to giving the customer always the desired product (not a substitute), but in a longer delivery time and with product and/or process redesign, PS (19) may be appropriate, otherwise PM and CO are considered. If in this latter case (29) the cheaper solution that keeps inventory closer to customers is preferred to product and/or process redesign and leagility and there are EOS in ordering, then CO (24) may be appropriate, otherwise PM (14) (cf. (23) to (25)). If the importance of product variety is denied in (2) and lead times are highly variable/uncertain or long (30), TS, VP, OS, and CO are considered (cf. (4)). In case (30) is negated and rather demand uncertainty reduction is important, PP 644, IP 645, CP, and CO 646 (cf. (4)) are considered as they only pool demands and thus reduce demand variability, but not lead time variability. According to Dilts (2005) CO may also reduce lead times (cf. (4)). 642 Cf. footnote CO may utilize EOS in procurement (Eppen and Schrage 1981: 67, Hu et al. 1997, 2005: 34, Gürbüz et al. 2007: 293, Cachon and Terwiesch 2009: 341). 644 Cachon and Terwiesch (2009: 331f.). 645 Evers (1996: 115, 1997: 57, 60, 1999: 121). 646 Cf. Cachon and Terwiesch (2009: 336, 339, 341f., 349). 65

81 4 Choosing Suitable Risk Pooling Methods If (30) is affirmed, (31) the fixed order cost is high (CO, TS, and VP are considered (cf. (5))), (32) the transshipment or transportation cost is high and there are EOS in ordering, CO (33) may be reasonable (cf. (6)). If (32) is negated and (34) your supplier, wholesaler, or warehouse locations have small-order drop-shipping or cross-filling capabilities 647 (cf. (11)), VP (35) may be appropriate, especially if it is less expensive than TS. If not, TS (36) may do (cf. (11) to (13)). If (31) is low (OS, TS, and VP are considered (cf. (5))) and (37) both demand uncertainty and lead time (uncertainty) reduction, fewer stockouts, and order placements are preferred to only lead time pooling, but avoiding premium transportation and in-transit inventory costs of stock transfers 648, then TS and VP are considered further and the already explained decision process (34) to (36) is triggered again. If (37) is answered in the negative, OS (38) may be economically sensible. If (30) is negated and (39) accommodating demand uncertainty 649 is preferred to reducing inventory and system utilization (arrival divided by service rate) is high, CP and CO are considered. While the relative benefit of inventory pooling tends to diminish with utilization, the relative benefit of capacity pooling tends to increase with utilization in a production-inventory system with endogenous supply lead times. 650 CP or manufacturing flexibility is more valuable with approximately equal total capacity and expected demand. 651 CO does not reduce inventory as much as IP, but keeps it near customers. 652 The postponed more responsive allocation of the central order to the delivery warehouses, retailers, or stores according to more recent demand information enables better matching of supply and demand 653 (also cf. (17)). If afterwards EOS in ordering and a preference for a possibly less expensive, fast implementable and changeable solution are affirmed in (40), CO (33) may be appropriate. If (40) is negated and (41) CP/(manufacturing) flexibility is cheaper than capacity, CP (42) might be applied 654. Goyal and Netessine (2005) may help to choose a type of manufacturing flexibility (volume and/or product flexibility) 655. If capacity is cheap- 647 Randall et al. (2002: 56). 648 Evers (1997: 72, 1999: 123f.). 649 Cachon and Terwiesch (2009: 344, 348). 650 Benjaafar et al. (2005: 565). 651 Cachon and Terwiesch (2009: 348). 652 Eppen and Schrage (1981: 61), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349). 653 Cachon and Terwiesch (2009: 341). 654 Cachon and Terwiesch (2009: 348). 655 Volume flexibility is [t]he ability to adjust the output volume of a product without incurring large costs, product flexibility the ability to manufacture different products and to efficiently shift production from products with low demand to products with high demand (Goyal and Netessine 2005: 2). For a monopolist, product flexibility reduces uncertainty in demand for individual products more and in aggregate de- 66

82 4 Choosing Suitable Risk Pooling Methods er than CP/flexibity, adding capacity (43) might be a better choice. 656 CP may be more appropriate for manufacturing, CO for trading companies (cf. (48)). If (39) is negated, PP and IP (cf. (17)) are considered, as inventory reduction is given priority. If then (44) product availability is preferred to product functionality, PP (45) may lead to a higher product availability than IP (46): It does not increase the distance between products and customers and may enable EOS in production and procurement of a single universal component or product, but might degrade product functionality, not achieve the same total demand as a set of focused designs, and eliminate some brand/price segmentation opportunities. 657 Returning to (4), if lead times are not highly variable/uncertain or long, rather demand pooling is important (PS, CP, CC, PM, and CO are considered), and (47) your products share components or qualities to satisfy the same or similar needs or you are willing to create these commonalities, then PS, CP, CC, PM, and CO may be applied. Substitute goods satisfy the same or similar needs and therefore are seen as an alternative or replacement by consumers. The reason for this replacement relationship is the functional replaceability between two goods, if they correspond in price, quality, and utility or performance so that they are able to meet the consumer's need. This thus enables substitution structurally. 658 CP is also based on commonalities: Common design, assembly processing, training in common methods, suppliers capable of coping with common design and processing and reacting to volume and complexity are needed. 659 CC designs products that share components. 660 PM advantages partly arise from CC. 661 CO does not require (component) commonality. However, the centrally ordered products usually are needed by several requisitioners (delivery warehouses, stores, or departments). Therefore one could say the products are common to two or more locations. mand less than volume flexibility. Moreover, product flexibility copes better with substitutable and worse with complementary products than volume flexibility. Using both volume and product flexibility can lead to diseconomies of scope (Goyal and Netessine 2005: 1). 656 Cachon and Terwiesch (2009: 348). 657 Cachon and Terwiesch (2009: 335). 658 Wildemann (2008: 72). 659 Mayne et al. (2008). 660 Chopra and Meindl (2007: 326ff.). 661 Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al. (1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al. (2008). 67

83 4 Choosing Suitable Risk Pooling Methods PM and CP perform better with similar demand. For PM that means that demand is of comparable size 662 or that the standard deviations of demand for items in the product line are similar 663, for CP approximately equal total capacity and expected demand 664 and similar demand variability 665. Capacity sharing among independent companies is more beneficial, if they are similar in their characteristics (work content, demand rates, or delay costs). 666 PM may reduce EOS 667 or increase the cycle/delivery lead time 668. If then (48) a less expensive, fast implementable and changeable solution is preferred to product and/or process redesign and leagility and you run a trading or retail company rather than a pure manufacturing company, then PS and CO may be applied, otherwise CP, CC, and PM. PS can be implemented faster than CP, CC, and PM. It may only incur the costs of persuading a customer to buy a substitute 669 and maybe cause customer dissatisfaction with the substitute purchase 670. CO may be less responsive, but also less expensive, implemented within a shorter time frame, and involve less departments (mainly purchasing and sales) than CP, CC, and PM. It does not require a product redesign either. CP 671, CC 672, and PM 673 may necessitate a costly product and/or process redesign and therefore also involve at least manufacturing and R&D in addition. As products are only delivered after a customer order is received, in general PM leads to a centralized logistics system 674 and may increase the distance between inventory and customers relative to CO 675 and even more so compared to PS. With CP a product is produced, 662 Chopra and Meindl (2007: 363f.). 663 Zinn (1990: 14), Alfaro and Corbett (2003: 18f., 24), Cachon and Terwiesch (2009: 342). 664 Jordan and Graves (1995: 583), Cachon and Terwiesch (2009: 348). 665 Iyer and Jain (2004), Jain (2007). 666 Yu et al. (2008: 26). 667 Zinn and Bowersox (1988: 124), Yang et al. (2005b: 994). 668 Zinn and Bowersox (1988: 126), Van Hoek (2001: 161), Rabinovich and Evers (2003b: 35), Yang et al. (2005b: 994), Graman and Magazine (2006: 1078), Pishchulov (2008: 13), Mahar and Wright (2009: 3061). 669 Eynan and Fouque (2003, 2005). 670 Swaminathan (2001: 133). 671 Jordan and Graves (1995), Mayne et al. (2008), Cachon and Terwiesch (2009: 349). 672 Bagchi and Gutierrez (1992: 817), Swaminathan (2001: 129, 131), Ma et al. (2002: 536), Simchi-Levi et al. (2008: 345f., 348). 673 Lee and Tang (1997: 40, 1998), Van Hoek (1998a), Kapuscinski and Tayur (1999), Jain and Paul (2001), Swaminathan (2001: 129f.), Kim and Benjaafar (2002: 12), Davila and Wouters (2007: 2245), Yang et al. (2005b: 993f.), Piontek (2007), Shao and Ji (2008), Simchi-Levi et al. (2008: 346). 674 Shapiro and Heskett (1985: 53), Zinn and Bowersox (1988: 126), Pfohl (1994: 145), Pagh and Cooper (1998: 14), Van Hoek (1998a: 95). 675 Eppen and Schrage (1981), Pishchulov (2008: 22), Cachon and Terwiesch (2009: 349). 68

84 4 Choosing Suitable Risk Pooling Methods stored, or transported, or a customer served where there is capacity, so that the distance between inventory and customers may increase. PM research is highly conceptual 676. Applications are mostly limited to manufacturing 677, e. g. in Zinn and Bowersox (1988: 121), Lee et al. (1993), Dröge et al. (1995), Feitzinger and Lee (1997), Garg and Tang (1997), Lee and Tang (1998: 172), Van Hoek (1997), Dominguez and Lashkari (2004), Caux et al. (2006), Chopra and Meindl (2007: 365), Davila and Wouters (2007), Harrison and Skipworth (2008: 193), Kumar et al. (2009), and Kumar and Wilson (2009). Bailey and Rabinovich (2005) exceptionally apply PM in internet book retailing. Currently, relatively simple postponement applications are practiced in wholesale and logistics services as supplementary services. More complex, high value adding manufacturing activities are still the primary domain of manufacturers and these are not often outsourced to logistics service providers 678. Our survey results in appendix A support that CC 679, PM, and CP 680 are predominantly applied in manufacturing, CO or consolidated distribution 681 and PS 682 rather in trade, so that their implementation might be more promising here. PS is more efficient than CC. 683 In case (48) is answered in the affirmative (PS and CO are considered) and (49) matching supply and demand and product functionality are preferred to a less costly, fast implementable and changeable solution with higher (substitute) product availability, but possible customer dissatisfaction because of substitution and there are EOS in ordering, then CO (33) may be appropriate, otherwise PS (50). PS offers the customer a product right away, however, not the originally desired one but a substitute, which may lead to customer dissatisfaction. CO gives the customer the desired product maybe in a longer lead time or the sale is lost. PS can be implemented and changed faster and less expensively than CO. The latter may benefit from EOS in procurement though (cf. (23)). 676 Yang et al. (2005b: 994). 677 Boone et al. (2007: 594). 678 Van Hoek and Van Dierdonck (2000: 205). 679 Gerchak and Henig (1989), McDermott and Stock (1994), Tsubone et al. (1994), Sheu and Wacker (1997), Swaminathan and Tayur (1998), Swaminathan (2001), Hillier (2002b), Ma et al. (2002), Labro (2004), Mohebbi and Choobineh (2005), Chew et al. (2006), Simchi-Levi et al. (2008: ), Nonås (2009), Wazed et al. (2008, 2009: 76). 680 Upton (1994, 1995), Jordan and Graves (1995), Weng (1998), Plambeck and Taylor (2003), Pringle (2003), Iyer and Jain (2004), Benjaafar et al. (2005), Jain (2007), Goyal et al. (2006), Van Mieghem (2007), Mayne et al. (2008). 681 Eppen and Schrage (1981), Cachon and Terwiesch (2009: ). 682 Anupindi et al. (1998), Smith and Agrawal (2000), Mahajan and Van Ryzin (2001a, 2001b), Rajaram and Tang (2001), Eynan and Fouque (2003, 2005), Zhao and Atkins (2009). 683 Eynan and Fouque (2005). 69

85 4 Choosing Suitable Risk Pooling Methods If (48) is negated (CP, CC, and PM are considered), (51) the costs to have CP or (manufacturing) flexibility are lower than the costs for CC (common components, product redesign, and possible cannibalization) and PM (product and/or process redesign or resequencing), then the already explained decision process (41) through (43) has to be completed. If (51) is answered in the negative (CC and PM are considered) and the product 684 (cf. (47)) and (52) (manufacturing) process is modular 685, the firm maximizes its performance by adopting 686 PM (53): It will help to maximize effective forecast accuracy and minimize inventory costs 687. In case the product is modular 688 (cf. (47)) but the process is not 689, then differentiation cannot be delayed, but CC (54) is the most effective approach 690. Simchi-Levi et al. (2008: 348) express this more cautiously: CC is likely to be effective. However, we follow the primary source Swaminathan (2001: 132). To determine the optimal level of CC you may refer to Boysen and Scholl (2009). Nevertheless, if the process (and the product) is modular, CC and PM may both be applied. To choose between them the CC 691 cost (product redesign 692 and possible cannibalization of higher priced components 693 ) has to be traded off against the PM cost (higher production, transportation, and process and/or product redesign cost (cf. (7))). This be- 684 Feitzinger and Lee (1997), Lee (1998), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek (1998a, 1998b, 2001: 173), Chiou et al. (2002: 113, 122), Yang et al. (2004: 1053), Simchi-Levi et al. (2008: 348), ElMaraghy and Mahmoudi (2009: 483). 685 Feitzinger and Lee (1997), Van Hoek et al. (1998), Swaminathan (2001: 131), Van Hoek (2001: 173), Simchi-Levi et al. (2008: 348). A modular product, e. g. a personal computer as opposed to a shirt, is assembled from a variety of modules such that there is a number of options the customer is interested in for each module. This is important for concurrent and parallel processing (Swaminathan 2001: 128, Simchi- Levi et al. 2008: 345). A modular (manufacturing) process, e. g. semiconductor wafer fabrication as opposed to oil refining, consists of discrete operations, so that inventory can be stored in semi-finished form between operations. Products are differentiated by undergoing a different subset of operations during the manufacturing process. Modular products are not necessarily made in modular processes (Swaminathan 2001: 128, Simchi-Levi et al. 2008: 345). 686 Swaminathan (2001: 131). 687 Simchi-Levi et al. (2008: 348). 688 Weng (1999), Swaminathan (2001: 131), Yang et al. (2005b: 993), Simchi-Levi et al. (2008: 348). 689 Swaminathan (2001: 131), Simchi-Levi et al. (2008: 348). 690 Swaminathan (2001: 132). 691 The common component may be more expensive than the dedicated ones that it replaces (Hillier 2002a, 2002b, Van Mieghem 2004: 419, Zhou and Grubbström 2004, Mohebbi and Choobineh 2005: 473). Still component commonality may reduce total cost (Van Mieghem 2004: 419, Hillier 2002a, 2002b). 692 Sometimes, it is necessary to redesign products and/or processes to achieve commonality (Bagchi and Gutierrez 1992: 817, Swaminathan 2001: 129, 131, Ma et al. 2002: 536, Simchi-Levi et al. 2008: 345, 348), which may result in a smaller and more economical set of components though (Whybark 1989). 693 Excessive part commonality can reduce product differentiation, so that less expensive customization options might cannibalize sales of more expensive parts (Ulrich and Ellison 1999, Kim and Chhajed 2000, 2001: 219, Desai et al. 2001, Krishnan and Gupta 2001, Ramdas and Sawhney 2001, Simpson et al. 2001, Swaminathan 2001: 131, Heese and Swaminathan 2006, Simchi-Levi et al. 2008: 348). 70

86 4 Choosing Suitable Risk Pooling Methods comes important if not form, but place and time PM are considered. CC and PM often are connected and can be applied together. Maybe applying both of them may be more economical than applying only one. PM implementation may require CC 694 ( postponement through standardization 695 ). According to Caux et al. (2006: 3244), PM in the form of delayed differentiation can be implemented by process restructuring, component commonality and product design. If (47) is negated, then CO and CP are considered, because they do not require CC, especially if transportation or storage capacity is pooled. Yet, we consider CP related to inventories under IP. If then (55) the costs of CO are lower than both the ones of CP and adding capacity and there are EOS in ordering, then CO (33) may be effective. Otherwise CP and adding capacity are considered and the already explained decision process (41) to (43) still has to be followed. Frequently the risk pooling methods cannot be separated mutually exclusively, because they are favorable under similar conditions as tables D.3 and D.4 already showed. If the decisions in the RPDST are not selective and disjunctive, the respective risk pooling methods are considered for both choices. The RPDST only shows tendencies and enables general statements about the advantageousness of risk pooling design options, since the specific size of the costs and benefits are unknown and the complex interdependencies are simplified. The advantageousness of specific risk pooling methods in a specific situation for a specific company depends on specific cost parameters and their interaction or ratios. 696 In a particular company case risk pooling design recommendations might differ from this RPDST. The identified conditions and recommendations for risk pooling methods depend on the selected reference framework. Therefore a study with the same topic might attain a different classification and thus different results. The framework gives general recommendations about the advantageousness of risk pooling methods. Afterwards a company should weigh the costs and benefits of the different suitable options expressed in monetary units to reach a decision about which risk pooling strategy to implement. Expenses for implementing the risk pooling strategy might exceed the achievable savings. 697 Some benefits besides decreased (inventory) cost such as increased flexibility, responsiveness, and customer service level are hard to quantify. Resequencing due to PM might lower inventory levels, but increase the inventory value per unit. However, if customiza- 694 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347). 695 Ma et al. (2002: 534). 696 Cf. e. g. Wanke (2009) on IP. 697 Cf. Simchi-Levi et al. (2008: 349). 71

87 4 Choosing Suitable Risk Pooling Methods tion is postponed, the generic products may have a lower value than the customized ones. Tariffs and duties for undifferentiated products might be lower. Still products and processes might be more expensive under some risk pooling methods. 698 Implementing risk pooling might lead to positive or negative effects not studied in detail in this RPDST, such as human resistance or negative impacts on the whole supply chain. It might be appropriate to apply risk pooling methods just to certain products (e. g. the ones with uncertain demand). 699 Combining several risk pooling methods might improve performance. 700 Using, for instance, time PM (e. g. emergency TS and inventory centralization), form PM (product customization), and enterprise-wide information systems together improved enterprisewide inventory management performance more than using each of these methods separately in an empirical model based on 216 large and established U.S. manufacturing firms. 701 (Logistics) PM might go hand in hand with IP (inventory centralization) or CO (centralized distribution). 702 A hybrid strategy of pooling demand by centralizing inventories (IP) but splitting supply by multisourcing (OS) can be worthwhile. 703 Substitutable products support the implementation of variety PM. 704 Demand substitution furthermore facilitates flexible manufacturing without competition and may facilitate its adoption with competition. 705 CP may exploit CC. 706 Kutanoglu (2008) considers both emergency lateral shipments from other local facilities and direct shipments (VP in the sense of Netessine and Rudi 2006) from one central warehouse of service parts to repair high-technology hardware systems such as computers and telecommunication devices in case of a stockout at a local facility within the time window necessary for the target service level. Alfredsson and Verrijdt (1999: 1430) find conjoint use of lateral TS and direct deliveries can reduce costs significantly, particularly for slow moving parts. Investing only in direct delivery flexibility may increase costs dramatically, unless pipeline flexibility is applied. Pipeline flexibility means that a customer backorder is satisfied by the part that arrives first either via normal replenishment or via direct delivery. Similarly, Wong et al. (2007b: 1056) remark emergency direct deliveries from the central 698 Simchi-Levi et al. (2008: 349). 699 Cf. Chopra and Meindl (2007: 366). 700 Cf. e. g. Hong-Minh et al. (2000). 701 Rabinovich and Evers (2003b: 38, 42f.). 702 Shapiro (1984), Zinn and Bowersox (1988), Van Hoek (1998a, 2001), Nair (2005: 451). 703 Benjaafar et al. (2004a: 1442). 704 Heskett and Signorelli (1984), Kopczak and Lee (1994), Goyal and Netessine (2005: 22). 705 Goyal and Netessine (2006: 1). 706 Mayne et al. (2008). 72

88 4 Choosing Suitable Risk Pooling Methods warehouse and the plant in case of stockouts in a two-echelon system are only worthwhile, if lateral TS between local warehouses are not possible. The RPDST neglects the degree to which the different favorable risk pooling methods should be applied and their opposite methods. Often two opposing methods are applied in combination to a certain degree (e. g. centralization and decentralization, consolidation and singularization, postponement and speculation). Speculative inventories, for instance, should be held in the logistics channel wherever their costs do not exceed the savings achievable by postponement. 707 Furthermore, the certain part of the product line or the generic product can be made less expensively to stock, the uncertain products or product variants to order. An empirical verification of the derived results pertaining to the design recommendations appears worthwhile. The theoretical analysis revealed fundamental interdependencies of risk pooling methods and facilitates the practical risk pooling design. Possible deviations from business practice can be disclosed by empiricism. The analytic process can be adapted accordingly. Therefore, we will apply the RPDST to a German paper wholesaler to determine risk pooling methods that may reduce the demand and lead time uncertainty it faces. 707 Bucklin (1965: 28). 73

89 5 Applying Risk Pooling at Papierco In this chapter we will first introduce Papierco to you and some problems it faces. Afterwards we will determine risk pooling methods with the help of the RPDST developed in the previous chapter to solve these problems and consider their application at Papierco in more detail. Finally we will summarize our results. 5.1 Papierco A German paper wholesale company (to protect confidentiality we call it Papierco in the following) pursues the business strategy of a decentralized, differentiated full-line distributor and system provider of paper, printing accessories, as well as screenprinting and advertising systems, which precludes central warehouses and minimal storage. This corporate strategy seems to be Papierco's competitive advantage, as its competitors cannot offer such a ubiquitous and fast delivery service as well as broad assortment. The decentralized warehouse network also constitutes a competitive advantage in the light of increasing fuel costs, autobahn toll, climate change, environmental legislation, and increased traffic volume. Papierco delivers its products from its warehouses with its own truck fleet or has them drop-shipped from paper plants to its customers. According to its management, Papierco is a full-line wholesaler, as its 32,739 customers (mainly printing offices) need all kinds of different product specifications mostly within 24 hours. If a product with a low turnover was eliminated from the assortment, some customers might not buy some other products either anymore due to product interdependencies. The alliance Papierco of several legally independent paper wholesalers and exchange of items between 21 regional warehouses in case of a stockout (emergency transshipments) allow the individual companies and locations to offer a larger product assortment than they could store on their own. Not every of the 7,000 product specifications Papierco offers is stored at every location. Products with a low turnover share are only stocked at few locations due to cost considerations. 708 This is called selective stocking 709, selective stock keeping 710, or specialization 711. The idea behind selective stock keeping is lowering inventory holding costs by treating products differently without impairing the service level 708 Pfohl (2004a: 122f.), Simchi-Levi et al. (2008: 233). 709 Ross (1996: 310f.). 710 Pfohl (2004a: 118ff.). 711 Anupindi et al. (2006: 191f.). 74

90 5 Applying Risk Pooling at Papierco considerably. 712 Transshipments between Papierco's locations are necessary, so that every location can offer the complete assortment. The shipping decision is postponed until a customer order is received. Every warehouse thus functions as both a regional and central warehouse and can access products in every other warehouse as if all warehouses were one single warehouse (virtual inventory or warehouse). Hence Papierco takes advantage of inventory pooling, but mitigates some of the disadvantages of a central warehouse through the use of transshipments and information technology Problems Papierco Faces Fierce Competition in German Paper Wholesale Paper wholesale in Germany is characterized by strong competition especially in office, illustration printing, and offset paper: Sales stagnate, sales prices decrease, raw material, energy, and logistics costs increase. A lot of customers go bankrupt and there is an ongoing concentration process in the printing industry. 714 Paper manufacturers, the paper wholesale's suppliers, suffer from bad profitability due to increasing costs, overcapacities, and price pressure 715, as well as competition pressure from Asia and Eastern Europe 716, which they seek to improve by mergers and markups. The current international economic downturn intensifies the cost and competition pressure in all industrial sectors. Insufficient capacity utilization is a strain on the paper wholesale, its customers, and suppliers. Increasing profit margin pressure is believed to promote the consolidation tendency on all levels of the value chain. 717 Thus paper wholesale faces strong competition and economically stricken customers and suppliers, whose negotiation power increases because of mergers. Competitiveness and economic success can be secured on this market by efficient supply, storage, and distribution planning enabled by risk pooling, particularly since logistics incurs the highest costs at Papierco Supplier Lead Time Uncertainty The lead time of paper manufacturers fluctuates strongly, ranges from 14 to 154 days, and is on average days. It fluctuates subject to price increases, drop-shipping sales, (international) demand, and production setup times. Supplier lead times are entered into the enterprise 712 Pfohl (2004a: 122). 713 Cf. Sussams (1986: 8f.), Simchi-Levi et al. (2008: 233). 714 BVdDP (2009). 715 Kibat (2007). 716 FPT (2007b: 7). 717 BVdDP (2009). 75

91 5 Applying Risk Pooling at Papierco resource planning (ERP) system by a central master data maintenance in three German Papierco locations. The actual lead time of each supplier should rather be recorded for every delivery to improve the purchasing policy. Because of long and uncertain lead times for certain products paper merchants sometimes place so called phantom orders for product quantities they do not actually need as a precaution, which intensifies the bullwhip effect 718 and leads to even longer and more variable lead times. This once resulted in all orders having to be cancelled and only entering real orders (with a corresponding real demand) again afterwards. Thus lead times normalized again Customer Demand Uncertainty Total Sales (t) 320, , , , ,000 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 5.1: Total Fine Paper Sales in Tons per Month in Germany (BVdDP 2010a: 8) 718 Lee et al. (1997a: 98). 76

92 5 Applying Risk Pooling at Papierco Total Sales (t) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 5.2: Papierco's Total Fine Paper Sales to Customers in Germany in Tons per Month Total demand for fine paper in Germany is seasonal: It is higher in January, February, and March, lower from April till July, and increases up to November in order to decrease again in December as figures 5.1 and 5.2 show. Total customer demand depends on the overall economic development, i. e. on the available financial means for e. g. new products and advertising budgets. Warehouse sales made up 42 %, drop-shipping sales 58 % of all sales in 2007 and 2008, 719 respectively 43 % and 57 % in Warehouse sales of individual products per week per warehouse are sporadic without a trend or seasonal pattern as figure 5.3 shows exemplarily. 719 BVdDP (2009). 720 BVdDP (2010b). 77

93 5 Applying Risk Pooling at Papierco Figure 5.3: Papierco's 2007 Warehouse Sales to Customers per Week of Seven Standard Paper Products from the Hemmingen Warehouse 78

94 5 Applying Risk Pooling at Papierco When demand for items is intermittent, because of low volume overall and a high degree of uncertainty as to when and at what level demand will occur, the time series is said to be lumpy, or irregular 721. Among others many products and stocking locations might explain the lumpiness of demand for individual Papierco products. 722 The lumpy demand condition occurs when two or three times the standard deviation of the historical data exceed the forecast of the best model that can be fit to the time series 723. Ballou (2003a: 9) states in the PowerPoint presentation to Ballou (2004b) a time series is lumpy, if the mean of the series is less than or equal to three times the standard deviation of the series. Although the items in figure 5.3 are considered standard, on average they did not sell 8.29 weeks or around 16 % of the year 2007 and their standard deviation of sales per week per warehouse was on average 0.94 times their mean. Fast moving copy papers selling nearly every week were the least lumpy with the standard deviation being only 0.37 times the mean on average. Uncoated Cut-Size White Wood-Pulp Paper was the lumpiest with no sale in 34 weeks or almost two thirds of the year 2007 and a lumpiness factor (standard deviation of demand divided by mean demand) of 2.11, followed by the Folding Box Board with no sale in 15 weeks and a lumpiness factor of On average the standard deviation of an item's sale per month per warehouse is 2.24 times the mean sale per month per warehouse in Nearly one third (31.45 %) of the products show a standard deviation that is more than three times the arithmetic mean of sales per month per warehouse. In these cases the standard deviation is on average 3.78 times the mean. Of a lot of articles no unit is sold for several months and then suddenly some month a lot of units are sold. On average 7.83 months or nearly two thirds of the year 2007 a specific product is not sold. We conclude that demand per product per month is very random and lumpy or sporadic and therefore difficult to predict accurately by mathematical methods due to the wide variability in the time series 724. Risk pooling methods might produce relief here. Ballou (2004b: 311) suggests to use the reasons for the lumpiness in the forecast, separate forecasting of lumpy and regular demand products, not react quickly to random demand shifts without assignable cause and use slowly reacting forecast methods such as exponential smoothing with a low smoothing constant or a regression model refit annually 721 Ballou (2004b: 288). For further definitions please refer to e. g. Ghobbar and Friend (2003: 2105), Kukreja and Schmidt (2005: 2059), Bridgefield (2006), Gutierrez et al. (2008: 409, 412). 722 Cf. Ballou (2004b: 288, 310). 723 Ballou (2004b: 310). 724 Ballou (2004b: 310). 79

