Evolutionary production planning and scheduling

Transcription

1 Evolutionary production planning and scheduling vorgelegt von Dipl.-Ing. Andreas Schöpperl aus Berlin von der Fakultät VII Wirtschaft und Management der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften - Dr.-Ing.- genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. H. Hirth Berichter: Prof. Dr. H.-O. Günther Berichter: Prof. Dr. C. Bierwirth Tag der wissenschaftlichen Aussprache: 26. August 2013 Berlin 2013 D83

2 Evolutionary production planning and scheduling eingereicht von: Dipl.-Ing. Andreas Schöpperl Dissertation zur Erlangung des akademischen Grades Doktor-Ingenieur (Dr.-Ing.) Doktor der Ingenieurwissenschaften Fakultät VII Wirtschaft und Management Technische Universität Berlin

3 To my love. To my son. To my mother.

4 Acknowledgement I wish to express my gratitude to Prof. Dr. Hans-Otto Günther for his support, guidance and for providing valuable insights and advice. Additionally, I would like to thank the PhD committee for the assessment of this dissertation. Furthermore, I offer my sincere thanks to Anna Barkhoff for her friendship, support and precious advice. Finally, I wish to thank my family and friends for their on-going support and encouragement.

5 Contents I. Concept Introduction Motivation Object of study Way of proceeding Production planning in a dynamic environment Production planning environments Uncertainty sources in production planning Common production planning approaches Static and flexible planning Rolling horizon planning Robust planning Reactive planning Production plan evaluation Plan variation impacts Measuring plan variations Combining multiple measures Planning policies Periodical planning policies Event-based planning policies Hybrid planning policies Classification of an evolutionary production planning Evolutionary production planning concept Characteristics Main characteristics Balancing evolutionary production planning goals Plan efficiency & variation trade-off Multi-step techniques Responsive evolutionary production planning Further characteristics Classification of evolutionary production planning applications Evolutionary production planning system development Evolutionary production planning simulation framework (EPPSF)

6 Contents II. Case studies Case 1 - Evolutionary scheduling of a beverages bottling facility Introduction Literature Model formulations Representation of time Scheduling model Schedule efficiency & variation objectives Compact scheduling model Model extension Experimental design Numerical study results Preliminary considerations and simulation excerpts Main results strategy comparison Result details & parameter impacts Schedule variation & production cost trade-off Fixation of schedule elements Two-step strategies with production cost bounds Limited number of planning periods with schedule variation considerations Number of planning periods Scheduling policies Demand characteristics Case summary Case 2 - Evolutionary scheduling of chemical commodity products Introduction Literature Model formulations Scheduling model Schedule efficiency & variation objectives Compact scheduling model Model extensions Inverse production sequences Variable production speed Experimental design Numerical study results Preliminary considerations Main results strategy comparison Detailed results & parameter impacts Schedule variation & production cost trade-off Fixation of schedule elements Two-step strategies with production cost bounds

7 Contents Limited number of planning periods with schedule variation considerations Inverse production sequences Number of planning periods Scheduling policies Demand characteristics Case summary Concluding remarks and outlook 167 Bibliography 169 6

8 List of Figures 1.1. Dissimilarity of successive plans Additional coordination and planning efforts and costs Case-specific planning system implementation Categorization of production planning environments Uncertainty causes Rigid planning Rolling horizon planning Robust planning for a worst case scenario Robust planning for estimated plan realizations Robust planning for estimated disruptions Reactive planning for a machine break-down Hierarchical grouping of plan variation measures Plan variation measure example Planning policy categories Periodical planning policy Event-based planning policy Hybrid planning policy Common production planning approaches & typical characteristics Evolutionary production planning logic Evolutionary production system planning information overview High vs. low schedule variation One dominant goal type One quantity unit for all objectives Example trade-off curve Example trade-off curves for different data sets Time-based goal balance Time dependent goal dominance Goal as constraint example Normalization of goal elements Periodical planning policies Event-based planning policies Hybrid planning policies Evolutionary planning system development Evolutionary production planning simulation framework (EPPSF) EPPSF-Planner example

