THE IMPACT OF LOCAL DECISION

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1 Eindhoven, November 2014 THE IMPACT OF LOCAL DECISION MAKING IN A PHARMACEUTICAL SUPPLY CHAIN by E.J.W. van Schijndel BSc. Industrial Engineering & Management Science Student Identity Number in partial fulfilment of the requirements for the degree of Master of Science in Operations Management and Logistics Supervisors Dr. M. Slikker, Eindhoven University of Technology Ir. Dr. S.D.P. Flapper, Eindhoven University of Technology

2 TUE. School of Industrial Engineering Series Master Theses Operations Management and Logistics Subject headings: supply chain management, local decision making, pharmaceutical industry, dual sourcing

3 ABSTRACT This report addresses the impact of local decision making, in the case where a pharmaceutical manufacturer has one internal supplier and one local external supplier. This is based on a case study within a pharmaceutical company, which we will call PharmInc. There are three myopic mathematical models described to analyze the decision making. One model uses the decisions as they are made at the moment within PharmInc, one model optimizes the KPIs of the manufacturer and the last model optimizes the KPIs of the whole company. The KPIs considered are profit and working capital. For the situation that we researched, we showed that when the manufacturer only regards his own KPIs, it is optimal to source more at the external supplier than the internal supplier, which causes a high stock build-up at the internal supplier. However, when the KPIs of the company as a whole are regarded, the decision making changes to ordering more from the internal supplier than the external supplier. Cost savings can be made for the company as a whole by providing incentives for the manufacturing part of the company that bring the local decision making closer to the centralized decision making. I

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5 MANAGEMENT SUMMARY In this report the results are presented of a master thesis project conducted within a pharmaceutical company, which we will call PharmInc. INTRODUCTION The supply chain under investigation is that of the intermediate product A that is produced in plant X. Plant X produces product A on full capacity. After production product A is sold to external customers or shipped to two internal plants, Y and Z. Plant Y is located in the same continent as plant X, whereas plant Z is located overseas. Here product A is turned into the end-product B. Plant Z in also has the possibility to source product A at an external supplier in the same country, since the production in plant X is not enough to supply the three parties fully (see Figure 1). Figure 1. Supply Chain product A PROBLEM STATEMENT The research focused on the local decision making that seemed to exist within this supply chain. PharmInc has implemented a decentralized control of the supply chain by dividing PharmInc into regional Business Units (BUs), who have their own target on EBITDA, working capital and investments and their own profit and loss statement. Plants X and Y belong to the same BU and plant Z belongs to a different BU. The personal targets and premiums for people working within these BUs are mostly based on the performance of their BU. The people in these BUs therefore have incentives to optimize locally. One example of this local optimization within the supply chain under investigation is the decision of plant Z to order a lower amount of product A at the end of the year in order to reach their target on on-hand inventory plus goods in transit of product A. It is not clear however how large the impact exactly is of the local decisions that are made within the product A supply chain on the performance of the business units and PharmInc. This results in the following main research question. III

6 What is the impact of local decision making within the product A supply chain on the performance of the business units and the whole company, as measured by the key performance indicators, and in which ways can this impact be mitigated? MATHEMATICAL MODEL To answer this question and in order to be able to quantify the impact of the local decision making, we developed a mathematical model. In this mathematical model we focused completely on the decisions that are made in plant Z, because based on a continuous full production in plant X this is the stock point where the inventories of the whole system can be lowered by smart external sourcing. We also saw in the problem statement that plant Z has some incentives to make local decisions. Plant Z has two suppliers of product A: plant X and an external supplier S. For the demand that has to be satisfied in a certain month, they can use both these suppliers. Therefore there are two decisions that we consider in the models: 1. The quantity sourced from plant X, arriving two periods later. 2. The quantity sourced from an external supplier S, arriving one period later. To be able to compare different ways of decision making, we developed three different models. Model 1: As-is One model takes the decisions as close to how the decisions are made within PharmInc at the moment. We have two variants of this model. One variant is that all the decisions are taken the same in every month. The other variant is that the decision in December changes in order to reach the target put on on-hand inventories plus goods in transit. This second variant is called Model 1 December. Model 2: Optimized, local The second model focuses on the decisions in order to optimize the KPIs of plant Z. Again we have two variants. The first takes the decisions every period in order to minimize the costs of plant Z, whereas in the second variant the decisions change in November and December in order to reach the target in December. This second variant is called Model 2 December. Model 3: Optimized, central The third model focuses on the decisions in order to optimize the KPIs of PharmInc. For this model we only have the variant in which the decisions are taken every period in order to minimize the costs. It does not make sense for PharmInc to alter their decision in December. RESULTS To quantify the impact of the decision making structures, we used simulation using Visual Basic for Applications in Excel. After simulation of the models we could compare the different ways of decision making. We analyzed both the impact of the local versus centralized decision making and the impact of the different decision in December. The costs are given as averages per year, whereas the stock height is given as average per month. IV

7 IMPACT OF LOCAL DECISION MAKING From Table 1 we can see immediately that it is far more optimal for plant Z to follow their own KPIs (Model 2) than the decision making of Model 1 and Model 3. The huge decrease in average inventories and inventory related costs are due to the fact that they order only a small amount of their product A in plant X. This results in a large build-up of stock in plant X, which can be seen by the high costs for PharmInc that are shown in Table 2 under Model 2. The higher total cost per year of Model 1 compared to Model 3 for both plant Z and PharmInc is mostly due to a better sourcing strategy for the externally sourced product A. From the fact that Model 1 has the highest total costs and inventory related costs for plant Z and PharmInc, we can conclude that the ordering policy used in PharmInc at the moment is not cost optimal for plant Z nor PharmInc. Table 1. Cost and OWC plant Z of Model 1 versus Model 2 versus Model 3 Model 1 Model 2 Model 3 Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 161,826 67, ,642 Table 2. Cost and OWC PharmInc of Model 1 versus Model 2 versus Model 3 Model 1 Model 2 Model 3 Total cost per year of PharmInc 100 8, Inventory related costs PharmInc , Average stock height PharmInc 161, ,517, ,160 IMPACT OF DIFFERENT DECISION IN DECEMBER When we look at the cost of plant Z it looks like the average total costs per year of Model 1 and Model 1 December are similar (see Table 3). However there is a relatively small increase in Model 1 December of 0.004% compared to Model 1. This small increase allows them to reach their target in December 90.7% of the times instead of 2.5% of the times. Interestingly, the focus on stock height in Model 1 December actually causes the average stock height of plant Z to be higher than in Model 1. Table 3. Cost and OWC plant Z of Model 1 versus Model 1 December Model 1 Model 1 December Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 161, ,029 The impact on PharmInc is larger than the impact of plant Z. We can see in Table 4 that the different decision in December gives relative extra total cost for PharmInc of 0.24 per year. This is mainly caused by the extra holding cost of one period in plant X over the amount that is not ordered in December. Again the target has a negative influence on the stock height. Besides the extra on-hand inventory in plant Z, we also have extra inventory in plant X. V

8 Table 4. Cost and OWC PharmInc of Model 1 versus Model 1 December Model 1 Model 1 December Total cost per year of PharmInc Inventory related costs PharmInc Average stock height PharmInc 161, ,628 The impact of the decision in December becomes more extreme because of a higher supply in December. This higher supply is caused by an on average lower order from plant Y and no orders from external customers. The higher supply in December has a big impact on the average on-hand inventory of both Model 1 and Model 1 December, since it takes a long time after this high supply to get on the regular on-hand inventory level again. Therefore we also considered steady supply in December, which means it has the same probability distribution as the rest of the year. When we look at Figure 2 we can see the impact of the different decision of December in Model 1 December more clearly with the steady supply. We scaled the y-axis in order to show the increase better, so note that it does not start at 0. We see that the average on-hand inventory of Model 1 is approximately the same in every period, the small differences are caused by the stochastic nature of the supply and the demand. In Model 1 December we see a decrease in average on-hand inventory in February and an increase in March, where the on-hand inventory becomes higher than that of Model 1. This difference with Model 1 becomes smaller every period, but does last until January. This lasting difference leads to an overall higher average on-hand inventory for Model 1 December compared to Model Average on-hand inventory plant Z per month Model 1 Model 1 December Figure 2. Average on-hand inventory of Model 1 versus Model 1 December with steady supply CONCLUSIONS & RECOMMENDATIONS A striking conclusion that can be drawn from the results shown here is that the target on stock height actually has a counterproductive effect, resulting in a higher average stock height. Considering the impact on plant Z of this decision in the situation as-is, we saw that the costs and stock height went up. It did however cause an improvement of reaching the target in December from 2.5% to 90.7%, with only VI

9 a small increase in the costs. For PharmInc the impact is much larger, the target on stock height causes higher costs because of extra stock in plant X for one period. 1 The impact for PharmInc when plant Z only focuses on their own KPIs is very large. A huge stock build-up in plant X is the consequence of this ordering policy, since plant Z order less than a quarter of their demand to product A in plant X. However, to focus on their own KPIs is by far the most optimal option for plant Z, because it leads them to reducing their inventory related costs and average stock height by more than half when comparing it to the other ways of decision making. We can also look at this the other way around: it costs plant Z more than double to make their decisions based on the KPIs of PharmInc. Based on the results and the conclusions we have the following recommendations for PharmInc to mitigate the impact of local decision making: Remove the target on the on-hand inventory plus goods in transit for plant Z, because plant Z can hardly influence this. Focus more on the external sourcing strategy of plant Z, in order to make sure plant Z tries to optimize the part of their costs and working capital which they can influence. In order to do so we propose a target on the part of on-hand inventory that is externally sourced. The exact height of this target needs further research. Provide a more steady supply to plant Z, especially at the end of the year, because this will reduce the impact of the local decision making in December. This can be done by reviewing the decision making of plant Y. It is also beneficial to sell more to external customers, this increases the profit and decreases the total stock in the product A supply chain. Evaluate whether the whole amount available should be shipped from plant X to plant Z, because unnecessary high amounts shipped from plant X to plant Z cause higher costs. This is especially beneficial for plant Z, but also gives plant X the opportunity to respond to changing demand of plant Y or external customers. Use an internal transfer price for the evaluations of the performance of the business units. Important remark is that in order to do so, PharmInc needs two different ways of bookkeeping which causes an extra administrational burden. Another option is to use a lower price for product A sourced at plant X when plant Z makes their business cases regarding product A. If they base their decisions on the business case with this lower price, their decisions will be likely to be closer to the central optimum. 1 All results should be interpreted with the assumptions that are made in mind. The assumptions are summarized in Appendix D. VII