95 5 Applying Risk Pooling at Papierco at the most, and maybe make up for forecast inaccuracy by a higher inventory level for low demand items. Croston (1972) and Johnston and Boylan (1996) recommend an exponential smoothing constant of 0.05 to 0.20 for lumpy demand. Silver et al. (1998: 127), however, report pertaining to intermittent and erratic demand that [t]he exponential smoothing forecast methods [ ] have been found to be ineffective where transactions (not necessarily unit-sized) occur on a somewhat infrequent basis. [ ] Infrequent in the sense that the average time between transactions is considerably larger than the unit period, the latter being the interval of forecast updating. Lumpy or highly uncertain demand can be coped with by obtaining information directly from customers, collaborating with other supply chain and channel members, collaborative forecasting, forecasting total demand and apportioning it by regions, delaying supply response, product differentiation, and forecasting as long as possible, supplying the more certain products first, developing quick response and flexible supply systems, and applying the forecasting methods with caution. 725 Most of these suggested solutions rely on risk pooling Distribution Requirements Planning (DRP) Tons Inventory Sales to Customers Sales to Colleagues Total Warehouse Sales Goods Received from Suppliers Goods Received from Colleagues Total Goods Received Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 5.4: 2007 Incoming Goods, Warehouse Sales, and Inventory at Warehouse Hemmingen 725 Ballou (2003a: 39-42, 2004b: 310f., ). 80

96 5 Applying Risk Pooling at Papierco Tons Inventory Sales to Customers Sales to Colleagues Total Warehouse Sales Goods Received from Suppliers Goods Received from Colleagues Total Goods Received Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Months Figure 5.5: 2007 Incoming Goods, Warehouse Sales, and Inventory at Warehouse Reinbek Figures 5.4 and 5.5 illustrate Papierco's demand forecasting and inventory management problems using two standard Papierco warehouses. The inventory level is always around 1,000 to 2,000 tons higher than total warehouse sales. This may be partly explained by the large product variety. The Total Goods Received and Total Warehouse Sales curves often are opposite in phase or time-lagged, i. e. when total warehouse sales go up, often goods receipts go down or vice versa. Sales departments, product managers, and purchasing departments of the different warehouse locations do not collaborate in planning demand and requirements. The sales departments merely plan the customers' financial development, i. e. sales and contribution margins per customer. On the basis of the product managers' aggregated sales planning on the product group level for all German locations skeleton agreements are centrally negotiated with the most important suppliers. The purchasing departments forecast demand on the product level on the basis of the past six months' sales and order accordingly. These three planning processes are unconnected. The sales departments do not report any expected exceptional demands to the purchasing departments either. The latter only plan products sold via warehouses, without considering substitution effects between similar 81

97 5 Applying Risk Pooling at Papierco products or between warehouse and drop-shipping sales 726. Drop-shipping sales are conducted only by the sales departments. Papierco should create a uniform cross-functional demand planning process, in which sales, product managers, and purchasing collaborate, to contain extraordinary demands through the sales assistants' and product managers' profound market knowledge and enable a better demand forecast and thus order policy. Although Adam and Ebert (1976) show that objective statistical forecasting models produce more accurate results than subjective judgemental forecasts, Bunn and Wright (1991) remark expert forecasts had a higher quality than previous research claims. That is why Silver et al. (1998: 133) suggest combining these two approaches. The individual locations conduct their distribution requirements planning (DRP) without any coordination, so that inventory reductions at one location strain the transshipment flows and impair other locations' DRP. Thus, one location might deplete another one's stock of a specific product via transshipments. In the following week the latter location might have to obtain this product via transshipments from another warehouse due to a customer demand and so on. Likewise a warehouse may receive a supplier's delivery, although it has plenty of inventory left, while another one does not. This process seems to have taken on a life of its own in a vicious circle with increasing transshipment volumes and inventory variability at most warehouse locations. The increased transshipments did not reduce the aggregate safety stock, although this might be assumed because of the demand balancing effect thanks to the creation of a virtual inventory through transshipments. Allegedly the customer service level increased, which is difficult to verify, as Papierco does not record it in any way. We will recommend a not necessarily geographically centralized procurement, which forecasts and orders for all of Papierco's German locations on the product level and directs the suppliers' deliveries to the warehouses according to current demand in section Demand Forecasting Methods Increasing forecast accuracy decreases the need for risk pooling 727 (e. g. emergency transshipments) and safety stock and increases customer service level (product availability). 726 Sometimes a drop-shipping sale is converted into a warehouse sale, if the drop-shipping lead times are high. 727 Cf. Graman and Magazine (2006: 1081). 82

98 5 Applying Risk Pooling at Papierco Today Papierco uses the forecast methods 4 (Moving Average) and 10 (Linear Smoothing) of the twelve ones the ERP software JD Edwards OneWorld offers. Method 1 (Percent Over Last Year), method 2 (Calculated Percent Over Last Year), method 3 (Last Year To This Year) and method 8 (Flexible Method or Percent Over Months Prior) are so called naïve estimates and project sales of previous years into the future either directly or after multiplying them with a factor. 728 These methods are rather inadequate for Papierco, as sales of individual products differ significantly from year to year. Method 12 (Exponential Smoothing with Trends and Seasonality) is not suitable either, as demand for individual products does not follow a trend or seasonal pattern. Method 4 (Moving Average), Method 7 (Second Degree Approximation), which expresses sales in a curve, method 9 (Weighted Moving Average), method 10 (Linear Smoothing), which assigns weights to the sales numbers linearly decreasingly with a formula, and method 11 (Exponential Smoothing 729 ) are similar. They are suitable for shortterm forecasts for mature products without trends or seasonal patterns. 730 They could enable a good demand forecast for Papierco with an order cycle of two weeks. Method 5 (Linear Approximation) establishes a trend on the basis of two data points. Small changes influence long-term forecasts strongly. Method 6 (Least Squares Regression) also calculates a linear trend. Turning points and changes in the demand function are recognized late with the Linear Regression. If the sales data form a curve or show strong seasonal fluctuations, systematic forecast errors appear. 731 Methods 5 and 6 may be suitable for Papierco because of the short order cycle of two weeks, although demand for individual products shows no or only a short-term trend. Analyzing the forecast methods for the seven standard products, we discovered that a forecast based on sales of the last twelve months leads to improved results compared to the current one with six months. This comes as no surprise as Gibson and Horner (2005: 1f.) state that JD Edwards OneWorld forecasting accuracy improves with the length of the used sales history. The software is capable of using up to two years of sales history. Method 11 (Exponential Smoothing) and method 6 (Least Squares Regression) led to the best results most frequently. Ballou (2004b: 311) also recommends these methods for forecasting lumpy demand. 728 Oracle (2009). 729 Exponential Smoothing automatically uses linearly decreasing weights and is a weighted average of actual sales and the previous period's forecast. 730 Oracle (2009). 731 Oracle (2009). 83

99 5 Applying Risk Pooling at Papierco The results of method 11 (Exponential Smoothing) might be improved by letting JD Edwards OneWorld determine the smoothing constant alpha based on past sales instead of determining it arbitrarily. Methods 9 (Weighted Moving Average), 4 (Moving Average), and 10 (Linear Smoothing) also led to good results in order of descending quality. A naïve estimation (projection of the previous year's sales into the current year) did not give good results. The results could be improved by multiplying the previous year's sales with a growth factor. We used the mean absolute deviation (MAD) of the forecast values from the actual sales in 2006 and 2007 and the forecast error (the sum of the difference of the actual and the forecast sale per week) to measure the quality of the respective forecast method. For other forecast performance measures please refer to Gutierrez et al. (2008: 413f.). Comparison of the forecast accuracy of forecast methods is difficult 732, as the forecast errors of the two methods may be correlated 733. Besides a linear combination of forecasts from two or more [forecasting] procedures can outperform all of those individual procedures 734. According to Kang (1986) a regular average of forecasts of several methods leads to high-quality results. Tiacci and Saetta (2009) evaluate the impact of usually neglected possible interactions between demand forecasting methods and stock control systems on global system performance. Accordingly, demand forecasting methods cannot be chosen only on the basis of traditional measures of forecast errors. Total costs and service level of the global inventory control system should also be considered. However, this is beyond the scope of this thesis and remains for further research. The products still have a lumpy demand pattern also according to Ballou's (2004b: 310) definition: [T]he forecast of the best model that could be fit to the time series was 3.39 times the standard deviation of the historical data. The MAD was on average half the size of the mean actual demand per week, i. e. even with the best tested forecast method, we would have ordered half a week's average demand too much or too little per product per week on average. The absolute forecast error was on average four times the mean actual demand per week, i. e. even though the forecast errors balance each other to a certain extent we would have had four week's average demand too much or too little over the whole year per product on average. 732 Silver et al. (1998: 131). 733 Peterson (1969). 734 Silver et al. (1998: 131). 84

100 5 Applying Risk Pooling at Papierco Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted Moving Average) should be admitted to the DRP forecast run besides today's exclusively used methods 4 (Moving Average) and 10 (Linear Smoothing), as they gave good results. Gibson and Horner (2005: 4) recommend using as many forecast methods as possible to maximize the chances that the Best Fit forecast that is calculated is really close to what reality will be. Of course, this has to be traded off with calculation time and software performance. The statistical forecast techniques discussed earlier may work well for stable, mature products with significant demand history, whereas qualitative methods based largely on human opinion and direct marketing intelligence (not a part of JD Edwards) usually make more sense for new or unstable demand products. [ ] In fact, conventional wisdom is that sales and marketing should ʻown the forecastʼ. Their input is especially important for new products or products with unstable demand. Sales and marketing should participate in the development of forecasts and they should also be formally ʻgradedʼ on their forecast accuracy performance results. [ ] And one final comment: always remember that there is far more to be gained by people collaborating and communicating well than there is by using all of the advanced formulas and algorithms yet developed 735. Since our analysis is only based on seven standard products, as no further data were provided, it should be extended to a larger, more representative number of products before implementation. Simple forecasting methods outperform statistically sophisticated procedures for individual items. The reverse is true for macro-level data and medium and long-term forecasting. Consequently, sophisticated forecasting methods do not outperform simpler ones in terms of forecast accuracy in general. 736 Nevertheless, one could check whether more sophisticated forecasting methods not available in JD Edwards OneWorld and developed for products with lumpy demand lead to more accurate results. The Croston (1972) method forecasts intermittent demand well 737 and is available in forecasting software packages 738. It generates separate forecasts for the demand size and the number of periods between demands, and uses the ratio as an estimate for the expected demand per period. It also updates the mean absolute deviation of the forecast error for the de- 735 Gibson and Horner (2005: 9). 736 Makridakis et al. (1982). 737 Willemain et al. (1994), Johnston and Boylan (1996). 738 Syntetos et al. (2005). 85

101 5 Applying Risk Pooling at Papierco mand size 739. Teunter and Sani (2009: 82) call Croston's method the standard method for forecasting intermittent demand and use its forecasts to calculate order-up-to levels that lead to close to target customer service levels. Gutierrez et al. (2008) apply neural network modeling to forecasting lumpy demand. Neural network forecasts generally outperform single exponential smoothing, Croston's method, and the Syntetos Boylan approximation 740. Syntetos and Boylan (2001, 2005) approximately correct an error in the mathematical derivation of and the resulting bias in Croston's estimates of expected demand. Gutierrez et al. (2008: 418) find neural network models generally perform better than the traditional methods. The Syntetos Boylan approximation performs better than Croston's and single exponential smoothing methods in lumpy demand forecasting. If the average nonzero demand is considerably smaller in the test than in the training sample, the traditional forecast methods perform better than the neural network forecasts with lower smoothing constants. However, Gutierrez et al. (2008: 412) only consider 24 SKUs. Analyzing other methods for lumpy demand forecasting not available in JD Edwards OneWorld lies beyond the scope of this thesis. Furthermore, it would be difficult and expensive to integrate these forecasting methods into the current ERP system and DRP. A better demand forecast leads to a higher product availability (customer service level) at the primary warehouse and thus reduces transshipments. Customer service level can be increased and at least safety stock can be reduced. Of course it would be desirable to always have the desired product at the right time at the right warehouse, so that no transshipments would be necessary at all. This however is impossible 741, as forecasts are generally incorrect 742. The longer the forecast horizon, the worse the forecast is 743. Aggregate are more precise than individual forecasts. 744 As the suggested forecast methods in JD Edwards OneWorld only lead to a limited forecast improvement and the more sophisticated methods for lumpy demand are difficult to implement at least in the short run and their benefit for Papierco is unknown, this company could resort to risk pooling methods that reduce demand uncertainty relying on aggregate forecasting 745, such as central ordering. 739 Teunter and Sani (2009: 82). 740 Syntetos and Boylan (2001, 2005, 2006), Syntetos et al. (2005). 741 Evers (2001: 316). 742 Anupindi et al. (2006: 168). 743 Anupindi et al. (2006: 169). 744 Cf. footnote Sheffi (2004: 95). 86

102 5 Applying Risk Pooling at Papierco 5.3 Solving Papierco's Problems Papierco could cope with lead time and demand uncertainty and its related forecasting and inventory problems and ensure its competitiveness and economic success by risk pooling Determining Suitable Risk Pooling Methods for Papierco The RPDST developed in section 4.4 is used to determine appropriate risk pooling methods for Papierco, which suffers from customer demand and supplier lead time uncertainty (1). Both demand and lead times fluctuate strongly. Product variety is important (2) for Papierco's competitive advantage and because its customers, who are mostly printing offices, need all kinds of paper specifications. Stockout penalty costs are high compared to inventory carrying costs and thus attainable inventory cost savings (3) from e. g. inventory pooling: The stockout cost (209 ) is estimated by the average contribution margin of one ton of warehouse sales to customers minus the sales assistant's premium. The average length of time a ton stays in inventory is estimated by the average inventory level divided by average annual demand. Papierco has an annual average turnover rate of 8, i. e. on average a ton of paper remains in storage for one eighth of a year or one and a half months. Storing one ton of paper costs 22 per month, so that the cost of holding a ton of paper in storage is 33 on average. The supplier lead time means and variabilities are high and therefore their reduction is important to Papierco (4). Papierco declared costs per order did not accrue. However, if all 2007 expenses of the purchasing departments are divided by the total amount of warehouse purchases from suppliers, we arrive at an order cost of 3.31 per ordered ton. This cost per order is relatively low (5) compared to the average value per ton of 1,058 in Demand uncertainty and lead time (uncertainty) reduction and fewer orders are preferred to only lead time pooling, but lower premium transportation cost and in-transit inventory cost (15), as Papierco suffers from both demand and lead time uncertainty, minimum order and saltus quantities have to be observed, and the in-transit carrying cost per unit and emergency transfer cost per unit are low. Order splitting (16) is not feasible because of among others the required minimum order quantities and full truck load supplier deliveries. The cheaper, faster implementable and changeable, and less cross-functional solution to cope with both demand and lead time uncertainty is preferred to product and/or process redesign of a postponement (14) strategy (10). Besides, manufacturing and assembly postponement can rather be applied by the paper producer, not the paper wholesaler. Papierco could postpone the labeling, packaging (ream 87

103 5 Applying Risk Pooling at Papierco wrapping paper), or delivery of products, e. g. by central ordering the allocation of ordered products can be delayed and conducted according to more current demand information. Mixing printer's ink from base colors can also be postponed to the delivery warehouses until a customer order arrives instead of ordering already mixed colors from the supplier. Cutting paper to the desired format could also be delayed until an order arrives. However, this can only be applied to an insignificant part of the product line. The other postponement options for Papierco will not reduce demand and lead time uncertainty much either. The paper producers do not possess small-order drop-shipping capabilities (11). They only drop-ship full truck loads to customers. However, there are endeavors of some paper wholesalers to conduct drop-shipping sales via its warehouses to gain the higher profit margin of warehouse sales and of paper producers to drop-ship less than truck load to paper wholesale customers to increase their profit. This causes resentment on both sides. Virtual pooling (12) by not holding any inventory, only arranging sales, and having all products drop-shipped from the paper producers to the customers is no viable strategy for the paper wholesaler, as it would make him dispensable and the paper producers do not possess the necessary distribution infrastructure. Furthermore, the restriction to deliver to customers usually within 24 hours could not be kept. Therefore lateral transshipments (13) or cross-filling seem to be the risk pooling method of choice for Papierco to deal with both demand and lead time uncertainty. Order costs may also be considered high in (5), because minimum order and saltus quantities make (placing) an order more expensive, as frequently more than forecast demand minus on hand inventory has to be ordered by the individual locations to meet these order restrictions, which results in unnecessary inventory costs. Increasing the needed order quantity per order by postponement (8) or central ordering (9) for several locations may better exhaust minimum order and saltus quantities and lead to economies of scale in ordering (6) due to price discounts. As Papierco prefers the less expensive, fast implementable and changeable solution and the possibilities for postponement (8) are still limited as described above, central ordering (9) might be a viable risk pooling method to achieve both efficiency and responsiveness to customers. Some of the transportation cost otherwise incurred for emergency transshipments between warehouses may be shifted unto the suppliers who deliver to Papierco's delivery warehouses. Therefore (9) central ordering might make sense, especially against the background of increasing fuel prices. Today Papierco's average transportation cost to deliver one ton of paper with its truck fleet within Germany is We arrived at this figure by dividing Papierco Germany's 88

104 5 Applying Risk Pooling at Papierco total transportation cost (driver costs, capital commitment, depreciation, maintenance and repair, motor vehicle tax, insurance, diesel, lubricant, tires, autobahn toll, parking, and miscellaneous operating costs) by the total annual warehouse sales in The transshipment cost per ton (transportation, shipment documentation, receiving, handling and administration costs) amount to per transshipped ton of paper on average. This is still relatively moderate (6), so that the decision process (10) through (13) can be followed again, which reconfirms transshipments (13) as a favorable risk pooling method. Papierco's management thinks that (2) product variety might be reduced in the office paper segment and where product specifications just differ in their format in one or two centimeters. The Paper Technology Research Association Forschungsvereinigung Papiertechnik e. V. (FPT) also denies the necessity of the current large product variety in German paper wholesale. 746 Affirming the importance of lead time (uncertainty) reduction (30) afterwards leads to the same train of thoughts in (31) to (38) as in (5) to (16) without considering postponement (cf. 2), which favors transshipments (36) and perhaps central ordering (33). If Papierco gives priority to reducing demand uncertainty, as demand variability is more severe and lead times and their variability are not recorded accurately nowadays, and therefore (30) is denied and accommodating demand uncertainty is preferred to inventory reduction (39) due to the fierce competition for customers, then central ordering (33) is favored again: It is less expensive, faster implementable and changeable than capacity pooling (41f.) and permits to achieve economies of scale in ordering (40). Besides, capacity pooling is rather suitable for manufacturing companies than for wholesalers. Papierco's locations cannot pool manufacturing capacity, as they do not produce paper. They could, however, pool or share printer's ink mixing, paper cutting, or ream wrapping capacity. This might not be economically worthwhile, since the costs of shipping mixed paint or cut to fit or ream wrapped paper between locations might destroy the capacity pooling benefits. Furthermore, delivery time to the customer might suffer, and this can only be applied to an insignificant part of the product line. Papierco's locations could pool transportation capacity, which is operationalized by transshipments, and inventory storage capacity, which corresponds to inventory pooling. Papierco's management would also like to reduce inventory. One has to carefully check whether this intention does not conflict with Papierco's business strategy and competitive 746 FTP (2007a, 2007b). 89

105 5 Applying Risk Pooling at Papierco advantage of being a 24-hour delivery full-range paper wholesaler in Germany and inventory savings outweigh possible lost sales. Remember that Papierco's inventory carrying costs are moderate relative to stockout and transshipment costs per ton. If one concludes that inventory reduction is more important than accommodating demand uncertainty (39), product pooling (45) and inventory pooling (46) might be suitable. Product pooling keeps inventory close to customers in the delivery warehouses, thus enables the nationwide 24-hour delivery service and product availability (44), pools demands, and improves forecast accuracy, but perhaps degrades product functionality. Because of the mentioned shortcomings and because it only pools demands, product pooling should not be applied on its own but together with another risk pooling method that reduces lead time uncertainty and only within a product segment that can be rationalized without hurting customer service level and product purchase interdependencies substantially. Rationalization in this context means deleting products from the product line or replacing several product variants by a universal product. Physical inventory pooling in a single central warehouse would preclude the 24-hour delivery service. However, selective stock-keeping in several delivery warehouses may be feasible, pool demands, enable to reduce at least safety stock and maintain the product variety and delivery speed, but increase transportation costs. Fast movers could be stored at every warehouse, while slow movers could be held at a limited number of warehouses only. If Papierco disavows the importance of lead time (uncertainty) reduction in (30), it may also do so in (4). Papierco's products share common qualities (47). The less expensive, fast implementable and changeable solution is preferred to product and/or process redesign and leagilty, and Papierco is a trading company (48). It does not produce its paper products itself and its products neither are modular nor do they share common components besides the raw materials, so that it cannot redesign the products and/or production processes. Hence, component commonality (54) or manufacturing postponement (53) is not sensible for Papierco. Postponing cutting paper to the right format, mixing printer's ink, and labeling and ream wrapping paper are conceivable but not expected to reduce demand or lead time uncertainty significantly. Product substitution (50) can be implemented quickly and cheaply, but displease customers as they do not receive the desired product in case of a stockout, but a substitute. In contrast to product substitution, central ordering (33) might reduce lead time (uncertainty) in addition to demand uncertainty and lead to economies of scale in ordering, but be more expensive, particularly since transaction and coordination costs are higher. 90

106 5 Applying Risk Pooling at Papierco On the whole, lateral emergency transshipments seem to be the most suitable risk pooling method for Papierco, followed by central ordering, especially if fuel and transportation costs continue to rise. Both methods may be applied in combination and enable to achieve the seemingly conflicting aims of reducing demand and lead time uncertainty as well as inventory investment and maintaining customer service level in terms of product variety, inventory availability, and delivery speed. Product substitution, product pooling, inventory pooling, and postponement may also be suitable in order of descending favorability, but not as a sole method due to their mentioned drawbacks. They may not reduce lead times or lead time uncertainty by themselves. In the following we will deal with the suitable risk pooling methods determined for Papierco in more detail Emergency Transshipments between Papierco's German Locations Papierco's German locations exchange products in case of a stockout, which supports the result of the RPDST. As the quantities exchanged by transshipments have risen over the last years, Papierco's management asked whether these transshipments are economically sound and whether they can be reduced or improved. In our opinion this stock exchange must not be considered detachedly from sales 747, demand, demand forecast, order policy and storage policy, as it is influenced by these factors. Therefore the systemic approach of logistics should be accommodated and the interdependencies between single components and the whole should be considered. 748 It is desired to contribute to a preferably spatially and temporally smooth, continuous, and aligned sequence of activities and processes which target satisfying customer needs Optimizing Catchment Areas A business policy has evolved historically that if the sales department of one location attends to a customer, the same location's logistics department also delivers products to this customer. Therefore, today some of Papierco's customers in the same five-digit zip code areas are allocated inefficiently to several of the current 21 German warehouse locations. Customers should, however, be supplied standardly by the warehouse closest to them. There is a high potential for 747 The sales assistant triggers a transshipment order, i. e. he orders stock from another warehouse, if he cannot satisfy a customer's demand from the primary warehouse. 748 Delfmann (2000: 322). 749 Delfmann (2000: 325). 91

107 5 Applying Risk Pooling at Papierco transportation cost degression in switching from today's suboptimal to the determined optimal customer allocation to Papierco's current 21 warehouses. Unfortunately, it cannot be numeralized exactly due to today's inefficient customer allocation to multiple locations, erroneous data management, and ignorance of the number of delivery trips to each customer, delivery routes and quantities, and truck utilization before and after optimization. Optimizing the customer allocations can lead to cost reductions fast and without much investment burden. The delivery route numbers merely have to be changed for some customers in the customer master data of the ERP software. Furthermore, optimal customer allocations may reduce transshipments. The optimal customer allocation according to the shortest distance was found with the software NCloc 750 and Euclidean metric and visualized with the zip code diagram Das Postleitzahlen-Diagramm in figure 5.6. The colored areas represent today's, the ones outlined in black the optimal catchment areas. 750 ATL (2009). 751 Wessiepe (2009). 92

108 5 Applying Risk Pooling at Papierco Figure 5.6: Comparison of Current and Optimal Catchment Areas of Papierco's Warehouses 93

109 5 Applying Risk Pooling at Papierco Increase in Transshipments and Its Causes Year Warehouse Sales to Customers (t) Transshipments (t) Transshipments (% of Sales to Customers) ,694 53, ,116 58, ,491 71, Table 5.1: The Extent of Transshipments at Papierco We can confirm that the transshipment quantities rose from 2005 to 2007 by % (from 2005 to 2006 by 9.54 % and from 2006 to 2007 by %). The warehouse sales to customers also increased from 2005 to 2007 by % (from 2005 to 2006 by 6.14 % and from 2006 to 2007 by 5.77 %). However, this does not fully explain the increase in transshipments, as the percentage of warehouse sales to customers enabled by transshipments increased as well (cf. table 5.1). In interviews with chief operating officers and directors of purchasing, sales, and logistics at Papierco's different locations it became clear that the increase in transshipments is caused by changing transshipment operations to direct invoicing in June of , some locations decreasing their inventory levels, and including more and more products in the product line 753. According to one chief executive officer the dramatic increase in transshipment volumes was the manifestation of the sales department's service delusion. However, thanks to transshipments Papierco had also gained market share in warehouse sales. Papierco's better development compared to its competitors was based on transshipments, as they enabled a higher product availability, broader product assortment, and faster delivery. This confirms that transshipments can lead to a competitive advantage as Guglielmo (1999), Kroll (2006), and Alvarez (2007) already insinuate. The cost that locations are charged for using an emergency transshipment (transshipment cost rate) is based on quantity units (positions, pallets, and kilograms) and purchase prices and does not reflect the actual logistical costs (picking, transportation, and reloading costs). Within a company group only the costs really incurred by the transshipments should 752 Sales people do not search at the own warehouse for an alternative product to the one originally desired by the customer in case of a stockout anymore. Today sales assistants order more via transshipments for reasons of simplicity than prior to the introduction of direct invoicing. This puts a strain on the product exchange flows between warehouses in terms of volume and costs. 753 These products tend to have small sales volumes and to steal sales from substitutes. Nonetheless, at least small quantities have to be stored at every location, which increases average stock, or the product has to be obtained via transshipments, which increases transshipment quantities. 94

110 5 Applying Risk Pooling at Papierco be charged, so that there is no incentive to prefer or reject the use of transshipments due to inadequate charges. Although Rudi et al. (2001) find transshipment prices that are supposed to always induce local deciders to make globally optimal inventory and transshipment decisions, Hu et al. (2007) give a counterexample. There may exist coordinating prices for only a small range of problem parameters, e. g. if the two locations are symmetric (both locations have the same cost and revenue coefficients, demand distributions, and capacity constraints, and changes in either demand or capacity distributions are simultaneously implemented in both locations). The higher the capacity uncertainty is, the higher the coordinating prices are. Increasing demand variability may increase or decrease coordinating prices depending on the distribution. A linear transshipment price schedule often will not achieve coordination of two locations' production and transshipment. Apart from this the transshipment lead time tends to be shorter than the supplier lead time. In Papierco's case the transshipment lead time ranges from a few hours to 4 work days at the most. The supplier lead time for the various products ranges from 14 to 154 days and is days on average. Therefore a transshipment from a sister location is preferred to a replenishment from a supplier in case of a stockout, as otherwise the sale is lost due to the usual delivery time restriction of 24 hours. Some managers remark that for some Papierco locations other ones were their best customers, as they made profits by transshipping products. One director of logistics claimed only locations obtaining a lot of products via transshipments criticized the transshipment charge rate as too high. It would be even higher, if the really incurred logistical costs were charged. This supports the call for fair transshipment charge rates. The transshipment costs ought to be debited to the sales assistants (deducted from the contribution margin which determines the sales assistants' premium) who release a transshipment order or at least made transparent to them. The objection that one should not inhibit the sales assistants in their sales function can be countered that other wholesalers commonly set up guidelines for the sales personnel. Furthermore, if a sales assistant chooses, for instance, a paper with a one centimeter larger format as an alternative to a stocked out product desired by a customer, the higher purchase price cannot be charged. Therefore, the contribution margin that determines the sales assistant's premium is lower and the sales assistant is enticed to obtain the originally demanded product via transshipment from another warehouse location. This highlights that the implementation of risk pooling methods is influenced by human resource and business 95