9 List of Figures EPPSF-Planner example General EPPSF simulation logic Example of a beverage bottling production cycle Time representation EPPSF-Planner - beverages bottling case Generation of demand orders Generation of order cancellations Simulation run excerpt base demand Simulation run excerpt demand change Simulation run excerpt production costs Simulation run excerpt lot starting time variation costs Simulation run excerpt schedule variation measures Average solution time per scheduling iteration Cost strategy & deterministic planning comparison Strategy comparison total production & schedule variation costs Strategy comparison lot variation costs Strategy comparison sub-lot variation costs Strategy comparison production costs Schedule variation & production cost objective weighting Schedule variation & production cost trade-off (SlStSiCost strategy) Schedule variation & production cost trade-off (SlSiCost strategy) Schedule variation & production cost trade-off (SlStCost strategy) Schedule variation & production cost trade-off (LStCost strategy) Schedule variation & production cost trade-off (SlSeCost strategy) Schedule variation & production cost trade-off (LSeCost strategy) Sub-lot starting time & size variation cost trade-off (SlStSi strategy) Schedule fixation strategies Production cost bounds schedule variation costs Production cost bounds production costs Production cost bounds SlStCb strategy Limited number of planning periods with schedule variation consideration Planning horizon length & production costs Planning horizon length & lot starting time variation costs Scheduling policy & cost measures Demand level & production costs Demand level & lot starting time variation costs Demand change offset impact Demand change level impact Demand granularity impact Exemplary changeover matrix Changeover matrix excerpt product cluster with sub-clusters EPPSF-Planner - chemical commodity case study

10 List of Figures 5.4. Generation of demand orders Generation of order cancellations Simulation run excerpt - schedule variation measures Average solution time per scheduling iteration Cost strategy & deterministic planning comparison Strategy comparison total production & schedule variation costs Strategy comparison schedule variation costs Strategy comparison production costs Schedule variation & production cost objective weighting Schedule variation & production cost trade-off (LStSiCost strategy) Schedule variation & production cost trade-off (LSiCost strategy) Schedule variation & production cost trade-off (LStCost strategy) Schedule variation & production cost trade-off (LSeCost strategy) Schedule fixation strategies Production cost bounds schedule variation costs Production cost bounds production costs Limited number of planning periods with schedule variation consideration Product sequence impact Planning horizon length & production costs Scheduling policy & cost measures Demand level impact Demand granularity impact Impact of demand change occurrence Impact of demand change level

11 List of Tables 3.1. Case study classification Model parameterization examples Production system parameters Demand data overview Model parameterization examples Production system parameters Production system parameters Product changeover Demand data overview

12 Part I. Concept 11

13 1. Introduction This work arose from research activities investigating the possibilities of a more continuous development of plans in modern production planning and scheduling applications. The following section 1.1 states the underlying motivation for this research while section 1.2 isolates the object of study and defines research goals. Finally, the last section 1.3 of this chapter describes the way of proceeding and the contents of the remaining chapters of this work Motivation Nowadays, companies often encounter highly competitive markets in very dynamic environments. Indeed, companies in many industries are faced with an increased product variety and complex, fast changing and ever more sophisticated environments, increasing demand variability as well as decreasing order timeframes, while the need to remain competitive results in an increased cost pressure. Furthermore, many companies are shifting from Make-To-Stock (MTS) to Make-To- Order systems (cf. Kaminsky and Kaya (2009)), in order to reduce inventory holding and associated costs. Production is thus based on actual customer demands instead of demand forecast. In consequence, a constant change in consumer behavior and demand variations (often on short notice) result in a requirement of quick responses and frequent planning decisions, while still remaining competitive. An on-going challenge is e.g. the need to quickly respond to demand-related influences, such as short-term customer orders and order modifications. A further characteristic of these competitive markets and the sophisticated customer side (cf. Adebanjo and Mann (2000)) is the need to quote short, reliable lead times (cf. Kaminsky and Kaya (2009)). Examples of markets with characteristics as described above may be found e.g. in the fast-moving consumer goods industry. It is a competitive industry, characteristic are low margins for relatively high volumes, a high product variety, small order sizes, short lead times, cost pressure and high demand variability. Quick responses to changing consumer behavior are required, in terms of demand, quality, flexibility, service and price (cf. e.g. van Dam et al. (1993), Keh and Park (1997)). Classically, if cost (or time, respectively) efficient planning is pursued, in order to produce with minimal costs, no attention is payed to previously released production plans. Respective planning processes typically result in a complete regeneration of production plans without consideration of former plans. Furthermore, the outcome of corresponding planning methods will usually react rather sensitive to even small data changes. In conjunction with a high demand variability, necessitating frequent planning decisions, 12