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11 ACKNOWLEDGEMENT This thesis marks the end of my master Operations Management & Logistics at the Eindhoven University of Technology. Therefore I would like to express my gratitude towards some people that have helped me during my thesis and during my whole student life. I would like to start with expressing my gratitude to my first supervisor Marco Slikker. I deeply appreciate the time he took for me, his critical feedback and especially his approach towards me and the project that made sure I kept making progress. Also many thanks to my second supervisor Simme Douwe Flapper for his structured, critical, and useful feedback. Furthermore I want to thank my supervisors and colleagues from the company I had the opportunity to conduct my master thesis. I am grateful to have been given this opportunity, especially because it gave me a valuable insight in the corporate world and their business way of thinking instead of the scientific way that we are taught during our studies. Since this thesis marks the end of my years as a student, I also want to take the time to thank some of the people that made my years as a student a time I will never forget. I want to thank all my friends for making my time as a student much fun. I will cherish the memories I made with you for the rest of my life. Most of the best memories of my student life were in some way a result of joining E.S.C. Most notably the memories I made with the girls of Briljant, who made me feel at home in Eindhoven from the start and have taught me more about myself than I will ever admit. I am also very grateful to have been involved in the relocation project and even more so to have done that within a board that could not have been better. Senaat 54, thank you for everything. Until this day I cannot think of another group with who I m able to spend a full year within 16 square meters and still want to see them after. Furthermore I want to thank my parents Coby and René, who have supported me in every choice I made and for giving me my whole life the freedom to do what I thought was right. I want to thank my brother Thomas for always giving me his honest and often blunt opinion, and for providing a home where I could finish my thesis. Last but certainly not least I also want to thank Daniel for his patience and for always finding a way to make me smile. Emmy van Schijndel Oisterwijk, 2014 IX

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13 TABLE OF CONTENTS Abstract... I Management Summary... III Introduction... III Problem statement... III Mathematical model... IV Results... IV Impact of local decision making... V Impact of different decision in December... V Conclusions & Recommendations... VI Acknowledgement... IX 1. Introduction Product A Specifications Supply chain description Thesis outline Problem Statement Example of local optimization Problem statement Research design Research questions Research deliverables Methodology Research methods Literature review Pharmaceutical and process industry Optimization of global supply chains Issues of global supply chains Advantages of a global supply chain Strategic and tactical optimization Coordination of global supply chains XI

14 Perspective of coordination Alignment of incentives Two supplier models Deterministic lead times Forecast updates Mathematical model Notation Order of events Relations between inventories Demand parameters Supply from plant X Minimum supply from plant X Key performance indicators Profit Operating Working Capital Three different models Model 1: As-Is Decision QtSZ Decision QtXZ Model 2: Optimized, Local Decision QtSZ Decision QtXZ Model 3: Optimized, Central Production decision plant X Decision QtSZ Decision QtXZ Determination of parameters Input parameters Supply from plant X Minimum amount from plant X Demand in plant Z Cost parameters XII

15 Price per kilo product A at supplier S Price per kilo product A at plant X Relevant unit cost order supplier S in period t Relevant unit cost order plant X Transportation cost Holding cost Penalty cost plant Z Overview of parameters Simulation of the models Validation & Verification Conceptual model validation Model Verification Operational validation Data validity Input Execution Accuracy of the simulation Output Output costs Output inventory level Results Impact of different decision making Impact of the target in December Focus on OWC Model Model Model Steady supply from plant X Sensitivity analysis Conclusions and Recommendations Conclusions & Recommendations Impact of decisions based on reaching the target of December XIII

16 Impact of decisions to optimize KPIs of plant Z Recommendations to mitigate impact Academic relevance Suggestions for further research Bibliography Appendix A: List of abbreviations Appendix B: List of figures Appendix C: List of tables Appendix D: List of assumptions Appendix E: Finding the minimum of cost function QtXZ Appendix F: Distribution of Dt, t + 1 and Gt + 2 1pZpZ + hz Appendix G: Demand data from plant Y Appendix H: Normality tests demand from plant Y Appendix I: Demand data external customers Appendix J: Normality tests demand external customers Appendix K: Data minimum supply from plant X Appendix L: Historical costs of externally sourced product A Appendix M: Historical data product A demand in plant Z Appendix N: Normality tests demand parameters plant Z Appendix O: Overview parameters Appendix P: Operational Validation Appendix Q: Sensitivity analysis holding cost rate XIV

17 1. INTRODUCTION In this report the results of a master thesis project and is aimed at local decision making within a pharmaceutical supply chain. This chapter will introduce the supply chain under investigation and the outline of this report. It is based on a case study within a pharmaceutical company that we will denote with PharmInc PRODUCT A The focus of this research will be on the supply chain of the intermediate product A SPECIFICATIONS Product A is an intermediate for producing product B, the end product for PharmInc. There are three different types of product B made: B1, B2 and B SUPPLY CHAIN DESCRIPTION Product A is produced in a plant in county X. Plant X produces product A on full capacity. Product A is produced via a process that is very difficult and expensive to stop. Also the fixed cost of plant X are high, therefore plant X produces as much product A as they can. This production is quite stable over the months. Table 5. Overview of locations and products Country X Y Z Plant X Y Z Products produced A B1, B2 and B3 B1, B2 and B3 In the plants in country Y and country Z product A is turned into one of the products B. Plant Y is located on the same continent as plant X. Plant Z is located overseas. Product A is shipped from plant X to Plant Y, plant Z, and third party customers who also make product B. Plant Z also sources from an external supplier in the same country (see Figure 3). An overview of the plants and what they produce is given in Table 5. There is a priority in shipping product A to the different parties. Because plant X is the only supplier of plant Y, plant Y has the first priority. After plant Y the external customers are supplied, because selling product A to external customers instead of supplying plant Z results in a higher profit and a lower operating working capital (OWC) for PharmInc. The remaining product A, with exception of some safety stock, is supposed to go to plant Z. The global planner of product A will determine this quantity each month and communicate this to plant Z. Plant Z then books the order and the quantity is shipped. Without this booking confirmation, plant X cannot send any product A to plant Z. Usually plant Z orders the amount that is available for them. In general this amount is lower than the total amount needed in plant Z, so they also need to order product A at an 1

18 external party, which is based in the same country Z. It is not possible for plant Z to order more product A at plant X than the amount available for them. Figure 3. Supply Chain product A 1.2. THESIS OUTLINE The first chapter provided the introduction to the supply chain under investigation. In Chapter 2 we will further investigate the problem by stating the problem and giving an example of local optimization. Based on this information the research design is developed in Chapter 3. A literature review of relevant literature is given in the Chapter 4. Mathematical models to be able to calculate the costs of the decisions made within the supply chain under investigation are developed in Chapter 5. We estimate the parameters that are specified in these models in Chapter 6. In Chapter 7 the results of the simulation of the mathematical models are given. Finally in Chapter 8 the conclusions and recommendations based on the outcomes of the simulations will be stated. 2

19 2. PROBLEM STATEMENT In this chapter we will give an example of the problem within the product A supply chain and introduce the problem statement. PharmInc has implemented a decentralized control of the supply chain by dividing their business into regional BUs, who have their own profit and loss statement and targets on EBITDA, working capital and investments. The personal targets and premiums for people working within these BUs are mostly based on the performance of their own BU. Therefore the people in these BUs have incentives to optimize locally. Since plant X and Y reside in the same continent and plant Z overseas, they belong to different BUs. One example of this local optimization is given in the next section EXAMPLE OF LOCAL OPTIMIZATION One situation where a business unit is focusing on their own targets instead of the benefit of the whole company arises at the end of the year. At that moment the BUs are trying to meet their targets, one of these targets is put on the operating working capital (OWC). One way to lower the OWC is by having less stock of intermediates and finished products. It can be seen clearly that BUs steer on this target when looking at the demand of plant Z for product A in Plant X communicates the amount of product A that is available for plant Z well in advance. Plant Z then plans on the amount of product A they have to buy from external suppliers. An order confirmation from plant Z is needed in plant X to send product A to plant Z. Without this confirmation it is not possible to ship product A. Normally plant Z orders the full supply that is available for them, but in 2013 at the end of the year we can see that plant Z orders a lot less than plant X has forecasted to supply them, see Figure 4. In this figure plant Z forecasted supply is the supply plant X planned for them, where plant Z actual demand is the actual order that plant Z placed. Forecasted supply versus actual demand plant Z 2013 Plant Z forecasted supply Plant Z actual demand Figure 4. Forecasted and actual demand of product A in plant Z over 2013 When the stock levels of both plant X and plant Z are compared, it is obvious that plant X is way over their target while plant Z just met their target, see Figure 5 and Figure 6. The stock of plant Z consists of

20 on-hand inventories plus the goods in transit (GIT) from plant X to plant Z. The stock of plant X only consists of their on-hand inventory. Stock development plant Z 2013 Stock plant Z Target stock plant Z Figure 5. Stock development of product A in plant Z over 2013 Stock development plant X 2013 Stock plant X Target stock plant X Figure 6. Stock development of product A in plant X over 2013 At first sight, this does not seem suboptimal for the whole company since the total stock level is the same whether the stock is in plant Z or plant X. The problem arises in the months after. To justify their decision to order less product A, plant Z showed a very low forecast on production of product B for the first quarter of the new year. When the quarter started, their actual production went up and they had to source additional product A locally since the lead time from plant X is 6 weeks. For example in the first three months of 2014, they used 45% more product A than forecasted in December A large part of this extra demand was sourced externally, the externally sourced amount of product A went up with 65%. Based on the large stock that is over target in plant X in November and December, it would have been possible to reduce the external sourcing with 40% for the first three months when all the stock that is over target in plant X was send to plant Z at the end of This leads to a decrease in the holding cost for PharmInc. A rough estimation with a cost price per kilo product A of 50 euros and holding/opportunity cost of 20% annually, this results in a loss of approximately 115,000 euros. Not only does this situation have a financial impact, it also causes friction between both BUs involved. The global planner who is in charge of product A already knows that this situation will happen again at the end of the year and this causes frustration even before the situation arises. 4

21 So despite of product A being available within the company it was in plant Z at the beginning of the year and thus could not be used. As a result a financial loss, frustration for the global planner and friction between the BUs is caused. This shows that the BUs can negatively influence the global central decision making, by providing information and making decisions that are only beneficial for their own BU PROBLEM STATEMENT In the example above we have illustrated the impact of the decision that was made by plant Z in December However, it is not clear how big the impact of this local decision making exactly is. Therefore we have the following problem statement: There is evidence that there is local decision making within the product A supply chain that is not optimal for PharmInc. At the moment it is however not clear what the impact of this local decision making on the performance of the business units and PharmInc exactly is. 5

