Building Resilient Supply Chains using Supply Chain and Traditional Risk Management and Insurance Techniques

Transcription

1 Building Resilient Supply Chains using Supply Chain and Traditional Risk Management and Insurance Techniques By K.P. Sapna Isotupa School of Business & Economics Wilfrid Laurier University Waterloo, ON, N2L 3C5 CANADA (519) ext Mary Kelly School of Business & Economics Wilfrid Laurier University Waterloo, ON, N2L 3C5 CANADA (519) ext Anne Kleffner * Haskayne School of Business University of Calgary Calgary, AB T2N 1N4 CANADA (403) kleffner@ucalgary.ca * Contact author.

2 Introduction and Overview Supply chain management encompasses the management of all businesses and activities involved in sourcing and procurement of raw material, transportation, storage, in-transit inventory and all logistics management activities from source to the end user. It involves coordination and collaboration with all business partners, which can be suppliers, intermediaries, third-party service providers, and customers. In the past two decades, firms have implemented practices such as lean management, just-in-time inventory, virtual inventory and global sourcing to reduce total supply chain costs. Any threat which could cause an interruption in the flow from raw material to the end user is a supply chain risk and any interruption in the flow of material is a supply chain disruption. The severity and the frequency of supply chain disruptions have increased as firms have built leaner supply chains. A 2011 study found that the top five causes of supply chain disruptions were adverse weather (51 percent); information technology or telecommunications outage (41 percent); transport network disruption (21 percent); earthquake or tsunami (21 percent); failure by outsourced service provider (15 percent). (Zurich, 2012). 1 The Business Continuity Institute s 2010 survey of its membership noted that 72 percent of respondents had noted at least one disruption in its supply chain that resulted in a loss of productivity or a loss in reputation and for 10 percent of respondents, a financial cost exceeding 500,000 Euros. Given the catastrophic potential of supply chain disruption, supply chain risk management is a critical issue for the survival and growth of companies. Furthermore, the difference between effective and ineffective risk management can make the difference between solvency and insolvency. Because of the high costs of supply chain disruption, in practice, risk managers implement solutions to both reduce the likelihood of a supply chain disruption and to ensure recovery after a disruption happens. Solutions that reduce the likelihood of failure contribute to the robustness of supply chains. Solutions that enable the firm to become operational after a loss contribute to the resilience of the supply chain. Many organizational responses are available to reduce the frequency or severity of supply chain disruptions. Ex ante responses include traditional risk management solutions, such as 1 An earlier Zurich survey found that the most common categories of disruptions over the period were accidents, such as fire or hazardous spills; labour issues, such as shortage of qualified workers or labour unrest; production problems, such as overly lean inventory or lead-time variability; and natural disasters, such as epidemics and extreme weather (Bolgar, 2011). 1

3 employee safety training, fire prevention, building and workplace design and hazardous materials management, and logistical solutions, such as inventory management and demand management, alternative transportation and supply management tools, such as dual sourcing. An important way for companies to build resilience is by putting financial solutions in place to provide ex post funding after a disruption has occurred. Insurance, for both direct and indirect losses, is often used for disruptions that are internal to the company. However, insurance, namely contingent business interruption insurance, has not been shown to be reliable in financing indirect losses that arise from disruptions that occur outside the company. As one risk manager noted, traditional insurance is too little and paid too late to be effective. Therefore firms may keep funds in highly liquid assets to be used as self-insurance, or they could arrange for funds (such as lines of credit) to be available after a disruption has occurred. One possible financing mechanism is contingent capital. Contingent capital is specifically designed to provide funds when pre-defined events, such as man-made or natural catastrophic events, trigger the need for capital. The upfront cost of contingent capital is less than insurance, but unlike insurance, funds accessed after the loss has happened need to be paid back. Contingent capital is a popular alternative for officers and Boards of Directors who do not wish to enact inflexible arrangements (like dual sourcing) for rare events. Managing supply chain disruptions in practice involves several functional areas of the business and the response depends on the potential severity of the disruption. However, there is very little academic literature that addresses these complex issues that arise in managing and surviving supply chain disruptions. Here we briefly survey both the supply chain risk management (SCRM) literature and the risk management and insurance (RMI) literature to provide insight into this issue. The academic supply chain risk management literature develops theoretical solutions to minimize the likelihood of supply chain disruption. The literature on supply chain risk focuses analytics, algorithms and simulation of processes to mitigate supply chain disruption. These are issues of robustness: how can a supply chain be designed to minimize the likelihood of failure. Tang (2006) notes that most of the quantitative models in the literature are designed for managing operational risks. Tang and Musa (2011) reiterate the findings of Tang (2006) and state that more quantitative papers on SCRM have started appearing since 2004, however the field is still largely dominated by qualitative papers. 2 Quantitative supply chain risk research has 2 Some of the recent and oft quoted works on supply chain risk management are Christopher et al, 2003; 2