111 5 Applying Risk Pooling at Papierco policy factors. Managers should formulate clear guidelines for the usage of transshipments in case a desired item is not available at the primary stocking location. A software tool should be created to help the sales assistant in deciding whether it is more economical to obtain a stocked out item via transshipments from another warehouse, search for a substitute at the own warehouse, cut paper to the right format, or ream wrap paper at the own location if possible Transshipments Are Worthwhile for Papierco A high customer service level at the warehouses can be achieved by either holding sufficient inventory there, which entails high inventory investment and carrying costs, or by postponement through centralized inventory holding, which presumes fast and thus expensive delivery of any amount of any product to any customer. A better alternative might be to hold some inventory at the warehouses and let the warehouses transship products in case of a stockout. 754 A mathematical model of the exact implications [ of transshipments] is extremely complicated 755. Evers (2001), Minner et al. (2003), and Minner and Silver (2005) consider transshipments between two locations for a specific product in a specific situation only and not whether transshipments might be worthwhile for a company with more locations and products in general at all. Minner et al. (2003: 394) note that their model may be extended to multiple locations with no fixed transshipment costs by successively determining which location maximizes the savings for each transshipped unit. The problem becomes more difficult with fixed costs, unless there are only a small number of warehouses as in Tagaras (1999). The structures in all past transshipment research are much simpler than the practical ones. 756 If the outlets use complete pooling, the exact form of the lateral transshipment policy does not significantly affect total system performance. 757 Deciding between never transshipping or always transshipping as many units as disposable if one location faces a stockout while another one has stock on hand 758 is almost as good as a more extensive investigation that considers the transshipment's prospective effect on the transshipping location's cost 759. Burton and Banerjee (2005: 169) also find that an ad hoc emergency transshipment approach may lead to lower shortage (higher customer service) and transshipment cost 754 Cf. Evers (2001). 755 Minner et al. (2003: 385). 756 Chiou (2008: 442). 757 Tagaras (1999). 758 Cf. Olsson (2009). 759 Minner et al. (2003: 394f.), Minner and Silver (2005: 1). 96

112 5 Applying Risk Pooling at Papierco (number of lateral transshipments) than a more systematic transshipment technique based on stock level equalization 760. Transshipping is better than not transshipping, but it increases transportation activity. 761 Backordered demand should not be partially fulfilled by transshipments. 762 In practice pull systems may offer simpler and more practical joint replenishment/transshipment policies than the push systems mostly considered in the literature. 763 At Papierco the charged transshipment costs (for transportation, shipment documentation, receiving, handling, and administration) amounted to 5 Mio. in 2007, i. e. about per ton that was delivered via transshipments (5 Mio. /71,967 t = /t). According to its inventory turnover curve (figure 5.7), Papierco needs around 10,291 t of average inventory for 71,967 t of warehouse sales to customers. This suggests that without transshipments Papierco would have had to store at least 10,291 t of additional average inventory. This derivation might not be fully justified, as we derive inventory figures for the system without transshipments from the figures for the existing system with transshipments and while safety stocks will be lower in general, regular stocks may increase with crossfilling of demand 764. Before transshipments were used, average inventory turnover in German paper wholesale was 5.4 from 1975 to Therefore one might estimate that Papierco would have needed 13,327 t (= 71,967 t/5.4) extra average inventory without transshipments. Consequently, Papierco would have incurred approximately 3.5 Mio. of additional inventory carrying costs in order to sell 71,967 t without transshipments: 13,327 t 1,058 /t (average product purchase price in the warehouse sales business division) 0.25 (average inventory carrying cost rate) = 3,524,992. However, these additionally stored tons would not necessarily have been the demanded ones in the right location. As the estimate of additional inventory carrying costs without transshipments is lower than the 2007 total transshipment cost, the latter should be reduced, e. g. by storing fast-movers such as copy papers at all locations (cf. section 5.3.5), avoiding unnecessary and uneconomical transshipments, improving demand forecasts, and using less expensive alternative risk pooling methods. 760 See, e.g., Jönsson and Silver (1987a). 761 Burton and Banerjee (2005: 169). 762 Wee and Dada (2005: 1529). 763 Bhaumik and Kataria (2006). 764 Ballou and Burnetas (2000, 2003), Ballou (2004b: ). 765 Röttgen (1987: 109). 97

113 5 Applying Risk Pooling at Papierco Centralizing all inventories in one or several central warehouses would decrease warehouse fixed costs, safety stock and thus inventory holding costs as well as inbound transportation costs to these central warehouses, but also the customer service level due to greater delivery distances to the customers (the stockout costs would be higher and the profit possibly lower) and increase outbound transportation costs to customers. Besides, a central warehousing strategy would conflict with Papierco's corporate strategy of a decentralized full-line 24-hour-delivery distributor. As stockout costs could not be estimated in the aggregate consideration without transshipments in general, we now consider the costs of transshipping versus not transshipping. Transshipments entail transportation, shipment documentation, receiving, handling and administration costs, the sending location's cost of reordering the transshipped product from the supplier, as well as an increased probability of a stockout at the sending location. 766 Transportation, shipment documentation, receiving, handling, and administration costs amount to per transshipped ton of paper on average. As derived in section the order cost per ton amounts to Even though Papierco's locations order and receive stock regularly about every two weeks and thus it is unlikely to place an order merely to make up for transshipped items, we consider this value as an upper bound to the order cost caused by transshipping. The increased probability of a stockout at the sending location is difficult to quantify in general and on average. In Papierco's case this cost is rather another transshipping cost again, as the sending location would ask another location for a transshipment, if later it ran out of stock of the product it had just transshipped. The increased stockout likelihood depends on the transshipment quantity, the current on-hand inventory of the transshipped product, customer demand for this item, and the stock receipts of this item (quantity on order and its arrival time). Transshipments made up 16.8 % of warehouse sales to customers in 2007, i. e. one could assume that Papierco had an average overall stockout probability of 16.8 % and therefore an inventory availability or fill rate before transshipments of 83.2 %. We assume that every location faces a stockout probability of 16.8 % for an item, neglecting the different influencing factors just mentioned, the derivation of this stockout probability from the situation with transshipments, and the difference between alpha and beta service level. If two locations 766 Evers (2001: 312f.). 98

114 5 Applying Risk Pooling at Papierco transship, they face a stockout with a probability of %, three with a probability of %, four with 0.08 %, five with %, six with %, seven with %, and 21 with %. This affirms that emergency transshipments lead to a high effective fill rate for the customer (97.18 % for two, % for three, and % for four locations that transship), even if the item fill rate is relatively low (83.2 %). 767 The main benefit (reduced stockouts and safety stock levels) can be reaped having just a few locations transship. It is neither necessary nor economical to have all 21 locations transship due to diminishing marginal returns to transshipping 768. If we consider the worst but unlikely case that at every location one after another a stockout occurs for the same item after having transshipped one ton of that item to the preceding location, then the reorder cost due to transshipment only accrues at the last (21 st ) location. The cost of increased probability of a stockout can be estimated by another transshipping cost of 69.48, since the likelihood that one transshipment triggers more than one additional stockout and thus transshipment is negligible as the example above shows. Therefore the average cost of transshipping can be estimated as: /t = /t (transportation and related costs) /t (reorder cost) /t (increased transshipment usage/stockout probability). Without transshipments Papierco incurs the cost of a stockout and the cost of holding a ton in inventory until later at the not transshipping location. The stockout cost (209 ) is estimated by the average contribution margin of one ton of warehouse sales to customers minus the sales premium. The impact of stockouts on the future purchasing behavior of customers is difficult to grasp and neglected here. Holding the ton of paper in storage until later costs 33 on average (cf. section 5.3.1). Therefore, the cost of not transshipping amounts to approximately 242 /t. Transshipping is on average economically sensible for Papierco, as it generally is less expensive ( ) than not transshipping (242 ) a ton of paper in case of a stockout. If only transportation-related costs evoked by transshipments and stockout costs due to not transshipping are considered and the other costs are neglected, a sales assistant should only make a transshipment order in case of a stockout, if the contribution margin is equal to or larger than /t. Then at least the average transportation-related costs for the transshipment are covered. 767 Cf. Ballou and Burnetas (2000, 2003), Ballou (2003b: 81, 2004b: ). 768 Tagaras (1989), Evers (1997: 71f.), Ballou and Burnetas (2000, 2003), Ballou (2004b: ), Kranenburg and Van Houtum (2009). 99

115 5 Applying Risk Pooling at Papierco In order to decide more accurately on emergency transshipments for a specific item in a specific situation the methods proposed by Evers (2001), Minner et al. (2003), and Minner and Silver (2005) can be used, provided that the necessary data are available. Minner et al. (2003: 395) present a heuristic decision rule for the quantity and source of a transshipment. In simulations, Minner et al.'s (2003: 390f., 393) method generally achieves lower average annual costs than Evers' (2001) one. Since the cost parameters are likely to remain constant in the short run, whether or not a particular transshipment is made depends principally on the on-hand inventory level at the shipping location. 769 However, before using transshipments, sales assistants should check their own warehouse for substitutes for the customer wish and try to persuade the customer to buy another product, which only incurs transaction costs (searching for substitutes in the information system). This product substitution might cause a slight dissatisfaction on the customer's part, but is certainly cheaper than a transshipment. If the alternative product is more expensive than the original customer wish, a higher profit is gained. If only the sales price for the originally desired product can be charged or the substitute is less expensive than the original purchase wish, Papierco has to accept a lower contribution margin. Of course the product should not be sold beneath cost price. If no substitute can be found, it should be checked whether the paper can be cut to the right size (form postponement 770 ), which costs around /t (neglecting waste), or ream wrapped (packaging postponement) for /t on average. Both options are cheaper than and therefore should be preferred to a transshipment in general. In order of increasing costs incurred by the considered risk pooling methods, Papierco's sales assistants should first try to substitute an unavailable product, then to customize or differentiate products, and then to resort to transshipments in case of a stockout. This shows that risk pooling methods can be combined effectively. Although this is a rather crude general average analysis, because exact data (especially probabilities) were not available, and we advert to the perils of using averages as noted e. g. by Savage et al. (2006), it shows some general relationships. Of course a decision for a particular risk pooling method (product substitution, postponement, or transshipment) in a certain situation depends on the specific cost parameters. 769 Evers (2001: 313). 770 See e. g. Chauhan et al. (2008). 100

116 5 Applying Risk Pooling at Papierco Centralized Ordering Papierco's Current Order Policy At Papierco a replenishment order is placed with a supplier (the daily DRP run generates an order message) whenever the reorder point is reached or in possibly short intervals (every two weeks) within the suppliers' minimum order quantity restrictions. The reorder point is the sum of safety stock, which is set by every Papierco member company independently, and average lead time demand (average sales per day during the lead time times the lead time in days). The purchase order planning code for a specific product is 1, if it is planned with DRP, and 0, if it is not planned with DRP. The latter case applies to about 20 % of the warehouse products, as for them the minimum order quantity is usually higher than the planned order quantity, e. g. if they have fixed order dates or the minimum order quantity is a full truck load. These products are planned manually with order lists. Safety stock is calculated as the product of average sales per day during the lead time, supplier lead time in days, and a safety factor. Thus double average demand during lead time results in double safety stock. According to experience the safety factor is set to ¼ for ream wrapped paper and 1/3 for not ream wrapped one. The safety factor is not entered into the ERP system for every product, but for parts of the product line manually every three months. However, safety stock should not be set arbitrarily, but according to a target customer service level (e. g. 90 % product availability for A items) and the statistical behavior of demand during lead time or rather the forecast error in the case of Papierco, because demand is forecast. The actual supplier lead time and whether and how often the safety stock is touched is not recorded either. No cost optimal order quantities or times are determined. Folding Box Board (cf. figure 5.3) has an average demand during one week lead time of sheets, a current safety stock of (= /4) sheets, and a reorder point of (= ) sheets. According to the empirical distribution function this corresponds to a service level of approximately 76 % or a stockout probability during lead time of 24 %. A reorder point of sheets or safety stock of (= ) sheets would be needed to reach an inventory availability of 80.8 % during lead time. According to the respective empirical distribution functions, the Uncoated Cut-Size White Wood-Pulp Paper has an inventory availability during lead time of 86 %, one continuous roll of approximately 84 %, the other of 73.1 %, Woodfree Matte Coated Cut-Size Paper of 72 %, the Woodfree White Cut- Size C-Quality Copy Paper of 76.9 %, and the Woodfree White Cut-Size A-Quality Copy Paper 101

117 5 Applying Risk Pooling at Papierco of 86.5 % with today's calculation of safety stock. The safety stock can be determined more definedly based on a target customer service level. According to the nonparametric Kolmogorov Smirnov test for the second continuous roll (asymptotic significance (two-tailed) p = 0.700) and the copy papers (p = and 0.616) the hypothesis H 0 that the sample stems from a population with normally distributed weekly demands cannot be rejected with a level of significance of 5 %. The Kolmogorov Smirnov test is also applicable to small samples, but might not be very definite if the unknown distribution function is not continuous (as in this case) or the data are not metric. 771 The hypothesis H 0 that the sample stems from a population with uniformly, Poisson, or exponentially distributed weekly demands is rejected with a level of significance of 5 % for all products but the second continuous roll (for the exponential distribution p = 0.436). However, there is one value outside the specified exponential distribution range that is skipped. In the Kolmogorov Smirnov test of exponential distribution for the other paper grades (variables) there are also values outside the specified distribution range that are skipped. The used Order Policy Code 4 (Periods of supply) combines the order quantities (forecast demands) for the time period defined in the Value Order Policy (for most Papierco products 10 days). The JD Edwards OneWorld manual says This order policy code was designed to use with high-use/low cost items for which the user is not concerned about carrying excess inventory 772. This partly explains why Papierco carries so much inventory, although it mainly sells low-turnover and not necessarily low-cost products. The other available Order Policy Codes are 0 (The DRP system will not plan this item.), 1 Lot-for-lot or as required (The system will create messages for purchase orders for the exact amount needed.), 2 Fixed order quantity (The system will create messages for purchase orders based on the value entered in the Value Order Policy in the Plant Manufacturing Data. If demand exceeds the fixed order quantity, the system will generate purchase orders in multiples of the fixed order quantity.), 3 Economic Order Quantity (EOQ), and 5 Rate scheduled item (The system will generate messages based on existing rates and rate generation rules for parent rate-scheduled items only.). The order quantity is the maximum of the ten day demand forecast and the minimum order quantity, which is rounded to the next higher order quantity that is divisible by the saltus quantity. For instance, if the minimum order and saltus quantity are 500 kg (only 771 Duller (2008: 108, 112). 772 Oracle (2009). 102

118 5 Applying Risk Pooling at Papierco complete pallets must be ordered) and forecast demand for ten days is 1,150 kg, then 1,500 kg are ordered. Such a policy that determines and controls the inventory level at each warehouse location in direct proportion to (forecast) demand is called stock-to-demand. 773 Papierco's inventory turnover curve in grey in figure 5.7 confirms this. For all its warehouses the average annual inventory in dependence of the annual throughput is plotted with green squares. A linear regression line is adequate for these data as the coefficient of determination R 2 = shows. However, it also suggests that not all warehouses execute this order policy consistently. 774 Individual turnover rates range from 5 to 21 with an average of Deviations of the individual turnover rates might be explained by different service levels or replenishment rules. 775 Warehouses, whose data points lie above the turnover curve, might attain a higher turnover and lower inventory holding costs, if they followed the stock-to-demand order policy more consistently. Warehouses, whose data points are plotted beneath the turnover curve, exhibit a higher-than-average turnover rate than attainable by this stock-to-demand policy. An EOQ policy would lower the average turnover rate to 6.53 as the turnover curve in black shows (a power function with the normative exponent suggested by Ballou (2000: 75) fitted to Papierco's data), probably because the stock-to-demand order policy is not followed consistently today and some warehouses have an unusually high turnover rate of 11, 15, or 21. Nevertheless, this paper distributor's average inventory levels appear rather high for the annual throughputs. The annual average turnover rate of the German wholesale of paper, cardboard, and office supplies from 1999 to 2006 was However, this group contains stationary wholesalers, which might raise the average turnover rate and make it unsuitable as a benchmark for just paper wholesalers. The U.S. merchant wholesalers of paper and paper products had an annual average turnover rate from 1992 to 2008 of Papierco has a rather low average turnover rate of This might be explained by the large product variety it offers. Papierco sells at least 7,000 different product specifications. Thus it is difficult to forecast demand for individual products. Furthermore, minimum order and saltus quantities have to be met. 773 Ballou (2000: 74). 774 Cf. Ballou (2000: 76). 775 Cf. Ballou (2000: 78f.). 776 Statistisches Bundesamt Deutschland (2009a, 2009b, 2009c, 2009d, 2009e, 2009f, 2009g, 2009h), calculated by us. 777 U.S. Census Bureau (2009), calculated by us. 103

119 5 Applying Risk Pooling at Papierco Average Inventory (t) y = 0.143x R² = y = x 0, Annual Warehouse Throughput (t) EOQ Current Stock-to-Demand Policy Pot.(EOQ) Linear (Current Stock-to-Demand Policy) Figure 5.7: Inventory Turnover Curves for Papierco EOQ = economic order quantity, Pot. = regression power function, Linear = linear regression line. Papierco has 196 sum suppliers, but 83 % of the annual procurement quantity is sourced from ten, 52 % from three, 40 % from two suppliers, and 20 % just from a single supplier. With big suppliers a quantity structure is negotiated. There is a one-to-one product-supplier relationship, i. e. every product is sourced from only exactly one supplier. Therefore, Papierco should collaborate closer with its suppliers, conduct a better supplier management, to enable shorter lead times, a better forecast, inventory policy and product availability. One Papierco member company's director of purchasing had created such a collaboration with Papierco's most important supplier that supplied the highest quantity. A monthly demand forecasting for product groups and a guaranteed maximum lead time of 14 days for fast and 28 days for slow movers was established. Previously this supplier's lead time had been 4 to 6, sometimes 8 to 12 weeks. Inventories could be reduced considerably. Unfortunately, the business relationship to this supplier was broken due to price policy reasons. This concept was neglected, and inventories rose again. One director of purchasing is against a partner-like collaboration with suppliers for they already took advantage of Papierco due to their big negotiation power. One director of sales remarked, paper wholesalers and manufacturers did not cope with recurring demand peaks correctly, such as in election times. When there were vacation close-downs, they could not prevent supply bottlenecks. This shows again that a close collaboration with 104

120 5 Applying Risk Pooling at Papierco suppliers is indispensable. Not least Weng and McClurg (2003) showed the value of supplier buyer coordination (in ordering) in coping with uncertain delivery time and demand Stock-to-Demand Order Policy with Centralized Ordering and Minimum Order and Saltus Quantities Risk pooling models are based on economic-order-quantity (trading off inventory holding against order costs) or newsvendor models (trading off overage against underage costs). In practice, however, a stock-to-demand order policy is followed frequently 778 as we also detected in interviews with logistics and purchasing managers and at Papierco. Orders and therefore cycle inventories are proportional to demand at each warehouse. 779 Expected demand at each warehouse location is forecast. Order quantities result from the difference of forecast demand and available inventory. Maister (1976: 132) and Evers (1995: 5) refer to this order policy as the replacement principle, where orders are set equal to demand during a certain time period. Such an order policy leads to a constant turnover. It is frequently pursued, as it is simple and easily executable 780 and because automated ordering systems have very low ordering costs and thus the EOQ is not used 781. The replacement principle is followed e. g. in Zinn et al. (1990: 139), Evers (1996: 117, 1997: 59), and Rabinovich and Evers (2003a: 226). If it is applied, centralization usually does not reduce cycle stocks: 782 The system wide order quantity of n warehouses and therefore average cycle stock in the decentralized system are equal to the ones in the centralized system, if exactly the forecast demand is ordered. Following a stock-to-demand order policy, safety stock is often calculated as the product of a safety factor and average demand during lead time at each warehouse as our interviews with logistics and purchasing managers showed. Doubling demand results in double safety stock. Safety stock is not determined by a desired target customer service level and the statistical behavior of demand during lead time or the forecast error. Centralization does not reduce system wide safety stock, if the safety factor is equal for all warehouses 778 Wanke (2009: 108). 779 Ballou (2000: 74). 780 Ballou (2000: 77f., 2004a: 20f.). 781 Herron (1987), Evers (1995: 14). Researchers disagree whether the EOQ model is rarely used (Herron 1987, Woolsey 1988, Zinn et al. 1990: 139, Evers 1995: 14) or often used (Osteryoung et al. 1986, Pan and Liao 1989, Lee and Nahmias 1993: 48, Dubelaar et al. 2001: 98, Slack et al. 2004). Of eleven companies that we surveyed (table D.1) five use a stock-to-demand, four an EOQ, one a dynamic order policy, and one the newsvendor model. 782 Maister (1976: 132), Evers (1995: 2, 14f.). 105

121 5 Applying Risk Pooling at Papierco and remains the same. The service level increases, however, due to the risk pooling effect. Perhaps this service level is higher than necessary. Often the stock-to-demand policy is subject to minimum order and saltus quantity constraints as in the case of Papierco. Then the order quantity q i for a specific product at warehouse i = 1,, n results from forecast demand minus available inventory d i for a specific period at warehouse i and a constant minimum order quantity m and saltus quantity s. The saltus quantity demands that only certain multiples are ordered like in Köchel (2007), e. g. only full pallets. If a stock-to-demand order policy with minimum order and saltus quantities is followed, centralization may lead to a reduction in average cycle stock. The order quantity and therefore average cycle stock in the decentralized system, where every location places orders for itself, is more than or equal to the ones in the centralized system, where a common joint order is placed for all locations 783, since often more than forecast demand minus available inventory is ordered in order to meet minimum order and saltus quantities. In the centralized system the constant minimum order and saltus quantities may be exhausted more. The order quantity q i for a specific product at warehouse i is,. (5.1) The total system wide order quantity in the decentralized system therefore is:,. (5.2) The total system wide order quantity in the centralized system is:,. (5.3) The total system wide order quantity in the centralized system is less than or equal to the one in the decentralized system, because the order quantity function (5.1) is subadditive:,,. (5.4) For the proof please refer to appendix E. The centralized ordering effect (COE), the percent reduction of the order quantity by centralized ordering, is: 783 For Özen et al. (2005: 1) inventory centralization also is a byword for joint ordering: Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand. 106

122 5 Applying Risk Pooling at Papierco ,, 100. (5.5) Centralized ordering can reduce demand and supply uncertainty and thus inventory and stockouts and increase customer service level by demand pooling, aggregate forecasting across all locations, and postponement of order allocation to the delivery warehouses. This will be shown in the following section Benefits of Centralized Ordering for Papierco The example of a woodfree white cutsize A-quality copy paper in table 5.2 demonstrates that the centralized ordering effect for a stock-to-demand order policy with minimum order and saltus quantities can be significant. This copy paper has the highest annual sales and contribution margin in warehouse sales of all products at most Papierco locations. Table 5.2 shows the actual warehouse sales for this copy paper for Papierco's 22 German locations and one Dutch location per month in The sales forecasts were obtained with exponential smoothing. The forecast method was initialized with the 2006 actual warehouse sales per month per location, i. e. data from 2006 were used to determine starting values for the exponential smoothing model. The exponential smoothing constant (column O) that minimized the forecast error (the standard error of the forecast (RMSE)) for the monthly forecasts of 2006 warehouse sales for every location was used for forecasting 2007 sales Cf. Ballou (2004b: 299). 107

123 5 Applying Risk Pooling at Papierco 1 A B C D E F G H I J K L M N O P Q R S 2 Minimum order quantity 22,500 kg Value 0.93 /kg All values in kg except for the exponential smoothing constant (sm. const.). 3 Saltus order quantity 500 kg Contribution margin 0.23 /kg Average monthly positive net stock (sum of the positive net stocks divided by twelve). 4 5 Work days Warehouse Location Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total/Average Sm. Const. MAD BIAS RMSE Safety Stock 7 Aalen 8 Actual sales 43,300 32,608 44,833 26,535 26,935 23,490 27,773 34,888 19,350 36,420 29,615 8, ,887 15,835 9 Forecast 27,465 27,624 27,674 27,845 27,832 27,823 27,780 27,780 27,851 27,766 27,852 27, , ,523 1,727 9, Forecast error 15,835 4,984 17,159-1, , ,108-8,501 8,654 1,763-19,730 20, Order quantity 27,500 43,500 33,000 45,000 26,500 27,000 23,000 28,000 35,000 22,500 33,000 30, , Net stock -15,800-4,908-16,741 1,724 1,289 4, ,862 8,788-5,132-1,747 20,113 3, Sales rate 1,968 1,630 2,038 1,397 1,347 1,119 1,262 1, ,655 1, Average cycle stock (CS) 8,952 11,868 9,037 14,992 14,757 16,544 13,913 11,380 18,463 13,539 13,154 24,183 14, Berlin 16 Actual sales 40,165 44,888 37,418 39,375 33,300 41,138 34,318 39,308 41,488 40,243 42,313 8, ,195 6, Forecast 35,059 35,110 35,208 35,230 35,271 35,252 35,311 35,301 35,341 35,402 35,451 35, , ,602 1,562 9, Forecast error 5,106 9,778 2,210 4,145-1,971 5, ,007 6,147 4,841 6,862-27,278 18, Order quantity 35,500 40,000 45,000 37,500 39,500 33,000 41,500 34,000 39,500 41,500 40,500 42, , Net stock -4,665-9,553-1,971-3,846 2,354-5,784 1,398-3,910-5,898-4,641-6,454 27,305 2, Sales rate 1,826 2,244 1,701 2,072 1,665 1,959 1,560 1,709 2,074 1,829 1, Average cycle stock 15,788 14,097 16,835 16,122 19,004 15,307 18,557 16,019 15,392 15,847 15,323 31,426 17, Bielefeld 24 Actual sales 44,288 28,438 53,200 25,388 27,913 21,163 22,028 45,038 18,665 40,700 31,663 15, ,322 16, Forecast 28,440 28,599 28,597 28,843 28,809 28,800 28,723 28,657 28,820 28,719 28,839 28, , ,472 2,467 11, Forecast error 15, ,603-3, ,637-6,695 16,381-10,155 11,981 2,824-13,029 29, Order quantity 28,500 44,500 28,500 53,500 25,500 28,000 22,500 22,500 43,000 22,500 37,000 31, , Net stock -15, ,426 3,686 1,273 8,110 8,582-13,956 10,379-7,821-2,484 13,178 3, Sales rate 2,013 1,422 2,418 1,336 1,396 1,008 1,001 1, ,850 1, Average cycle stock 9,397 14,493 8,073 16,380 15,230 18,692 19,596 10,930 19,712 13,425 13,501 21,097 15, Bremen 32 Actual sales 22,150 17,000 22,450 12,913 13,988 17,938 12,663 24,038 11,238 14,188 24,013 16, ,404 4, Forecast 19,224 19,253 19,231 19,263 19,199 19,147 19,135 19,070 19,120 19,041 18,993 19, , ,382-1,693 4, Forecast error 2,926-2,253 3,219-6,350-5,211-1,209-6,472 4,968-7,882-4,853 5,020-2,218-20, Order quantity 22,500 22,500 22,500 22,500 22, ,500 22,500 22, ,500 22, , Net stock 350 5,850 5,900 15,487 23,999 6,061 15,898 14,360 25,622 11,434 9,921 15,596 12, Sales rate 1, , , , Average cycle stock 11,425 14,350 17,125 21,944 30,993 15,030 22,230 26,379 31,241 18,528 21,928 24,009 21, Cologne 40 Actual sales 127, , ,830 96, , , , ,203 84, , ,465 97,890 1,532,903 58, Forecast 105, , , , , , , , , , , ,773 1,405, ,095 10,658 45, Forecast error 21,428 6, ,311-25,670 4,715-7,876-13,299 58,566-38,773 19,687-8,120-22, , Order quantity 106, , , ,000 94, , , , ,500 80, , ,500 1,556, Net stock -21,123-6, ,098 25,722-4,276 8,346 13,678-58,525 39,255-19,548 8,487 23,097 9, Sales rate 5,778 5,732 10,992 5,062 6,200 5,328 4,803 7,661 4,236 6,332 5,158 5, Average cycle stock 44,605 50,926 25,768 73,812 57,927 64,285 66,512 40,147 81,615 51,851 65,220 72,042 57, Dietzenbach (Frankfurt) 48 Actual sales 37,325 44,800 36,765 35,105 28,875 58,725 26,413 82,000 23,588 37,725 34,888 39, ,282 22, Forecast 36,609 36,616 36,698 36,699 36,683 36,605 36,826 36,722 37,174 37,039 37,045 37, , ,555 3,629 15, Forecast error 716 8, ,594-7,808 22,120-10,413 45,278-13, ,157 2,049 43, Order quantity 37,000 37,000 45,000 37,000 35,000 28,500 59,000 26,500 82,500 23,500 37,500 35, , Net stock , ,005 8,130-22,095 10,492-45,008 13, ,291-1,782 3, Sales rate 1,697 2,240 1,671 1,848 1,444 2,796 1,201 3,565 1,179 1,715 1,586 2, Average cycle stock 18,352 15,183 18,493 19,558 22,568 11,743 23,699 8,784 25,698 18,555 19,735 17,844 18, Dortmund 56 Actual sales 2,238 2,775 8,503 3,800 4,050 6,040 4,225 3,300 3,440 5,190 2,813 2,690 49,064 2, Forecast 3,625 3,611 3,603 3,652 3,653 3,657 3,681 3,686 3,682 3,680 3,695 3,686 43, , , Forecast error -1, , , , , Order quantity 22, , , , Net stock 20,262 17,487 8,984 5,184 1,134 17,594 13,369 10,069 6,629 1,439 21,126 18,436 11, Sales rate Average cycle stock 21,381 18,875 13,236 7,084 3,159 20,614 15,482 11,719 8,349 4,034 22,533 19,781 13, Ernstroda (Erfurt) 64 Actual sales 6,900 4,888 15,125 7,213 11,788 10,650 14,313 16,263 27,225 18,238 18,525 19, , Forecast 18,712 12,806 8,847 11,986 9,599 10,694 10,672 12,492 14,378 20,801 19,520 19, , , ,254 6, Forecast error -11,812-7,918 6,278-4,773 2, ,641 3,771 12,847-2, Order quantity 22, , , ,500 22,500 23,000 22,500 22, , Net stock 15,600 10,712-4,413 10, ,936-3,377 2,860-1,865 2,897 6,872 10,109 5, Sales rate , , Average cycle stock 19,050 13,156 3,865 14,481 5,039 16,261 4,236 10,992 11,860 12,016 16,135 19,741 12, Fellbach (Stuttgart) 72 Actual sales 32,800 37,603 41,795 39,615 39,400 30,535 45,043 49,350 42,663 49,505 52,850 14, ,009 11, Forecast 36,395 36,035 36,192 36,752 37,039 37,275 36,601 37,445 38,636 39,038 40,085 41, , ,071 1,930 10, Forecast error -3,595 1,568 5,603 2,863 2,361-6,740 8,442 11,905 4,027 10,467 12,765-26,511 23, Order quantity 36,500 32,500 38,000 42,000 40,000 39,500 30,000 46,000 50,500 43,000 50,500 54, , Net stock 3,700-1,403-5,198-2,813-2,213 6,752-8,291-11,641-3,804-10,309-12,659 26,991 3, Sales rate 1,491 1,880 1,900 2,085 1,970 1,454 2,047 2,146 2,133 2,250 2, Average cycle stock 20,100 17,465 16,130 17,172 17,604 22,020 15,143 14,603 17,788 15,706 15,502 34,416 18, Garching (Munich) 80 Actual sales 56,395 51,943 69,108 46,790 53,673 53,540 56,500 47,680 50,575 59,443 41,563 37, ,573 15, Forecast 40,932 48,664 50,303 59,706 53,248 53,460 53,500 55,000 51,340 50,958 55,200 48, , , , Forecast error 15,463 3,279 18,805-12, ,000-7, ,485-13,637-11,019 3, Order quantity 41,000 64,500 53,500 78,500 40,000 54,000 53,500 58,000 44,000 50,500 63,500 35, , Net stock -15,395-2,838-18,446 13, ,949 7, ,147 13,790 11,427 3, Sales rate 2,563 2,597 3,141 2,463 2,684 2,550 2,568 2,073 2,529 2,702 1,889 1, Average cycle stock 15,147 23,280 18,871 36,659 26,447 26,821 25,446 31,211 26,084 22,287 34,572 30,109 26, Hemmingen (Hanover) 88 Actual sales 60,453 62,338 75,190 42,813 52,063 47,125 59,500 76,913 41,063 45,175 56,228 36, ,186 24, Forecast 41,620 45,386 48,777 54,059 51,810 51,861 50,914 52,631 57,487 54,202 52,397 53, , ,119 3,407 15, Forecast error 18,833 16,952 26,413-11, ,736 8,586 24,282-16,424-9,027 3,831-16,838 40, Order quantity 42,000 64,000 66,000 80,500 40,500 52,000 46,000 61,500 81,500 38,000 43,500 57, , Net stock -18,453-16,791-25,981 11, ,018-8,482-23,895 16,542 9,367-3,361 17,314 5, Sales rate 2,748 3,117 3,418 2,253 2,603 2,244 2,705 3,344 2,053 2,053 2,556 1, Average cycle stock 14,881 16,949 16,490 33,113 26,175 28,581 22,038 18,625 37,074 31,955 24,934 35,477 25, Kiel 96 Actual sales 17,728 19,563 26,308 21,080 17,575 24,715 27,015 29,045 21,305 18,883 29,563 14, ,793 5, Forecast 23,673 23,614 23,573 23,601 23,575 23,515 23,527 23,562 23,617 23,594 23,547 23, , ,505-1,351 5, Forecast error -5,945-4,051 2,735-2,521-6,000 1,200 3,488 5,483-2,312-4,711 6,016-9,594-16, Order quantity 24,000 22,500 22,500 22,500 22,500 22,500 22,500 22,500 25,500 22,500 22,500 24, , Net stock 6,272 9,209 5,401 6,821 11,746 9,531 5,016-1,529 2,666 6, ,707 6, Sales rate ,196 1, ,177 1,228 1,263 1, , Average cycle stock 15,136 18,991 18,555 17,361 20,534 21,889 18,524 13,068 13,319 15,725 14,035 16,714 16, Leizen 104 Actual sales 2,488 2,388 6,025 5,100 4,075 3,700 3,238 4,375 5,613 8,563 7,550 3,125 56,240 2, Forecast 4,920 4,896 4,871 4,882 4,885 4,876 4,865 4,848 4,844 4,851 4,888 4,915 58, , , Forecast error -2,432-2,508 1, ,176-1, ,712 2,662-1,790-2, Order quantity 22, , , , Net stock 20,012 17,624 11,599 6,499 2,424 21,224 17,986 13,611 7, ,385 11,260 12, Sales rate Average cycle stock 21,256 18,818 14,612 9,049 4,462 23,074 19,605 15,799 10,805 3,749 18,160 12,823 14, Lohfelden (Kassel) 112 Actual sales 4,650 1,288 4,700 2,763 1, ,013 2,775 1,963 2,200 2,900 2,400 29,990 2, Forecast 2,252 2,276 2,266 2,290 2,295 2,292 2,273 2,270 2,275 2,272 2,271 2,277 27, , Forecast error 2, , , , Order quantity 22, , , Net stock 17,850 16,562 11,862 9,099 7,149 6,761 4,748 1,973 22,510 20,310 17,410 15,010 12, Sales rate Average cycle stock 20,175 17,206 14,212 10,481 8,124 6,955 5,755 3,361 23,492 21,410 18,860 16,210 13, Lunteren (NL) 120 Actual sales 1, , ,163 2, ,138 1,863 1,075 14,203 1, Forecast , ,169 1,308 10, Forecast error 1, , , , , Order quantity 22, , Net stock 20,987 20,887 18,262 18,162 18,162 16,999 14,849 14,336 13,373 11,235 9,372 8,297 15, Sales rate Average cycle stock 21,744 20,937 19,575 18,212 18,162 17,581 15,924 14,593 13,855 12,304 10,304 8,834 16,