22 3. RESEARCH DESIGN This chapter shows how the research is designed and which methodology is used to conduct the research RESEARCH QUESTIONS The following main research question can be derived from the described problem statement. What is the impact of local decision making within the product A supply chain on the performance of the business units and the whole company, as measured by the key performance indicators, and in which ways can this impact be mitigated? To answer the main research question, we have the following sub research questions: 1. Which model can be used to optimize the situation described in the problem statement? a. What is the supply chain structure of PharmInc? b. What is the scope of the optimization? c. Which performance indicators are important for PharmInc? d. What are the cost drivers for the supply chain? e. What are the decision variables? 2. What is the current performance of the situation described? 3. Given the model, what could be the optimal performance under decentralized control? 4. Given the model, what could be the optimal performance under centralized control? 5. What is the difference between (2), (3) and (4)? 6. Which measures can be taken to minimize the difference found in (5)? Question 1 will be answered in Chapter 5, questions 2 through 5 will be answered in Chapter 7 and finally question 6 and the main research question will be answered in Chapter RESEARCH DELIVERABLES The following deliverables are expected. 1. A model describing the situation 2. Outcome of how much cost reduction is possible by optimal set up 3. Measures to bring the current situation closer to the optimal situation METHODOLOGY The regulative cycle of van Strien (1997) follows five phases for a solution oriented project. These phases are problem definition, analysis, design, implementation and evaluation. For the design and implementation phase, the approach of Mitroff (1974, via Bertrand & Fransoo, 2002) is used which consists of the stages conceptualization, modeling, model solving, and implementation. The model of Mitroff is shown in Figure 7. 6

23 Figure 7. Model of Mitroff for research design (1974) In my research, the stages consist of the following: 1. Conceptualization Literature review Identification of variables that need to be included in the model 2. Modeling Define causal relationship between variables and formulate a quantitative model Build the model in a software program that can solve it Validate the model for the current situation 3. Model solving Collect real life data Solve model using these real life data for the decentralized and centralized case Implement measures and solve model again 4. Implementation Reflect on the outcomes obtained from the model and translate these outcomes into recommendations and insights for PharmInc and in general. When having completed the steps above, also the regulative cycle is completed RESEARCH METHODS We have used several research methods during this research. Desk research Relevant articles were reviewed in Van Schijndel (2014). Furthermore documents of PharmInc are used to get insights in the supply chain structure, the ordering behavior and the costs that are used within PharmInc. 7

24 Interviewing Unstructured interviews were held, first to gain more knowledge about the company and to scope the research. Hereafter more unstructured interviews were held in order to gain more specific knowledge of PharmInc, the product A supply chain and the cost structure within PharmInc. Mathematical modeling and simulation All the information gained from desk research and interviews was turned into mathematical models. The outputs from the simulations of the models are used to derive conclusions and recommendations. 8

25 4. LITERATURE REVIEW In preparation of this thesis, relevant academic literature was reviewed in Van Schijndel (2014). A short summary of this literature review is given below. Also a part is added on two-supplier models, since we see this structure in the product A supply chain PHARMACEUTICAL AND PROCESS INDUSTRY The process industry is characterized by chemical or biological processes, rather than the assembly of different parts as with discrete manufacturing. The outcomes of the processes are usually bulk quantities instead of countable units. Typically, because of the process, the product cannot be disassembled back into its raw materials. The pharmaceutical industry is a subcategory of process industries. In the pharmaceutical industry the process is used to make medicines. There are several distinct features of the pharmaceutical industry that distinguish the pharmaceutical products from products in other chemical process industries: Related to development there are high cost and low success rates, there is much time and money concerned with clinical trials, the industry is heavily regulated with differences across nations and regions, there is limited shelf life due to deterioration, the length of manufacturing time is on the high end of the average process industry manufacturing time, up to 6 to 9 months, often there is a global business structure, and generic competition arises when a patent expires (Laínez, Schaefer, & Reklaitis, 2012). There is also a specific structure in the production of pharmaceuticals. Companies are typically divided into primary and secondary producers. The primary producers are responsible for manufacturing the active pharmaceutical ingredient (API). The production of API involves chemical synthesis and separation stages and/or biochemical processes. These processes are often defined by long processing times and extensive inventories in between the stages. This primary manufacturing step is seen as the most valueadding step. Secondary producers are involved in turning the API into the final product, which usually also includes packaging. The manufacturing locations are often geographically dispersed around the world. One of the operational issues has to do with this division of primary and secondary producers. The customer end, at the secondary producer, is a typical pull process, driven by the customers demand. As the primary producers have long production cycle times, it is difficult to ensure the responsiveness to the pull process. This causes the primary manufacturer to work with a push process, driven by medium and long-term forecasts. This makes it difficult to respond to short term opportunities (Shah, 2004). In the last decade, there has been a growing interest in the specific issues that occur in the pharmaceutical industry. The research on the pharmaceutical industry is carried out from different academic perspectives, where SCM is the second most researched topic (Narayana, Pati, & Vrat, 2012). Narayana, Pati, & Vrat (2014) found that logistics management was the most researched theme within the Pharmaceutical Supply Chain area. Those studies mostly focused on optimization strategies across the pharmaceutical processes. Especially the uncertainty of clinical trials and their impact on capacity expansion decisions is researched. To make optimal use of the patent life span of a product and cope with the uncertainty in the best way, strategic decisions should be taken before the outcome of the 9

26 clinical trials, where tactical decisions should be taken after the outcome of the clinical trials. Decentralized control or coordination of a pharmaceutical supply chain is not found OPTIMIZATION OF GLOBAL SUPPLY CHAINS Since the pharmaceutical supply chain is typically a global supply chain, we have focused on the optimization of global supply chains ISSUES OF GLOBAL SUPPLY CHAINS Global supply chain models are more complex than the local supply chain models. The flow of information and money is much more important and difficult to coordinate. (Vidal & Goetschalckx, 1997). In a global supply chain the distances between the different facilities are also much larger. These geographic distances cause the transportation cost and the lead time to increase, which gives more complicated inventory cost trade-offs. The location of their customers and suppliers, the availability of inexpensive labor, and costs of transporting along diverse modes should also be considered ADVANTAGES OF A GLOBAL SUPPLY CHAIN There are also advantages of having a global supply chain. Setting up a global supply chain can minimize the landed costs of products which are delivered to different market locations, while keeping a high level of local customer satisfaction by maintaining close relationships with them. Furthermore a global supply chain can take advantage of the differences between the operational regions by recognizing and profit from differences in technology expertise, local tax rates, and labor costs. To benefit from these differences the supply chain must be effectively coordinated. Besides that, the enterprise must be flexible enough to respond to changes in the environment (Cohen & Mallik, 1997) STRATEGIC AND TACTICAL OPTIMIZATION Optimization can be done on a strategic, tactical and operational level. Here we will discuss the strategic and tactical optimization. The strategic decisions are made long term, two to ten years, and include where plants or warehouses should be opened or closed, which technologies to be employed, which suppliers to use, and the capacity of plants and warehouses. These decisions form the design of the supply chain network. The objective of the strategic decisions is to maximize total profit, including border crossing fees when operating a global supply chain (Goetschalckx & Fleischmann, 2005; Schmidt & Wilhelm, 2000; Vidal & Goetschalckx, 1997). The tactical decisions are less long term then strategic decisions, but take the design from the strategic level as a given. The tactical level consists of decisions on production levels at all plants, assembly policy, the inventory levels, and batch sizes. An example of a tactical decision is whether to produce large batches which are hold in central warehouses or to produce on demand at numerous locations. It is important to have some measure of customer satisfaction and feed this back to the strategic level, in order to improve the network design (Schmidt & Wilhelm, 2000) COORDINATION OF GLOBAL SUPPLY CHAINS Most optimization models assume that decision making within a supply chain is done centralized or hierarchically (Whang, 1995). In practice however, a supply chain consisting of several companies will 10

27 not have such a centralized decision-making function. Even when optimizing a supply chain consisting of one company, the different divisions can still have their own objectives and base their decisions on that. Therefore this chapter will investigate ways to coordinate the different entities in a global supply chain. Intra-firm coordination is the coordination between different divisions in a company. There is information sharing and transparency between the different divisions, but each division still has his own goals and a certain level of autonomy. Effective management of the coordination of activities throughout the intra-firm supply chain can result in lower distribution and production costs, tax minimization through transfer pricing and reduced currency risks by a combination of financial and operational hedging of these risks (Cohen & Mallik, 1997) PERSPECTIVE OF COORDINATION The literature describes three different perspectives that are used in optimization models. The first perspective is the single-person perspective. This perspective assumes that one person has all the information and is able to make all the decisions centrally for the company. The second perspective is the team-perspective, where there are multiple parties in an organization. Those multiple parties do share the same goal, but have limited information and actions and therefore need to coordination and communicate with each other to reach their shared goal. The team-perspective assumes full cooperation between the different parties. The last perspective is the nexus-of-contract perspective, which assumes each party tries to maximize its own objective. The research on this perspective mostly focusses on aligning the incentives of the parties with the global goal, for example by performance measurement schemes or transfer prices (Whang, 1995) ALIGNMENT OF INCENTIVES According to literature the incentive policy for a subsidiary should not be fully dependent on the enterprise wide result. It is suboptimal to tie the incentives of subsidiary management only to the consolidated profit. Since the consolidated profit consists of the subsidiaries as well as the parents profit, a subsidiary can free-ride on the achievements of the parent and other subsidiaries. It does not motivate them to improve their performance due to the fact they have little to no control over the other entities they are also rewarded on (Hyde & Choe, 2005). So the incentive policy should in some way be based on divisional results, or a combination of divisional and enterprise wide results. The divisional results are determined by rules that are set by the company. Thus a way of aligning the incentives is through a set of corporate rules. Such a set of rules is called a (performance) measurement scheme and includes transfer pricing, accounting methods and various operational constraints. Lee and Whang (1999) consider three properties to create a good performance measurement scheme. The first property is that the scheme must be cost conservative. It means that all costs must be traced back to individual sites and does not require any subsidies or taxes from the headquarters. The second property is incentive compatibility, which is at the core of a good performance measurement scheme. It says that under an incentive compatible scheme each manager finds it beneficial to pursue the optimal decision rules that are specified for the complete system. The last property is informational decentralizability. This ensures that the scheme can be implemented without information from other sites. 11