4 gained prominence in the operations management journals since 9/11. However, very few papers include analytical models that address systems with more than one echelon. For models with more than two echelons, simulation is the widely used method to study supply chain disruptions. Deleris and Erhun (2005) use Monte Carlo simulation to model a supply chain where a disruption at one node disrupts work on an entire branch of the supply chain. Schmitt, Snyder and Shen (2011) use simulation to establish the benefit of having multiple, decentralized stocking locations under supply uncertainty. This is the opposite of the classical risk-pooling effect, which describes the reverse tendency under demand uncertainty. The narrowness of the solutions provided in the SCRM literature has been noted by Bernes and Khan (2007) in their article which addresses defining a research agenda for supply chain risk management. They identify two major shortcomings in the supply chain risk management literature. First, it doesn t locate itself within the wider literature on the theory of risk and the practice of risk management; and second, it doesn t incorporate risk management tools and techniques from other disciplines of research. The management of corporate risk is also studied extensively in the risk management and insurance literature. The current academic literature on managing risk within complex organizations tends to focus on enterprise risk management. Recent contributions include a theoretical framework to study capital allocation decisions under enterprise risk management (Ai, et al., 2012) an assessment of the value added to the firm by implementing enterprise risk management (Hoyt and Liebenberg, 2011; Mcshane, et al. 2011) and determinants of enterprise risk management adoption (Pagach, and Warr, 2011). Supply chain risk is not analyzed. One of the few papers to consider the complementarities of SCRM and RMI solutions is Dong and Tomlin (2012). They model the relationship between business interruption insurance and operational measures for managing disruption risk. They develop a model that reflects the interplay between insurance purchase decisions and operational decisions, decisions that they note are often made independently. Their model solves for the optimal inventory, deductible and coverage limits and they show that in some cases insurance and operational measures can be complements, even though intuitively one might expect them to be substitutes. When disruption is a rare event that lasts for a long period of time, the value of emergency sourcing increases. Barry, 2004; Cavinato, 2004; Christopher and Lee, 2004; Kleindorfer and Van Wassenhove, 2004; Spekman and Davis; 2004; Zsidisin et al., 2004; Hendricks and Singhal, 2005; Towill, 2005; Peck, 2005; and Tomlin,

5 Insurance is one way of obtaining resources for emergency sourcing and hence multiple sourcing (operational risk management) and insurance are complementary in this case. We also examine the relationship between SCRM and RMI strategies for managing supply chain risk. Following the SCRM literature, we build a supply chain simulation model. Our model expands on the literature in that it incorporates both SCRM and RMI options for addressing supply chain risk. In our model there are multiple suppliers, a single manufacturer, retail outlets and many consumers. Embedding a traditional SCRM model within the wider literature is valuable because it allows us to address the issue of resilience or recovery after a disruption. Our results show that the best combination of solutions is a function of both the frequency of loss (length of time between disruptions) and the severity of loss (length of disruption). Firms minimize the impact of high frequency, low severity disruptions by dual sourcing materials. Having funds available after a loss (through contingent capital or similar arrangements) is the best option to minimize the impact of catastrophic low frequency and very high severity disruptions. For medium frequency and medium severity disruptions, we find that a combination of both dual sourcing and loss financing minimizes the impact of the disruption. To our knowledge, this is one of the few papers integrating these two streams of literature: the supply chain algorithmic models with the insurance-based risk management literature. 3 By extending operation management models to include the traditional risk management and insurance literature, our work will add to the growing research on the true impact of disaster recovery planning on the operations of business. Problem Statement and Methodology In order to manage the risk of supply chain disruptions, companies can use a number of different strategies. Tomlin (2006) distinguishes between operational mitigation strategies, which are strategies undertaken to increase the robustness of the supply chain, and operational contingency strategies, which are tactics that the firm employs only in the event a disruption occurs. We focus on the use of dual sourcing as the operational contingency strategy used by the firm. Operational mitigation strategies, such as rerouting by changing transportation 3 There are some papers in the operations management science journals which take a broader view of supply chain risk such as Christopher and Peck (2004) and Kleindorfer and Saad (2005), but these papers tend to be more descriptive in style. 4