124 5 Applying Risk Pooling at Papierco 1 A B C D E F G H I J K L M N O P Q R S 6 Warehouse Location Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total/Average Sm. Const. MAD BIAS RMSE Safety Stock 127 Mannheim 128 Actual sales 14,475 8,225 21,500 23,625 18,025 18,463 17,050 22,575 12,025 16,913 23,900 11, ,964 7, Forecast 16,620 16,598 16,514 16,564 16,635 16,649 16,667 16,671 16,730 16,683 16,685 16, , , , Forecast error -2,145-8,373 4,986 7,061 1,390 1, ,904-4, ,215-5,569 8, Order quantity 22,500 22, ,500 22,500 22,500 22,500 22,500 22, ,500 22, , Net stock 8,025 22, ,150 8,187 13,637 13,562 24,037 7,124 5,724 17,036 10, Sales rate , , Average cycle stock 15,263 26,413 11,550 11,504 13,163 17,419 22,162 24,850 30,050 15,581 17,674 22,630 19, Nuremberg 136 Actual sales 2,540 4,488 8,425 9,135 9,488 8,668 10,638 6,400 10,188 7,843 11,113 7,675 96,601 1, Forecast 10,388 9,603 9,092 9,025 9,036 9,081 9,040 9,200 8,920 9,047 8,926 9, , ,094-1,158 3, Forecast error -7,848-5, ,598-2,800 1,268-1,204 2,187-1,470-13, Order quantity 22, , , , , , Net stock 19,960 15,472 7,047 20,412 10,924 2,256 14,118 7,718 20,030 12,187 1,074 15,899 12, Sales rate Average cycle stock 21,230 17,716 11,260 24,980 15,668 6,590 19,437 10,918 25,124 16,109 6,631 19,737 16, Ottendorf-Okrilla (Dresden) 144 Actual sales 1, , , ,188 2, , Forecast , Forecast error , , Order quantity 22, , Net stock 20,887 20,687 20,037 18,849 18,224 17,724 16,524 16,461 15,273 12,810 11,847 11,347 16, Sales rate Average cycle stock 21,694 20,787 20,362 19,443 18,537 17,974 17,124 16,493 15,867 14,042 12,329 11,597 17, Queis (Halle) 152 Actual sales 34,400 33,738 34,800 40,538 24,025 28,750 30,938 36,663 25,863 29,650 39,575 23, ,178 9, Forecast 28,771 29,334 29,774 30,277 31,303 30,575 30,393 30,447 31,069 30,548 30,458 31, , ,378 1,488 6, Forecast error 5,629 4,404 5,026 10,261-7,278-1, ,216-5, ,117-8,132 17, Order quantity 29,000 35,000 34,000 35,500 41,500 23,500 28,500 31,000 37,000 25,500 29,500 40, , Net stock -5,400-4,138-4,938-9,976 7,499 2, ,852 5,285 1,135-8,940 8,322 2, Sales rate 1,564 1,687 1,582 2,134 1,201 1,369 1,406 1,594 1,293 1,348 1,799 1, Average cycle stock 12,331 13,081 12,908 11,720 19,512 16,624 15,288 13,056 18,217 15,960 12,009 19,941 15, Reinbek (Hamburg) 160 Actual sales 60,375 50,345 55,478 48,475 64,020 62,413 70,720 81,763 41,658 61,405 62,938 42, ,205 16, Forecast 43,764 48,748 49,227 51,102 50,314 54,426 56,822 60,991 67,223 59,553 60,109 60, , ,003 3,247 13, Forecast error 16,611 1,597 6,251-2,627 13,706 7,987 13,898 20,772-25,565 1,852 2,829-18,343 38, Order quantity 44,000 65,500 50,500 57,500 47,500 68,500 64,500 75,000 88,000 34,000 62,000 64, , Net stock -16,375-1,220-6,198 2,827-13,693-7,606-13,826-20,589 25,753-1,652-2,590 18,795 3, Sales rate 2,744 2,517 2,522 2,551 3,201 2,972 3,215 3,555 2,083 2,791 2,861 2, Average cycle stock 16,294 24,011 22,021 27,065 20,053 24,232 23,142 23,218 46,582 29,122 28,992 40,103 27, Sasbach (Strasbourg) 168 Actual sales 16,790 16,953 18,805 18,165 14,225 15,950 15,005 12,015 7,950 10,223 13,553 12, ,357 2, Forecast 15,090 16,790 16,953 18,805 18,165 14,225 15,950 15,005 12,015 7,950 10,223 13, , , , Forecast error 1, , ,940 1, ,990-4,065 2,273 3, , Order quantity 22,500 22,500 22,500 22, ,500 22, , , , Net stock 5,710 11,257 14,952 19,287 5,062 11,612 19,107 7,092 21,642 11,419-2,134 7,643 11, Sales rate Average cycle stock 14,105 10,734 24,355 28,370 12,175 19,587 26,610 13,100 25,617 16,531 4,643 14,005 17, Tettnang (Lake Constance) 176 Actual sales 5,238 4,900 6,425 2,238 3,513 4,968 4,235 4,313 4,300 4,988 3,200 3,163 51,481 1, Forecast 3,306 3,692 3,934 4,432 3,993 3,897 4,111 4,136 4,171 4,197 4,355 4,124 48, , , Forecast error 1,932 1,208 2,491-2, , , , Order quantity 22, , , , Net stock 17,262 12,362 5,937 3,699 22,686 17,718 13,483 9,170 4, ,182 16,019 11, Sales rate Average cycle stock 19,881 14,812 9,150 4,818 24,443 20,202 15,601 11,327 7,020 2,381 20,782 17,601 14, Trierweiler (Trier) 184 Actual sales 19,150 19,728 41,668 19,038 21,400 22,665 27,153 27,925 8,113 30,838 18,025 23, ,128 9, Forecast 21,553 21,529 21,511 21,713 21,686 21,683 21,693 21,748 21,809 21,672 21,764 21, , ,687 1,587 8, Forecast error -2,403-1,801 20,157-2, ,460 6,177-13,696 9,166-3,739 1,698 19, Order quantity 22,500 22,500 22,500 35,000 22,500 22,500 22,500 23,000 28,000 22,500 22,500 22, ,500 SUM(S7:S184) = 188 Net stock 3,350 6,122-13,046 2,916 4,016 3, ,727 14,160 5,822 10,297 9,372 4, , Sales rate ,894 1,002 1,070 1,079 1,234 1, , , Average cycle stock 12,925 15,986 10,029 12,435 14,716 15,184 12,809 8,923 18,217 21,241 19,310 21,085 15, Total demand 654, , , , , , , , , , , ,638 7,643, , Aggregate forecast 571, , , , , , , , , , , ,449 7,478, ,502 13, , Forecast error 82,484 15, ,370-80,558-36,715-9,711-2, , ,999 51,494 22, , ,369 43, Pooled order quantity 572, , , , , , , , , , , ,500 7,847, Non-pooled order quantity 721, , , , , , , , , , , ,500 7,974, Net stock -82,097-15, ,065 80,763 36,859 9,794 2, , ,445-51,292-21, ,991 40, Sales rate 29,732 30,192 39,710 29,851 29,745 29,265 28,173 35,800 25,257 31,011 30,140 23, Average CS central ordering 251, , , , , , , , , , , , , Average CS decentral ordering 411, , , , , , , , , , , , , Negative net stock 202 Pooled system 654,175 kg 203 Non-pooled system 845,636 kg Table 5.2: Effects of Centralized Ordering at Papierco The order quantity for every month is the demand forecast for that month minus the net stock (at the end of the period after demand has been satisfied but before the order arrives at the beginning of the new period) left from the previous period plus the quantity to meet the minimum order and saltus quantity. Supplier lead time is neglected 785. If net cycle stock is negative (the actual sales exceeded the order quantity and the cycle stock on hand), this demand is either satisfied via transshipments, covered by safety stock 786, or backor- 785 Actually a location might run out of stock before the end of the period and have to wait until the beginning of the next period to place and receive a new order. This time might be seen as a replenishment order lead time. 786 Safety stock is neglected here at first. However, safety stock may also be defined as the average level of the net stock just before a replenishment arrives (Silver et al. 1998: 234, cf. Chopra and Meindl 2007: 305). Here we adhere to the definition Safety inventory is inventory carried to satisfy demand that exceeds the amount forecasted for a given period (Chopra and Meindl 2007: 304). 109

125 5 Applying Risk Pooling at Papierco dered. In any case this quantity has to be ordered in addition for the next period to replenish the stock of the location that has transshipped this item or the safety stock or satisfy the backordered demand. It is assumed that there are no available inventories or backorders of the copy paper at the beginning of the year The net stock of the respective period is the order quantity minus the actual sales plus the previous period's net stock. If the forecast of next period's sales can be met with net stock no order is placed with the supplier (the order quantity is zero). This occurs at the locations Bremen, Dortmund, Ernstroda, Leizen, Lohfelden, Lunteren, Mannheim, Nuremberg, Ottendorf, Sasbach, and Tettnang, where the monthly forecasts and actual sales are lower than the minimum order quantity (except in Bremen in August and November and Ernstroda in September). For central ordering (total demand) the monthly actual sales are the sum of the individual locations' monthly sales (row 191). The total 2007 order quantity of this copy paper with central ordering for all locations (pooled order quantity) 7,847,500 kg (cell N194) is lower than the sum of the total order quantities of the individual locations ordering separately (non-pooled order quantity) 7,974,000 kg (cell N195). The centralized ordering effect (equation (5.5)) amounts to 1.59 %. With central ordering Papierco could have saved ordering 126,500 kg, 117,645 (= 126,500 kg 0.93 /kg) purchasing costs, as well as average cycle inventory and the associated inventory carrying cost just for this one product by improved exhausting of the minimum order and saltus quantity. For some months the non-pooled order quantity is lower than the pooled one. This is evoked by some locations not placing an order in some months and serving demand from a minimum order quantity and net stock, as the forecasts and actual sales are much lower than the minimum order quantity. However, in these cases higher inventory carrying costs have to be borne, as the ordered minimum order quantity minus sales remains in stock for several periods. Negative net stock also postpones order quantities to later periods. Besides, a higher order quantity than the forecast to meet minimum order and saltus quantities works as a buffer for positive forecast errors (if the actual demand exceeds the forecast): The absolute value of the negative net stock is always less than the forecast error in these cases. Nevertheless, on the whole a lower total order quantity is needed to serve the same total annual demand with central than with decentral ordering. We approximated the average cycle stock per warehouse location as follows: We calculated the sales rate (actual sales divided by work days). Sales can only occur on work days. We determined the work days per month for the year 2007 (row 5). In case the work days in the different German federal states differed, we took the maximum. We then determined the inventory 110

126 5 Applying Risk Pooling at Papierco level at the end of each working day after sales, deducting the sales rate from the previous end of day inventory. Whenever the end of day inventory was negative we replaced it with zero physical inventory. The inventory level at the beginning of the month is the order quantity plus the previous month's end inventory level. We thus assumed that backordered demand (negative end of month net stock) is satisfied instantaneously at the beginning of the new month when the order quantity arrives. Finally we determined the arithmetic mean of the end of work day inventory levels as the average cycle inventory. This also confirms that today average inventory at Papierco is so high relative to actual sales partly due to minimum order and saltus quantities. The total average cycle stock with central ordering (row 198) is lower than with decentral ordering (row 199) in every month and for the whole year 2007, because of improved exhausting of minimum order and saltus quantities. For this copy paper Papierco could have saved 131,059 kg of average cycle stock and the corresponding inventory carrying costs of 30,471 (= 131,059 kg 0.93 /kg 0.25) in The sum of the average monthly positive net stock of the individual locations (184,234 kg) in column N is larger than the average monthly positive net stock with central ordering in cell N196 (40,987 kg). The sum of the forecast error statistics mean absolute deviation (MAD 142,459), bias (BIAS 29,560), and root mean square error (RMSE 190,306) for the individual locations in columns P, Q, and R is higher than the error statistics for the central order (95,502, 13,781, and 130,602 respectively) in cells P, Q, and R This confirms 788 that the aggregate forecast of monthly sales of this copy paper for all 23 considered locations is more accurate than the disaggregate forecast for the individual locations. This leads to a higher inventory availability, i. e. a smaller total stockout or backorder quantity (negative net stock) and thus smaller stockout or backorder costs in the system with central ordering (654,175 kg) than in the system with decentral ordering (845,636 kg), if safety stock is neglected. According to the One-Sample Kolmogorov-Smirnov Test, the H 0 -hypothesis that the forecast error at the locations Aalen, Berlin, Bielefeld, Bremen, Cologne, Dietzenbach, Dortmund, Ernstroda, Fellbach, Garching, Hemmingen, Kiel, Leizen, Lohfelden, Lunteren, Mannheim, Nuremberg, Ottendorf, Queis, Reinbek, Sasbach, Tettnang, and Trierweiler 787 MAD is [ ] the average of the absolute differences between the actual [ ] and the forecast sales. BIAS is the average of the differences between actual and forecast sales. RMSE is [the] square root of the average of the squared differences between the actual and the forecast sales (Ballou 2004c: 5f.). 788 Cf. footnote

127 5 Applying Risk Pooling at Papierco and of total demand is normally distributed cannot be rejected with an asymptotic significance (two-tailed) p of 0.984, 0.317, 0.879, 0.872, 0.485, 0.268, 0.582, 0.996, 0.513, 0.974, 0.970, 0.922, 0.973, 0.695, 0.966, 0.984, 0.681, 0.864, 0.832, 0.711, 0.758, 0.991, 0.851, and respectively. The One-Sample Kolmogorov-Smirnov Test for the exponential distribution shows a higher asymptotic significance (two-tailed) for Cologne (p = 0.820), Dortmund (p = 0.936), Fellbach (p = 0.824), Leizen (p = 0.993), Lohfelden (p = 0.911), Nuremberg (p = 0.839), Reinbek (p = 0.830), Trierweiler (p = 0.977), and total demand (p = 0.993). However, for Fellbach and Reinbek there are 3, for Cologne, Dortmund, Lohfelden, Trierweiler, and total demand 6, for Leizen and Nuremberg 7 values outside the specified distribution range. These values are skipped. Kiel shows a higher asymptotic significance (two-tailed) of in the One-Sample Kolmogorov-Smirnov Test for the uniform distribution. As Poisson variables are non-negative integers and negative values occur in the data, the One-Sample Kolmogorov-Smirnov Test cannot be performed for the Poisson distribution. In conclusion, the forecast error can be assumed to be rather normally distributed at the different locations. According to Thonemann (2005: 258) most applications assumed a normally-distributed forecast error. Nevertheless, we use the empirical distribution function of the forecast error to determine the safety stock. The empirical distribution function F(y) gives the probability that the forecast error is less than or equal to y, i. e. F(y) = P (forecast error Y y). In order to have an inventory availability of 91.7 %, we determine the y for P = 91.7 %. If we carry y as safety stock, this will cover demand that exceeds the forecast with a probability of 91.7 %, as the forecast error is less than or equal to this safety stock with the probability of 91.7 %. The safety stock that ensures a service level of 91.7 % is shown in column S for every location. The sum of the individual locations' safety stocks (245,561 kg) in cell S188 is larger than the safety stock with central forecasting and ordering for all locations (201,579 kg) in cell S191, as the aggregate forecast is more accurate than the disaggregate one. Papierco could have saved 43,982 kg of safety stock and the associated inventory holding cost of 10,226 (= 43,982 kg 0.93 /kg 0.25) just for this copy paper in Although Papierco forecasts demand and therefore should use safety stock as protection against the forecast error and not demand uncertainty 789, it uses the average past demand for the copy paper to determine safety stock. 789 Cf. Thonemann (2005: 255f.). 112

128 5 Applying Risk Pooling at Papierco With decentralized ordering there would have been 123,215 kg negative net stock that could not have been absorbed by the safety stock for all locations in We arrived at this figure by adding the negative net (cycle) stock and safety stock for every location for every month, whenever the absolute value of the former was greater than the one of the latter, and then adding up all the negative sums. With centralized ordering 80,486 kg of demand would have exceeded available inventory (cycle stock and safety stock). In the decentralized system the 123,215 kg of demand could have been satisfied by transshipments from other warehouses, backordered, or lost. In the centralized system, transshipments would not have been possible, as demand would have exceeded the order quantity and safety stock for all locations, and demand could have been only backordered or lost. Therefore one could argue that in this regard the service level in the decentralized system would have been higher. Transshipping 123,215 kg of this copy paper in the decentralized system would have cost at least 8,561 = t /t (cf. section ). Losing the contribution margin of selling the 80,486 kg of this copy paper would have cost 80,486 kg 0.23 /kg = 18,512 in the centralized system. Thus the net stockout costs (lost contribution margin in the centralized system minus the transshipment cost in the decentralized one) amount to 9,951 = 18,512-8,561 at the most. If all the unsatisfied demand had been backordered in both systems, backorder costs would have been higher in the decentralized than in the centralized system because of the backordered volume. Overall, Papierco could have saved at least 30,746 in inventory holding costs just for this one copy paper in 2007, if it had used centralized planning and ordering instead of the current decentralized one: 30,746 = 30,471 (saved inventory holding costs for average cycle stock) + 10,226 (saved inventory holding costs for safety stock) - 9,951 (net stockout costs). This example highlights that centralized ordering enables to reduce order quantities and thus average cycle inventory and inventory carrying costs by exhausting minimum order and saltus quantities better as well as to reduce safety stock and improve overall customer service level (inventory availability) or reduce negative net stock as the aggregate forecast is more accurate than the disaggregate one. Therefore, we propose a central distribution requirements planning with aggregate forecasting and central ordering for all Papierco locations. After placing a joint order, central planning would receive a notification of dispatch from the producer when the ordered products are produced and the trucks are ready to deliver them. Then Papierco tells the supplier which warehouses to deliver to according to current demand. Full truck loads can 113

129 5 Applying Risk Pooling at Papierco be delivered to single warehouses or one truck can deliver to several warehouses on a delivery route. The delivery destination decision is postponed until the ordered products are produced and ready to be delivered from the production facility to the delivery warehouses (geographic or logistics postponement). Today each warehouse location forecasts its warehouse sales and places orders with the suppliers individually. The warehouse receives a dispatch notification from the supplier before the delivery truck leaves the production facility to deliver the ordered products to the warehouse. The delivery destination is determined at the time of placing the order. With today's decentralized release orders within the centrally negotiated framework contracts every Papierco location orders all products for itself. With centralized ordering each location or company of the eight ones comprising Papierco could process the orders for one part of the product line, e. g. a main product group, for all considered 23 locations. This would lead to the following advantages: Fewer orders at the suppliers (1/23 of today's decentralized orders), lower order costs, improved utilization of minimum order and saltus quantities, lower average inventory, higher turnover, lower capital commitment, lower inventory holding costs. Only one procurement manager per product line part or product, higher specialist knowledge about this part of the assortment, improved forecasting, improved matching of supply and demand, improved potential utilization (negotiation power), closer collaboration with suppliers, long-term planning with suppliers, cost degression potentials for Papierco and its suppliers, reduced lead times. Directing supplier deliveries to certain warehouse locations at short notice (higher flexibility, product availability, and customer service level, reduced transshipments and inventories). This approach would maintain the importance of the legally independent companies forming Papierco and their decentral locations. The employees of the purchasing departments do not have to relocate to a physically central ordering department, but can remain at their locations. They may become more motivated by their increased responsibility, as they do not place replenishment orders for their own location only anymore, but for all Papierco locations albeit just for a certain part of the product line. Thus possible disadvantages of centralized ordering such as decreased responsiveness and sales due to lacking local know- 114

130 5 Applying Risk Pooling at Papierco ledge 790 can be mitigated as well. Procurement employees may have more time for improved forecasting and collaboration with suppliers and other departments or their number may be reduced. The number of the suppliers' trips to the warehouses would probably remain unchanged. Perhaps the supplier would charge a fee for delivery routes, if a truck load is to be transported to more than one Papierco location. This charge is unlikely to outweigh all the other stated benefits. The products, however, have to be managed more intensively by procurement managers. Operations and rules in all locations have to be standardized. Necessary data have to be available and correct. Orders would still be placed according to order suggestions generated by DRP consistent with customer orders, demand forecasts, inventory levels, and supplier lead time. Of course the ERP software has to be adapted to plan across all Papierco locations. The paper industry shows long production lead times, expensive holding costs for inventory surplus, and highly random demand at the retailers. Orders can be backlogged only for a few days at the most in case of a stockout or the sale is lost. These conditions favor centralized ordering according to Eppen and Schrage (1981: 51) and Schoenmeyr (2005: 5). Total demand is less variable than demand at the individual stores, which makes consolidated distribution most effective according to Cachon and Terwiesch (2009: 340). The time from placing an order with the supplier until production of the order is finished is longer than the delivery time from the production facility to the delivery warehouses. This corresponds to Cachon and Terwiesch's (2009: 340) observation that consolidated distribution is most effective [ ] if the lead time before the distribution center is much longer than the lead time after the distribution center. Replenishment coordination is most beneficial for high fixed order/transportation cost, large truck capacities, and many retailers. 791 The minimum order and saltus quantity restrictions Papierco has to observe can be subsumed under large fixed order or transportation cost and truck capacities, and Papierco has many delivery warehouses in Germany. In contrast to Eppen and Schrage (1981), Gürbüz et al. (2007: 305), and Cachon and Terwiesch (2009) our considerations do not contain a distribution center (here we follow Schonmeyr's (2005: 4) proposition), Papierco uses a stock-to-demand order policy with minimum order and saltus quantities and transshipments between regional warehouses, weekly demand often does not follow a theoretical distribution (cf. section ), demand at the 790 Ganeshan et al. (2007: 341). 791 Gürbüz et al. (2007: 305). 115

131 5 Applying Risk Pooling at Papierco different warehouses is correlated, and supplier lead time is largely neglected. Our centralized ordering model does not increase the distance a unit must travel from the supplier to the delivery warehouses, unless it is delivered on a delivery route with several stops. Eppen and Schrage (1981) consider centralized ordering policies in a periodic-review base-stock multi-echelon, multi-period system in the conglomerate for steel industry with independent normally distributed stationary random demands and identical proportional costs of holding and backordering at N warehouses, and no transshipments between the warehouses. In Eppen and Schrage (1981) products are ordered and quantity discounts are possible. Papierco just calls quantities of products from the supplier within the bounds of previously centrally negotiated skeleton agreements. Possible quantity discounts have been granted before. Diruf (2005, 2007) and Heil (2006: 169) examine only the demand-pooling savings of postponement, centralized ordering, and lateral transshipments between cooperating possibly independent fashion retailers with normal and lognormal 792 demand, equally big sales areas 793, and a newsboy structure. In their model the central ordering system leads to lower costs than the local ordering system with transshipments unless over- and underage costs are equal. In this case both systems achieve the same improvements compared to a system without risk pooling. 794 Hu et al. (2005) deal with the impact of emergency transshipments on (s, S) (order-upto) ordering policies and centralized ordering. Gürbüz et al. (2007: 296, 305) consider only one outside supplier, but inventory and transportation costs and four order-up-to policies. Cachon and Terwiesch (2009) consider consolidated distribution in retail with 100 stores, an order-up-to-model, Poisson demand at the retail stores per week 795, normallydistributed demand at the retail distribution center 796, lead times, and backordering 797. One could still determine an optimal delivery allocation procedure and order policy for Papierco, but this would go beyond the scope of this thesis. The reader is referred to e. g. Silver et al. (1998) for a detailed treatment of inventory control policies. 792 Heil (2006: 145f.). 793 Heil (2006: 169). 794 Diruf (2005: 59f.), Heil (2006: 110). 795 Cachon and Terwiesch (2009: 336). 796 Cachon and Terwiesch (2009: 338). 797 Cachon and Terwiesch (2009: 336f.). 116