14 1. Introduction... Arrival of a new order Scheduled production lots (colors indicate specific products)... Successive Production schedules Modification of an order... Figure 1.1.: Dissimilarity of successive plans this leads to an increased variation in resulting planning decisions and rather dissimilar or unrelated seeming successive production plans (cf. figure 1.1). On the other hand, alterations between two successively released production plans do not only concern the production system which is executing these plans but usually also influence further planning activities (e.g. material sourcing, personnel planning or financing) within a company which rely on a released production plan. Thus, if alterations to an already released production plan are made, further coordination will usually arise (e.g. with other company departments) when an adjusted plan is verified and released. Furthermore, an altered plan then may necessitate the execution of other dependent planning activities to incorporate the plan alterations, which in turn strains corresponding personnel and planning capacities (cf. figure 1.2). In consequence, additional costs arise, due to the occupation of planning capacities but also as a result of alterations to the respective plans made by dependent planning activities (e.g. additional costs for material delivery on short notice). In turn, alterations to these plans of dependent planning activities influence further dependent planning activities as well, resulting in even more additional planning, coordination and planning efforts and costs. In fact, some of these plan alterations may again affect the validity of released production plans and require further coordination and potentially renewed production planning activities. For these reasons the described interdependencies have to be considered in production planning considerations as well. Ideally an integrated planning might encompass all relevant coherences in order to accomplish an integrated efficient planning of all respective planning activities within a company. However, such integrated planning models are usually far too complex to allow for an integrated approach. Furthermore, not all of the required information regarding these interdependencies and resulting costs will be available or even ascertainable in a specific planning case. Thus, it may not even be possible to completely assess realistic costs as a result of specific plan adjustments. Commonly, this information deficit is countered by the estimation and application of penalty costs to plan alterations, by the fixation of plan components or by focusing solely on the minimization of certain plan alterations or costs. The estimation quality of penalty costs is important in the first type of approaches, as respective planning methods may react rather sensitive to penalty cost variations. A fixation of plan components restricts respective plan alterations without the need for cost estimations, though the time period in which plan components may be fixed is limited by the due dates and occurrence of 13

15 1. Introduction Figure 1.2.: Additional coordination and planning efforts and costs (short-term) demand variations to be planned. While a focus on cost minimization does not consider described interdependencies in planning and perhaps implicitly assumes a handling of occurring demand variation events during plan execution, the exclusive minimization of plan alterations focuses on plan repairs and may not be very cost efficient if frequent plan adaptions become necessary. In practical applications, it is e.g. not uncommon to focus solely on the reduction of plan alterations, as reliable plans are desired in order to reduce coordination efforts. This repair of production plans is then usually coupled with a periodical complete regeneration of new production plans. However, frequent occurrence of new demand information, such as new orders or order modifications, induces the need for an on-going inclusion of respective demand information into a continuously developed production plan. On the other hand, due to cost pressure in highly competitive markets, cost considerations cannot be neglected in the development of production plans. Hence a requirement in the considered highly dynamic environments and competitive markets is the continuous adaptation of production plans in a cost-efficient but also reliable way under constant consideration of new demand-related information. The way such a planning goal is pursued is, of course, specific to each individual planning application, including implemented planning methods, consideration of specific costs and plan alterations as well as the desired balance of cost-efficiency and plan reliability (cf. figure 1.3). While research work exists which considers the inclusion of new demand information into an existing production plan (usually production scheduling problems) for some planning applications, there is still considerable demand for research on further planning 14

16 1. Introduction Figure 1.3.: Case-specific planning system implementation applications and case studies intent on a more continuous plan development, in respect to plan efficiency and reliability, in challenging markets. Furthermore, while a specific planning system implementation is very dependent on the individual planning application in focus, the formulation of a general concept summarizing and classifying common characteristics of such planning applications is important in order to support a general overview and categorization (cf. Vieira et al. (2003) for a framework for the related research field of rescheduling problems) Object of study This work aims at the formulation of a general concept describing the continuous development of production plans under consideration of frequent demand variations in competitive markets. This planning field is called Evolutionary production planning in the remainder of this work. Considered evolutionary production planning problems will usually reside on the operative planning level, with short-term (or short- to mid-term) planning timeframes, though depending on each specific planning application, the definition of what is considered as a short timeframe may vary considerably (e.g. a number of shifts, days, weeks etc.). Beside the formulation of a general concept, in the core part of this work specific production planning applications are addressed, planning methods developed and numerical case studies conducted. A variety of planning strategies is compared as well as the sensitivity of planning results to environmental influences and planning parameters. A framework supporting the design, implementation and evaluation of specific evolutionary planning systems is developed and applied in the investigated case studies. As applications of the evolutionary production planning concept, two case studies are investigated. While classically lot sizing and scheduling of production orders have often 15