28 Transfer prices are one element of a performance measurement scheme. Lee and Whang (1999) give a quite straightforward rule for transfer pricing, where the transfer price is the same as the cost price. More elaborate rules on transfer prices are also discussed and we have found that there is a trade-off between the incentive and tax purpose of transfer pricing. To make optimal use of transfer pricing, it is best to use dual transfer prices, one for internal evaluation and one for tax purposes, and be very considerate about the rules tax authorities have enforced on transfer prices TWO SUPPLIER MODELS The supply chain under investigation is one with multiple supply options, when we look at the stock point of plant Z. Minner (2003) gives an extensive review on multiple-supplier inventory models. In these models the suppliers can have deterministic and stochastic lead times. The research on models that use deterministic lead times are focused on determining the optimal order policy or determine the optimal parameters for a given policy. The research on models with suppliers that have stochastic lead times focuses more on reducing the uncertainty of the lead times of arriving order. For this thesis we are interested in the part that describes single-stage inventory models with deterministic lead times. There is no literature found that focuses on the local decision making when there is one internal and one external supplier DETERMINISTIC LEAD TIMES Most models with deterministic lead times are restricted to a model with two suppliers, no setup costs per order and consecutive lead times. This means the difference in lead times is only one period. This is often even more reduced to a situation where there is a regular supply with a lead time of one period and an emergency supply who supplies instantaneous. Barankin (1961) formulates the problem for a given time horizon of T periods. Extensions of this model have been made by several authors. One extension that we are interested in is the extension with forecast updates made by Sethi, Yan & Zhang (2003) FORECAST UPDATES Sethi, Yan & Zhang (2003) make use of forecast updates in their two-supplier model. There is an initial forecast, which is the same for all periods. Before the decisions are made on the fast and the slow order an update on the forecast is received. After the decision another forecast is received which shows the actual demand. The fast order will arrive before the second update. They use a dynamic programming equation to calculate the cost over a time horizon T. They conclude that the optimal policy parameters for this problem are only dependent on the most recent forecast update and not the inventory position. 12

29 5. MATHEMATICAL MODEL In Chapter 3 we saw the impact of the order quantity decision that plant Z made in December In order to assess the decision making of plant Z in general, we have used a mathematical model to model the decisions of the amount to source at plant X and at the local supplier. In this way we can make general statements about the decision making and whether this negatively impacts the whole company. We will focus on the decisions that plant Z makes regarding the order quantities of product A, because based on a continuous full production in plant X, this is the stock point where the inventories of the whole system can be lowered by smart external sourcing. We also saw in Chapter 2 that plant Z has some incentives to make local decisions. Plant Z has two suppliers of product A: plant X and an external supplier in country Z. We will denote this external supplier with an S. For the demand that has to be fulfilled in a certain month, they can order from both of these suppliers. See Figure 8 for the part of the supply chain of product A that we are interested in for the mathematical model. Plant X The lead time from plant X to plant Z is approximately 6 weeks. In order to be able to work with whole periods (months) in the model, we change this lead time to 2 months. From the moment product A is ordered in plant X, it is counted as stock of plant Z. Plant Z has both a minimum and a maximum amount of product A that can be ordered from plant X. Supplier S The lead time from an external supplier in plant Z to the plant in plant Z is approximately two weeks. Again, to be able to work with full periods, we assume the lead time to be 1 month. We assume that they can order an unlimited amount from this supplier. Figure 8. Part of the product A supply chain under investigation 13

30 5.1. NOTATION Below in Table 6 the notation is given which is used throughout the models. Table 6. Notation Notation Description D r,t Demand forecasted in period r for period t in plant Z d t Realized demand in plant Z during period t = f t + r 1 2 t + r t F Random variable forecast plant Z, realization of this random variable in period t-2 is shown by f t GIT t Goods in transit (GIT) to plant Z at end of period t. Only the goods from plant X to plant Z are included in the GIT. h Z Holding cost on on-hand inventory and GIT of plant Z h X Holding cost on on-hand inventory of plant X IP t Inventory position of plant Z at end of period t. This consists of the on hand inventory plus the goods in transit. m XZ Minimal supply from plant X OH t On hand inventory in plant Z at end of period t. Backorders are not allowed so OH t 0 p Z Penalty cost on part of demand that cannot be fulfilled in plant Z SZ Q t Quantity sourced externally from supplier S at end of period t. This will be available at the beginning of period t + 1 XZ Q t Quantity shipped from plant X to plant Z at period t. This quantity will arrive at the beginning of t + 2 R 1 First update of the forecast f t, made in t-1. Realization of this random variable in 1 period t-1 is shown by r t R 2 Second update of the forecast f t + r 1 t, made in t to reveal the actual demand. 2 Realization that is made in period t is shown by r t XZ S t Available supply in period t from plant X to plant Z x + Max{0, x} 5.2. ORDER OF EVENTS We have the following order of events each period (t) in plant Z XZ SZ 1. The order from plant X Q t 2 and the order from supplier S Q t 1 arrive 2. Actual demand d t is revealed 3. Actual demand d t for the period is fulfilled 4. On-hand inventory OH t is calculated XZ 5. Plant X communicates the available supply S t 6. Demand forecasts are updated for next two periods: D t,t+1 and D t,t+2 SZ XZ 7. Decision is made on the order quantities Q t and Q t 8. Inventory position IP t is calculated The events are visualized on a timeline in Figure 9. 14

31 5.3. RELATIONS BETWEEN INVENTORIES Figure 9. Timeline and legend of events in plant Z The relations between the on-hand inventory and inventory position are shown below. Because we do not allow for backorders, all excess demand is lost and the on-hand inventory cannot be negative. OH t = (OH t 1 + Q t 2 + Q t 1 d C t ) + (5. 1) GIT t = Q XZ t 1 + Q t (5. 2) IP t = OH t + GIT t = (OH t 1 + Q XZ t DEMAND PARAMETERS + Q SZ t 1 d C t ) + + Q XZ XZ t 1 + Q t (5. 3) Because decisions on delivery quantities are made a maximum of two periods before the actual demand occurs, we are not interested in forecasts of the demand more than two periods ahead. The forecast that is made in period t-2 of the demand in period t is the realization f t of random variable F. The next period (t-1) we get more information on the demand, resulting in a forecast update r t 1, which is the realization of random variable R 1. Finally in period t when the demand has to be satisfied we get our last update to reveal the actual demand. This is forecast update r t 2, a realization of random variable R 2. 15

32 For now we assume all variables to be normally distributed and independent in order to be able to easily sum the random variables. We will later test the assumptions and fit a distribution to the random variables. The distribution of the random variables thus looks like this: F~N(μ F, σ F ) R 1 ~N(μ R 1, σ R 1) R 2 ~N(μ R 2, σ R 2) D s,t describes the probability distribution of the demand in period t with the information known at period s, with s < t. In case s = t it is not a probability distribution anymore, since the actual demand is known then. In Figure 10 we can see which information leads to which forecast distribution or actual demand. D t 2,t = f t + R 1 + R 2 ~N (f t + μ R 1 + μ R 2, σ 2 R 1 + σ 2 R 2) D t 1,t = f t + r t 1 + R 2 ~N(f t + r t + μ R 2, σ R 2) 5.5. SUPPLY FROM PLANT X Figure 10. Forecast updates The amount of product A that is available to ship from plant X to plant Z, S t XZ, plays a big role in the model. The supply from plant X to plant Z is usually known a few months ahead, for the planners in plant Z to know what to source externally. However, it is possible that this supply changes before the order decision is made. We assume here that the actual supply of period t is communicated in period t, before the decision is made on Q t XZ. We will later see which values this supply takes. The amount that plant Z orders less than S t XZ cannot be used to sell externally, since the demand of the external customers is already satisfied. Besides this we also assume that the demand for product A in plant Y and for external customers is never higher than the amount produced, so it will also not be used the next period to satisfy the demand. Therefore when plant Z orders less than the supply from plant X, the supply in the next period will be higher with the amount they have not ordered. 16

33 MINIMUM SUPPLY FROM PLANT X S XZ t = S XZ t + (S XZ t 1 Q XZ t 1 ) (5. 4) From product A there are three products made: B1, B2 and B3. B1 can be made from product A from plant X and from the local supplier. B2 and B3 can only be made with product A from plant X. Therefore we need a minimum supply of product A from plant X for these two products, which will be denoted by m DC. We will assume this is the same every period and hence not compensated if there s a high order from plant X a period before KEY PERFORMANCE INDICATORS There are two relevant key performance indicators (KPIs) for plant Z when it comes to ordering product A PROFIT For profit there are two measures that PharmInc uses. One is the EBITDA, the earnings before interest, tax, depreciation and amortization. The other is the net profit, so all costs are taken into account then. We will focus on the EBITDA here, so when mentioning profit this means the EBITDA. Profit always exists of two factors: revenue minus cost. When able to fulfill all demand, the revenue comes directly from the demand which is an external factor and not influenced by the decision on product A. When part of the demand cannot be satisfied, the missing revenue can be translated into penalty costs. This means that we can maximize the profit, by minimizing all relevant costs including the penalty costs OPERATING WORKING CAPITAL Another important performance measure is the Operating Working Capital, or OWC. This consists of the stock value plus accounts receivable minus accounts payable. In this research the payables and receivables are out of scope, thus we only consider the stock value of product A. Target on OWC There is a target on the stock height of product A at all the stock points. These targets are linked to personal incentives and are measured at the end of every quarter. However, we see clear evidence that the consideration to reach this target is particularly strong in December. Therefore we assume that the overall target is reached, when it is reached in December. Based on the information available within PharmInc we set the target to 140,000 kilos THREE DIFFERENT MODELS We are going to compare three different ways of decision making for plant Z: 1. As-is This reflects the way the decisions are made now, based on agreements that are made within PharmInc, for example on safety stock. 17

34 2. Optimized, local This reflects the way the decisions can be taken based on optimizing the KPIs of plant Z. With this model we therefore disregard the cost plant X has. 3. Optimized, central This model disregards the different business units and optimizes the KPIs of the whole company, so plant X and Z together. 18

35 5.8. MODEL 1: AS-IS In this model we try to stay as close to the decision making as it is done now within PharmInc DECISION Q t SZ Currently the decision on Q t SZ is made to get the expected on-hand inventory of the next period on a certain target or safety stock level. The safety stock level for product A in plant Z is decided upon to be 29,400 kilos. This means that they aim to have 29,400 kilos of product A on-hand at the end of period t+1. To reach this stock, the forecast of the demand in period t is used as if it was the real demand of period t+1. Formulation of problem Q t SZ influences the on-hand inventory of one period later, so t+1. We know the following relation for the on-hand inventory at period t+1: OH t+1 = (OH t + Q XZ t 1 + Q SZ t d t+1 ) + (5. 5) The forecast that is known at period t for period t+1 is used as if this was the actual demand of period t+1. This forecast has the value of f t+1 + r t+1, therefore the calculated on-hand inventory for period t+1 is as given in (5. 6). OH t+1 = (OH t + Q XZ t 1 + Q SZ t (f t+1 + r 1 t+1 ) ) + (5. 6) Outcome This on-hand inventory is brought up to 29,400 by ordering Q t SZ, this gives the following value for Q t SZ : Q CC 1 t = (29,400 + f t+1 + r t+1 OH t Q XZ t 1 ) + (5. 7) No real optimization is done here while making the decision, it is assumed that the target stock of 29,400 kilo is already chosen as to optimize the cost of plant Z. Also the stochastic nature of the demand is not taken into account DECISION Q t XZ As explained before, the site in plant X produces product A at full capacity and all stock that is remaining after supplying plant Y and external customers is supposed to go to plant Z. The agreement is made with plant Z to accept the amount that is available for plant Z from plant X. For reasons discussed earlier the decision on Q t XZ is not the same throughout the year. Although there is an agreement that plant Z should take all the supplies that comes from plant X (S t XZ ), they also have to consider their working capital and therefore their inventory position. We have seen that this consideration is stronger at the end of the calendar year, particularly in December. Since it causes a lot of tension between the business units, only in the last month of the year they order less than what is supplied from plant X. 19