6 patterns, sourcing outside the supply chain, or product redesign, can be funded by ex ante contingent financing arrangements. To examine the effectiveness of different strategies for managing supply chain risk, we use simulation and compare the solutions for various risk management techniques in mitigating the effects of a disruption to one part of a supply chain. In particular, we study the effect of a disruption at a supplier on a manufacturer and retailers. We build four different simulation models using the discrete event simulation software, ARENA, by Rockwell Automation Technologies Incorporated. The simulation methodology is used because of the complexity of the modeling. It is not possible to obtain closed form analytic solutions. The simulation models are initially designed to provide the best operational strategy in a world with no disruption, and then examine the impact of randomly occurring disruptions to the model. We describe the base model first. Our focus is risk management options for the manufacturer. We start by building a base model to quantify the flow of goods from a single supplier to the manufacturer and retailers when there is no disruption at the supplier as shown in Figure 1 and Figure 2 below. Demand for the manufacturer is generated by many retailers who have the option of going elsewhere for their supply if the manufacturer doesn t have items on hand. Most retailers are willing to wait for a fixed length of time within which they expect to obtain their order. If the manufacturer is unable to provide them with their order in that length of time, they take their business elsewhere. insert Figure 1 and Figure 2 about here The assumptions of the base model (with no risk management) are common to inventory management simulations. 4 The manufacturer has a maximum inventory capacity of S boxes of goods, encompassing both those goods in production and finished goods. Each box contains n individual units of the good to be sold to the customer. When the inventory level at the manufacturer reaches the reorder level, s, an order of size S-s = Q units is placed with the supplier. The time it takes the supplier to replenish the stock has a normal distribution with mean, m. The demand for items by the retailer from the manufacturer occurs according to a stochastic process; specifically, the time between orders follows an exponential distribution with known mean, λ. Each retailer demand is for one box. Once the manufacturer receives the 4 For more information on the subject, we direct the interested reader to Zipkin (2000). 5

7 demand from a retailer, the demand is dispatched to the retailer after T units of time. T is the fixed transportation time to deliver goods from the manufacturer to the retailer If the manufacturer has neither the raw material nor the finished goods at the time that demand arrives from a retailer, retailers are prepared to wait for a further W units of time at the end of which they take their demand elsewhere and the manufacturer loses the sale. The simulation model for the above process is built and run for 1000 days in order to obtain the various operating characteristics for the manufacturer, such as the average inventory level, the percentage of retailer demand which is met immediately after realization of the demand, the percentage of retailer demand that is met within the fixed length of time that retailers are willing to wait for their items, and the percentage of lost sales because of stock unavailability. A disruption at the supplier would cause some lost business to the manufacturer, and the longer that a supplier is not operational, the greater the losses to the manufacturer. The aim of this paper is to suggest risk management strategies that will minimize lost sales to the manufacturer arising from supplier disruptions. A firm can undertake SCRM or RMI, or a combination of both, to shorten the length of the disruption. The likelihood or frequency of a disruption is not controllable by the manufacturer. Furthermore we assume that there exists an infinite number of retailers or in essence, even if a retailer s demand is unsatisfied, the retailer will purchase from the manufacturer in the future. In order to examine the effects of different risk management strategies on the severity of supply chain disruptions, we build four models. The first model is one where the base model as described above is modified slightly and a disruption is introduced at the supplier. The time between two successive disruptions at the supplier is an independently and identically distributed random variable with known mean, y. The time for which the supplier is not operational is a constant (z units of time). In this initial model, the manufacturer undertakes no risk management to mitigate against this potential disruption. In the second model, which we refer to as the RMI model, the firm uses contingent financing to reduce the severity of a disruption after the disruption occurs. The focus here is building a resilient supply chain. The contingent financing can be used to source supplies from a supplier outside of the supply chain, or it can be used to cover additional operating expenses such as product redesign. In the simulation model, the impact of RMI is to decrease the length of time for which supplies are unavailable. Specifically, the change between the first and the second model is that the length of the disruption is halved. The time between two successive 6