17 1. Introduction been considered in separate planning steps, lately increased attention has been given to integrated planning models in order to allow for a more efficient planning. The discussed case studies are concerned with integrated lot-sizing and scheduling of beverages and chemical commodity products, respectively. Specifically, the block planning principle as a practical tool for lot-sizing and scheduling product variants in a predetermined sequence is adopted for the modeling of the two cases. In conjunction with the second discussed application, characteristics such as series dependent as well as limited product changeovers are considered Way of proceeding In chapter 2 existing concepts and planning approaches for a production planning in dynamic environments, found in the literature or in practice, are discussed. The chapter closes with a discussion of the relation as well as overlaps of these existing planning approaches with an evolutionary production planning and indicates the demand for a tailored concept focusing only on the specific aspects of evolutionary production planning applications. Chapter 3 then presents the general concept and planning framework for an evolutionary production planning. In part II, the core of this work, two case studies, implementing the evolutionary planning concept for a beverages production (cf. chapter 4) and a chemical commodities production system (cf. chapter 5), are presented. In numerical studies, various planning strategies are evaluated and compared. Finally, in chapter 6 the insights gained during these research activities are summarized and future research possibilities are indicated. 16

18 2. Production planning in a dynamic environment In practical applications, companies usually encounter a dynamic environment. When production activities are being planned, it is rarely the case that a once determined production plan remains unchanged until the end of the last production activity, specified by the plan. Instead companies are faced with the necessity to adapt their production plans to cope with new information regarding the dynamic environment, which becomes available as time progresses. Updated demand information, such as new, changed or even cancelled production orders, create the necessity to replan production activities. Other changes to the planning environment may be aspects of the production site, e.g. disturbances, such as machine break-downs, variable processing times etc. In this chapter, important concepts and existing planning approaches concerned with production planning in a dynamic environments are discussed. The chapter then closes with an assessment of planning approaches with respect to a suitability to accomplish evolutionary planning goals Production planning environments Production planning environments can be of static or dynamic nature. Static environments have a finite set of demand elements and planning periods to be considered. In dynamic environments the set of demand elements and future planning time is infinite and available information is changing as time progresses. In addition, if the environment is static and deterministic, all relevant planning information is available and certain at the time of planning. If some information is uncertain, such as variable processing times for certain production tasks, the environment is called stochastic. In a dynamic environment, demand related information is variable, albeit the kind of variability may differ in dependence on a specific planning problem considered (e.g. order arrival time, amount, due date etc.). Demand variability can be further distinguished by the possibility or impossibility of alterations to already available demand information (e.g. order cancellations, due date changes, order amount changes etc.). Again, in addition to demand related information, other information may be uncertain as well. For more information, the reader may confer Vieira et al. (2003) or Pfeiffer et al. (2007). The type of environments that is the focus of this work is highlighted in figure 2.1. Note that the term no alterations in figure 2.1 means that while new planning information becomes available as time progresses, it is not subject to later alterations once it is known (e.g. incoming demand orders are not subject to later modification or cancellation). 17

19 2. Production planning in a dynamic environment Figure 2.1.: Categorization of production planning environments 2.2. Uncertainty sources in production planning As stated in 2.1, dynamic environments are characterized by uncertainties regarding future planning relevant information. These uncertainties can be demand related but may also have other sources. As a simple categorization, these uncertainty sources are distinguishable as being internal or external. A typical example of external sources are demand related influences on the environment. Internal sources refer to the production system itself (e.g. variable processing times, available production capacity etc.). According to Aytug et al. (2005), uncertainties can be further categorized by introducing the three dimensions cause, context and impact. Causes for uncertainties are attributed to objects, such as processes, machines, demand etc. and variability in respective states in which these objects may be in the future (e.g. normal production, machine break down, new demand order etc.). Furthermore, interdependencies between objects may evoke consecutive reactions of other objects if an objects changes its state. Typical objects of uncertainty can be grouped into the categories of being demandrelated, material-related or production resource/process-related (cf. figure 2.2). As discussed before, demand-related uncertainty causes are within the main focus of this work. Examples for these are deviations from expected due dates and demand amounts due to order modifications by customers or realizations of predicted demands which differ from the predictions, order cancellations, new urgent orders or even changes in order priorities. Material-related uncertainty causes include variations concerning the quality (e.g. 18