132 5 Applying Risk Pooling at Papierco Alfaro and Corbett (2006: 24) find that within certain quite wide ranges of suboptimality of inventory control policies, risk pooling is better than optimizing the policy. This range expands with the number of SKUs. Papierco carries thousands of SKUs. Harrison and Skipworth (2008: 193) also find that form postponement in three companies improved responsiveness of manufacturing, although it had not been implemented theoretically ideally. Finally, risk pooling reduces decision errors, biases, and local suboptimization of boundedly rational decision makers and thus total costs by pooling decision errors across locations, even if demands are perfectly positively correlated or deterministic (behavioral benefits of inventory pooling) 798. Therefore, introducing risk pooling methods at Papierco at first, does not hurt Product Pooling For the last years more and more products have been added to Papierco's product line without dropping any other ones. The product range meanwhile comprises around 20,000 current products, some with few sales, and is planned to be diversified further especially in the business units printing accessories and screens and signs. This diversification leads to higher inventories, as every warehouse has to store at least some units of every product in order to be able to deliver every product specification, or more transshipments. Product availability decreases as forecasts for more and more individual items are less accurate. Every firm wishes to be ʻcustomer focusedʼ or ʻcustomer oriented,ʼ which suggests that a firm should develop products to meet all of the needs of its potential customers. Truly innovative new products that add to a firm's customer base should be incorporated into a firm's product assortment. But if extra product variety merely divides a fixed customer base into smaller pieces, then the demand supply mismatch cost for each product will increase. Given that some of the demand supply mismatch costs are indirect (e.g., loss of goodwill due to poor service), a firm might not even realize the additional costs it bears due to product proliferation 799. Already in 1987 Röttgen remarked due to the cut-throat competition fine paper wholesalers are forced to distinguish themselves from their competitors. This is possible by intensifying some selected distribution functions rather than accepting additional ones. Thus paper wholesalers seek to diversify their product line more and more to exhaust the cus- 798 Su (2008: 33). 799 Cachon and Terwiesch (2009: 335f.). 117

133 5 Applying Risk Pooling at Papierco tomer potential as much as possible. 800 Fine paper wholesale has to abandon the idea to be a specialist for all paper grades. This implies prioritizing within the product range instead of a sprawling product line diversification. An escalating diversification will lead to disproportionately high costs and continue to keep the return low. 801 According to the FPT-Workshop No. 4 in Munich on October 24, 2007 the variety of paper grades is narrower in the U.S. and is not demanded by customers (printing offices) in Germany either. The majority of printing offices deny the necessity of the present variety of grades. For them operativeness, color consumption, quality consistency, and mixability of paper grades are decisive and not a new brand or grade. 802 A FPT study supports this: A change in demand behavior for paper grades seems to gain momentum away from the unclear vast variety of grades towards a homogenization. The printing industry foremost demands good operability and printability of the paper in the printing machine. Paper grades with standard functionality (reproducible operability and printability) and multifunctionality are the focus of the forthcoming development. 803 Furthermore a too large product variety might backfire, as customers might not like to choose from many alternatives. 804 Toyota's and Nissan's fast introduction of a series of products, for instance, was counterproductive as it confused customers. 805 For all these reasons Papierco should rationalize its product line by product pooling taking into account its business strategy, demand and buying interdependencies between products, customer needs, and cooperation with suppliers 806 also in order to simplify its procurement planning. Serving demand with fewer products reduces demand variability, which leads to better performance in terms of matching supply and demand (e.g., higher profit or lower inventory for a targeted service level) Inventory Pooling Nowadays there are bilateral agreements between some Papierco member companies to store slow-moving items for one another. However, there is no transparency, which articles are stored at which location, and the partly sought selective stock keeping is not pursued strategically and economically. 800 Röttgen (1987: 83). 801 Röttgen (1987: 124). 802 FPT (2007b). 803 FPT (2007a). 804 Chain Drug Review (2009a), Hamstra (2009), Ryan (2009). 805 Pine II et al. (1993), Lau (1995). 806 Kulpa (2001), Hamstra (2009), MMR (2009), Pinto (2009a, 2009b), Thayer (2009: 23). 807 Cachon and Terwiesch (2009: 330, 335). 118

134 5 Applying Risk Pooling at Papierco If a new product is launched, it is stored at only three locations first. If it has been selling well for half a year, further locations start inventorying it and it may be stocked at every Papierco location in the end. Papierco's uniform price list suggests immediate availability of all paper grades at every warehouse location. Due to the increasing range of products, however, availability of every product at every location cannot be assured anymore. Some products are only available at one warehouse in Germany. Thus demands for transshipments rise and the 24-hour delivery service cannot be guaranteed anymore. Transshipment errors increase, especially if a product is transshipped via other warehouses. Often truck capacity is exceeded. Papierco's competitive advantage of delivering any paper grade mostly within 24 hours is fading. The product master record contains 61,132 different products. Thereof merely 23,740 ones show stock on hand at at least one warehouse. Of these only 9,868, of the 61,132 only 14,565 ones, are planned automatically with DRP. The product master record should be rid of inactive products with no sales. Product purchase planning and storing is distributed unequally between the eight Papierco member companies as figures 5.8 and 5.9 show. If it was distributed more evenly at least for fast movers, product availability could be increased and transshipments decreased (cf. section ). Along the same line, Pasin et al. (2002) simulate pooling of equipment for homecare service for a group of local community service centers (CLSCs) in the Montreal, Canada region. Overall pooling reduces shortages (rental costs) with the same inventory level, but the larger CLSCs with considerable equipment overcapacity may lose, because they almost never need to borrow equipment from other CLSCs, but have to bear the disadvantages (wear-and-tear costs). A more even distribution of over-capacity reached by inter-clsc sales or an equivalent financial compensation is much more effective than minimum stock, maximum contribution or maximum debt rules in producing an overall reduction in costs without penalizing any of the partners in the pooling process. We would have liked to design an optimal policy of strategic stock-keeping (inventory pooling through selective stock keeping). However, the necessary data such as the turnover or (average) inventory per SKU were not available. 119

135 5 Applying Risk Pooling at Papierco Number of Products Papierco Member Company (Code) Number of products planned with DRP (planning code = 1) Number of products not planned with DRP (planning code = 0), but with stock on hand Figure 5.8a: Product Purchase Planning at Papierco's Member Companies Number of Planned Identical Products Number of Papierco Member Companies Figure 5.8b: Product Purchase Planning at Papierco's Member Companies 120

136 5 Applying Risk Pooling at Papierco Number of SKUs Inventory (t) Warehouse Number of routinely stocked SKUs (product code P = purchase including raw materials) Number of SKUs with stock on hand Inventory (t) Figure 5.9: Stockkeeping at Papierco's Warehouses in February Challenges in IT and Organization Today too little process-oriented information exchange between departments inhibits business processes. Data are not transparent enough. If they are recorded at all, often they can only be obtained from the diverse, little integrated electronic data processing (EDP) systems with great effort. Too many subsystems and interfaces result in data transfer problems, too much data maintenance, and high costs. A lot of workarounds were programmed in the standard ERP system for Papierco, as many locations wanted to keep some unique business processes. However, the standard ERP system should standardize the business processes or one does not derive the full benefit from the standard software. 808 CLM (1995: 6) also concludes that the vast majority of available technology capable of facilitating process integration is underutilized. Papierco's different data analysis tools often show different numerical results for the same data query specifications. Data are often not available on a disaggregate individual product basis, but only for product groups. Analyses are hampered by different product codes for the same product for drop-shipping and warehouse sales, different periods (days, weeks, and months), units (sheets and kilograms), and product groupings and levels in dif- 808 Fleisch et al. (2004), Laudon and Laudon (2010: 369). 121

137 5 Applying Risk Pooling at Papierco ferent parts of the EDP system, too little knowledge about the analysis tools at Papierco's locations, as well as a bad data structure and maintenance. The delivery situation is not transparent enough: There are customer and delivery addresses. The delivery addresses are not assigned to customers uniquely. Sales can only be attributed to customer and not to delivery addresses. Some data are not recorded at all, such as cycle, safety, and average stock, as well as turnover per product, utilization of safety stock, cycle time, actual supplier lead times, and actual transshipment costs. Some computerized reports give wrong (calculated, not actual) safety stock levels for product groups, so that often the shown safety stock is higher than the actual total inventory on hand. Certain costs can only be obtained by checking every single cost unit. Higher cost awareness might lead to higher return. Setting up a systematic controlling might be worthwhile. Data and information are passed on by employees only hesitantly and after direct request. Important extra information to get a complete idea often is omitted. This might be interpreted as a defense strategy to secure the job and power position by exclusive knowledge. Any criticism can be invalidated by pointing out that certain information had not been considered. Similar micropolitical games were observed e. g. by Reihlen (1997: 3) in a heating technology company. Change in logistical practices often faces resistance. 809 This can be remedied with a company culture that promotes transparency. Papierco consists of eight different and legally independent companies, but is and wants to be seen as a single uniform company. However, employees rather feel obliged to their individual member companies that pay their salaries. This sometimes leads a member company to transship products for its own warehouse locations first and leave the goods bound for other member companies' locations behind. Products ought to be transshipped according to urgency and not company affiliation. Papierco should not optimize locally but globally. Logistics is seen very restrictively within Papierco as storing, handling, and transporting goods. Taking on its interdepartmental function, logistics should collaborate closely with and support management, sales, purchasing, finance, accounting, and controlling. During this study differences in managing Papierco's different locations became obvious. Papierco should standardize its operational policy, measure performance uniformly, and restructure its distribution system cautiously. For this a consistent and faultless data maintenance and accessibility is essential. Some data are deficient for logistical management. 809 CLM (1995: v, 6), Ballou et al. (2004b: 550), Graman and Magazine (2006: 1077). 122

138 5 Applying Risk Pooling at Papierco Most of these challenges are common in a lot of companies. Papierco is addressing them successfully and is a profitable company. 5.4 Summary The paper wholesale company Papierco can increase its competitiveness and reduce customer demand and supplier lead time uncertainty by the risk pooling methods transshipments, product substitution, postponement, centralized ordering, product pooling, and inventory pooling. The proposed optimization of the customer allocation to the individual warehouses can lead to considerable transportation cost savings near-term and without much investment burden. Customers should be served by the warehouse nearest to them. The following suggestions can be made to reduce inventory and transshipments, which have increased for the last years, and maintain or improve the customer service level and profitability: (1) The organizational structure and logistics should support the business processes as well as possible. (2) The company culture should promote transparency and a process view. (3) Improve the fragmented, little integrated, little standardized, not process- but function-oriented system landscape. This would also lower the disproportionately high IT costs. (4) Necessary data should be collectable faultlessly. (5) The demand planning 810 and purchasing policy should be improved, as this will result in higher product availability (customer service level) and less transshipments and inventory. (6) Create a uniform cross-functional demand planning process, in which sales, product managers, and purchasing collaborate to contain extraordinary demands through the sales assistants' and product managers' profound market knowledge and enable a better demand forecast and thus order policy. (7) Communicate and coordinate inventory reductions at the different member companies and warehouses. If a company is member of a purchasing group, it cannot act autonomously anymore. 810 Methods 11 (Exponential Smoothing), 6 (Least Squares Regression), and 9 (Weighted Moving Average) should be admitted to the DRP forecast run besides today's exclusively used methods 4 (Moving Average) and 10 (Linear Smoothing), as they gave good results. The forecast should be based on the last 12 to 24 months of sales history, if system performance permits this. 123

139 5 Applying Risk Pooling at Papierco (8) Establish (not necessarily physically) centralized procurement, which forecasts and orders for all of Papierco's German locations on the product level and directs the suppliers' deliveries to the warehouses according to current demand (consolidated distribution with pooling over the outside-supplier lead time). (9) Foster a close, reliable, long-term collaboration and exchange of information between suppliers, Papierco, customers, and individual departments. (10) Safety stock and transshipments can be reduced without hurting product availability by decreasing lead time (uncertainty) through improved collaboration with suppliers and reducing demand uncertainty by better forecasts and information gathering and usage. (11) Determine safety stocks more definedly according to the target customer service level, forecast error, supplier lead time, and lead time variability. (12) Enable determining the correct inventory levels per product and utilization of safety stock. (13) Rationalize the product line considering the business strategy, customer needs, product interdependencies, and cooperation with suppliers (product pooling). (14) Establish transparency regarding the storage locations of products. (15) Pursue selective stock keeping (inventory pooling) strategically economically. (16) Use alternatives to transshipments (product substitution and form postponement). (17) Papierco's emergency transshipments are economically worthwhile on average. (18) However, they should only be used, if the contribution margin of a sale is at least /t. (19) Establish transshipment cost rates that reflect the true costs. (20) Set up clear rules for the sales assistants for using transshipments. (21) Transshipment costs should be made transparent to the sales assistants and perhaps be deducted from the premium-determining contribution margin. We would have liked to always evaluate the cost savings attainable by these suggestions for improvement in money units, but necessary cost data and information were not provided. A consultancy described similar problems of obtaining data at Papierco. 124

140 5 Applying Risk Pooling at Papierco Human resource factors, transaction costs, and local suboptimization seem to be important in risk pooling and transshipments. These factors are commonly neglected in the risk pooling literature. This application shows that risk pooling can be used effectively as a guiding umbrella principle in systematically restructuring a distribution system to cope with supplier lead time, customer demand, and forecast uncertainty, as well as product variety and reduce costs and inventory, increase customer service, and make a company more competitive. Risk pooling methods can be used side by side to take advantage of their benefits, while making up for disadvantages of other ones. Our Risk Pooling Decision Support Tool is suitable to determine appropriate risk pooling methods for a company that faces lead time and demand uncertainty. Some of the methods determined with the help of this tool are already applied by Papierco nowadays (transshipments, product substitution, inventory pooling, and postponement), but can and should be improved. The other ones still make sense after a more thorough investigation (centralized ordering and product pooling). Centralized ordering can reduce average cycle inventory, even if a stock-to-demand order policy is followed and minimum order and saltus quantities have to be observed. It also enables to decrease safety stock and improve inventory availability, as the aggregate forecast for the central order is more accurate than the disaggregate one for the decentral orders. 125

141 6 Conclusion Our main novel contributions lie in the (1) comprehensive and concise definition of risk pooling distinguishing between variability, uncertainty, and risk, (2) holistic review and valuechain-oriented structuring of the plethora of research on risk pooling methods in business logistics, especially on inventory pooling, according to their uncertainty reduction abilities, (3) developing tools to help in comparing and choosing appropriate risk pooling methods and models for different economic conditions based on a contingency approach, (4) applying these tools to German paper wholesale, and (5) conducting a survey on the recognition and usage of the various risk pooling concepts and their associations in 102 German trading and manufacturing companies. Risk pooling in business logistics can reduce total variability of demand and/or lead time and thus uncertainty and the possibility of not achieving business objectives (risk) by consolidating individual variabilities (measured with the standard deviation) of demand and/or lead time. These individual variabilities are consolidated by aggregating demands (demand pooling) and/or lead times (lead time pooling). This reduction in uncertainty allows to reduce inventory without reducing the customer service level (product availability) or to increase the service level without increasing the inventory or a combination of both and to cope with product variety. Risk pooling is explained by the Minkowski-inequality, the subadditivity property of the square root of nonnegative real numbers, and the balancing effect of higher-than-average and lower-thanaverage values of a random variable. Risk pooling usually shows increasing returns, but diminishing marginal returns. Its benefit generally increases with decreasing correlation of pooled demands and/or lead times and concentration of uncertainty as well as increasing variability. Risk pooling in business logistics comprises well over 600 publications mostly containing modeling research. After the concept borrowed from modern portfolio and insurance theory has been mainly applied to inventory pooling, meanwhile research focuses on postponement, transshipments, and the coordination of risk pooling arrangements and cost and profit allocation through contracts. The researchers are of different backgrounds, orientation, and prominence, so that they use inconsistent terms, frameworks, and structures and make our thorough literature review, structuring, and definitions essential. We identified ten risk pooling methods: (1) inventory pooling, (2) virtual pooling, (3) transshipments, (4) centralized ordering, (5) order splitting, (6) component commonali- 126

142 6 Conclusion ty, (7) postponement, (8) capacity pooling, (9) product pooling, and (10) product substitution. These methods can be implemented everywhere along the supply chain and mainly pertain to the value activities storage (inventory pooling), transportation (virtual pooling and transshipments), procurement (centralized ordering and order splitting), production of goods and services (component commonality, postponement, and capacity pooling), and sales (product pooling and product substitution). We presented a classification of risk pooling methods according to their ability to pool demands and/or lead times. They all but order splitting can reduce demand uncertainty, order splitting only lead time uncertainty, capacity pooling, component commonality, inventory pooling, product pooling, and product substitution only demand uncertainty. Transshipments, virtual pooling, postponement, and central ordering may dampen both uncertainties. (1) Inventory pooling is the consolidation of inventories, e. g. by inventory or warehouse system centralization or selective stock keeping, in order to reduce inventory holding and shortage costs through risk pooling. Its risk pooling effect in terms of inventory savings can be quantified with the square root law (SRL), portfolio effect (PE), and inventory turnover curve. The SRL states that the total system wide stock of n decentralized warehouses is equal to that of a single centralized one multiplied with the square root of the number of warehouses n. Despite confusion in the literature it applies to regular stock, if an economic order quantity (EOQ) order policy is followed, the fixed cost per order and the per unit stock holding cost, demand at every decentralized location, and total system demand is the same both before and after centralization. It is valid for safety stock, if demands at the decentralized locations are uncorrelated, the variability (standard deviation) of demand at each decentralized location, the safety factor, and average lead time are the same at all locations both before and after consolidation, average total system demand remains the same after consolidation, no transshipments occur, lead times and demands are independent and identically distributed random variables and independent of each other, the lead time variance is zero, and the safety-factor approach is used to set safety stock for all facilities both before and after consolidation. It applies to total stock (the sum of regular and safety stock), if the assumptions stated above of the SRL both as applied to regular and safety stock hold (cf. appendix B). It does not hold, if its assumptions are not fulfilled. If an EOQ policy is followed and constant fixed costs per order, holding costs, and total demand are assumed for all locations before and after centralization, the total order fixed 127

143 6 Conclusion cost usually is lower because of less orders and the inventory holding cost is lower due to a smaller total EOQ in the centralized than in the decentralized system (cf. appendix C). Savings in safety stock through inventory pooling stem from balancing demand variabilities (risk pooling). Although some researchers 811 claim the SRL estimated real savings well, in 13 of 14 practical cases we reviewed it overestimated actual inventory savings often significantly. This means its assumptions are not fulfilled in these cases or there were other inventory- or service-related changes. In a survey that we conducted with eleven companies from different countries and industries (see table D.1) only one fulfilled all, two fulfilled none of the five assumptions necessary for applying the SRL to regular stock. The participants fulfilled at least two and at the most seven of the eleven assumptions of the SRL when applied to safety stock. It seems that seldom is it appropriate to apply the SRL, because mostly not all its assumptions are fulfilled. Nonetheless, the other SRL- and PE-models that we synoptically compared in terms of their assumptions in table D.2 might be applied as their assumptions are fulfilled. Researchers questioning the SRL either question its assumptions or do make other assumptions and therefore arrive at different results. Zinn et al.'s (1989) PE shows the reduction in aggregate safety stock by centralizing several warehouses' inventories in one warehouse in percent, if lateral transshipments are not usual, there is no lead time uncertainty, customer service level is not affected by a change in the warehouse number, demand at each warehouse is normally distributed, and the order quantity equals demand during lead time. The inventory turnover curve shows average inventory in dependence of the inventory throughput for a specific company. It can be constructed from a company's stock status reports and be used to estimate the average inventory (not only safety stock as with the PE) for any (planned) warehouse throughput without the limitations of the SRL. (2) Virtual pooling extends a company's warehouse or warehouses beyond its or their physical inventory to the inventory of other own or other companies' locations by means of information and communication technologies, drop-shipping, and cross-filling. (3) Transshipments are inventory transfers among locations (e. g. between warehouses or stores) for example in case of a stockout. 811 For example Sussams (1986: 10), Pfohl (1994: 141). 128

144 6 Conclusion (4) Centralized ordering places joint orders for several locations and later allocates the orders (perhaps by a depot) to the requisitioners or distribution points in consolidated distribution according to current demand information. (5) Order splitting is partitioning a replenishment order into multiple orders with multiple suppliers or into multiple deliveries. (6) Component commonality designs products sharing parts or components. This reduces the variability of demand for these components. (7) Postponement delays decisions in production, logistics, or distribution as long as possible, e. g. developing, purchasing, ordering, fulfillment assignment, production, manufacturing, assembly, packaging, labeling, pricing, and shipping. Because of a shorter forecast period and an aggregate forecast more accurate information can be used. (8) Capacity pooling is consolidating production, service, or inventory capacities of several facilities. Without pooling every facility fulfills demand just with its own capacity. With pooling demand is aggregated and fulfilled by a single (perhaps virtually) joint facility. A higher service level can be attained with the same capacity or the same service level can be offered with less capacity. (9) Product pooling is unifying several product designs to a single generic or universal design or reducing the number of products thereby serving demands that were served by their own product variant before with fewer products. In (10) product substitution one tries to make customers buy another alternative product, because the original customer wish is out of stock or although it is available (demand reshape). Using contingency theory, we explored conditions that favor these individual risk pooling methods, their advantages and disadvantages, and basic trade-offs in detail. Based on this synopsis the Risk Pooling Decision Support Tool (RPDST) was developed for choosing an appropriate risk pooling strategy for a specific situation. This tool was effectively utilized to choose suitable risk pooling methods for a large German paper distributor. This application showed that risk pooling can be used effectively as a guiding umbrella principle in systematically restructuring a distribution system to cope with supplier lead time, customer demand, and forecast uncertainty, as well as product variety and reduce costs and inventory, increase customer service, and make a company more competitive. Human resource factors, transaction costs, and local suboptimization seem to be important in risk pooling and transshipments. These factors are commonly neglected in the risk pooling literature. Risk pooling methods can be and are used 129

145 6 Conclusion side by side to take advantage of their benefits, while making up for disadvantages of other ones. This is in line with our survey findings. Centralized ordering can reduce average cycle inventory even if a stock-to-demand order policy is followed and minimum order and saltus quantities have to be observed. It also enables to decrease safety stock and improve inventory availability as the aggregate forecast for the central order is more accurate than the disaggregate one for the decentral orders. The literature review and this application showed the theoretical benefits risk pooling can bring. However, survey research on the knowledge and application of risk pooling is scarce. Therefore, we explored whether the different risk pooling concepts are known, applied, and associated in a survey of 102 German manufacturing and trading companies: A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It appears that mainly transshipments and postponement are associated with risk pooling. Although at least in our sample the risk pooling concepts are known fairly well (central ordering, product substitution, and selective stocking the most), only selective stocking, transshipments, and central ordering are widely applied. Transshipments are more, postponement and product pooling less applied than suggested by some publications mostly for other regions. Less sample companies have centralized their warehouse system than European ones. For our sample we cannot confirm a major decentralization trend as one may expect due to increasing fuel costs. Companies seem to be consistent in their strategy of centralization, decentralization, or no change in warehouse number over time. The utilization and knowledge of a risk pooling concept are correlated. This suggests that improving the knowledge of risk pooling may increase its application. Research needs to convey under what conditions and how the different risk pooling concepts can be applied successfully. This research constitutes one step in this direction. Prominently associated is past decentralization with future decentralization, the utilization of product substitution and demand reshape, past centralization and decentralization (the only negative correlation), the application of the inventory turnover curve and transshipments, commonality and product pooling, risk pooling and transshipments, turnover curve and order splitting, selective stocking and virtual pooling, transshipments and virtual pooling, risk pooling and postponement, product substitution and transshipments, product substitution and virtual pooling, as well as postponement and commonality and vice versa. 130

146 6 Conclusion We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of form postponement at best only weakly for our sample. Trading companies seem to apply product substitution and transshipments more than manufacturing companies. The opposite is true for commonality and postponement. This was considered in the RPDST. In contrast to Van Hoek (1998b) our sample shows no significant difference in the application of postponement by electronics, automotive, food, and clothing manufacturers. More large companies appear to use risk pooling and postponement than smaller ones, perhaps because they can better afford to invest in expensive risk pooling methods as suggested by Huang and Li (2008b: 12). More small companies have centralized their warehouse or logistics system in the past than large ones in our sample. The survey is of limited representativeness and generalizability, as a genuine simple random sample of the relevant population of German manufacturing and trading companies could not be drawn. Survey research is very laborious and prone to many biases and errors and has low response rates that disappoint the researcher and impair the results. Our experience supports that face-to-face methods tend to achieve higher response rates. As this treatise constitutes a first attempt to structure the vast risk pooling research in business logistics, develop tools to choose between the various risk pooling methods, and get an idea about their recognition and application in German companies, we make the following suggestions for further research: Our RPDST and its underlying contingency factors should be empirically validated with additional companies in different industries. Conditions and implementation modalities favoring the different risk pooling methods should be further explored, especially for product pooling, central ordering, (particularly non-manufacturing) capacity pooling, virtual pooling, and substitution/demand reshape, as our considerations are not exhaustive. The effectiveness and efficiency of the different methods should be compared. Evers (1999), Swaminathan (2001), Eynan and Fouque (2005), and Wanke and Saliby (2009) made a good start here. Perhaps a normative model could be developed that integrates and compares the ten identified methods in terms of their costs and benefits in order to choose an optimal one. However, such a model might be either too complex or simple. Perhaps combining simulation and analytic frameworks may better account for the complicated interaction effects 131

147 6 Conclusion among various factors. 812 Centralized ordering and transshipments at Papierco could be simulated as well. In general, risk pooling models should become more realistic in terms of their assumptions, accessibility for practitioners, and allowing (practitioners) to quantify the benefits of risk pooling. 813 We considered choosing suitable risk pooling methods for individual companies for certain economic conditions and sometimes their relation to their immediate supply chain members at the most. However, a risk pooling strategy that is beneficial for an individual supply chain member might not be profitable for others or the whole supply chain. 814 Therefore, it should not be implemented by one company unilaterally and further research should focus on the supply chain as a whole: Which conditions render a risk pooling method or a combination of risk pooling methods beneficial for all members of a supply chain? How do you get independent parties to agree on or join a risk pooling strategy? If some supply chain members are better and other ones worse off after risk pooling, how do you distribute the gains to encourage risk pooling and make it beneficial for everybody? The contracting side of risk pooling still leaves room for further research. Another interesting question to explore would be whether the risk pooling methods make individual companies and the whole supply chain more resilient to external uncertainties other than demand and lead time uncertainty. Sheffi (2006, 2007) explores this question for several risk pooling methods and individual companies 815. Snyder and Shen (2006: 42) conclude that [s]upply chain resilience [to supply disruptions and demand uncertainty] can be improved significantly without large increases in cost by centralization (risk pooling) and decentralization (risk diversification). How should supply chains or logistics systems be designed, so that risk pooling is exploited optimally and uncertainties are minimized? 812 Cf. Hwarng et al. (2005). 813 Cf. Heil (2006: 81, 169). 814 Some or all supply chain members may be hurt by centralized ordering (Gürbüz et al. 2007: 305), inventory pooling (Anupindi and Bassok 1999, Pasin et al. 2002, Simchi-Levi et al. 2008: ), postponement (García-Dastugue and Lambert 2007), transshipments (Grahovac and Chakravarty 2001, Dong and Rudi 2002, 2004, Zhang 2005, Shao et al. 2009), and virtual pooling (Randall et al. 2002: 56). 815 He examines how an enterprise can be made more resilient to disruptions (supply shortages, production disruptions, energy price increases, exchange rate fluctuations, strikes, and natural disasters) especially by risk pooling (Sheffi 2006: 117f., 210, 212, 248, 303, 317), flexibility (Sheffi 2006: 117ff., 199ff.), postponement (Sheffi 2006: 297), commonality (Sheffi 2007: ), standardization (Sheffi 2007: ), interchangeability (Sheffi 2006: 210), multiple suppliers (Sheffi 2007: 99f., ), inventory/forecast aggregation (Sheffi 2006: 117f.), exchange of parts (Sheffi 2006: 248), and reduction of product variants (Sheffi 2006: 119). 132

148 6 Conclusion An empirical analysis of risk pooling in the German auto industry might be interesting, because of the current changes in model mix (high gas prices), production volume (recession), and steel prices. How can you prepare your production system for something like this? How does the current economic downturn affect risk pooling? We already noted that this might have contributed to increased research and implementation of risk pooling. How do increased transportation costs affect risk pooling? If they are lasting and warehouse networks are therefore decentralized, how is this decision affected by risk pooling and how does network redesign affect risk pooling? Another more representative survey with a higher response rate could also shed light onto the companies' reasons for and against as well as the manner, degree, benefits, and costs of applying the risk pooling concepts, as we intended in the six-page version of our survey that yielded a uselessly low response rate. As risk pooling can affect the whole supply chain, another survey could consider a supply chain wide perspective rather than single companies. Risk pooling is usually shown or proved with the standard deviation. For other measures of dispersion, such as the variance of independent random variables or the range, there might be no risk pooling effect. Therefore one could consider risk pooling with measures of dispersion other than the standard deviation. Risk pooling should also be further explored with different order policies. Finally, the SRL- and PE-models can be extended to include further assumptions. One should also check whether the conditions or assumptions necessary for the SRL to hold (necessary conditions) are also sufficient conditions, i. e. if the SRL holds, these conditions also automatically apply. 133