36 Formulation of problem As we stated before, the agreement within PharmInc is to order everything that plant X can supply to plant Z. At the end of the year, plant Z puts their own targets on operation working capital above the interests of PharmInc. This results in a different decision in the month December. When they reach the target there is a personal incentive placed upon reaching this target. We assume that it does not matter how far below the target they are in order to get the incentive. Therefore we assume that the target is reached XZ XZ when the on-hand inventory plus outstanding orders Q 11 and Q 12 is below or on 140,000 in December. Q XZ 12 = (140,000 OH 12 + Q XZ 11 ) + (5. 8) And the supply restrictions still hold: m XZ Q DC XZ 12 S 12 (5. 9) When the amount needed to stay under the target is higher than the supply, the decision will be the same as the rest of the year. Usually this is not the case though. We assume that the personal incentive is that important, that the decision will always be made to stay under target unless it is not enough to satisfy the demand for products B2 and B3, which can only be made with product A from plant X. Outcome This makes the decision throughout the year (t 12): Q XZ XZ t = S t (5. 10) XZ The ordered amount in December Q 12 will be the following: Q XZ 12 = Min{Max{m XZ, (140,000 OH 12 Q XZ 11 ) + }, S XZ 12 } (5. 11) 20

37 5.9. MODEL 2: OPTIMIZED, LOCAL In this model we look at the decisions plant Z would make if they are only optimizing their own KPIs. The KPIs profit and OWC are not necessarily aligned. When aiming for low stocks and therefore low OWC, the probability of being out of stock is higher which can lead to higher costs and therefore lower profit. We assume that profit is most important throughout the year, and OWC only plays a role in December. That OWC only plays a role in December is a result of the personal premium that is connected to reaching the target on OWC in December. Throughout the year the focus is more on having a sound BU with resulting profit. We saw in the literature that for a model with a constant forecast and forecast updates there is an optimal ordering policy for the two-supplier model over a certain horizon. Since we want to use forecasts that are not the same in every period, to better represent the ordering policy of PharmInc, we cannot use this model. Therefore, we propose a myopic model that optimizes the costs over 1 period for the decision Q t SZ and two periods for Q t XZ. We made some assumptions to be able to use this myopic model. These assumptions are provided throughout this report and summarized in Appendix D DECISION Q t SZ We saw in our first model that the optimization of this order quantity is done by setting a target level on on-hand stock. In this model, we do not set a fixed target level, but use the KPIs to find the optimal onhand stock target. The KPIs of plant Z were profit and OWC. With the decision on Q t SZ we have chosen to only focus on the profit and not to incorporate OWC. Because the decision on Q t SZ only influences the on-hand inventory it would be the same as using an extra penalty on the on-hand inventory, resulting in higher holding cost. By varying the holding cost rate we can also imitate the importance of OWC during the year. Therefore we use an objective function that maximizes the profit of plant Z and thus minimizes the relevant costs for the decision Q t SZ. Relevant costs are in this case the costs that are influenced by the decision on Q t SZ. Cost function Q t SZ We assume that product A is maximum one period on-hand if it is not used immediately after delivery. In other words, the amount of product A on-hand at the end of period t+1, will be used by the end of period t+2. During the simulation of the model we will see whether this assumption is justified. This is the case when the end on-hand inventory is always lower than the demand of the next period. The penalty cost for ordering not enough product A from the external source is always incurred only once. Since we do not allow for backorders, it is not possible that the backorder of period t+1 is still there at period t+2. When we assume that the inventory is not carried over for more than one period, we can use a myopic model that only considers the costs that are made at period t+1. This results in a newsvendor problem, 21

38 where the selling season is period t+1 and all cost are incurred at the end of this period. The relevant cost when making the decision on Q t SZ are the holding costs of on-hand inventory at the end of the next month and penalty cost for being out of stock. This is denoted with h Z and p Z respectively. The objective when ordering Q t SZ is to minimize the expected value of these costs of period t+1. The expected costs at the end of period t+1 are denoted by the following cost function. E[Cost SZ t+1 ] = (h Z E[(OH t + Q XZ t 1 + Q SZ t d t+1 ) + ]) + (p Z E[(d t+1 OH t Q XZ t 1 Q SZ t ) + ]) (5. 12) Formulation of the problem All the information above combined results in the following optimization problem. Minimize Subject to h Z E[(OH t + Q XZ t 1 + Q SZ t d t+1 ) + ] + p Z E[(d t+1 OH t Q XZ t 1 Q SZ t ) + ] Q t SZ 0 Minimize: Subject to h Z 0 OH t +Q XZ t 1 +QSZ t (OH t + Q XZ t 1 + Q t SZ x) g t+1 (x)dx + p Z (x OH t + Q t 1 + Q SZ t ) g t+1 (x)dx OH t +Q XZ t 1 +QSZ t Q t SZ 0 Outcome As already stated, this problem can be optimized following the analogy of a newsvendor function as described amongst others in Silver, Pyke, and Peterson (1998, p. 385) and the critical ratio of underage c and overage costs u. We can regard the holding costs as the overage costs and penalty costs as c u + c o underage cost. We defined G t+1 (x) as the cumulative distribution function of D t,t+1 which gives us Function (5. 13). XZ 1 ( Q t SZ = (G t+1 pz p Z + h Z) OH t Q t 1 + XZ ) (5. 13) 22

39 The ratio ( pz p Z +h Z) shows how high the probability is that we have that the demand in period t+1 is smaller than the on-hand inventory before demand is satisfied. When we vary the height of the holding cost, this ratio will change which causes a higher or lower service level DECISION Q t XZ The decision on Q t XZ will be taken to optimize the cost during the year and in December the target on OWC will play a role. First we will explain the relevant costs for this decision and find the Q t XZ which minimizes these costs. Hereafter we analyze how a focus on the target on OWC changes the decision in December. Profit The relevant costs for the decision on Q t XZ are all the costs that are affected by the decision on Q t XZ. XZ Besides the direct cost of the decision Q t we also have to consider the cost of an alternative decision if XZ that is possible. When Q t is ordered, plant Z pays a certain price to plant X. However, every kilo that they do not buy at plant X they can order one period later at the local supplier S and pay two periods later, causing them to have the money two periods longer. Therefore it depends on the price of product XZ A at plant X and at the external supplier whether ordering Q t causes a loss or a profit compared to SZ. ordering Q t+1 Other cost that plant Z pays when ordering Q t XZ are the import duties that not have to be paid when ordering at a local supplier and inland handling costs. Plant X pays the transport fees only to get product A to country Z. In order to get product A at the plant, plant Z has to pay inland handling costs. For the local supplier plant Z does not pay any handling or transportation costs. SZ We will denote the costs of ordering Q t+1 with c SZ XZ and the cost of ordering Q t with c XZ. SZ Anticipation on order Q t+1 We have to anticipate on the decision on Q SZ t+1, since this decision is influenced by the choice of Q XZ t. In SZ period t+1, the decision of Q t+1 is made according to (5. 13). 1 ( In period t+1 G t+2 pz p Z +h Z) has a constant value, since it is only dependent on the distribution of R2. In period t the realization of R 1 is not known yet, thus G t+2 the probability distribution G t+2 1 ( pz p Z +h 1 ( pz p Z +h Z) as seen from period t converts into Z). For the on-hand inventory in period t+1 there is still uncertainty in the realization of R 2 to reveal the actual demand in period t+1. Therefore this is also a probability distribution and is denoted with OH t+1. Because there are probability distributions in the choice of Q SZ t+1, this will also be a probability distribution: Q t+1 SZ SZ. The value of Q t+1 is the following: Q t+1 SZ = [G t+2 1 ( pz p Z + h Z) OH t+1 Q t XZ ] + (5. 14) 23

40 Cost function Q t XZ When we combine all costs above, we get the complete cost function of Q t XZ : E[Cost t (Q XZ t )] = Q XZ t c XZ + E[Q t+1 SZ ] c SZ (5. 15) Restrictions We have two restrictions when it comes to the order Q XZ t. The first restriction is that it cannot be more than the amount available in plant X, so S XZ t. Furthermore we need the minimum amount m XZ, thus we get the same restriction as in (5. 9). In the case S t XZ < m XZ, the restriction Q t XZ m XZ will not be satisfied. We do not account extra cost for this (see Appendix D). Formulation of the optimization problem Minimize Subject to Q XZ t c XZ + E[Q t+1 SZ ] c SZ m XZ Q t XZ S t XZ Outcome In Appendix E the proof is given that formula (5. 16) gives the minimum value of the cost function. This represents the probability that we have a positive order Q SZ t+1. P {G t+2 1 ( P {G t+2 1 ( pz p Z + h Z) OH t+1 Q XZ t > 0} = cxz c pz XZ p Z + h Z) (OH t + Q t 1 SZ (5. 16) + Q SZ t D t,t+1 ) + Q XZ t > 0} = cxz csz (5. 17) We assume that the lost sales are negligible in order to be able to get D t,t+1 out of the function. This causes Q t XZ to be chosen higher than actually needed, because now the on-hand inventory of period t+1 can also have values smaller than zero. See appendix D for an elaboration on this assumption. P {G,t+2 1 ( pz p Z + h Z) (OH t + Q XZ t 1 P {G t+2 1 ( P {G t+2 1 ( pz XZ p Z + h Z) OH t Q t 1 pz + Q SZ t D t,t+1 ) Q XZ t > 0} = cxz csz (5. 18) Q SZ t + D t,t+1 Q DC t > 0} = cxz csz (5. 19) XZ p Z + h Z) + D t,t+1 > OH t + Q t 1 + Q SZ t + Q DC t } = cxz csz (5. 20) SZ This says we have a positive order of Q t+1 when the amount we want to have at the start of period t+2 24