8 disruptions is still a random variable with mean y and the time for which the supplier is unavailable is z/2. In the third model, the SCRM model, the focus is building robust supply chains. Specifically, the manufacturer undertakes dual sourcing (contracts with two suppliers). The manufacturer orders Q1 units from Supplier 1 and Q2 units from Supplier 2 (where Q1 + Q2 = Q). The lead times for the two orders are normally distributed each having a mean of m. The time between two disruptions is an independently and identically distributed random variable with mean y and the duration of disruption remains constant (z units of time). In this model, if one supplier fails, the manufacturer, because it has a relationship with another supplier, can request inputs from the other supplier. We assume that, after the appropriate lead time, the second supplier will be able to supply the total quantity Q demanded by the manufacturer In the fourth model which we refer to as the combined model, a combination of RMI and SCRM is simulated by decreasing the length of the disruption if a disruption occurs (to simulate RMI) and by using two suppliers (dual sourcing). The input variables into this model are different from the inputs for models 2 and 3 to recognize the resource constraints of the manufacturer. Specifically, in model 2, a fixed resource α was incurred to secure financing to decrease the duration of the disruption to z/2. In model 3, the same fixed resource α was incurred to use two suppliers each having a lead time of m units. In this model, we use the same resource α and divide it between decreasing the duration of the disruption and increasing the number of suppliers. The length of the disruption is 0.75 z units of time. Two suppliers are used and each has a mean lead time of 1.33 m which results in a replenishment rate of 1.5µ. All four models are run for 1000 days and different operating characteristics for each model are recorded. We vary the expected number of days between disruptions and also the duration of disruption to examine which risk management solution is optimal based on a combination of both likelihood and severity of a disruption. In each case we determined the percentage of demand which is met with no wait, percentage of demand which is met after a wait and the percentage of demand which is lost (in other words, the percentage of shortage). The ranking of the models based on the maximum proportion of demand being met without wait and on minimum proportion of demand lost are the same. 7

9 Results We conducted simulation experiments for four different values of the average time between two successive disruptions, y. Specifically, we look at an average time between disruption of 20 days, 100 days, 200 days and 500 days. For each of these values of y, we varied the length or severity of disruption, z, from 0 days to the average frequency of disruption. For example if the average time between disruptions was 200 days, we examined disruption severities between 0 and 200 days. Full results of these simulations are given in the Appendix. We summarize these results in Table 1. Table 1 highlights which of the three policies, RMI, SCRM or the combined model yields the lowest shortage rates for different frequency and severity combinations. The first row of the table denotes the average frequency (time between disruptions), y. For each average frequency, the first column represents the number of days of disruption for the base model, and the second column gives the optimal policy (the policy that minimizes the percentage of customers whose demand is not met). Recall that if the disruption length in the base model is z =10 days, then the disruption length for the RMI model is z/2 = 5 days; the disruption length for the SCRM model is z = 10 days; and the disruption length for the combined model is 3z/4 = 7.5 days. Table 1 Summary of Results Average frequency 20 days Average frequency 100 days Average frequency 200 days Average frequency 500 days Disruption length, z (days) Best policy Disruption length, z (days) Best policy Disruption length, z (days) Best policy Disruption length, z Best policy 0 to 2 SCRM 0 to 11 SCRM 0 to 22 SCRM 0 to 46 SCRM 3 to 9 combined 12 to 42 combined 23 to 90 combined 47 to 230 combined 10 to 20 RMI 43 to 100 RMI 90 to 200 RMI 231 to 500 RMI From Table 1, we note that the optimal policy is a function of both the frequency and severity of disruption. When there is a low severity disruption that is the severity of the disruption is about 11% of time between disruptions - the SCRM model performs best. This is not surprising as this type of disruption is usually an operational disruption (process issues, lead 8