20 2. Production planning in a dynamic environment Figure 2.2.: Uncertainty causes amount of rejects) and availability (e.g. material shortage, delivery delay) of required raw materials and other production input materials. Production resource/process-related uncertainty causes comprise processing variances (e.g. processing time and quality), function (e.g. machine failures) and capacity (e.g. personnel shortage) of production resources, among others (cf. Vieira et al. (2003); Neuhaus (2008); Gebhard and Kuhn (2009, p.29ff.)). Furthermore, the impact of uncertainties is not only related to a specific object and state changes but also its context the specific situation of the production system and environment at the time of a state change of an uncertainty object. Machine failures which occur during night shifts may be more serious then during day shifts, e.g. due to less personnel being available for repair. Processing times and quality may depend on the expertise of assigned personnel. Short-term demand changes are more serious to adjust to than demand changes which affect orders with due dates lying further in the future. Impacts of uncertainties comprise finishing time, quality and availability of products as well as availability and processing time of production facilities. According to Aytug et al. (2005), uncertainty should be explicitly considered during problem modeling and execution of planning activities, including sources, impacts and interdependencies. 19

21 2. Production planning in a dynamic environment Figure 2.3.: Rigid planning 2.3. Common production planning approaches This section presents common planning approaches found in the literature, concerned with various aspects of production planning in a dynamic environment Static and flexible planning Static planning assumes a static, deterministic environment all relevant information is known in advance and not subject to changes. When performing a static planning, a plan is regarded as fixed once it is created. It is assumed that a plan is carried out as planned, until the end of the planned time period is reached. This approach is also called predictive planning in the literature, especially in the area of reactive planning. Schneeweiß (1992) also distinguishes between static and rigid planning approaches a rigid planning being a static planning that is repeatedly performed in a dynamic environment, without attention to its dynamic nature (and the possibility of further alterations). Instead, the infinite set of planning periods is partitioned into distinct finite subsets for which a static planning is then executed (cf. figure 2.3). While carrying out a static plan, it may of course become necessary to make adjustments, but these are not considered in an explicit planning process, but implicitly assumed to being performed during plan execution. This approach has the advantage of simplicity and apparent reliability once a plan is created. Depending planning activities can rely on the apparent constancy of a released plan. On the other hand, the approach remains only realistic as long as hardly any changes to the planning information occur. In contrast to a static planning approach, flexible planning techniques try to account for the dynamic nature of environments, incorporating changes to the available planning information by revising created plans or taking pro-active measures during plan creation. 20

22 2. Production planning in a dynamic environment In the following sub-sections, major planning concepts which apply to one degree or another flexible planning techniques, are discussed Rolling horizon planning A typical planning technique is the classical rolling horizon planning approach. It is found in many planning areas, in the literature as well as in practice. It accounts for the dynamic nature of planning environments by the use of moving, overlapping planning time windows. As time progresses, production activities are repeatedly planned. Overlapping planning periods account for the fact that planning information for overlapped periods may have changed since the last planning iteration and already created plans are in need of a revision. Figure 2.4 illustrates a rolling horizon planning. Sethi and Sorger (1991) list the quality of demand forecasts, often declining with the distance in time of future planning periods, as one reason for requiring a gliding planning technique with overlapping planning time periods and frequent plan revisions. Rolling horizon planning is also used in other planning fields, such as financing. Rolling horizon approaches are most common in mid- or long-term planning application (cf. e.g. Liu et al. (2009)), but occasionally also in short-term planning applications (cf. e.g. Gomes et al. (2010)) If mid- or long term planning is performed, planned activities are typically only released and executed for the first planned period. If short term planning is performed, usually more than one planned period is released and may induce further replanning and coordination activities, if revised at a later time. Thus, when plans with overlapping periods are subsequently revised, these depending planning and coordination activities will have to be performed repeatedly. In rolling horizon planning applications, usually a discrete time frame is used, dividing the planning time into a series of planning periods. Planning activities are then performed periodically, each time moving (rolling) forward the planning time window (or the planning horizon, respectively) by a specific number of planning periods, discarding expired periods and including an equal number of new periods at the end of the planning time window. The planning time windows, considered in each planning iteration, overlap by a specific number of planning periods, defining the number of repeatedly revised periods. Thus, planning decisions in earlier planning periods are not included in the set of overlapping periods and binding, while decisions in later periods are preliminary and going to be revised during subsequent planning iterations. A classical argument supporting this approach is that it enables the periodical update and correction of production plans by incorporation of new planning information. In consequence, plans for planning periods which have been planned before are discarded and completely new plans are created instead. For more information on rolling horizon planning confer Stadtler (1988); Steven (1994); Sethi and Sorger (1991); Kurbel (2005); Kistner and Steven (2001); Kurbel (2011); Schneeweiß (1992). The length and number of planning periods varies depending on the planning area and level and of course the specific planning problem under consideration. Furthermore the length of planning periods can be either constant throughout the planning time window, 21