41 plus the demand of period t+1 is more than we have on-hand plus the goods that are in transit at the SZ moment. We want the probability of a positive order of Q t+1 to be cxz c SZ. P {G t+2 1 ( pz XZ p Z + h Z) + D t,t+1 OH t + Q t 1 + Q SZ t + Q XZ t } = (1 cxz ) csz (5. 21) To be able to calculate which value Q t XZ should take, we have to know the distribution of G t+2 1 ( pz p Z +h Z) + D t,t+1 expressed in variables we know in period t. The distribution of the separate 1 ( probability distributions G t+2 1 ( pz pz p Z +h Z) and d t,t+1 is described in Appendix F. Since both G t+2 p Z +h Z) and D t,t+1 are normally distributed and independent, the sum of the two variables is again normally distributed. G t+2 1 ( pz p Z + h Z) + D t,t+1 ~N (f t+1 + r t f t+2 + z + μ R 1 + μ R 2, σ 2 R 1 + σ 2 R 2 ) (5. 22) We define Y t (x) to be the cumulative distribution function of G t+2 Y t (OH t + Q XZ t 1 With this formula we can calculate the optimal Q t XZ. 1 ( pz p Z +h Z) + D t,t+1. + Q SZ t + Q XZ t ) = 1 ( cxz ) csz (5. 23) + XZ Q t = (Y 1 t (1 ( cxz c SZ )) OH t Q XZ t 1 Q SZ t ) (5. 24) The actual order placed is in line with the restrictions: Q XZ t = min{s XZ t, max{q XZ t, m XZ }} (5. 25) End of the year XZ As in model 1, the objective for the order Q t in December will change. plant Z will try to get their onhand inventory plus goods in transit on a certain target. We have set this target at 140,000 kilos. Since plant Z now does not have to consider the tension that is caused by ordering less than the supply from plant X, they will try to always reach this target. Therefore their decision already changes in November. We want a high probability that the on-hand inventory of period 12 plus the order in November is less than 140,000 m XZ XZ. Therefore we set this probability to and Q 11 is decided accordingly. P {OH 12 + Q XZ 11 (140,000 m XZ )) = (5. 26) P{OH 11 + Q XZ 10 + Q SZ 11 + Q XZ 11 D 11,12 140,000 m XZ ) = (5. 27) 25

42 P{D 11,12 OH 11 + Q XZ 10 + Q SZ 11 + Q XZ ,000 m XZ } = (5. 28) G t+1 is again the cumulative distribution function of the random variable D t,t+1 that is normal 1 distributed with mean f t+1 + r t+1 + μ R 2 and standard deviation σ R 2. So G 12 is the cumulative distribution of D 11,12. Q DC 11 = G 1 12 (0.001) + (140,000 m XZ ) (OH 11 + Q XZ 10 + Q SZ 11 ) (5. 29) We have to take the minimum and maximum supply into account and when the optimal value according to the cost is less than the optimal value specific for November, we should order the optimal value according to the cost. This results in formula (5. 30). Q XZ 11 = Min {S XZ t, Max {m XZ, Min{Q XZ 11, G 1 12 (0.001) + (140,000 m XZ ) (OH 11 + Q XZ 10 + Q SZ 11 )}}} For December we have the following decision for Q XZ 12. (5. 30) Q XZ 12 = (140,000 OH 12 + Q XZ 11 ) + (5. 31) With the supply restrictions again as in (5. 9). XZ The ordered amount Q 12 will be the following: Or in words: Q XZ 12 = Min {S XZ t, Max {m XZ, Min{Q XZ 12, (140,000 OH 12 Q XZ 11 ) + }}} (5. 32) XZ XZ When the cost optimal Q 12 is smaller than Q 12 as specified by the target, we order the cost optimal quantity, which is Q XZ 12. When the amount we want to order is smaller than the minimum supply, we order the minimum supply m XZ. When this amount is smaller than the supply, we order the supply S t XZ. 26

43 5.10. MODEL 3: OPTIMIZED, CENTRAL In this model, the decisions in plant Z are taken centrally, so these decisions are made in order to maximize the profit of PharmInc PRODUCTION DECISION PLANT X Now that we consider the whole company, also the decisions in plant X have to be taken into account. This is the decision on the supplied amount, which leads back to the decision on how much to produce. We stated before that PharmInc has decided at the moment to produce as much as possible, because of the high fixed costs and relatively low variable cost. Since the fixed costs are such a significant part of the total product costs, we will assume that it is always beneficial to produce as much as possible DECISION Q t SZ When we want to maximize the profit of PharmInc we have to assess the relevant cost of the decision Q t SZ for the whole company. We have again the same assumption that inventories are at most on hand during one period. Since we see backorders as lost sales, also the cost of backorders are only made one period. Since there are no other options than the local sourcing to satisfy the demand in period t+1, the only relevant costs are the holding and penalty cost of period t+1. Therefore we can use the same model as in model 2. See Decision Q t SZ in Model 2 according to formula (5. 13) DECISION Q t XZ When taking the decision on Q t XZ there are other business units concerned, namely the BU of plant X. Therefore it does not mean automatically that minimizing the cost for plant Z also minimizes the cost of PharmInc as a whole. We considered the supply from plant X as a given with no options to decrease the production or sell the remaining product A to an external customer. This means that when plant Z does not order the full supply of product A, it will be added to the supply that is available for plant Z one period later. The product A is already made and with no options to decrease the production it means that the cost price of making product A in plant X is not relevant. Also the internal payment from plant Z to plant X is not relevant since it is an intercompany money transfer, so cost in plant Z and revenue in plant X. Therefore the relevant cost are the transport cost and import duties paid over every kilo of product A that is shipped from plant X to plant Z which will be denoted with c T. Furthermore the price of 1 kilo product A bought at a local supplier and the holding cost at plant X. When plant Z does not order the full supply from plant X, we have extra holding costs of h X. Cost function Q t XZ When we combine the information above, we get the following cost function. E[Cost t (Q XZ t )] = (S XZ t Q XZ t ) h X + Q XZ t c T + E[Q t+1 SZ ] c SZ (5. 33) 27

44 Every kilo ordered extra in plant X results therefore in an extra cost of c T and a reduction in the cost of h X. When we assume the extra stock in plant X will be there for a maximum of one period, we can also deduct the holding cost in plant X from the transportation cost per kilo product A from plant X. This results in the following cost function. E[Cost t (Q XZ t )] = Q XZ t (c T h X ) + E[Q t+1 SZ ] c SZ (5. 34) XZ Restrictions on Q t The restrictions are again the same as in (5. 9). Again, in the case that S XZ t < m XZ the restriction on m XZ is left out. We will not take extra costs into account for this, see Appendix D for an elaboration on this. Formulation of the optimization problem Minimize Subject to Q XZ t (c T h X ) + E[Q t+1 SZ ] c SZ m XZ Q t XZ S t XZ Outcome The structure of the cost function is the same as in Model 2, but with different costs. Therefore the SZ outcome will also have the same structure. The probability of getting a positive order Q t+1 is now given by ct h X in order for Q c SZ t DC to be optimal. This results in: 1 P {G t+1,t+2 ( pz p Z + h Z) OH t+1 Q XZ t > 0} = ct h X c SZ (5. 35) Q t XZ = (Y t 1 (1 ( ct h X c SZ )) OH t Q XZ t 1 Q SZ t ) + (5. 36) The actual order placed has to be in line with the restrictions placed on Q t XZ Q DC t = min {max{m XZ, Q XZ } t, S XZ t } (5. 37) 28

45 6. DETERMINATION OF PARAMETERS In order to be able to calculate the outcomes of the model, we need to define some parameters. These parameters are split up in input parameters and cost parameters and will be determined in this chapter INPUT PARAMETERS The input parameters are the parameters that will be the same for every type of model we have. They consist of the supply from plant X, the two-month forecast, the forecast updates and the demand. For the testing of normality of the distributions, we use the Shapiro-Wilk test, which is more accurate than the Kolmogorov-Smirnov test and therefore works especially well for small datasets. When using the Shapiro-Wilk test on large sample sizes the test is limited, because then the test often give a nonnormality result due to small deviations (Field, 2009). Our sample size consists of maximum 24 data points, so our sample size is not especially large. The Shapiro-Wilk test tests whether the data significantly differs from a normal distribution. When this test is not significant it says that the data is distributed normally. Since the Shapiro-Wilk test tests whether the data significantly differs, the higher the significance level is chosen the lower the probability that it is indeed a normal distribution. We have chosen as a significance level 0.05, which is a common level to use. We do note however that all parameters that we consider distributed normally under this assumption also pass the Shapiro-Wilk test with a significance level of 0.10, which is quite high. The input parameters are all based on fictitious numbers that do not represent the actual values of these numbers for PharmInc. These numbers are created in consultation with experts within PharmInc SUPPLY FROM PLANT X The production of product A is a continuous process, where the aim is to produce as much as possible. We assume that the production is the same in every month. We assume a constant production of 189,000 kilos every month. From this production, first the demand of plant Y Q t XY is subtracted. After this, the demand of the external customers Q t XE is satisfied and then the amount available for plant Z is calculated. We assume that everything left can be used to ship to plant Z. S t XZ = 189,000 Q t XY Q t XE Demand from plant Y We differentiate between the demand from plant Y during the year and the demand from plant Y in December. We have seen that the demand in December is considerably lower in December than in other months (see Appendix G). When we disregard the demand in December we have 22 data points of the demand of plant Y in the years 2012 and We tested whether this demand was distributed normally. The demand seemed to be skewed to the right and did not pass the Shapiro-Wilk test for normality. Therefore we used 29

46 transformations on the data points. This transformed dataset seems to be distributed normal with the following parameters: The normality test can be found in Appendix H. TQ t XY ~N(113.43; 65.73) Since we only use the value of Q t XY and do not have to base calculations on the value, we can use the transformed value to calculate the values of Q t XY. Q t XY = 127,202 (TQ t DS ) 2 Because we only have two data points for the demand in December, we cannot fit a distribution to the data. Therefore we assume that this demand in normally distributed, with the mean and standard deviation from the two data points we have. Q XY 12 ~N( ; ) Demand from external customers The demand numbers from external customers in 2012 and 2013 in shown in Appendix I. Also the demand from external customers is different during the year than the order in December. In XE December the order of the past two year has been 0. Therefore we will set Q 12 to 0. The distribution of the demand of external customers in the other months is analyzed with SPSS and is tested for normality. With the Shapiro-Wilk test for small sample sizes, we have determined that the demand is distributed normally with the following parameters (see Appendix J): MINIMUM AMOUNT FROM PLANT X Q t XE ~N( , ) From product A there are three products made. Products B2 and B3 can only be produced with product A from plant X. Therefore we need a minimum supply of product A from plant X for these two products. We will assume that this amount is the same every month and is 14,000 kilos DEMAND IN PLANT Z m DC = 14,000 The numbers over 2012 and 2013 gives the two-month forecast, one-month forecast and actual demand as shown in Appendix G. June 2013 is dismissed from the data due to external factors that caused the actual demand to be very low. The updates are considered additive and therefore calculated accordingly. R 1 = one-month forecast two-month forecast R 2 = actual demand one-month forecast 30