10 time variability, logistics issues) and supply diversification in practice performs best in these cases. For disruptions of moderate severity - when the length of the disruption is between 12% and 45% of time between disruptions - the combined model with supplier diversification and some RMI yields the lowest shortage rates. For catastrophic disruptions - when the disruption lengths are long and are over 50% of time between disruptions - the pure RMI model works best. This is similar to what is observed in practice. For catastrophic losses, firms typically use loss financing and not operational measures to ensure survival. Resilience is more important than robustness for catastrophic losses. In terms of developing a comprehensive supply chain risk management strategy, we are not suggesting that companies choose one solution and ignore the others. In practice, companies expect to have some frequent, low severity disruptions for which their best response is to increase robustness. For medium frequency and severity events, a firm will undertake both RMI and SCRM. For the very low probability, catastrophic losses, contingent financing is the best solution. Because contingent financing is most valuable for long disruptions, this provides guidance to firms in crafting their contingent capital arrangements. Conclusion and Future Work This paper develops a supply chain simulation model to examine the impact of supply chain disruptions caused by accidents, logistical or labour issues, man-made or natural catastrophes, on a manufacturer s ability to satisfy retailer demand. We examine the impact of, and trade-offs between, SCRM solutions and RMI solutions on a firm s ability to minimize the sales lost due to a supplier disruption. Our results show that the solution is a function of both the frequency of loss (length of time between disruptions) and the severity of loss (length of disruption). As in practice, we find that SCRM solutions, such as dual sourcing, are optimal when the duration of disruption (severity) is low and arranging loss financing (RMI solution) is optimal when the duration of disruption is expected to be high. For moderate severity, a combination of SCRM and RMI minimizes the percentage of loss sales. Because this work is preliminary, there are many avenues of exploration available that we identify below. The analysis presented here does not incoproate any cost analysis as the costs for RMI and operational risk management are industry specific. Using a cost model makes it 9

11 difficult to quantify lost sales or waiting time costs. Future work will include building a better model of the trade-offs (e.g. budget constraint) between SCRM and RMI expenditures. An examination of firms that have survived catastrophic failures within the supply chain also suggests that there is a role for ex post loss reduction measures. Future models will attempt to model this explicitly. We also expect that the trade-off between ex ante and ex post expenditures is a function of the ability of the manufacturer to rebuild customer loyalty after a disruption. Thus our future work will incorporate customer (including retailer) loyalty strategies that manufacturers can use in order to reduce losses from supply chain disruption. We will undertake a qualitative study of customer loyalty under supply disruptions and identify possible strategies for customer retention. By integrating the traditional risk management and insurance literature with operations management models, we are able to provide insights into the challenges associated with supply chain risk management. 10

12 Figures Figure 1 - Supply Chain with Supplier, Manufacturer and Retailer Retailer Manufacturer Supplier Figure 2 Reordering Criteria for Manufacturer and Retailer 11

13 References Ai, J., Brockett, P. L., Cooper, W. W., & Golden, L. L. (2012). Enterprise Risk Management through Strategic Allocation of Capital. Journal of Risk and Insurance 79(1): Barry, J. (2004). Supply Chain Risk in an Uncertain Global Supply Chain Environment, International Journal of Physical Distribution & Logistics Management 34(9): Bernes, B. and Khan, O (2007).: Risk and Supply Chain Management: Creating a Research Agenda, The International Journal of Logistics Management 18(2): Bolgar, Catherine (2011). Insights: Supply Chain Risk. Zurich Insurance Company. Retrieved from 0Chain/Insights%20Final%201%2024%2011.pdf. Business Continuity Institute (2010). Supply Chain Resilience 2010: BCI Survey of Resilience Professionals. Available on-line at Cavinato, J.L. (2004). Supply Chain Logistics Risks: From the Back Room to the Board Room, International Journal of Physical Distribution & Logistics Management, 34 (5): Christopher, M., U. Juettner, H. Peck (2003). Supply Chain Risk Management: Outlining an Agenda for Future Research, International Journal of Logistics: Research & Applications 6(4): Christopher, M. and H. Lee (2004). Mitigating Supply Chain Risk through Improved Confidence, International Journal of Physical Distribution & Logistics Management, 34(5): Christopher, M., and H. Peck (2004). Building the resilient supply chain. International Journal of Logistics Management 15(2): Deleris, L.A. and F. Erhun (2005). Risk Management in Supply Networks Using Monte-Carlo Simulation. In: Kuhl, M.E., Steiger, N.M., Armstrong, F.B., Joines, J.A. (Eds.), Proceedings of the 2005 Winter Simulation Conference. Institute of Electrical and Electronics Engineers, Inc, Piscataway, New Jersey, pp Dong, L. and B. Tomlin (2012). Managing Disruption Risk: The Interplay Between Operations and Insurance, Management Science. Articles in Advance: Hendricks, K., and V. Singhal (2005). Association Between Supply Chain Glitches and Operating Performance Management Science 51 (5): Hoyt, R.E. and A.P. Liebenberg (2011). The Value of Enterprise Risk Management. Journal of Risk and Insurance 78(4):