23 2. Production planning in a dynamic environment Figure 2.4.: Rolling horizon planning or the aggregation level of planning periods may vary, allowing for a detailed planning in earlier periods and coarser planning for later composite periods. Typically, a new predictive plan is created at each planning iteration, as for a static planning, assuming all information to be known and not subject to changes it may be viewed as a mix between a rigid and flexible planning. Created production plans for planning periods which have already been planned in previous planning iterations are usually not considered during a planning iteration instead a complete replanning is performed. The application of rolling horizons and rolling horizon decision making has been addressed intensively in the past (cf. Sethi and Sorger (1991)). Rolling horizon planning is used in many applications in practice as well as in the literature (cf. e.g. Clark (2005b); Li and Ierapetritou (2010); Millar (1998); Clark and Clark (2000); Balakrishnan and Cheng (2009); Stauffer and Liebling (1997)). A lot of works in the literature are also concerned with the related problem of examining the impact of and finding an efficient length for the planning horizon parameter. For an overview, confer Chand et al. (2002). Another topic that has received considerable attention is concerned with the effect that planning methods tend to react rather sensitive to even slight changes in planning data, resulting in rather dissimilar plans because of slight data alterations. Consequently, frequent replanning due to rolling horizon techniques (especially frequent in short-term planning) then often leads to a lot of changes to plans for planning periods which have been revised. This effect of plan variations is called nervousness (cf. Inderfurth and Jensen (1996); Kurbel (2011)) and has been studied extensively in the literature, especially in the area of material requirement planning (MRP) systems, but other areas as well (cf. Pujawan 22

24 2. Production planning in a dynamic environment Figure 2.5.: Robust planning for a worst case scenario (2004); Kimms (1998); Kropp et al. (1983); Sridharan et al. (1987); Carlson et al. (1979); Blackburn et al. (1986); Federgruen and Tzur (1994); Ho and Ireland (1993, 1998); Kaipia et al. (2006)). Measures against planning nervousness include the application of penalty costs for alterations to the original plan (cf. e.g. Kazan et al. (2000)) as well as fixation planning periods or fixations of plan components (cf. e.g. Gomes et al. (2010)) Robust planning Robust planning approaches assume a non-deterministic (stochastic or dynamic) environment and try to anticipate disturbances by taking proactive measures to counter the impact of planning uncertainties. A production plan is created to be robust with the goal of minimizing the effect of major disturbances (usually due to resource-related disruptions) and simple process variances (e.g. variable processing times) on the plan validity in respect to performance measures in terms of efficiency or predictability. Ideally, a robust plan should need none or only minor adjustments during execution, if a disturbance occurs. A lot of literature on robust planning is focused on the area of machine scheduling and the minimization of disruptions to machine availability. For more information on robust planning, confer Aytug et al. (2005); Samsatli et al. (1998); Scholl (2001); Herroelen and Leus (2005); Gebhard and Kuhn (2009). Several groups of solution strategies, dealing with robust planning, can be found in the literature. The first group of strategies considers a set of planning scenarios which differ in the realization of disturbances and tries to create a valid plan under the assumption of a worst-case scenario. Individual solutions of this worst-case scenario are rated by their performance over the whole set of considered scenarios (cf. e.g. Kouvelis et al. (2000)). Figure 2.5 shows a simple planning example considering 3 scenarios which differ in the assumed processing time of order 1 and the occurrence of an urgent order 3. The final plan includes the assumptions of the worst case the longer processing time assumed by scenario 2 for order 1 as well as the inclusion of the urgent order 3. 23