149 Appendix A: A Survey on Risk Pooling Knowledge and Application in 102 German Manufacturing and Trading Companies 134

150 1 Introduction After reviewing the limited recent survey research in OR, business logistics, SCM, and particularly risk pooling mostly with low response rates, we describe our findings from a survey on risk pooling knowledge and application we conducted among 102 German manufacturing and trading companies. Such a survey has been demanded by some researchers and to our knowledge has not been conducted before. 1.1 Motivation: Scarce Survey Research on Risk Pooling There is little empirical and especially survey research in OR 816, business logistics 817, and risk pooling 818. The samples and response rates are usually small or not mentioned 819. No surveys have been conducted on risk pooling in business logistics in general yet. Only few surveys touch types of risk pooling. Most of these surveys deal with postponement, although the majority of empirical research on postponement relies on case stu- 816 Cachon (2004), Netessine (2005). 817 Griffis et al. (2003: 237). 818 Labro (2004: 358). 819 The following researchers conducted surveys on logistics topics with the following returns: Jackson (1985, 53 usable responses), Dubelaar et al. (2001, 72 usable of 101 surveys), Griffis et al. (2003: 241f., response rate: %), Kisperska-Moroñ (2003: 130, 538 questionnaires, on average three respondents in one company), Bagchi and Skjoett-Larsen (2005, 149 responses, response rate: 5.7 %), White (2005, 429 answers, response rate: %), Hilmola and Szekely (2006, 67 usable responses, response rate: 8.9 %). Johnson et al. (2006, 297 usable responses, response rate: 55 %, 305 usable responses, response rate: 51 %, 284 usable responses, response rate: 44 %), Shao and Ji (2006, 321 surveys, response rate: 89.2 %), Böhnlein and Lünemann (2008, 51 responses), Chikán (2009, 51 responses, response rate: %). Surveys on postponement received 65 (Kisperska-Moroñ 2003: 130), 76 (Yang et al. 2005b), 80 (Van Hoek 1998b), 102 (Chiou et al. 2002), 106 (Huang and Li 2008b), 111 (completed 24-page workbooks in interviews with world class companies, CLM 1995: 8, 384), 129 (McKinnon and Forster 2000: 5, Delphi survey with logistics experts), 256 (Rabinovich and Evers 2003b), 306 (Nair 2005), 322 (in the base-line survey in Germany, CLM 1995: 381f.), 358 (Oracle 2004, response rate: 2.24 %), 782 (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000, response rate: 53 %), and 3,693 (altogether in the base-line survey, CLM 1995: 381f.) usable responses. The surveys with high returns were conducted via logistics associations (CLM 1995, Rabinovich and Evers 2003b, Oracle 2004, Nair 2005) or via phone with very few questions (Van Hoek 2000b). They were administered in Europe (McKinnon and Forster 2000: 5), Greater China (Mainland China, Hong Kong, and Taiwan) (Huang and Li 2008b), Taiwan (Chiou et al. 2002), the U. S. (an expert study by Morehouse and Bowersox 1995, Van Hoek 1998b, Rabinovich and Evers 2003b, Nair 2005), the UK (Yang et al. 2005b), the Netherlands (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000), and Upper Silesia, Southern Poland (Kisperska-Moroñ 2003) among manufacturing (Van Hoek 1998b, Van Hoek and Van Dierdonck 2000, Chiou et al. 2002, Kisperska-Moroñ 2003, Rabinovich and Evers 2003b, Nair 2005, Yang et al. 2005b, Huang and Li 2008b), trading (Van Hoek and Van Dierdonck 2000, Nair 2005), and transport and logistics services companies (Van Hoek 2000b, Van Hoek and Van Dierdonck 2000). Graman and Magazine (2006: 1068, 1070f., 1075) conducted depth interviews with five managers of a small U.S. manufacturer of mops and brooms on issues influencing successful postponement implementation. 135

151 Appendix A dies 820, such as Dapiran (1992), Cooper (1993, examples), Feitzinger and Lee (1997), Garg and Tang (1997), Van Hoek (1997, 1998a, 1998b), Van Hoek et al. (1998), Magretta (1998), Brown et al. (2000), Waller et al. (2000), Ghemawat and Nueno (2003), Huang and Lo (2003), and Huang and Li (2008a). Whereas some researchers find postponement application has increased, will increase, or postponement is widely applied 821, others state it is not applied as much (as expected) 822 and will be even less used in the future 823. This is explained by a general lack of understanding of postponement regarding its conception, gains, and costs 824, perceived technology limitations, ineffective organization alignment 825, as well as difficulties in managing the relations to suppliers and customers 826 and in estimating the costs and benefits of postponement 827. Van Hoek (1998b: 513) finds that [d]ownstream activities such as distribution and packaging are largely postponed (56.93 per cent of the flow of goods and per cent). Upstream activities such as engineering and purchasing are postponed to a lesser extent (37.49 per cent of the flow of goods and per cent). Overall however, the findings indicate that postponement is applied at multiple points in the chain and to a significantly high share of the flow of goods. Yang et al. (2005b: 1000) remark that postponement is mostly applied as make to order and ship to order. 820 Van Hoek (2001). 821 CLM (1995: 213), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), Van Hoek and Van Dierdonck (2000), McKinnon and Forster (2000: 7f.), Chiou et al. (2002), Huang and Li (2008b). CLM (1995: 213) finds Research clearly supports the generalization that firms are rapidly adopting both form and time postponement, although 10.3 % of North American and 85 % of non-north American world class companies have decreased or substantially decreased the use of postponement and 31 % of North American and 0 % of non-north American (European/Pacific Basin) world class companies have increased or substantially increased the use of postponement (Workbook Section 4: Organization, Question 31, Electronic Appendix Disk to CLM 1995). Yet, only few non-north American companies completed the workbook (CLM 1995: 384). 822 Van Hoek et al. (1998: 34, 51), Bowersox et al. (1999), Battezzati and Magnani (2000: 423), Brown et al. (2000: 78), Van Hoek (2000b, in third party logistics or TPL), Van Hoek and Van Dierdonck (2000, in TPL), Oracle (2004), Yang et al. (2004, 2005a, 2005b: 991), Boone et al. (2007: 594), Yang et al. (2007: 972). Van Hoek et al. (1998: 51, 34) observe that although the theoretical benefits of postponement [were] introduced [already] in the 1950s and 60s, this highly attractive principle has hardly been applied to date. [P]ostponement applications are still in the infancy stage (Van Hoek et al. 1998: 51). It has an enormous potential, still largely under-exploited, in Italy (Battezzati and Magnani 2000: 423). Boone et al. (2007: 594) remark the slow rate of postponement adoption among practitioners. [P]ostponement is an underutilized concept (Yang et al. 2007: 972). 823 Postponement applications are still not as widespread as expected. [ ] The respondents also expected postponement to be less used in three years (Yang et al. 2005b: 991). 824 Oracle (2004: 2, 7). 825 Capgemini (2003), Matthews and Syed (2004: 30). 826 Yang et al. (2005b: 991), Waller et al. (2000), Van Hoek et al. (1998). 827 Van Hoek et al. (1998). 136

152 Appendix A Rabinovich and Evers (2003b: 41f.) find that time postponement (emergency transshipments) contributes to the implementation of form postponement. Huang and Li (2008b: 5, 16f.) discover that the degree of postponement application is higher in China than CLM (1995), Yang et al. (2005a), and Van Hoek (1998b) remarked in Western countries and increases. Chiou et al. (2002: 122) also conclude that form postponement strategies are practiced widely by IT firms in Taiwan. Huang and Li (2008b: 12) sent their questionnaires only to 411 companies that had confirmed on the phone that they applied postponement. They, Chiou et al. (2002), and Yang et al. (2005b) do not state how many companies in their research countries actually apply postponement. In a personal correspondence on September 4, 2009 Dr. Biao Yang, The York Management School, University of York, UK, explained that speaking from their experience, given the working definitions of different postponement strategies they provided 828, very few companies would claim that they are not using any postponement. The Council of Logistics Management (CLM) conducted a base-line survey in North America (Canada and the U.S.), Europe (France, Germany, the Netherlands, Norway, Sweden, and the UK), and the Pacific Basin (Australia, Japan, and Korea) from May to September Of the 21,592 mainly manufacturing companies contacted, 3,693 answered (response rate: 17.1 %). In Germany 3,000 surveys were mailed and 322 returned (response rate: 10.7 %). 829 It also did interviews with 111 companies from 17 countries in North America, Europe, and the Pacific Basin from early 1994 until spring 1995 that were believed by a group of logistics experts to have a high potential to possess world class logistical capabilities and asked them to complete a 24-page workbook % of North American and 29.1 % of non-north American world class companies consider location flexibility ( [t]he ability to service customers from alternative warehouse locations, i. e. in our opinion transshipments or virtual pooling) less or least impor- 828 In their survey Yang et al. (2005b: 1002f.) ask for the percentages of goods related to engineer, purchase, make, final manufacturing/assembling, package/label, and ship to order to elicit the extent of postponement application in the respondents' companies. Thus they equate make-to-order with postponement or delayed differentiation, while Cachon and Terwiesch (2009: 344) distinguish these strategies: Although they are conceptually quite similar, [d]elayed differentiation is thought of as a strategy that stores nearly finished product and completes the remaining few production steps with essentially no delay. Make-to-order is generally thought to apply to a situation in which the remaining production steps from components to a finished unit are more substantial, therefore involving more than a trivial delay. Hence, delayed differentiation and make-to-order occupy two ends of the same spectrum with no clear boundary between them. 829 CLM (1995: 381f.). CLM was named Council of Supply Chain Management Professionals (CSCMP) in CLM (1995: 8f., 384). 137

153 Appendix A tant, 35.3 % or 37.5 % respectively more or most important. The North American and non- North American world class companies see mostly the logistics department as responsible for location flexibility (77.19 and % responsibility). Fifty-one percent of North American and 58.3 % of non-north American world-class companies believe they perform better or much better than their competitors in terms of location flexibility. 831 According to McKinnon and Forster (2000: 17), the proportion of retail sales bypassing conventional shops and being delivered directly to the home is likely to increase significantly until Direct distribution to the home from nationally based suppliers is likely to experience the fastest growth 832. That means that virtual pooling in the form of drop-shipping is expected to increase. In a small phone survey by Randall et al. (2006) of 64 (56 responses, 54 usable responses, response rate: 84.4 %) publicly held e-tailers that made up 60 % to 70 % of U.S.- wide e-tailing revenue, 36 companies (67.7 %) chose to hold inventory. That means 33.3 % of the surveyed e-tailers conducted virtual pooling. In the CLM base-line survey, % of North American, % of European, and % of Pacific Rim companies agree or strongly agree that on an equal volume basis they had inventory located at fewer sites in 1993 (today) than in 1988 (five years ago). 833 That means that % of the surveyed European companies conducted inventory pooling. The world class companies' [l]ogistics strategy includes a priority to reduce [ ] [t]he number of logistics facilities more so in Europe and the Pacific Basin, where the mean answer was 3.55 than in North America, where the mean answer was 3.23 on a scale from 1 (Strongly Disagree) to 5 (Strongly Agree). 834 McKinnon and Forster (2000: 6f.) find The centralisation of inventory is likely to outstrip that of production. At a European level, the degree of inventory concentration is forecast to increase by a third, twice as much as at a national level. A significant minority of the panel (around 15 %) indicated that within countries there would be net decentralisation of inventory, with firms increasing their number of stockholding points. The prevailing view, however, was that inventory centralisation, which has been one of the main logistical trends over the past 30 years, would continue apace for at least the next 5 years. 831 Workbook Section 3: Relative Performance Competencies, Question 20, Electronic Appendix Disk to CLM (1995). 832 McKinnon and Forster (2000: 9). 833 Logistics Practices Results, Question 7, Electronic Appendix Disk to CLM (1995). 834 CLM (1995: 387). 138

154 Appendix A A Warehousing Education and Research Council survey with 139 U.S. participants in manufacturing, retail, wholesale, public utilities and government showed that the number of warehouses continues to shrink, although there are a few new large facilities in West or Mid Atlantic regions. 835 Contrarily, according to a survey by Lemoine and Skjoett-Larsen (2004) among logistics managers of mechanical, electronic, and medical equipment companies in Denmark in 2001 (46 usable questionnaires, response rate: 10 %) the number of suppliers, production facilities and warehouses has not been changed in the last three to five years in Europe, but has been increased or will be increased outside Europe. Bandy (2005) conducts an anonymous survey among 24 students that shows that a simple spreadsheet in-class simulation helps students understand the impact of pooling safety stock. Reviewing literature and interviewing Belgian companies, Naesens et al. (2007) find that companies are reluctant to implement inventory pooling in a horizontal collaboration. Nonetheless, companies seem to have conducted inventory pooling within companies to a broad extent. Twenty-seven percent of North American and 29.1 % of non-north American worldclass companies consider substitution flexibility ( [t]he ability to substitute product or service offerings in the event of a delay or stockout versus backorder or line cancellation ) less or least important, 46.2 % or 25 % respectively more or most important. Responsibility for substitution flexibility rests 49.9 % with logistics, % with marketing according to North American, or % or % respectively according to non-north American world-class companies % of North American and 37.5 % of non-north American world-class companies believe they perform better or much better than their competitors in terms of substitution flexibility. 836 Only few surveys provide information on how many companies apply the respective risk pooling method. Nearly 50 % of more than 350 companies from all over the world have not implemented postponement strategies. 837 Hence, about half of these companies use postponement. More than 40 % of the companies surveyed by Kisperska-Moroñ (2003: 131) gear total production towards customer orders. Surveyed companies manufacture on average 16 % to 835 Modern Materials Handling (2002). 836 Workbook Section 3: Relative Performance Competencies, Question 29, Electronic Appendix Disk to CLM (1995). 837 Oracle (2004). 139

155 Appendix A stock and 84 % to order, engineering 97 %, metal 74 %, plastic products 83 %, and electrotechnical companies 77 % to order. Thus one could infer that about 40 % of the surveyed companies in Upper Silesia, Poland apply manufacturing postponement. From 1988 to 1993 inventory was centralized or pooled by % of the European companies surveyed by the CLM. 838 Virtual pooling is applied by 33.3 % of the U.S. e-tailers that Randall et al. (2006) interviewed. None of the surveys gives detailed information on Germany, although Germany is the fourth largest economy in the world according to its nominal GDP in USD in and is very progressive, advanced, and sophisticated in logistics, especially in operating efficiency and cost and customer service, and, like other European countries, in the functional integration of logistics work within the firm and environmental issues like reverse logistics 840. European countries have opportunities for improvement in the external integration of logistics systems and development of supply chain relationships throughout Europe Objective We would like to determine to what extent the different risk pooling concepts are known and applied by 102 German manufacturing and trading companies and examine for our sample the following remarks, suggestions, and demands: Van Hoek (1998b) finds that postponement is extensively applied in electronics and automotive and less extensively applied in food and clothing. We would like to find out whether this applies to our sample as well. Alfaro and Corbett (2003: 12f., 15) observe that several approaches to the widely recognized challenge of managing product variety rely on the pooling effect. Pooling can be accomplished through the reduction of the number of products or stock-keeping units (SKUs), through postponement of differentiation, or in other ways [component commonality and inventory pooling]. These approaches are well known and becoming widely applied in practice. However, there are no studies yet whether product pooling and component commonality really are widely applied in practice. 838 Logistics Practices Results, Question 7, Electronic Appendix Disk to CLM (1995). 839 IMF (2009). 840 CLM (1995: 365). 841 CLM (1995: 366). 140

156 Appendix A Herer et al. (2006) remark Transshipments are not widely adopted in practice because the IT infrastructure is inadequate and there are no realistic models to take advantage of transshipment benefits. However, there are no studies yet whether transshipments really are not widely used in practice. Thomas and Tyworth (2006) demand a survey to determine whether order splitting is employed in practice 842. Boone et al. (2007) review postponement literature published from 1999 to 2006 and conclude research should be extended to non-manufacturing postponement and investigate the slow rate of postponement adoption among practitioners. Huang and Li (2008b: 12) only surveyed large electronic/information technology, clothing, and electric appliances companies. They remark large companies may apply postponement more than small ones, since they may be better able to afford the redesign of products and/or processes usually required by postponement 843. Hence, further studies could compare the differences of postponement application between large-scale and small and medium companies Yet, despite the impressive amount of past and present work on pooling lead-time risk by order splitting, it is difficult to find any substantive evidence of successful applications in academic or practitioner literature (Thomas and Tyworth 2006: 246). Although studies in both tracks provide hypothetical evidence that pooling lead-time risk by splitting orders simultaneously may be worthwhile, it is difficult, if not impossible, to find substantive empirical validation of the proposition (Thomas and Tyworth 2006: 254). Collectively, these limitations make the value proposition rather dubious. Thus future research in this area should include case studies, simulations, and surveys to determine whether companies use such order splitting methods and the business setting where successful applications appear (Thomas and Tyworth 2006: 254f.). 843 Ernst and Kamrad (2000), Aviv and Federgruen (2001b). 844 Huang and Li (2008b: 19). 141

157 2 The Survey There has not been a survey on how many companies know and apply the various risk pooling methods yet, especially not in Germany. In order to respond to the aforementioned demands and remarks, we conducted a survey among German manufacturing and trading companies from September 2008 to August 2009 and obtained 102 completed questionnaires (response rate: 21.3 %) from logistics or supply chain management professionals. Since an earlier sixpage survey that was ed to 3,600 companies had a response rate of only 0.3 %, we asked 478 manufacturing and trading company representatives in person to complete the one-page questionnaire in figure A.4 or forward it to the appropriate person mainly on company and job fairs in various German cities. Respondents were promised a summary of the survey results as an incentive. 845 Our experience supports that face-to-face methods usually achieve higher response rates Research Design The respondents worked for companies from the following branches of economic activity according to the German Classification of Economic Activities Edition 2003 of the German Federal Statistical Office (Statistisches Bundesamt Deutschland): 845 Cf. Yang et al. (2005b: 996). 846 Kisperska-Moroñ (2003: 130), Groves et al. (2004: 165). 142

158 Appendix A Classification Description Number % Number % Variance (%) 11 Extraction of crude petroleum and natural gas; service activities incidental to oil and gas extraction, excluding surveying Manufacture of food products and beverages 5, Manufacture of tobacco products Manufacture of wearing apparel; dressing and dyeing of fur Manufacture of pulp, paper and paper products Publishing, printing and reproduction of recorded media 2, Manufacture of chemicals and chemical products 1, Manufacture of rubber and plastic products 2, Manufacture of other non-metallic mineral products 1, Manufacture of basic metals Manufacture of fabricated metal products, except machinery and equipment 6, Manufacture of machinery and equipment n.e.c. 5, Manufacture of office machinery and computers Manufacture of electrical machinery and apparatus n.e.c. 1, Manufacture of radio, television and communication equipment and apparatus Manufacture of medical, precision and optical instruments, watches and clocks 2, Manufacture of motor vehicles, trailers and semitrailers 1, Manufacture of other transport equipment Manufacture of furniture; manufacturing n.e.c. 1, Recycling Electricity, gas, steam and hot water supply 1, Building of complete constructions or parts thereof; civil engineering 6, Wholesale of pharmaceutical goods 3, Wholesale of paper and paperboard, stationery, books, newspapers, journals and periodicals The whole population a Responding companies 2, Non-specialized wholesale of wood, construction materials and sanitary equipment 1, Wholesale of agricultural machinery and accessories and implements, including tractors 1, Retail sale in non-specialized stores with food, beverages or tobacco predominating 24, Retail sale of clothing 25, Retail sale of hardware, paints and glass 11, Retail sale of games and toys 3, Total 116, Table A.1: Comparing Respondents with the Total Population of Manufacturing and Trading Companies in Germany a Source: Statistisches Bundesamt Deutschland (2009i: 371, 408f.). Companies with in general 20 employees and more. Status of 09/30/2006 (trade), 09/30/2007 (manufacturing). 143

159 Appendix A As 78.7 % of the sampling frame population did not respond and the sample is small, it is not too representative of neither the whole population in the different branches of economic activity the respondents' companies belong to in table A.1 nor of the target population of German manufacturing and trading companies. 847 Not all areas of domestic production and trade are covered. Our sample consists of too many manufacturing companies, especially from vehicle construction (34, 35), although this is an important industry in Germany, manufacture of machinery (29, 31, 32), and recycling (37) and too few trading companies, particularly in food (52.11), clothing (52.42), and hardware retail (52.46) as the variance in the last column shows. Deviations of responding companies from the whole population in Huang and Li (2008b: 13) are of similar magnitude. In contrast, the responding companies in Yang et al. (2005b: 997) closely reflect the whole population. Of the 28 mentioned surveys in this section 848 only Huang and Li (2008b) and Yang et al. (2005b) (7.14 %) compare the responding companies' characteristics to the whole population (retrospective quota sampling). We have to highlight that the whole population in table A.1 only consists of companies with 20 or more employees, while our sample encompasses three companies (respondents 2, 65, and 100 from industrial sectors 52.42, 27, and ) with less than 20 employees. If we omitted them, the variance would increase and the representativeness decrease even more. A detailed classification of the branches of economic activity with all German companies with any number of employees is not publicly available. The German Federal Statistical Office told us we could apply for a special query with charges. A retrospective quota sampling with more detailed subgroups of industrial economic activity than in table A.1 and all German companies, which cannot be conducted due to lacking data, might reveal that our sample is more representative of these subgroups. The size of the responding companies ranges from 5 to 182,739 employees. 2 % have less than 10, 9 % less than 50, 31 % less than 250, 32 % less than 500, and 68 % have There were 52,362 manufacturing (9.94 % of manufacturing and trading companies) and 474,065 (90.06 %) trading companies with in general 20 or more employees in Germany in 2007 or 2006 respectively (Statistisches Bundesamt Deutschland 2009i: 409, 371). In our sample there are 75 (73.53 %) manufacturers and 27 (26.47 %) trading companies. 848 Jackson (1985), CLM (1995), Morehouse and Bowersox (1995), Van Hoek (1998b, 2000b), McKinnon and Forster (2000), Van Hoek and Van Dierdonck (2000), Dubelaar (2001), Chiou et al. (2002), Griffis et al. (2003), Kisperska-Moroñ (2003, two surveys), Rabinovich and Evers (2003b), Lemoine and Skjoett- Larsen (2004), Oracle (2004), Bagchi and Skjoett-Larsen (2005), Nair (2005), White (2005), Yang et al. (2005a, 2005b), Himola and Szekely (2006), Johnson (2006), Randall et al. (2006), Shao and Ji (2006), Naesens et al. (2007), Böhnlein and Lünemann (2008), Huang and Li (2008b), and Chikán (2009). 144

160 Appendix A or more employees. The majority of the sample consists of larger companies, while the majority of the whole population comprises small ones. 849 Nevertheless our survey can at least show the risk pooling knowledge and activities of the surveyed companies for a given moment in time. They are relatively heterogeneous in terms of industry membership and number of employees (size), so that risk pooling knowledge and activities of a wide company spectrum and size specific specialties can be detected. 850 Besides, the respondents do not deviate from the overall population extremely regarding the branches of activity. Therefore, the absence of data from the nonrespondents may not contaminate the conclusions drawn from the sample too much. 851 The questionnaire was scrutinized by three academics and three logistics managers, pretested among eleven companies, and adjusted according to the suggestions and detected problems before the final distribution to insure content validity. 852 Validity measures whether the questions capture what they are intended to capture. 853 Of the 28 surveys mentioned previously % deal with their validity. Reliability measures whether respondents are consistent or stable in their answers 854. Only % of the 28 surveys mentioned address their reliability. We did not measure reliability as respondents usually are not willing to be interviewed twice or to answer a questionnaire enlarged by asking for the same construct twice. 855 We could not check for systematic reporting errors 856 (response bias), as external data, which the survey responses could be compared to, are not available 857. None of the 28 surveys mentioned refers to their response bias. We did not check for non-response bias, because we could not collect the nonrespondents' characteristics 858. Non-response bias is the distortion of the sample and therefore the basic population because some people do not respond or do not answer certain questions. The answers of respondents may differ from the ones of nonrespondents. There is no consensus on when nonresponse reduces survey quality and therefore on appropriate response 849 In 2006 there were 4,307 (0.63 %) active industrial and 1,362 (0.18 %) trading companies with 250 and more, 680,561 (99.37 %) or 735,820 (99.81 %) ones respectively with less than 250 employees subject to social security (Statistisches Bundesamt Deutschland 2009i: 493). In our sample % of the industrial and % of the trading companies have 250 and more employees. 850 Cf. Böhnlein and Lünemann (2008: 6). 851 Cf. Vockell and Asher (1995: ch. 8). 852 Cf. Yang et al. (2005b: 995, 998), Huang and Li (2008b: 13). 853 Groves et al. (2004: 254). 854 Groves et al. (2004: 261). 855 Groves et al. (2004: 266), Yang et al. (2005b: 998). 856 Groves et al. (2004: 259). 857 Cf. Groves et al. (2004: 266). 858 Cf. Groves et al. (2004: ), Schneekloth and Leven (2003). 145

161 Appendix A rates. 859 Nevertheless, our response rate is above the unfavorable response rates below 20 % 860, within the 10 % to 30 % of the past mean 861 and the 4 % to 32.7 % of large samples in the Journal of Business Logistics from 1997 to , and higher than a lot of the mentioned surveys' ones 863. Nonresponse rates often are ignored, because it is assumed that the reason for the nonresponse is not associated with the measured statistical values and therefore it does not affect the quality of the survey's results. 864 Of the 28 surveys we mentioned ten (35.71 %) deal with their non-response bias. Most of these determine the nonresponse bias, checking whether the answers of first respondents and late respondents differ, although late respondents may not be an appropriate estimate for nonrespondents. Nonetheless, the answers of our 51 first and 51 last respondents are independent (the null hypothesis that there is no significant relationship between the answers cannot be rejected) in Pearson's and Yates' chi-square and Fisher's exact test at the 5 % level, except for the question about their risk pooling knowledge 865 and centralization in the past 866. In all other cases the distribution of the answers within the two groups does not differ significantly: The two-sided asymptotic significance of the respective test statistic is greater than 0.05 in each case, so that it is safe to say that any differences are due to chance variation, which implies that the two groups answered equally. With our sample size of 102 the confidence interval or margin of error is 9.7 on the 95 % confidence level for an estimated percentage of 50 %, i. e. one can be 95 % certain that if 50 % of the sample picks an answer between 40.3 % (50-9.7) and 59.7 % (50+9.7) of the whole population would have also picked that answer. However, the true percentage of the population only is the sample's percentage plus/minus the confidence interval, if a genuine simple random sample of the relevant population was drawn. This cannot be confirmed for our sample, so that this confidence interval is an underestimate. No errors and biases of coverage, sampling, nonresponse, or measurement [ ] are included in the margin of error 867. When random sampling is not used, one has to depend on logic apart from 859 Fowler (1993), Schneekloth and Leven (2003), Groves et al. (2004: ). 860 Yu and Cooper (1983). 861 Flynn et al. (1990). 862 Griffis et al. (2003: 242). 863 Cf. Yang et al. (2005b: 998). 864 Groves et al. (2004: ), Schneekloth and Leven (2003). 865 In this case Pearson's chi-square test gives χ 2 = with df = 1 and p = , Yates' correction for continuity χ Y = with df = 1 and p = , and Fisher's exact test p (two-tailed) = In this case χ 2 = with df = 1 and p = , χ Y = with df = 1 and p = , and p = in Fisher's exact test. 867 Groves et al (2004: 382). 146

162 Appendix A mathematical probability to assess to what extent the sample deviates from the population it was drawn from Data Analysis and Findings Risk Pooling Knowledge and Utilization in the German Sample Companies Percent of Responding Companies Knowledge Utilization Figure A.1: Risk Pooling Knowledge and Utilization in the German Sample Companies The most known concepts related to risk pooling in the whole sample are central ordering, product substitution, selective stocking, transshipments, and order splitting, followed by product pooling, commonality, virtual pooling, capacity pooling, risk pooling, postponement, demand reshape, the portfolio effect (PE), inventory turnover curve, and square root law (SRL) in order of descending percentage of respondents that know these concepts. Surprisingly, the SRL (28 %) is less known than the PE (54 %), although it is the simpler concept and there are more and earlier publications on it in business logistics. Perhaps the PE is more popular, as it is a generalization of the SRL and originated in finance. 868 Vockell and Asher (1995: ch. 8). 147