47 The two-month forecast and the forecast updates are tested for normality with the Shapiro-Wilk test. When considering a significance level of 0.05 we can see in Appendix H that the two-month forecast and R 2 are distributed normally. F ~ N( ; ) R 2 ~ N( ; ) However, R 1 is not distributed normally according to the Shapiro-Wilk test. We fitted R 1 with other distributions by testing them visually with a Q-Q, which showed R 1 seems to be closest to a normal distribution. Therefore we still propose the use the normal distribution, although the Shapiro-Wilk test showed a negative result. We use the mean and variance from the sample. R 1 ~N( ; ) Furthermore we needed to test whether the forecast updates were independent to be able sum them. We tested the correlation of the forecast updates and these were not significant correlated (see Table 31 in Appendix N). Therefore the distribution of R 1 + R 2 as needed for D t 2,t is: R 1 + R 2 ~N( ; ) The distribution of the forecasts of the demand is therefore also known. D t 2,t ~ N(f t ; ) D t 1,t ~ N(f t + r t ; ) 6.2. COST PARAMETERS The cost parameters are all the relevant cost as used in the decision making of the different models PRICE PER KILO PRODUCT A AT SUPPLIER S The price per kilo product A sourced at the local supplier changes each month. This is amongst others caused by the volatility of the raw materials of product A made in plant Z. We assume that the price is the same every month and is denoted with p SZ PRICE PER KILO PRODUCT A AT PLANT X The following formula is used by PharmInc to calculate the transfer price for product A from plant X. The transfer price is denoted by p XZ and is based on the price p SZ that is paid at the local supplier. p XZ = ((psz efficiency factor) inland handling cost) 1 + import duties The efficiency factor is used to cover the fact that it takes plant X longer than the local supplier to ship product A and is set on

48 RELEVANT UNIT COST ORDER SUPPLIER S IN PERIOD T+1 We know the price p SZ of buying product A locally. Since these costs are used when making the decision on the amount to source from plant X, we do have to consider that when ordered at the local supplier product A has to be paid two periods later. To account for the fact that we can pay product A supplied from plant Z two periods later, we use the weighted average cost of capital (WACC). c SZ = p SZ ((1 + WACC) ) p SZ RELEVANT UNIT COST ORDER PLANT X The cost of buying 1 kilo of product A is different from the transfer price. For each kilo they buy at plant X, they pay the import duties and inland handling cost. This is therefore added to the transfer price. When we use the price of 1 kilo of product A bought at a local supplier p SZ as a reference price we also have to account for the yield differences of product A bought at plant X or supplier S. The quality of product A produced in plant X is higher and this translates into a yield improvement. This yield improvement translates into a higher profit per kilo product A. This profit improvement in deducted from the price. c XZ = p XZ import duties + inland handling cost profit improvement Since the transfer price p XZ is calculated from the price that plant Z pays to local suppliers, we can also calculate the cost c XZ directly from this price p SZ. c XZ = p SZ 0.99 profit improvement Because of this, the relevant unit cost of an order at plant X is a little bit lower than the relevant unit costs of an order at supplier S one period later TRANSPORTATION COST The costs that have to be paid by PharmInc for transporting every kilo of Q t XZ are the transportation cost to plant Z, including inland handling cost, and the import duties. We will denote these costs by c T HOLDING COST The cost of holding 1 kilo of stock can consist of many factors. Main contribution to the holding cost is the opportunity cost of the capital that is tied up in the inventory. The opportunity cost is the return on an investment that could have been made when the money was not invested in inventory. The WACC shows the minimal return an investment got to have in order to be accepted by management. This is therefore part of the holding cost rate as opportunity costs. Furthermore there are operational costs that are being made, for example for storing product A. These costs are also included in the holding cost rate. The yearly holding cost percentage H is estimated at 15%. We assume this is the same in every location. We will later do a sensitivity analysis to see how vulnerable the model is to changes in the holding cost percentage. 32

49 Holding cost plant Z The holding cost in plant Z per month per kilo of product A is based on the holding cost rate and the price paid for product A. However, we saw before that the price paid in plant X is not exactly the price paid at the external supplier. From historical data we saw that the amount sourced from plant X and plant Z is approximately 50/50. Therefore we use the average price of plant X and the external supplier. The price we use for plant X is the transfer price plus the inland handling cost and import duties as paid by plant Z. The average price of 1 kilo product A sourced at the local supplier is p SZ. h Z = average price ((1 + H) ) = average price ((1.15) ) Holding cost plant X The holding cost in plant X consists of the cost price of product A as and H. h X = cost price product A ((1 + H) ) = cost price product A ((1.15) ) PENALTY COST PLANT Z The penalty cost is dependent on the cost of not being able to sell product B. Therefore we assume that plant Z produces at full capacity and every kilo of product B they cannot deliver immediately results in a lost sale. However, it does not result in losing the customer and has therefore no influence on the future distribution of the demand. Furthermore, an order can be fulfilled when it is not fully completed, so that the order is not completely lost when there is not enough product A to meet the full demand. The penalty cost is related to the loss of the contribution margin of product B. As a benchmark we use the average selling price to customers in country Z of the product B1. When the amounts of product B being produced are not enough to meet the demand, the allocation strategy is to serve the high-end customers first. Since the customers of country Z have one of the lowest selling prices, we can expect these customers to be served last. B1 is the most sold product B, over 80%, and has the lowest contribution margin. Therefore we can expect that this is the product that is not produced, so we use the data of product B1. The cost of a lost sale is then the contribution margin of product B1, otherwise sold to customers in country Z. We also need to account for the yield, the amount of kilos product A that is needed to produce product B1. Contribution margin B1 = Average selling price B1 country Z variable cost B OVERVIEW OF PARAMETERS p Z = Contribution margin B1 ( 1 yield ) The overview of all the parameters that were specified in this chapter can be found in Appendix O. 33

50 7. SIMULATION OF THE MODELS With the parameters defined we simulated the decision making according to the models specified in Chapter 6. The simulation is done in Excel with Visual Basic for Applications. We have first verified and validated the model, which is shown in the next section. Furthermore, in this chapter we will discuss the values of the input parameters for the simulation models which were specified in Chapter 6, the execution of the simulation and what the outcomes of the simulations are. The results of the simulations will be discussed by comparing the models and thus the different ways of decision making VALIDATION & VERIFICATION Sargent (2013) introduces a framework to validate the simulation model (see Figure 11). First he defines conceptual model validation, which should validate whether the assumptions underlying the conceptual model are correct for the problem it intends to solve. With model verification we have to determine whether the conceptual model is correctly implemented in the simulation program. Finally there is operational validation, where we have to determine whether the output of the simulation is accurate enough for its intended purpose. The validation that is important in all three steps is data validity, where we have to ensure that all data is correct. Figure 11. Framework validation and verification (Sargent, 2013) CONCEPTUAL MODEL VALIDATION We have made a lot of assumptions that allowed us to use the model as we described it. These assumptions can be found in Appendix D. There is also described how realistic these assumptions are and what the impact of these assumptions is. 34

51 MODEL VERIFICATION Because the simulated models do not make use of optimization procedures, we can quite simply verify whether the model calculates the values as specified in the chapter Mathematical Model. We have checked the calculations by hand and these matched the calculations as made by the simulation OPERATIONAL VALIDATION The validation of the model is done by checking the behavior of the model in extreme cases. This way we can check whether the behavior of the model makes sense in these cases. The extreme cases we consider are zero supply from plant X, extreme high demand in plant Z and deterministic demand. The outcome of these cases are presented in Appendix P DATA VALIDITY The validity of the data is discussed with professionals throughout the organization and throughout the project. Since we estimated the holding cost rate, we performed a sensitivity analysis on the holding cost rate. The holding cost rate varied between 0.15 and 0.25 with increments of This sensitivity analysis can be found at the end of this chapter INPUT We used per simulation the same input for all the models so that we can directly compare the results obtained with the different models. Because we worked with normal distributions the input parameters can also take negative values, which is not possible in the real world. Therefore we assumed for all the parameters, except the forecast updates, that the probability of having a value smaller than 0 is 0. In practice this means that we simulate the random variables from the distribution and when these are negative, we will ignore these values and simulate another value until the value is positive. The supply from plant X is the production at plant X minus the demand from plant Y and the demand from external customers. Since we have assumed that this demand would never be higher than the production, we simulate the demand and when this is more than the production, the supply is set to zero. This leads to a small increase in the probability of having 0 supply. For the updated forecast (f t + r t 1 ) and the actual demand (f t + r t 1 + r t 2 ) we also had to make sure there were not negative. Since we allowed the forecast updates to be negative, we checked after the simulation of the forecast updates whether the updated forecast and actual demand were positive. If this was not the case, the forecast updates were again simulated until we had a positive result. This causes the actual demand in the simulation to be higher than what would be expected from the distributions of F, R 1 and R EXECUTION After the input data is generated the other variables as described in Chapter 6 are specified. These are needed to make the decisions in the models. Every period in the model represents a month. Because the decisions are not the same throughout a year, we used a modulo 12 operation for our simulation to represent in which month of the year we are. 35

52 This means that period 13 is the same as period 1, 14 the same as period 2 et cetera. This makes the month December 12 mod 12 = 0. January to November are numbered 1 to 11. We have first considered five different models, with the decisions described below. Model 1 Model 1, the as-is situation, with the decisions the same in every period. This means there is no different decision in December in order to reach the target on the inventory. The decisions in period t mod 12 = 0,,11 are made according to formulas (5. 7) and (5. 10). Model 1 December Model 1 with the decision in December different in order to reach the target in December. The decisions in period t mod 12 = 1,,11 are the same as in Model 1. The decisions in period t mod 12 = 0 are made according to (5. 11). Model 2 Model 2, optimized local, with the decisions the same in every period. Again we have no different decision in December in order to reach the target. The decisions in period t mod 12 = 0,,11 are made according to formulas (5. 13) and (5. 25). Model 2 December Model 2 with the decisions different in order to reach the target of December. In this model the decisions are different for November and December. The decisions in period t mod 12 = 1,,10 are the same as in Model 2. The decisions in period t mod 12 = 11 are made according to formula (5. 30). The decisions in period t mod 12 = 0 are made according to formula (5. 32). Model 3 Model 3 with the decisions the same in every period. Here we do not consider the target in December, because it is not rational for PharmInc to make decisions in order to reach this target. The decisions in period t mod 12 = 0,,11 are made according to formulas (5. 13) and (5. 37) ACCURACY OF THE SIMULATION We first tested whether we needed a warm-up period for the simulation, by checking the variation in the on-hand inventories of the different models visually. There did not seem to be a warm-up period necessary, since there was no obvious steady state period after a certain amount of periods. 36