25 2. Production planning in a dynamic environment Figure 2.6.: Robust planning for estimated plan realizations Figure 2.7.: Robust planning for estimated disruptions A second group of strategies tries to determine expected plan realizations and to minimize the difference between predicted and realized plans in respect to a defined performance measure (cf. e.g. Wu et al. (1999)). Figure 2.6 shows a simple planning example considering 2 possible realizations for the processing time of a production order 1. The final plan includes an estimate based on those 2 realizations for the processing time. The third group of strategies tries to estimate the effect of certain disruptions. The production plan is then created in a way that, if the regarded disruptions occur, the plan does not have to be adjusted during execution (cf. e.g. Mehta and Uzsoy (1998)). The impact estimation of certain disruption will usually be based on the past performance of regarded production resources. As an example, a planning strategy could try to estimate the impact of machine failures on the prolongation of process completion times, include this information into the planning method creating the predictive plan and thus ensure good estimates of realized completion times (e.g. by inclusion of buffer times). These strategies try to ensure good estimates of the realized production flow by lowering the resource capacity. Figure 2.7 shows a simple example considering 2 past machine breakdowns with different repair times. The final plan includes a buffer time which is estimated from these past repair times. 24

26 2. Production planning in a dynamic environment Note that in approaches of the second and third group, the modeling of some planning parameters no longer treats these as deterministic but instead as random variables. Often, empirically determined statistical distribution functions are used in planning models. The characteristics of robust planning described in this sub-section lead to the conclusion that such strategies are only applicable as long as actual disruptions and realized variances from estimated effects do not exceed a certain level. If disturbances occur, which have effects that are much stronger than estimated, or which are completely unexpected, the created production plan cannot be carried out as planned. Furthermore, there are often many different uncertainties effecting a production system, making it difficult to create plans which are robust in respect to all, or at least to a set containing the most important uncertainties and effected system parameters (cf. Neuhaus (2008)) Reactive planning Reactive planning assumes a production environment which is dynamic but production planning does not take proactive measures as in robust planning approaches. In case of a disturbance (e.g. a machine break-down), of an amount which makes a plan adjustment necessary, the current production plan is adjusted, incorporating the changes to the planning information. The main goal of reactive planning is the restoration of plan feasibility in case of occurring disturbances, albeit usually the retention of plan performance (in respect to defined planning goals) is desired as well. A replanning is initiated on a periodical basis or tied to specific events. Sometimes a mixture of both is used (cf. 2.5 for more information on planning policies). Reactive planning approaches can be divided into dynamic planning and predictivereactive planning approaches. In the case of a pure dynamic (also called online or completely reactive ) planning, no predictive plan is created. Instead always only the next decision is planned and executed. Further information about the environment is not taken into account. Often, rule-based strategies are used for decision making. This lessens the computational burden and increases solution speed of planning methods (cf. Holthaus and Rajendran (2000)). In the case of predictive-reactive planning approaches, first a predictive plan is created and subsequently executed. Note that predictive planning is sometimes also referred to as offline planning (in contrast to online planning). Usually, all relevant information is included in the planning process with the goal to create an optimal plan in respect to the efficiency goals defined. The computational burden is higher but such methods can significantly outperform rule-based approaches by including much more information in the planning process and realizing existing optimization potential (cf. Ovacik and Uzsoy (1997)). However, if uncertainty increases, the performance-advantage of optimal methods may decline in specific cases (e.g. high processing time variances, cf. Lawrence and Sewell (1997)). Due to the occurrence of a disturbance, the plan is then adjusted as required. The applied methods for plan adjustments may again be simple rules, heuristics or optimal methods. The plan adjustment may be partial, meaning that it is restricted to a part of the plan, or comprise the complete plan. If a complete replanning is performed, a completely new predictive plan is created. Figure 2.8 shows a simple example of a 25