163 Appendix A A lot of respondents obviously did not realize that risk pooling may comprise all these different concepts. Otherwise they would have noted that they know and apply risk pooling, whenever they checked to know or apply any of these concepts. Risk pooling is a hypernym and not a risk pooling concept itself. The most applied risk pooling concepts in the whole sample are selective stocking, transshipments, central ordering, commonality 869, and centralization, followed by product substitution, virtual pooling, capacity pooling, product pooling, postponement, order splitting, risk pooling, the PE, inventory turnover curve, demand reshape, decentralization, and the SRL in order of descending percentage of surveyed companies applying these concepts. While the knowledge of the different risk pooling concepts is fairly good 870 (only the SRL and the inventory turnover curve are known by less than 50 %), they are not widely applied. Only the well established concepts selective stocking, transshipments, and central ordering show application rates over 50 %, namely 66 %. This disagrees with Herer et al. (2006), who remark Transshipments are not widely adopted in practice because the IT infrastructure is inadequate and there are no realistic models to take advantage of transshipment benefits. Some companies which do not employ central ordering remarked it increased transportation and delivery costs too much. This could be counteracted with a centralized ordering system like the one we designed for Papierco earlier. Transportation costs do not increase (substantially) or the supplier incurs them. Postponement is only applied by 35 % of the companies. Thus we cannot conclude that firms are rapidly adopting both form and time postponement 871 and widely apply it 872 in Germany as CLM (1995: 209) reports for North America and Europe, McKinnon and Forster (2000: 5) for Europe, and Chiou et al. (2002) and Huang and Li (2008b) for China. More sample companies in Germany (65 %) have not implemented postponement strategies than suggested by Oracle (2004) (nearly half of 358 mainly manufacturing companies from all over the world). We agree with Van Hoek et al. (1998), Bowersox et al. (1999), Battezzati and Magnani (2000), Brown et al. (2000: 78), Oracle (2004), Yang et al. 869 Wazed et al. (2009: 70) find Although the benefits of commonality are widely known, many companies are still not taking full advantage of it when developing new products or re-designing the existing ones. We can agree with them for our sample. 870 Alfaro and Corbett (2003: 12f., 15) already remark that risk pooling approaches such as product pooling, postponement, component commonality, and inventory pooling are well known [ ] in practice. 871 CLM (1995: 213). 872 Alfaro and Corbett (2003: 12). 148

164 Appendix A (2004, 2005a, 2005b, 2007), and Boone et al. (2007) that postponement is not applied as much (as expected). Some respondents told us they did not use postponement as it entailed completely different production and storage concepts and therefore usually was uneconomical. Research has to determine more clearly the changes necessary for postponement, methods for calculating the costs of postponement, and conditions that render postponement economical. Practice seems to lack the knowledge to implement postponement economically. Perhaps more concepts have to be developed that may make postponement less expensive, such as operations reversal. This is in line with Oracle (2004: 7f.). Our survey suggests that the reason for the low application may not lie in the basic knowledge of this concept (55 % know it), but it is less known than most of the other concepts except for demand reshape, the PE, inventory turnover curve, and SRL. Component commonality is well known and applied by nearly every second surveyed company. Thus, we can support Kim and Chhajed (2001: 219), who remark The use of commonality in product line extensions is a growing practice in many industries, and Alfaro and Corbett (2003: 12, 15), who observe it is becoming widely applied in practice. Nevertheless some companies who do not use it pointed out it was too expensive. This confirms that the cost of common components can be high 873. Location flexibility achieved by transshipments and virtual pooling seems to be more important in the sample companies in Germany than suggested by CLM 874 for North American and non-north American world class companies. McKinnon and Forster (2000: 9, 17) predicted virtual pooling in the form of drop-shipping to increase. Randall et al. (2006) found that 33.3 % of the 56 interviewed U.S. e-tailers relied on virtual pooling. More generally we find that 46 % of the surveyed manufacturers and traders apply virtual pooling in Germany. Our sample only contains a single toy e-tailer. Fewer German sample companies (48 %) have centralized their stockholding than European ones overall (68.31 %) 875. Our findings agree with McKinnon and Forster (2000: 6f.), Modern Materials Handling (2002), and Alfaro and Corbett (2003: 12f.) that inventory centralization is an important trend. However, we can also confirm the minority opinion of 15 % of the panelists in McKinnon and Forster (2000: 6f.) that there will be a slight net decentralization of inventory in Germany in the future. Thirty-five percent of the German 873 Van Mieghem (2004: 419). 874 Workbook Section 3: Relative Performance Competencies, Question 20, Electronic Appendix Disk to CLM (1995). 875 Logistics Practices Results, Question 7, Electronic Appendix Disk to CLM (1995). 149

165 Appendix A sample companies have not changed the number of warehouses or production facilities in the past. Lemoine and Skjoett-Larsen (2004) reached a similar result in Denmark. Some of the companies that did not or will not centralize declared it increased transportation costs too much. Most companies have already centralized or to a lesser extent decentralized their warehouse or logistics system in the past. Only six percent intend to centralize their logistics system in the future. Merely seven percent plan to increase the number of warehouse or production locations in the future. This is in opposition to the expectation that the increasing fuel and transportation costs induce companies to decentralize their warehouse or logistics systems. The risk pooling advantages derived from physical inventory pooling may outweigh the increased transportation costs. Product substitution flexibility seems to be more important in Germany than suggested by CLM 876 for North American and non-north American world class companies. Companies applying demand reshape mostly indicated they persuaded customers to buy another substitute product even though the original customer wish was available to increase the profit margin and not for risk pooling reasons as intended by Eynan and Fouque (2003, 2005). We have to disagree with Alfaro and Corbett (2003: 12) who observe the reduction of the number of products or stock-keeping units (SKUs), also known as product pooling 877, and postponement of differentiation are becoming widely applied in practice. Product pooling is applied by 40 % and postponement by 35 % of the companies in our sample. We can answer the call of Thomas and Tyworth (2006: 254f.) for empirical research to determine whether companies use such order splitting methods, pointing out that only 35 % of German companies in our sample do apply them. However, our survey does not inform about the conditions and success of these order splitting applications. Some interviewees said they did not know when and how it was favorable to apply the various risk pooling concepts. Research needs to address these issues further. More research is needed to convey to practice when and how the different risk pooling concepts may be implemented successfully. Our research constitutes one step in this direction. 876 Workbook Section 3: Relative Performance Competencies, Question 29, Electronic Appendix Disk to CLM (1995) 877 Cachon and Terwiesch (2009: 330, 467). 150

166 Appendix A Association between the Knowledge of Different Risk Pooling Concepts The knowledge of risk pooling is significantly associated with the knowledge of postponement (Goodman and Kruskal's Tau (τ) = 0.147, approximative significance based on chi-square approximation (p) = 0.000), product pooling (τ = 0.104, p = 0.001), transshipments (τ = 0.091, p = 0.002), the turnover curve (τ = 0.087, p = 0.003), commonality (τ = 0.066, p = 0.010), demand reshape (τ = 0.061, p = 0.013), and virtual pooling (τ = 0.050, p = 0.025) in order of descending significance. Goodman and Kruskal's Tau was chosen, as it offers advantages over all other measures of association for nominal variables. It can be interpreted easily, its maximum is one, it takes the value 0, if the variables are independent, and it is suitable, if the number k of the independent variable x's categories is not equal to the number m of the dependent variable y's categories. Its only disadvantage is its complicated calculation, which is remedied with modern statistics software. 878 Goodman and Kruskal's Tau measures the association of two categorical variables in terms of an improvement of prediction relative to a random distribution of people (or responding companies in this case) based on the marginal distribution. 879 It is a measure of proportional reduction of error (PRE). 880 The above Tau of 0.147, for instance, means that the postponement knowledge of 14.7 % more of responding companies is predicted correctly, if we predict the postponement knowledge of a company not only according to the general distribution of postponement knowledge, but according to the conditional distribution of postponement knowledge that is distinguished by the risk pooling knowledge. 881 Postponement might be the most popular type of risk pooling, as its recognition shows the highest correlation with the knowledge of risk pooling. Forty-two of the 59 responding companies who know risk pooling also know postponement. Twenty-nine of the 43 logistics professionals not knowing risk pooling do not know postponement either. The knowledge of risk pooling is also highly significantly associated with knowing product pooling (τ = 0.104, p = 0.001) and transshipments (τ = 0.091, p = 0.002). Further significant correlations at least at the 5 % level between the knowledge of the different risk pooling concepts can be read from table A.2 at the end of this section. 878 Müller-Benedict (2007: 203, 206). 879 Müller-Benedict (2007: 203). 880 Müller-Benedict (2007: 200). 881 Cf. Müller-Benedict (2007: 204). 151

167 Appendix A Most significantly correlated is the knowledge of product pooling and transshipments (τ = 0.163, p = 0.000), risk pooling and postponement (τ = 0.147, p = 0.000), transshipments and capacity pooling (τ = 0.139, p = 0.000), as well as transshipments and postponement (τ = 0.135, p = 0.000) and vice versa in order of descending strength of correlation. In this sample the knowledge of postponement and capacity pooling (τ = 0.116, p = 0.001), product substitution and demand reshape (τ = 0.112, p = 0.001), product pooling and demand reshape (τ = 0.104, p = 0.001), postponement and order splitting (τ = 0.101, p = 0.001), selective stocking and transshipments (τ = 0.098, p = 0.002), as well as demand reshape and transshipments (τ = 0.095, p = 0.002) is relatively strongly correlated. These concepts seem to be related and therefore to be known together: Postponement and capacity pooling are popular and applied together e. g. in the auto industry. Both in product substitution and demand reshape goods are substituted. One can offer a limited number of products by product pooling or offer a variety of products (but not store all of them) and apply demand reshape or transshipments. In order splitting certain steps in the order and supplier delivery process may be postponed. If SKUs are only stocked at certain locations (selective stocking), transshipments may be necessary between these locations. Usually, we call a correlation in the social and economic sciences strong, if the measure of correlation is > 0.5. In social and economic sciences any two characteristics are in general only weakly connected, i. e. the measure of correlation is < 0.3 for a lot of bivariate distributions of socio-scientific data, because social and economic interrelations are not transparent at first glance, but multidimensional, flexible, and versatile. 882 Furthermore, the other nominally scaled measures of correlation show much higher values than Tau, but are difficult to interpret except for Lambda. However, Lambda has the disadvantage of taking the value 0, even if both variables are not independent. 883 In our research the Tau values are one half to one third of the other measures' ones. A statistical correlation does not necessarily mean that there is a real cause and effect relationship between two variables: First of all, with a 95 % confidence interval there is still a 5 % chance that a measured correlation is coincidental. Secondly, without a theory one cannot determine the cause and the effect. Thirdly, there might be a spurious causation, i. e. two characteristics change in the same way, although they are not connected. They both are connected to and influenced by a third characteristic. In order to elucidate these effects also statistically one has to analyze more than two variables collectively by 882 Müller-Benedict (2007: 197f.). 883 Müller-Benedict (2007: 203ff.). 152

168 Appendix A multivariate data analysis. 884 Multivariate analysis methods for only nominal data seem less powerful and clear than the ones for metric data 885 and are not widely available in software packages 886. If all variables are nominal, contingency table, configuration frequency, log-linear, latent structure (if additional latent variables are used), and cluster analysis can be employed. Most multivariate analysis methods require higher scales of measurement. 887 They should not be used without understanding them, their assumptions, controversies, and theoretical foundations as modern software facilitate and some researchers do. 888 Knowledge of a risk pooling concept certainly is not only connected to the knowledge of other risk pooling concepts and a company's industrial sector and size (number of employees), but also to other factors. Likewise, the application of a risk pooling concept might be correlated to additional factors besides the awareness of this and other concepts, the application of other concepts, and a company's sector of economic activity and size. These other factors remain subject to further research. 884 Reynolds (1984: 72ff.), Müller-Benedict (2007: 267ff.). 885 Reynolds (1984: 78), Holtmann (2007). 886 Breakwell (2007: 441). 887 Holtmann (2007). 888 Breakwell (2007: 441f.). 153

169 Appendix A Risk Pooling Risk SRL PE Selective Commonality Turnover Product Product Demand Transshipmentment Postpone Virtual Capacity Central Order Pooling Stocking Curve Pooling Substi tution Reshape Pooling Pooling Ordering Splitting 1 SRL 1 PE 1 Selective Stocking Commonality Turnover Curve Product Pooling Product Substitution Demand Reshape Transshipments Postponement Virtual Pooling Capacity Pooling Central Ordering Order Splitting (0.010) (0.003) (0.001) (0.013) (0.002) (0.000) (0.025) (0.031) (0.008) (0.040) (0.040) (0.032) (0.009) (0.015) (0.049) (0.002) (0.039) a (0.010 b ) (0.015) (0.017) (0.031) (0.034) (0.003) (0.003) (0.031) (0.039) (0.022) (0.019) (0.019) (0.033) (0.007) (0.001) (0.017) (0.022) (0.001) (0.000) (0.016) (0.020) (0.022) (0.001) (0.003) (0.013) (0.049) (0.039) (0.001) (0.001) (0.002) (0.007) (0.035) (0.002) (0.009) (0.002) (0.000) (0.002) (0.000) (0.000) (0.000) (0.008) (0.039) (0.031) (0.022) (0.016) (0.000) (0.001) (0.040) (0.001) (0.025) (0.040) (0.019) (0.003) (0.040) (0.034) (0.019) (0.000) (0.001) (0.032) (0.033) (0.007) (0.040) (0.007) (0.032) (0.003) (0.007) (0.020) (0.035) (0.001) (0.007) 1 Table A.2: Significant Correlations at the 5 % Level of the Knowledge of Risk Pooling Concepts a. Goodman and Kruskal s Tau b. Approximative significance based on chi-square approximation Association between Knowledge and Utilization of Risk Pooling Concepts There is a strong highly significant correlation between the knowledge of a risk pooling concept and its application as the diagonal in the correlation matrix in Table A.3 at the end of this section shows. This suggests that increasing practitioners' knowledge and understanding of risk pooling by praxis-oriented research may increase its application. The strongest correlation exists between the knowledge and the application of virtual pooling (τ = 0.431, p = 0.000). That means the error of predicting the variable utilization of virtual pooling can be reduced by 43.1 %, if the distribution of the variable knowledge of virtual pooling is known. Forty-six of the 65 respondents who know virtual pooling also apply it. Of the 37 respondents who do not know virtual pooling 36 also do not apply it. Consequently, one professional did not recognize the concept perhaps by its name, but when reading the explanation he came to realize that his 154

170 Appendix A company applies this concept. There are a few cases like that pertaining to the other risk pooling concepts as well. The next highest correlations exist between the knowledge and application of the SRL (τ = 0.319, p = 0.000) and of commonality (τ = 0.317, p = 0.000). The recognition of transshipments is significantly correlated with both the application of selective stocking (τ = 0.088, p = 0.003) and risk pooling (τ = 0.071, p = 0.008), the knowledge of postponement with the use of risk pooling (τ = 0.079, p = 0.005). This highlights again that the respondents seem to mainly associate the popular concepts of postponement and transshipments with risk pooling. The knowledge of transshipments might favor the implementation of selective stocking, since products have to be exchanged between locations as they are only stored at few locations for economical reasons. Utilization Utilization Knowledge Risk Pooling SRL PE Selective Stocking Commonality Risk Pooling a SRL PE Selective Commonality Stocking (0.000 b ) (0.000) (0.000) (0.000) Turnover Curve Product Pooling Product Substitution Demand Reshape Transshipments (0.008) Postponement (0.005) Virtual Pooling (0.032) Capacity Pooling Central Ordering Order Splitting (0.003) (0.000) Turnover Product Product Demand Curve Pooling Substitution Reshape (0.000) (0.002) (0.001) (0.043) (0.054) (0.000) Transshipments (0.016) Postponement (0.000) (0.000) Virtual Capacity Central Pooling Pooling Ordering (0.021) (0.000) (0.047) (0.000) (0.000) Order Centralization Splitting past (0.029) (0.048) (0.000) Centralization future Decentralization past (0.042) Decentralization future Table A.3: Significant Correlations at the 5 % Level (except in the case Product Substitution/Demand Reshape) between Knowledge and Utilization of Risk Pooling Concepts a. Goodman and Kruskal s Tau b. Approximative significance based on chi-square approximation. 155

171 Appendix A Association of the Utilization of Different Risk Pooling Concepts Most significantly and strongly associated is past decentralization with future decentralization (τ = 0.253, p = 0.000), the utilization of product substitution and demand reshape (τ = 0.212, p = 0.000), past centralization and decentralization (τ = 0.185, p = 0.000), the application of the inventory turnover curve and transshipments (τ = 0.132, p = 0.000), commonality and product pooling (τ = 0.127, p = 0.000), risk pooling and transshipments (τ = 0.121, p = 0.000), the turnover curve and order splitting (τ = 0.117, p = 0.001), selective stocking and virtual pooling (τ = 0.113, p = 0.001), transshipments and virtual pooling (τ = 0.113, p = 0.001), risk pooling and postponement (τ = 0.109, p = 0.001), product substitution and transshipments (τ = 0.096, p = 0.002), as well as product substitution and virtual pooling (τ = 0.096, p = 0.002) and vice versa as shown in Table A.4 at the end of this section. Eighty-four (99 %) of the 85 companies which did not decentralize in the past do not intend to decentralize in the future. Eleven of the 17 companies which did decentralize will continue to decentralize in the future. Eighty-four (88 %) of the 95 companies which do not intend to decentralize their warehouse or logistics system, did not decentralize in the past either. Six (86 %) of the seven companies planning to decentralize in the future, already decentralized in the past. It seems that these companies follow their warehouse or logistics system strategy of decentralization or no decentralization consistently over time. Fifty-one (94 %) of the 54 respondents who do not apply product substitution do not apply demand reshape either. Twenty of the 48 respondents using product substitution use demand reshape as well. Fifty-two of the 80 companies which do not reshape demand do not substitute products in case of a stockout either. Twenty of the 22 demand reshaping companies also use product substitution. It seems that companies which do not persuade customers to buy a substitute product in case of a stockout mostly do not do so either, if the desired product is available. This might occur, if a company does not sell substitute products. Ninety-one percent of demand reshapers also apply product substitution, perhaps because both strategies are similar in that they both substitute products. If a company centralized in the past (49 companies), there was absolutely no decentralization in the past. If a company conducted no centralization in the past, there was mostly no decentralization either: Of the 53 companies which did not centralize in the past only 17 decentralized in the past, 36 ones (68 %) did not. Past centralization and decentralization thus show a rather negative correlation as the Phi value of (p = 0.000) sug- 156

172 Appendix A gests 889. Forty-nine (58 %) of the 85 companies which did not decentralize centralized in the past and none of the 17 companies which decentralized centralized in the past. It appears that decentralization excludes centralization and vice versa. The strategy of decentralization, centralization, or no change is followed fairly consistently over time. Thirty-four (97 %) of the 35 companies which do not transship do not use the inventory turnover curve. Forty-three of the 67 transshipping companies utilize the turnover curve. Thirty-four of the 77 responding companies which do not use the inventory turnover curve do not take advantage of transshipments either. Twenty-four (96 %) of the 25 companies using the turnover curve transship. One could assume that companies using the inventory turnover curve attach great importance to inventory turnover. If therefore they tend to mainly store fast movers at every location, this might explain why they also use transshipments to exchange e. g. slow movers between locations. Forty (77 %) of the 52 companies which have not implemented component commonality do not use product pooling. Twenty-nine of the 50 companies using common components also use product pooling. Forty of the 61 companies which have not implemented product pooling have not implemented component commonality either. Twenty-nine (71 %) of the 41 product pooling companies use common components as well. This comes as no surprise as product pooling may rely on common components to satisfy customers that were previously offered their own product variant with a single common product 890. Furthermore, both methods take advantage of standardization. [S]tandardization enables risk pooling across products, leading to lower inventories, and allows firms to use the information contained in aggregate forecasts more effectively 891. Thirty-one (89 %) of the 35 companies not relying on transshipments likewise declared that they did not apply risk pooling. Thirty-one of the 67 companies using transshipments also use risk pooling. Thirty-six of the 67 companies which indicated that they are not using risk pooling do not use transshipments either. Thirty-one (89 %) of the 35 ones using risk pooling do use transshipments as well. This highlights again that the responding professionals strongly associate risk pooling with transshipments. Fifty-seven (74 %) of the 77 companies which do not use the turnover curve do not apply order splitting either. Sixteen of the 25 companies employing the turnover curve split orders as well. Fifty-seven (86 %) of the 66 companies not splitting orders do not use 889 Although we deal with nominal variables, we can exceptionally refer to a negative correlation here (cf. Schulze 2007: 127). 890 Cachon and Terwiesch (2009: 330, 335). 891 Simchi-Levi et al. (2008: 357), cf. Reiner (2005: 434), Sheffi (2006, 2007: ). 157

173 Appendix A the turnover curve. Sixteen of the 36 companies that utilize order splitting use the inventory turnover curve as well. Splitting an order into multiple orders or goods receipts may not only decrease supplier lead time variability but also reduce average inventory and therefore increase inventory turnover. The inventory turnover is reflected in the inventory turnover curve. Inventory policies, which may be determined and controlled with the inventory turnover curve, might lead to order splitting. Twenty-seven of the 55 not virtually pooling companies do not store SKUs selectively at warehouses. Thirty-nine (83 %) of the 47 companies which apply virtual pooling also apply selective stocking. Twenty-five (71 %) of the 35 logistics professionals indicating that their company does not rely on selective stocking do not pool virtually either. Thirtynine of the 67 companies using selective stock-keeping also apply virtual pooling. Virtual pooling may entail selective stocking and vice versa: On the one hand, access to other locations' inventories via virtual pooling may favor a specialization in stock holding. On the other hand, stocking products only at few locations due to cost considerations may necessitate that these locations can access each other's inventories. For instance, a company may choose to stock only fast movers at all regional warehouses and have slow movers dropshipped to customers or cross-filled. Thus inventories and demands at different locations are pooled virtually. Seventy-seven percent (27) of the companies not using transshipments (35), do not pool virtually either. Fifty-eight percent (39) of the companies transshipping (67) use virtual pooling in addition. Twenty-seven of the 55 responding companies which do not use virtual pooling do not use transshipments either. However, thirty-nine (83 %) of the 47 virtually pooling companies rely on transshipments. Extending a company's warehouse or warehouses beyond its or their physical inventory to the inventory of other own locations or of other companies' locations via information technology and the internet (virtual pooling) often entails stock transfers between locations (transshipments). Virtual pooling resembles transshipments, if it comprises drop-shipping 892 or cross-filling 893. Of the 67 respondents who indicated not having implemented risk pooling 51 ones (76 %) have not implemented postponement either. Twenty (57 %) of the 35 ones who use risk pooling also use postponement. Fifty-one (77 %) of the 66 survey participants indicating no postponement utilization also denied the use of risk pooling. Twenty (56 %) of the 36 companies having implemented postponement also confirm the usage of risk pool- 892 Netessine and Rudi (2006: 845). 893 Ballou and Burnetas (2000, 2003), Ballou (2004b: ). 158

174 Appendix A ing. Consequently, the responding logisticians strongly associate risk pooling with postponement. Twenty-six (74 %) of the 35 companies that do not use transshipments do not substitute products either. Thirty-nine of the 67 transshipping companies also use product substitution. Twenty-six of the 54 companies not substituting products do not use transshipments either. Thirty-nine (81 %) of the 48 product substitutionists use transshipments in addition. This shows that product substitution and transshipments can be applied side by side just like in the case of Papierco. For this company product substitution is the cheaper option, so that it should only use transshipments as an alternative, if it is not possible to substitute products in case of a stockout. The same applies to virtual pooling: Thirty of the 48 companies which rely on product substitution pool virtually as well. Thirty-seven (69 %) of the 54 ones not substituting products, do not apply virtual pooling either. Thirty-seven (67 %) of the 55 companies not pooling virtually do not use product substitution either. Thirty of the 47 ones pooling virtually also substitute products. We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of form postponement at best only weakly for our sample: Postponement is only weakly and at the 5 % level just not statistically significantly associated anymore with transshipments (τ = 0.035, p = 0.059) and selective stocking (τ = 0.035, p = 0.059). Twenty-eight (42 %) of the 67 companies stocking selectively thereby centralizing inventory also apply postponement. Twenty-seven (77 %) of the 35 ones not using selective stocking do not use postponement either. The same applies to transshipments. Postponement is statistically significantly independent of past (τ = 0.000, p = 0.903) and future centralization (τ = 0.009, p = 0.350). The contrary is true for its association with risk pooling (τ = 0.109, p = 0.001) and component commonality (τ = 0.068, p = 0.009). Forty of the 66 not postponing companies do not use component commonality. Twentyfour (67 %) of the 36 postponing companies also employ common components. Forty (77 %) of the 52 companies not applying component commonality do not apply postponement either. Twenty-four of the 50 users of common components also rely on postponement. This shows that the implementation of postponement and commonality may go hand 159

175 Appendix A in hand 894 as we already highlighted describing the Risk Pooling Decision Support Tool. The implementation of postponement may even require component commonality. 895 Risk Pooling 1 SRL (0.010) PE Selective Stocking Commonality Turnover Curve (0.009) Product Pooling Product Substitution (0.022) Demand Reshape Transshipments (0.000) Postponement (0.001) Virtual Pooling (0.014) Capacity Pooling Central Ordering Order Splitting Centralization past Centralization future Decentralization past Decentralization future Risk SRL PE Selective Commonality Pooling Stocking a (0.010 b ) (0.005) (0.023) (0.047) (0.006) (0.009) (0.008) (0.001) (0.033) (0.049) (0.000) (0.009) Turnover Product Product Demand Curve Pooling Substitution Reshape (0.009) (0.045) (0.000) (0.003) (0.001) (0.000) (0.025) (0.022) (0.005) (0.023) (0.000) (0.002) (0.002) (0.047) 0.04 (0.045) (0.000) (0.005) (0.005) Transshipments (0.000) (0.006) (0.009) (0.000) (0.002) (0.001) Postponement (0.001) (0.009) 1 Virtual Capacity Central Order Centralization Pooling Pooling Ordering Splitting past (0.014) (0.001) (0.003) (0.002) (0.005) (0.001) (0.008) (0.022) (0.022) (0.016) (0.008) (0.001) (0.008) (0.016) (0.000) Centralization future 1 Decentralization past (0.033) 0.05 (0.025) (0.005) (0.000) (0.000) Decentralization future (0.049) (0.000) 1 Table A.4: Significant Correlations at the 5 % Level between the Utilization of Risk Pooling Concepts a. Goodman and Kruskal s Tau b. Approximative significance based on chi-square approximation. 894 Zinn and Bowersox (1988: 124f.), Lee (1996, 1998), Van Hoek (1998b, 2001: 173), Van Hoek et al. (1998), Feitzinger and Lee (1997), Pagh and Cooper (1998), Swaminathan and Tayur (1998), Aviv and Federgruen (2001a, 2001b: 579), Swaminathan (2001), Yang et al. (2005b: 993), Simchi-Levi et al. (2008: 345). 895 Swaminathan (2001: 132), Simchi-Levi et al. (2008: 347). 160

176 Appendix A Risk Pooling Knowledge and Utilization in the Responding Manufacturing and Trading Companies Figure A.2: Risk Pooling Knowledge and Utilization in the Sample Manufacturing and Trading Companies 161

177 Appendix A When we subdivide the original sample for subanalyses in this section, we decrease our sample size and therefore enlarge our confidence intervals 896. At the 5 % level Pearson's and Yates' chi-square and Fisher's exact test revealed significant differences between manufacturing and trading companies in employing product substitution (Pearson's chi-square χ 2 = 8.01, degrees of freedom df = 1, p = ), commonality (χ 2 = 7.84, df = 1, p = ), and transshipments (χ 2 = 6.19, df = 1, p = ), in the knowledge of commonality (χ 2 = 5.47, df = 1, p = ), and in the utilization of postponement (χ 2 = 4.52, df = 1, p = ) in descending order of asymptotic significance (two-sided). The 75 manufacturing companies surveyed know central ordering, product substitution, selective stocking, and order splitting the most, followed by transshipments, product pooling, commonality, capacity pooling, virtual pooling, risk pooling, postponement, demand reshape, the PE, inventory turnover curve, and SRL. The 27 trading companies recognize central ordering, product substitution, selective stocking, transshipments, order splitting, product pooling, the PE, virtual pooling, capacity pooling, demand reshape, commonality, risk pooling, the inventory turnover curve, postponement, and the SRL in decreasing order of awareness. The manufacturing and trading companies do not differ statistically significantly at the 5 % level in their knowledge of the various risk pooling concepts, except for commonality. Seventy-six percent of the manufacturing and 52 % of the trading companies are aware of this concept. Selective stocking (63 %), central ordering (61 %), transshipments (59 %), and commonality (57 %) are the concepts most frequently applied by the manufacturers. Capacity pooling (47 %), centralization, virtual pooling, product pooling, postponement, product substitution, order splitting, risk pooling, the PE, inventory turnover curve, demand reshape, the SRL, and decentralization follow in order of descending employment. Trading companies apply transshipments (85 %), central ordering (78 %), selective stocking (74 %), and product substitution (74 %) the most, followed by centralization (63 %), virtual pooling, order splitting, risk pooling, the PE, product pooling, demand reshape, commonality, capacity pooling, the inventory turnover curve, postponement, decentralization, and the SRL. 896 Vockell and Asher (1995: ch. 8). 897 However, in this case χ Y = 3.58 with df = 1 and p = , but p = in Fisher's exact test. 162