14 Kleindorfer, P. R. and G. H. Saad (2005). Disruption Risk Management in Supply Chains, Production and Operations Management 14: Kleindorfer, P. R. and L. Van Wassenhove (2004). Risk Management in Global Supply Chains; in H. Gatignon, J. Kimberly (eds.), The Alliance on Globalization, Cambridge University Press, chapter 12. McShane, M.K., A. Nair, and E. Rustambekov (2011). Does Enterprise Risk Management Increase Firm Value? Journal of Accounting, Auditing and Finance 26(4), Pagach, D. and R. Warr (2011). The Characteristics of Firms that Hire Chief Risk Officers. Journal of Risk and Insurance 78: Peck, H. (2005). Drivers of Supply Chain Vulnerability: An Integrated Framework, International Journal of Physical Distribution & Logistics Management, 35(4): Schmitt, A.J., L.V. Snyder and Z.J.M. Shen, Z (2011). Centralization Versus Decentraliza- tion: Risk Pooling, Risk Diversification, and Supply Chain Disruptions. Working Paper, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA. Spekman, R. and E. Davis (2004). Risky Business: Expanding the Discussion on Risk and The Extended Enterprise. International Journal of Physical Distribution & Logistics Management 34 (5): Tang, O., and S.N. Musa (2011). Identifying Risk Issues and Research Advancements in Supply Chain Risk Management, International Journal of Production Economics 133: Tomlin, B. (2006). On The Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks, Management Science 52(5): Towill, D.R. (2005). The Impact of Business Policy on Bullwhip Induced Risk in the Supply Chain, International Journal of Physical Distribution and Logistics Management, 35(8): Zipkin, P. (2000) Foundations of Inventory Management. McGraw-Hill, New York. Zsidisin, G.A., L.M. Ellram, J.R. Carter and J.L. Cavinat (2004). An Analysis of Supply Risk Assessment Techniques, International Journal of Physical Distribution & Logistics Management 34(5): Zurich Financial Services Group and Business Continuity Institute (2012). Supply Chain Resilience 2011 Study. 13

15 Appendix The tables in the appendix provide the detailed support for Table 1 in the body of the paper. Appendix Table 1, Appendix Table 2, Appendix Table 3, and Appendix Table 4 detail the percentage of demand that is lost for various different lengths of disruption, for each of the four models, when the average time between disruptions are 20 days, 100 days, 200 days and 500 days respectively. The first column in each of the tables below gives the disruption length, z, for the base model. Recall that implementing SCRM does not change the length of the disruption. Using RMI alone reduces the length of disruption in half, and using a combination of SCRM and RMI reduces the length of the disruption from z to 3z/4. For example in Appendix Table 1, the last row is the case where the length of the disruption, z is 15 days for the base model and the SCRM model; the disruption length is days for the combined model and the disruption length is 7.5 days for the RMI model. In each of the 4 tables, the maximum shortage rates is the least for the RMI model, and then the combined model, followed by the SCRM. The greatest variability in shortage rates is for the base model. In each of the tables, we highlight the policy that minimizes the shortage rate for the given frequency and severity combination. The first column in Table 1 is created by identifying the best policy for different lengths of disruption in Appendix Table 1. For example, when the disruption length, z, is 10 days, the best policy is RMI. Columns 2, 3 and 4 in Table 1 are created in a similar fashion from Appendix Table 2, Appendix Table 3, and Appendix Table 4 respectively. 14

16 Appendix Table 1 Average Time between Disruptions is 20 days Percentage of time demand from retailer is lost Disruption Base Model SCRM Combined RMI Length, z (in days) Appendix Table 2 Average Time between Disruptions is 100 days Percentage of time demand from retailer is lost Disruption Base Model SCRM Combined RMI Length, z (in days)

17 Appendix Table 3 Average Time between Disruptions is 200 days Percentage of time demand from retailer is lost Disruption Base Model SCRM Combined RMI Length, z (in days) Appendix Table 4 Average Time between Disruptions is 500 days Percentage of time demand from retailer is lost Disruption Base Model SCRM Combined RMI Length, z (in days)