27 2. Production planning in a dynamic environment Figure 2.8.: Reactive planning for a machine break-down reactive plan adjustment in reaction to a machine break-down. Also confer Neuhaus and Günther (2006) for an example of a reactive scheduling system for applications in the process industry. The majority of reactive planning papers in the literature is concerned with scheduling problems. Most of these, according to Aytug et al. (2005), focus on resource-related uncertainties, such as variable processing times or major disruptions, namely mean times for machine failures and repair operations. However some works also include or specifically address the inclusion of new orders into a predetermined productions schedule (cf. e.g. Vin and Ierapetritou (2000); Artigues and Roubellat (2002); Roslöf et al. (2002); Mendez and Cerda (2003); Janak et al. (2006); Ferrer-Nadal et al. (2007); Caricato and Grieco (2008); Gomes et al. (2010)). For more information on reactive planning, confer Aytug et al. (2005); Neuhaus (2008); Pfeiffer et al. (2007); Sabuncuoglu and Bayiz (2000); Herroelen and Leus (2005). Also note that robust and reactive planning approaches may be combined, resulting in so-called robust-reactive planning methods Production plan evaluation Given a decision problem in the area of production planning, a typical goal in the creation of a production plan is to not only find a valid plan under given conditions, but to also find the best possible plan in respect to defined planning goals. In order to be able to compare different plans for a specific planning problem, evaluation criteria are required, in order to evaluate plan performances (cf. Neuhaus (2008), p.47 et sqq.). In many cases, in the literature as well as in practice, classical efficiency criteria are used, usually requiring the calculation of cost- or time-related efficiency measures (e.g. inventory holding costs or production makespans). A listing of efficiency measures can be found in Blömer (1999). As described in robust planning aims at creating plans which are insensitive to environmental influences. In order to evaluate the robustness of a plan, respective robustness measures are required. As discussed before, robust planning is either focused on preserving the feasibility of a plan (e.g. by insertion of buffer times) or on the reduction of performance measure deterioration. Thus, robustness measures may roughly 26

28 2. Production planning in a dynamic environment be grouped into measuring robustness of feasibility or robustness against performance deterioration, respectively (for a listing of robustness measures, confer e.g. Mignon et al. (1995)). Another criterion for the evaluation of a production plan is its flexibility. Flexibility describes the ability of a plan to be adjustable in reaction to occurring events. A flexible plan is easily adjustable to changing environmental influences (cf. Jensen (2001)). A third criterion, plan stability, describes the similarity between an original plan and a resulting plan after adjustments have been made. A stable plan is very similar to its original plan. Plan variations may be due to replanning activities, resulting in differing plans or ad hoc adjustments during execution, in order to retain plan feasibility. A contrary defined criterion is the aforementioned nervousness of a plan. An adjusted plan which is very dissimilar to its original plan has a high nervousness. To express the amount of plan variations, appropriate (stability or nervousness) measures may be calculated. For a listing of stability measures, confer e.g. Neuhaus (2008) (p.50 et sqq.). The following sub-section will focus on effects of plan variations, while will present a short overview on plan variation measures Plan variation impacts As discussed before, variations from an original released plan may arise due to variances during execution (e.g. processing time variances) or plan adjustments in reaction to occurring events. This sub-section will focus on the impacts of such plan variations. Typically, after a production plan has been created, a revision phase follows during which the plan is verified and altered if required. After this revision phase, the plan is released and thus made available to the production system as well as other depending planning activities (e.g. material sourcing, personnel disposition or financing activities) within the company (or within the supply chain, respectively). If an already released plan is adjusted, another revision phase follows, verifying the altered plan. The type and amount of variations between the original and altered plan determine the verification efforts. A higher dissimilarity usually induces more verification efforts. In addition to a verification, the plan alterations have to be coordinated with other depending planning activities. This generates additional coordination efforts (as well as associated costs) between the involved planning authorities as well as with the executing production system. Beside coordination efforts, a revision of depending plans may induce further costs. These occur for a wide range of reasons, e.g. higher material costs for deliveries on short notice, penalty costs for plan alterations from external peers in the supply chain etc. Additionally, depending planning activities may also have to be repeated, again inducing further planning efforts for depending planning activities. The revised plans of other planning activities of course may themselves lead to additional coordination and planning efforts and additional costs. Furthermore, released plans are also used for the communication of delivery dates to customers. Frequent changes to these will likely degrade the customer service quality or add further penalty costs. In conclusion, in practical applications a low plan variation is usually desired to mitigate negative effects, such as additional coordination and planning efforts as well as additional costs. 27