178 Appendix A All concepts are more widely used in the trading companies than in the manufacturing companies, except for the SRL, commonality, the inventory turnover curve, product pooling, postponement, and capacity pooling. As already mentioned above, this relationship is statistically significant only for product substitution, commonality, transshipments, and postponement at the 5 % level. This supports our hypothesis from the Risk Pooling Decision Support Tool that component commonality, postponement, and capacity pooling are rather applied by manufacturers and might be more suitable in a manufacturing environment. However, the utilization of capacity pooling in manufacturing and trading companies is just not statistically significantly different at the 5 % level anymore (χ 2 = 3.53, df = 1, p = ). Forty-one percent of the manufacturing companies apply postponement. This matches the more than 40 % of the manufacturers surveyed by Kisperska-Moroñ (2003: 131) in Upper Silesia, Poland that gear total production towards customer orders. Thirty-seven percent of the 27 electronics (classification numbers 30, 31, and 32) and automotive (34) and 40 % of the five food (15) and clothing (18) manufacturers employ postponement. Consequently, with our sample we cannot support at the 5 % level Van Hoek (1998b), who finds that postponement is extensively applied in electronics and automotive and less extensively applied in food and clothing. The utilization of postponement by electronics and automotive and food and clothing manufacturers in our sample is independent in the Fisher Exact Probability Test 898 (p (two-tailed) = 1). It differs neither in these two nor in the four groups significantly at the 5 % level. However, Van Hoek's (1998b) observation may apply to the whole population, as the confidence interval for the aforementioned conditions is very broad with for electronics and automotive and for food and clothing. For the same reasons as given earlier this confidence interval can only serve as a crude estimate here. Only five answers from food and clothing manufacturers are probably not enough to compare postponement application between different industrial sectors. 898 The Fisher Exact Probability Test is used, because some contingency table (crosstab) cells have expected counts less than 5. Nevertheless, Pearson's and Yates' chi-square test led to the same conclusion. 163

179 Appendix A Knowledge and Utilization of the Different Risk Pooling Concepts in Small and Large Responding Companies Figure A.3: Knowledge and Utilization of the Different Risk Pooling Concepts in Small and Large Responding Companies 164

180 Appendix A The answers of the 33 small (having less than 500 employees) and 69 large companies (having 500 or more employees according to the Deutsches Institut für Mittelstandsforschung (German Institute for Midium-sized Businesses Research)) are independent (the null hypothesis that there is no significant relationship between the answers cannot be rejected) in Pearson's and Yates' chi-square and Fisher's exact test at the 5 % level, except for the usage of risk pooling (χ 2 = 5.63, df = 1, p = ), centralization in the past (χ 2 = 4.75, df = 1, p = ), and postponement (χ 2 = 4.24, df = 1, p = ). This means only for these last three variables the distribution in the two groups of small and large companies differs statistically significantly 900, most significantly for risk pooling. The small companies tend to have more knowledge of selective stocking, demand reshape, central ordering, product pooling, and order splitting, while a higher percentage of large ones know the SRL and postponement. The large companies apply all concepts more than small companies (especially risk pooling, postponement, transshipments, capacity pooling, the PE, and product pooling) except for centralization in the past, demand reshape, commonality, product substitution, and central ordering in order of descending percentage difference of companies applying the respective concept. Hence, we can agree with Huang and Li (2008b: 12) that large companies may apply postponement more than small ones, since they may be better able to afford the redesign of products and/or processes usually required by postponement However, in this case χ Y = 3.37 with df = 1 and p = , but p = in Fisher's exact test. 900 This means that one can be certain that this statistic is dependable, the difference is genuine and not by coincidence. It does not mean that the difference is large, important, or useful (Walonick 2009). 901 Ernst and Kamrad (2000), Aviv and Federgruen (2001b). 165

181 3 Critical Appraisal We need to point out that the assumption of the significance test of random sample data may be violated. For population data any crosstable differences are real and thus significant. With non-random sample data we cannot establish significance. 902 However, significance tests are sometimes used as rough approximations. 903 For criticism of significance testing you may e. g. refer to Carver (1978), Cohen (1994), and Thompson (1996). Statistical significance does not tell if a research's results will reoccur 904 or the strength and generalizability of relationships in a sample and hence may divert attention from more crucial concerns 905. Although a thorough research process was followed, the limited representativeness of this survey has to be acknowledged. This should be remedied in another survey by a higher response rate. However, this might be difficult, as response rates for academic studies are low 906 and have been declining over the last years 907. Perhaps there are so few surveys in logistical research, since it is very difficult to obtain a random or at least representative sample because of low response rates as we experienced. A lot of companies are swamped with surveys and/or have a policy of not answering surveys. Some researchers pay companies to take part in surveys or give them other perquisites, which might also lead to a response bias. Practitioners should not criticize business research as too theoretical on the one hand and not take part in surveys on the other hand. As it is laborious to design and administer surveys, the usually low response rates disappoint the researcher and imperil the strength of the research findings 908, and survey research is prone to so many biases and errors 909, one perhaps should consider other empirical research. Netessine (2005: 6), for instance, suggests using university research database, publicly available, consulting company, or industry journal data. Still for a Ph.D. student with little funds it is difficult to access some of these data sources that are subject to charges. Besides, some specific data are not available at all or insufficient. For example, we could not obtain any information about the number of warehouses from business and logis- 902 Garson (2009). 903 Dorofeev and Grant (2006: 253f.), Garson (2009). 904 Carver (1978). 905 Thompson (1994). 906 Bickard and Schmittlein (1999), Goldsby and Stank (2000). 907 Baruch (1999). 908 Griffis et al. (2003: 237). 909 Groves et al. (2004: 39ff., 377f., 380). 166

182 Appendix A tics associations and federal statistical offices in Germany and the U.S. to derive how inventories changed in dependence of the number of warehouses compared to SRL predictions or how the number of warehouses changed over time. Some researchers expected the number of warehouses to increase with increasing fuel costs. Furthermore, the number of companies in the industrial sectors in different publications of the German Federal Statistical Office differs, as it receives its information from different data sources. If the industrial sectors are broken down further, only companies with 20 or more employees are considered. 910 If all companies with any number of employees are considered, they are not subdivided into detailed industrial sectors. 911 This impaired our retrospective quota sampling. Another survey could also shed light onto the companies' reasons for and against as well as the manner, degree, benefits, and costs of applying the risk pooling concepts, as we intended in the six-page version of this survey that yielded a uselessly low response rate. As risk pooling can affect the whole supply chain, another survey could consider a supply chain wide perspective rather than single companies. A lot of respondents do not perceive all the questioned concepts as risk pooling ones. It appears that mainly transshipments and postponement are associated with risk pooling. Although at least in our sample the risk pooling concepts are known fairly well (central ordering, product substitution, and selective stocking the most), only selective stocking, transshipments, and central ordering are widely applied. Transshipments 912 are more important and applied, postponement 913 and product pooling 914 less than suggested by some publications mostly for other regions. Nearly half the sample centralized its warehouse or logistics system in the past. This is less than overall in Europe 915. In contrast to the expected trend to decentralize due to increasing transportation costs, only seven percent will increase, six percent even decrease the number of warehouse or production locations in the future. It seems that the companies are very consistent in their strategy of centralization, decentralization, or no change over time. 910 For example Statistisches Bundesamt Deutschland (2009i: 371). 911 For example Statistisches Bundesamt Deutschland (2009i: 378). 912 CLM (1995), Herer et al. (2006). 913 CLM (1995: 209), McKinnon and Forster (2000: 5), Chiou et al. (2002), Alfaro and Corbett (2003: 12), Oracle (2004), Huang and Li (2008b). 914 Alfaro and Corbett (2003: 12). 915 CLM (1995). 167

183 Appendix A The utilization and knowledge of a risk pooling concept are correlated. This suggests that improving the knowledge about risk pooling may increase its application. Research needs to convey to practitioners under what conditions and how the different risk pooling concepts can be applied successfully. This research constitutes one step in this direction. Prominently associated is past decentralization with future decentralization, the utilization of product substitution and demand reshape, past centralization and decentralization (the only negative correlation), the application of the inventory turnover curve and transshipments, commonality and product pooling, risk pooling and transshipments, the inventory turnover curve and order splitting, selective stocking and virtual pooling, transshipments and virtual pooling, risk pooling and postponement, product substitution and transshipments, product substitution and virtual pooling, as well as postponement and commonality and vice versa. We can support Rabinovich and Evers' (2003b) finding that time postponement (emergency transshipments and inventory centralization) contributes to the implementation of form postponement at best only weakly for our sample. Trading companies seem to apply transshipments and product substitution more than manufacturing companies. The opposite is true for commonality and postponement. In contrast to Van Hoek (1998b) our sample shows no significant difference in the application of postponement by electronics, automotive, food, and clothing manufacturers. More large companies appear to use risk pooling and postponement than smaller ones, perhaps because they can afford to invest in expensive risk pooling strategies as suggested by Huang and Li (2008b: 12). More small companies have centralized their warehouse or logistics system in the past than large ones in our sample. Our survey shows that different risk pooling methods are and can be applied together as we already suggested in the Risk Pooling Decision Support Tool and the Papierco example. 168

184 4 Questionnaire 1 Line of business 2 Number of employees in Germany 3 Your position (e. g. logistics manager) Survey on Risk Pooling in Business Log by Dipl.-Kfm. Gerald Oeser Do you know the following concepts? Does your company use them? Known? In use? 4 Risk Pooling (Demand and/or lead time variability is reduced, if one aggregates demands and/ or lead times e. g. across locations, because it becomes more likely that higher-than-average demands Yes No Yes No and/or lead times will be offset by lower-than-average ones. This reduction in variability allows to reduce safety stock and therefore reduces average inventor y without reducing the service level.) 5 Square Root Law (Total (safety) stock in n warehouses = (safet y) stock in 1 centralized Yes Yes warehouse * square root of the number of warehouses n.) No No 6 The Portfolio Effect shows the reduction in aggregate safety stock by consolidating several warehouses' Yes Yes inventories in one warehouse in percent. No No 7 Selective Stock Keeping/Specialization (Reducing inventory carr ying cost treating products Yes Yes differently without reducing the service level substantially. For example, products with a low turn- No No 8 Component Commonality (Products are designed sharing com ponents. This reduces the vaty Yes Yes riability of demand.) No No 9 The Inventory Turnover Curve shows average inventory in dependence of the inventory Yes Yes throughput for a specific company. It can be used to estimate the average inventory for any No No (planned) warehouse throughput (shipments from the warehouse or sa les). 10 Product Pooling (Unification of several product designs to a single generic or universal design Yes Yes or reducing the number of products thereby serving demands that were previously served by their own product version with fewer products.) No No 11 Product Substitution (One tries to make customers buy another alternative product, because Yes Yes the original customer wish is out of stock No No of demand and inventory costs.) 12 Yes No Yes No 13 Transshipments/Inventory Sharing Inventory transfers among locations (e. g. between Yes Yes warehouses or stores) for example in case of a stockout. No No 14 Delayed Product Differentiation and Postponement Yes Yes No No 15 Virtual Inventory/Warehouse/Pooling: Yes Yes No No 16 Capacity Pooling Yes No Yes No 17 Central Ordering for several locations and later allocation of the orders (perhaps by a depot) Yes Yes to the distribution points or requisitioners according to recent demand inform ation. No No 18 Order plitting Yes Yes No No 19 a) Did you centralize your warehouse/logistics system (reduce the number of warehouse or Yes production locations)? b) Do you intend to centralize your warehouse/logistics system? Yes 20 a) Did you decentralize your warehouse/logistics system (increase the number of warehouse Yes or production locations)? b) Do you intend to decentralize your warehouse/logistics system? Yes No No No No Please push to send answers Figure A.4: Questionnaire 169

185 5 Answers KNOWLEDGE UTILIZATION Respondent Industry classification Employees Risk Pooling SRL PE 1 = Yes, 0 = No Selective Stocking Commonality Turnover Curve Product Pooling Product Substitution Demand Reshape Transshipments Postponement Virtual Pooling Capacity Pooling Central Ordering Order Splitting Risk Pooling SRL PE Selective Stocking Commonality Turnover Curve Product Pooling Product Substitution Demand Reshape Transshipments Postponement Virtual Pooling Capacity Pooling Central Ordering Order Splitting , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Centralization past Centralization future Decentralization past Decentralization future 170

186 Appendix A Industry Classification Description 11 Extraction of crude petroleum and natural gas; service activities incidental to oil and gas extraction, excluding surveying 15 Manufacture of food products and beverages 16 Manufacture of tobacco products 18 Manufacture of wearing apparel; dressing and dyeing of fur 21 Manufacture of pulp, paper and paper products 22 Publishing, printing and reproduction of recorded media 24 Manufacture of chemicals and chemical products 25 Manufacture of rubber and plastic products 26 Manufacture of other non metallic mineral products 27 Manufacture of basic metals 28 Manufacture of fabricated metal products, except machinery and equipment 29 Manufacture of machinery and equipment n.e.c. 30 Manufacture of office machinery and computers 31 Manufacture of electrical machinery and apparatus n.e.c. 32 Manufacture of radio, television and communication equipment and apparatus 33 Manufacture of medical, precision and optical instruments, watches and clocks 34 Manufacture of motor vehicles, trailers and semi trailers 35 Manufacture of other transport equipment 36 Manufacture of furniture; manufacturing n.e.c. 37 Recycling 40 Electricity, gas, steam and hot water supply 45.2 Building of complete constructions or parts thereof; civil engineering Wholesale of pharmaceutical goods Wholesale of paper and paperboard, stationery, books, newspapers, journals and periodicals Non specialized wholesale of wood, construction materials and sanitary equipment Wholesale of agricultural machinery and accessories and implements, including tractors Retail sale in non specialized stores with food, beverages or tobacco predominating Retail sale of clothing Retail sale of hardware, paints and glass Retail sale of games and toys Table A.5: Survey Participants' Answers to the Questionnaire 171

187 Appendix B: Proof of the Square Root Law for Regular, Safety, and Total Stock Based on a numerical example in Ballou (2004b: 379f.) and in a manner different from the flawed 916 one in Maister (1976), we formally prove that under certain assumptions the SRL applies to regular, safety, and total stock. Let average regular stock at location i be the economic order quantity (EOQ) Q i divided by two:, (B1) where d i is demand at warehouse i, S the fixed order cost, I the inventory carrying cost rate and C the product value per unit. Regular system inventory for n decentralized warehouses equals Regular stock in one centralized warehouse is. (B2) 916 Das (1978: 334) correctly remarks But Maister's proof is incorrect due to a combination of faulty algebra and possible misprints without pointing out the mistakes. Indeed, we found e. g. that it is supposed to be... instead of... (Maister 1976: 129) and instead of (Maister 1976: 130). The expression (Maister 1976: 130) is also incorrect. Furthermore, it has to be instead of (Maister 1976: 129). Changing a three-location to a one-location system reduces inventory by 42 (not 43) % and changing a ten-location to a four-location system reduces inventory by 37 (not 38) % according to the SRL (Maister 1976: 131). Maister (1976: 132) wrongly states, although he earlier notes that 1 (Maister 1976: 127). He also explains If the original decentralised system had 16 locations, and inventory costs account for one-half of total costs in this system, then inventory savings from centralisation equal 1. But transportation must represent 1, or in the decentralised system. Hence, we can afford to almost double transportation expenses and still retain a system cost less than in the original system (Maister 1976: 133). However, we can only afford 1.75 times and not almost double the transportation cost or, in other words, we could only increase transportation cost by 75 % at the most. But if all inventory savings were spent on increased transportation costs, we would not retain a system cost less than in the original system. The centralized and decentralized system costs would be equal and we would be indifferent between them. Nevertheless, Das (1978: 333) also misprinted 1 and incorrectly uses the equality instead of the approximation sign, although the power (square root) function cannot equal a linear one. Furthermore,,,..., should be,,..., and should be (Das 1978: 334). Das (1978: 332) also refers to a proof to his solution in the appendix, but the journal does not contain it. Professor emeritus Chandrasekhar Das, College of Business Administration, University of Northern Iowa, Department of Management, agreed with us and kindly rewrote the proof, as it was not available at the publisher anymore in 2009 (personal correspondence on February 27, 2009). 172

188 Appendix B Regular stock in one centralized warehouse times a factor α equals regular system stock in n decentralized warehouses:. (B3) (B4). If demand at each warehouse is equal (d), the regular system inventory for n decentralized warehouses equals the one in one centralized warehouse times the square root of the number of warehouses n:. (B5) This means the SRL applies to regular stock, if an EOQ order policy is followed, the fixed cost per order and the per unit stock holding cost (inventory carrying cost rate times the product value per unit), demand at every location, and total system demand is the same both before and after centralization. 917 However, according to Maister (1976: 128f.) the SRL can also be a good approximation when demand rates at all the field locations are not equal. If regular inventory in each of n locations in the decentralized system (RS s ) is considered the following relationship holds:. This corresponds to equation 9-28 in Ballou (2004b: 380):. Safety stock in warehouse i is, where z is the same safety factor for every warehouse, s di the standard deviation of demand at warehouse i, and LT the constant replenishment lead time for every warehouse. System safety stock in n decentralized warehouses is (B6) (B7). (B8) 917 Cf. Maister (1976: 125, 127, 131). 173

189 Appendix B If the demands are uncorrelated, safety stock in the centralized warehouse is. (B9) Safety stock in one centralized warehouse times a factor α equals systemwide safety stock in n decentralized warehouses:. (B10) If the standard deviation of demand at each warehouse is equal (s d ), the systemwide safety stock in n decentralized warehouses is equal to the safety stock in one centralized warehouse times the square root of the number of warehouses n: (B11). This means the SRL applies to safety stock, if demands at the decentralized locations are uncorrelated 918, the variability (standard deviation) of demand at each decentralized location 919, the safety factor (safety stock multiple) 920 and average lead time are the same at all locations both before and after consolidation, average total system demand remains the same after consolidation 921, no transshipments occur 922, lead times and demands are independent and identically distributed random variables and independent of each other 923, the variances of lead time are zero 924, and the safety-factor (kσ) approach is used to set safety stock for all facilities both before and after consolidation 925. If demands at the warehouses are correlated, the SRL does not even yield an approximation. The safety stock savings through centralization decrease with increasing correlation between demands at the warehouses and become zero with perfectly positive correlation. 926 Total inventory is the sum of regular and safety stock. 927 Therefore total inventory in the decentralized system TI d with n warehouses equals total inventory in one centralized warehouse TI c times the square root of the number of warehouses n: 918 Maister (1976: 132). 919 Maister (1976: 130). 920 Maister (1976: 132). 921 Evers and Beier (1993: 110), Evers (1995: 4). 922 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 923 Evers and Beier (1993: 110), Evers (1995: 4). 924 Zinn et al. (1989: 2), Evers and Beier (1993: 110), Evers (1995: 4). 925 Maister (1976: 129). 926 Maister (1976: 130). 174

190 Appendix B. (B12) The SRL applies to total inventory, if the assumptions stated above of the SRL both as applied to regular and safety stock hold. For a critical review of these assumptions please refer to Maister (1976: 125, 132f.), Das (1978: 331f.), McKinnon (1989: 102ff.), and Evers (1995: 2, 14f.). It should be checked whether the conditions or assumptions necessary for the SRL to hold (necessary conditions) are also sufficient conditions, i. e. whether, if the SRL holds, these conditions also automatically apply. This analysis, however, is beyond the scope of this thesis. Ballou (2004b: 380) incorrectly states The square-root rule [ ] measures only the regular stock reduction, not both regular and safety stock effects [ ]. Assuming that an inventory control policy based on the EOQ formula is being followed and that all stocking points carry the same amount of inventory, the square-root rule can be stated as follows: [ ] where AIL T = the optimal amount of inventory to stock, if consolidated into one location in dollars, pounds, cases, or other units AIL i = the amount of inventory in each of n locations in the same units as AIL T n = the number of stocking locations before consolidation. Traditionally the SRL has been mainly applied to safety stock, but as proven above it is also valid for regular stock or both regular and safety stock, if the respective necessary assumptions stated above hold. If it is only applied to regular stock as in Ballou's case, all the assumptions of the SRL as applied to regular stock enumerated above must apply, not only the two mentioned by Ballou here. Ballou's formulation of the second assumption may confuse, as Maister (1976: 125) assumes the demand rates at all the field locations are equal Ballou (2004b: 380). Total inventory might also include pipeline, speculative, and obsolete stock (Ballou 2004b: 330f.), which is neglected here. 928 Professor emeritus Ronald H. Ballou, Weatherhead School of Management, Case Western Reserve University, agreed with us in a personal correspondence on May 15,

191 Appendix C: What Causes the Savings in Regular Stock through Centralization Measured by the SRL? The total EOQ in the decentralized system is. (C1) The EOQ in the centralized system is. (C2) Due to the subadditive property of the square root, the sum of the square root of the demands at the locations i is greater than or equal to the square root of the sum of these demands:. (C3) Therefore, the total EOQ in the decentralized system (the sum of the EOQs of the locations i) is greater than or equal to the EOQ in the centralized system:. (C4) However, the total EOQ in the decentralized and centralized system are only equal, if demands or demand forecasts at at least n-1 locations are zero 929, which is unusual: 2 0 If n-1 d i equal zero, (C4) becomes. (C5) for this single non-zero d i. If all d i are zero, (C4) becomes (C6) 0. Therefore, if demands (at at least two locations) are larger than zero, the EOQ and therefore the average regular inventory and thus the inventory holding costs are lower in the centralized system. However, under the above condition the EOQ per decentralized location i is less than the one for the centralized one, as n > 1: (C7) 929 This theoretically questions Wanke and Saliby's (2009: 680) general statement that [t]he cycle stock savings are based on the fact that the square-root of the aggregate demand is always smaller than the sum of the square roots of individual demands. 176

192 Appendix C The total number of orders in the decentralized system is The number of orders in the centralized system is.. (C8). (C9) (C10) Due to the subadditive property of the square root, the total number (the sum of the numbers) of replenishment orders in the decentralized system is greater than or equal to the number of orders in the centralized one:. (C11) In analogy to (C5)-(C7), if demands (at at least two locations) are larger than zero 930, the total number of replenishment orders in the decentralized system is greater than the number of orders in the centralized one resulting in lower total order fixed costs in the centralized system. However, in this case the number of orders (lead times) per decentralized location i is smaller than the number of orders for the centralized one 931, as n > 1:. (C12) The savings in regular stock stem from the assumption of an EOQ order policy, constant fixed costs per order, holding costs (inventory carrying cost rate times product value per unit), and total demand for all locations before and after centralization. In the centralized system, usually the total order fixed cost is lower because of less orders and the inventory holding cost is lower due to a smaller EOQ than in the decentralized system Ronen (1990), Zinn et al. (1990), and Evers (1995) neglect this. 931 Cf. Ronen (1990: 132). Zinn et al. (1990: 139) state that inventory centralization will increase the number of lead times per year if an EOQ ordering quantity is used. [A]n increase in the number of lead times with the same expected annual demand decreases the average base stock (Zinn et al. 1990: 141). This is true for the centralized warehouse compared to each decentralized one. 932 Evers (1995: 5). 177

193 Appendix D: Tables Table D.1: Fulfillment of the SRL's Assumptions by Eleven Surveyed Companies Survey respondents Number Country Denmark Germany Germany France Sweden U.S. U.S. Italy U.S. U.S. Germany Industry Paper Paper Paper Reusable wholesale production production packaging Automotive Utilities Electronics Paper Semiconductors telecom wholesale Wireless Paper wholesale Employees 65 40, ,000 60,000 1,850 60, ,500 6,000 1,652 Position Supply Vicepresident Director of Director of Functional Chain Supply Logistics Logistics Marketing Materials Administrator Supply Logistics Logistics & Integrator Optimization Manager Chain Manager Analyst Manager Manager IT Lead Chain Manager Central warehouses Regional warehouses Assumptions of the SRL when applied to Safety Stock Demands iid (are independent and identically distributed random variables) Locations' demands uncorrelated Locations' demand variance the same Zero supplier lead time variance Locations face same average lead time Lead times iid Lead times and demands independent of each other Safety factor approach used Locations use same safety factor No transshipments between locations Safety Stock/ Regular Stock Regular Stock 1=Yes, 0=No Average total system demand remains the same after consolidation Locations' demands the same EOQ Order Policy Locations' fixed order cost the same Locations' per unit holding cost the same

194 Appendix D Table D.2: Comparison of Important Inventory Consolidation Effect, Portfolio Effect, and Square Root Law Models 179

195 Appendix D Continuation of Table D.2 180

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197 Appendix D Continuation of Table D.2 182

198 Appendix D Continuation of Table D.2 183

199 Appendix D Table D.2 shows the different SRL and PE models and the assumptions they are based upon. With the help of this table one can choose the model best fit for assessing inventory changes from centralization or decentralization for given conditions. The corresponding formulae for calculating the inventory savings achievable by inventory pooling can be found on the respective publication's page noted in the first or second row of this table. In order to facilitate readability the assumptions are grouped according to the rubrics stock-, inventory-policy-, demand-, and lead-time-related. The columns or models are arranged chronologically according to their year of publication, so that the development and adding or dropping of assumptions over time can be retraced where possible. The models are also grouped by colors according to their main contribution or focus, although this is not too definite, as they are very different or overlapping and the terms SRL and PE are sometimes used interchangeably. Maister (1976) showed the SRL for the EOQ and the safety factor approach for both cycle and safety stock, Eppen (1979) for the newsvendor model and expected costs, Zinn et al. (1989) the PE as a generalization of the SRL, Mahmoud (1992) the Portfolio Quantity and Portfolio Cost Effect, Evers (1995) the Consolidation Effect, Caron and Marchet (1996) the impact of centralization on safety stock in a special two-echelon system, i. e. the ratio of safety stock levels in a coupled system and an independent system, first (pioneers). Das (1978) and Ronen (1990) 933 (critics) critically review Maister's (1976) SRL and Zinn et al.'s (1989) PE respectively. Evers and Beier (1993, 1998) and Tallon (1993) consider variable lead times, Evers (1996, 1997) transshipments, Tyagi and Das (1998), Das and Tyagi (1999), Wanke (2009), and Wanke and Saliby (2009) optimal consolidation schemes, and Croxton and Zinn (2005) inventory pooling effects with the SRL in network design. Of course all researchers may be considered critical pioneers as they all contribute something novel and critically review previous work, which is the essence of scientific research. Mahmoud (1992: 198, 212) also considers the optimal consolidation scheme and criticizes that the PE is not sufficient to define it. Evers and Beier (1993) and Evers (1995) criticize Maister's (1976) SRL. Evers and Beier (1993) and Tyagi and Das (1998) consider multiple consolidation points and the equal partitioning of demand assumption. Wanke and Saliby (2009) also deal with regular transshipments. Important distinguishing assumptions made or not made by the various models are highlighted in grey. 933 Ronen (1990) and Zinn et al. (1989, 1990) have a scientific dispute. For details please refer to the respective publications. 184

200 Appendix D Table D.3: Conditions Favoring the Various Risk Pooling Methods 185

201 Appendix D Continuation of Table D.3 186

202 Appendix D Continuation of Table D.3 187

203 Appendix D Continuation of Table D.3 188

204 Appendix D Continuation of Table D.3 189

205 Appendix D Continuation of Table D.3 190

206 Appendix D Continuation of Table D.3 191

207 Appendix D Continuation of Table D.3 192

208 Appendix D Continuation of Table D.3 193

209 Appendix D Continuation of Table D.3 194

210 Appendix D Table D.4 The Risk Pooling Methods' Advantages, Disadvantages, Performance, and Trade- Offs 195

211 Appendix D Continuation of Table D.4 196

212 Appendix D Continuation of Table D.4 197

213 Appendix D Continuation of Table D.4 198

214 Appendix D Continuation of Table D.4 199

215 Appendix D Continuation of Table D.4 200

216 Appendix D Continuation of Table D.4 201

217 Appendix E: Subadditivity Proof for the Order Quantity Function (5.1) The total system-wide order quantity in the centralized system is no greater than the one in the decentralized system, because the order quantity function (5.1) is subadditive:,,. (5.4) In order to prove this, we first resort to two warehouses with forecast demand minus available inventory (net demand) and and seek to prove:,,,. (E1) The order quantity function (5.1) is a compound function consisting of an outer maximum function and an inner ceiling function, which we henceforth denote by and, respectively. The ceiling expression is a constant. Recall that a function is called subadditive, if it obeys the inequality for any, from the function's domain. (E2) We first show that is subadditive, i. e. that the following holds for any, :. This can be verified by a case differentiation: (E3) For s d, s d, for s d, s d s d,s d, s d,s d where notation a b stands for a divides b or, equivalently, b is a multiple of a and designates negation. (E4) (E5) We now prove that, is subadditive as well, i. e. that the following holds for any, :,,,. g,g For g,g c,,,. g c,g For g c,g c,,,. (E6) (E7) (E8) 202

218 Appendix E Then for the compound function holds:, (E9) since (E10), where the first inequality is due to subadditivity of and non-decreasing behavior of and the second inequality is due to subadditivity of. It is now straightforward to generalize (E9) to any number of summands. Given, we by induction on n have: (E11), which hence gives (E12) and proves (5.4) to hold. 203

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