53 We used pilot runs in order to determine the run length and the accuracy of the simulations. Formula (7. 1) is derived from a t-test and shows the amount of runs needed when m pilot runs resulted in standard deviation S and mean X of a certain output of the simulation. We use a common used significance level α of 0.05 and the maximum error of the simulated mean to the real mean ε = We used the onhand inventory of Model 1, since this is both influenced by the stochastic nature of the supply from plant X and the demand. We can then calculate the needed replications of the models N according to formula (7. 1). S(m) t α m 1,1 2 N = ( ) X (m) ε 2 (7. 1) We did 5 pilot runs of a model with 12,000 periods, which runs under three minutes. This gave an N of 6.26 rounded up to N = ( ) = 6.26 This means we have to run the simulation with 12,000 periods 7 times in order to get an error term of less than 2%. In some cases we wanted to run the model with different parameters but with the same input data. Then we rather use a simulation with a lot of periods and only 1 run. We did 5 pilot runs of a model with 30,000 periods, which takes per run approximately 6.5 minutes for creating the input data and running all models together. When we only want to do 1 run, this resulted in an error of the mean ε of 2.7% OUTPUT The output that is generated by the simulation is the following: Average lost sales per period: LS Average on-hand inventory per period: OH Average on-hand inventory plant X per period: S XZ Q XZ Average amount of goods in transit per period: GIT Average order in plant X per period: Q XZ Average order in plant Z per period: Q SZ Service level o Percentage of months that plant Z is able to fulfill the complete demand Percentage of times the target was reached in December o This is the case when the on-hand inventory plus GIT in December are less than 140,000 All values that are noted in the results are these average values per period. So when we for example state on-hand inventory of plant Z this means the average on-hand inventory of plant Z per period. 37

54 OUTPUT COSTS We used these values to calculate the cost of plant Z and PharmInc. Just as in the models, we disregarded the cost of making product A in plant X. There are two differences between the costs of plant Z and PharmInc. Firstly plant Z pays for Q XZ the price plus the transportation cost within plant Z and the import duties (c XZ ), while PharmInc only pays the total transportation costs and import duties (c T ) for each kilo of product A sourced in plant X. Secondly plant Z has no costs for the on-hand inventory in plant X, where PharmInc has to pay holding cost over this quantity. Yearly total cost plant Z = 12 (LS p Z + (OH + GIT) h Z + Q XZ c XZ + Q SZ p SZ ) Yearly total cost PharmInc = 12 (LS p Z + (OH + GIT) h Z + (S XZ Q XZ ) h X + Q XZ c T + Q SZ p SZ ) We differentiate between the total cost per year and the inventory related cost. Since the purchasing cost of product A accounts for a big part of the total cost, we will also show the yearly cost without these purchasing cost. Since the cost for lost sales, on-hand inventories and GIT are all related to the inventory, we call those cost the inventory related cost. Inventory related costs plant Z = 12 (LS p Z + (OH + GIT) h Z ) Inventory related costs PharmInc = 12 (LS p Z + (OH + GIT) h Z + (S XZ Q XZ ) h X ) The difference between the inventory related costs of plant Z and PharmInc are the holding costs that are paid by PharmInc for the inventory in plant X. This means than the inventory related costs of PharmInc are always greater than or equal to the costs of plant Z. They are only equal to the inventory related costs in plant Z when there is no inventory in plant X. All the costs are presented in tables and will be given relative to one model in the table. As the costs of that one model are set to 100, the other costs in the table are percentages of these costs OUTPUT INVENTORY LEVEL To make remarks about the inventory besides the inventory related costs, we will also show the average stock height per month of plant Z and PharmInc. The stock height will be given in kilos of product A. For the average stock height of plant Z and PharmInc we used the following calculations. Stock height plant Z = OH + GIT Stock height PharmInc = OH + GIT + (S XZ Q XZ ) 7.5. RESULTS The differences between the models as explained in Chapter 5 are quantified and discussed in this section. 38

55 IMPACT OF DIFFERENT DECISION MAKING To analyse the impact of the different ways to make the decisions for the ordered product A at plant Z, we compared Model 1, Model 2 and Model 3. In Table 7 we can see the average values per month of the three different models, the service level and how often the target was reached in December. Table 7. Performance Model 1 versus Model 2 versus Model 3 Model 1 Model 2 Model 3 Lost sales On-hand inventory plant Z 58, , ,252.2 On-hand inventory plant X ,450, ,518.1 GIT 103, , ,389.4 Amount ordered at plant X 51, , ,694.0 Amount ordered at supplier S 21, , ,578.8 Service level Percentage of times target reached in December Interesting values that can be seen in Table 7 are that plant Z does not order all the supply from plant X in Model 2 which causes a high stock build-up in plant X, the low amount of lost sales of Model 1 and the high amount of times that Model 2 reached the target in December compared to Model 1 and Model 3. Stock build-up plant X in Model 2 From the values of Model 2 it becomes obvious that it is not optimal for plant Z, based on their KPIs, to order the full supply from plant X every month. More interestingly is that from a cost perspective for plant Z product A from plant X has such a small benefit over the externally sourced product A that plant Z often only orders the minimum amount necessary. This results in a large stock build-up in plant X. The number of average on-hand inventory of plant X shown in Table 7 is dependent on the number of periods simulated, since it grows with every period simulated. We knew product A from plant X only had a small cost advantage over product A from supplier S, however we did not expect this small cost difference to lead to such low orders at plant X compared to the other two models. Model 1 has highest service level We can see in Table 7 that Model 1 has the highest service level and also the lowest lost sales. Compared to Model 2 and 3 it is a decrease of lost sales of respectively 69.3% and 49.9%. However, the higher service level of Model 1 is also reflected in the higher on-hand inventory at plant Z. Model 1 is also the only model that does not have inventory in plant X, since they always order the provided supply from plant X. Since we used the target safety stock for Model 1 as a given and saw that there is often an over-forecast for the demand, we expected a higher on-hand inventory level for Model 1 and therefore also a higher service level. Times target reached in December In the models compared, no decision is altered in December in order to reach the target. We do see that, despite not focusing on reaching the target, Model 2 reaches the target of 140,000 kilos on-hand plus 39

56 GIT in 99.8% percent of the times, where for Model 1 and Model 3 this is respectively only 2.5% and 6.8%. From the average values for on-hand inventory and GIT of plant Z it becomes clear why Model 2 reaches their target more often than Model 1 and 3. Because of the low amount ordered in plant X, the average on-hand inventory in plant Z and the GIT is much lower. With the values from Table 7 we can calculate the average yearly cost for plant Z and for PharmInc. These costs are shown in Table 8 and Table 9 for plant Z and PharmInc respectively. We set the average total costs and inventory related costs as 100 in Model 1. The values of Model 2 and 3 are relative to Model 1. Impact of different decision making on costs plant Z For plant Z we can see clearly that Model 2 has lower cost and much lower average inventory than Model 1 and Model 3 (see Table 8). Table 8. Cost and OWC plant Z of Model 1 versus Model 2 versus Model 3 Model 1 Model 2 Model 3 Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 161,826 67, ,642 The impact does not seem to be that big when we only look at the total cost per year. However, when we disregard the cost plant Z has for the purchasing of product A, the impact of the decision making becomes rather large, see the inventory related costs. Since we did not expect the order at plant X to be that much smaller in Model 2 compared to the other models, we did not expect this extreme cost difference. We did expect Model 3 to have lower costs than Model 1, mainly due to the external sourcing strategy that is in Model 3 based on minimizing cost. Inventory related costs plant Z Lost sales On-hand plant Z GIT Model 1 Model 2 Model 3 Figure 12. Components of inventory related costs for plant Z 40

57 Model 1 versus Model 2 The differences for plant Z between Model 1 and Model 2 are 0.47 and for the total cost per year and the inventory related costs respectively. The decrease of total cost per year seems small, but the total costs are in absolute numbers much higher than only the inventory related costs. The large difference between the inventory related costs is mostly due to an extreme decrease in GIT, from 103,389 kilos in Model 1 to 34,483 kilos in Model 2 (see Figure 12). There is also a large decrease in the on-hand inventory of plant Z. This can be caused by not ordering the full supply from plant X and therefore being able to better steer the on-hand inventory or by a better ordering policy for Q t SZ. Model 2 versus Model 3 The comparison of Model 2 and Model 3 shows that following the KPIs of PharmInc instead of their own KPIs is costing plant Z on average more per year. The difference in inventory related costs between Model 3 and Model 2 is again very high, going from to 95.14, an increase of 210%. Model 1 versus Model 3 The higher total cost per year of Model 1 if compared to Model 3 is mostly due to a better sourcing strategy for the externally sourced product A. Model 3 has mainly a reduction for the purchasing of product A externally and for the lower on-hand inventory. A graphic overview of the different components of the inventory related costs for plant Z are shown in Figure 12. We can see there that the largest part of the inventory related cost for Model 1 and 3 comes from the GIT. Impact of different decision making on costs PharmInc For the costs of PharmInc we only compared Model 1 to Model 3, we will disregard the cost and stock height for PharmInc of Model 2 because they increase with every period resulting in very high costs and stock height for PharmInc (see Table 9). We did not anticipate this large stock build-up in plant X for Model 2, however again we expected that Model 3 would have lower cost than Model 1. Table 9. Cost and OWC PharmInc of Model 1 versus Model 2 versus Model 3 Model 1 Model 2 Model 3 Total cost per year of PharmInc 100 8, Inventory related costs PharmInc , Average stock height PharmInc 161, ,517, ,160 We have seen in Table 7 that in Model 3 PharmInc has on average 5,518 kilos of product A on-hand in plant X. This means that in Model 3, plant Z does on average not order the full supply from plant X every month. Therefore it is not always optimal for PharmInc to order the full supply from plant X when focussing on optimizing their costs. Model 1 versus Model 3 When we look at the cost for PharmInc of Model 3 we see that Model 3 has lower total costs and lower inventory related costs than Model 1 (see Table 9). This difference in costs can be a result of the agreement to order the full supply in Model 1 or of the different external sourcing strategy. The graphic overview of the different components of the inventory related costs for PharmInc of Model 1 and Model 41

58 3 are shown in Figure 13. The costs of Model 2 are omitted because of the very high cost. Again a large part of the inventory related cost, more than half, comes from the GIT. From the fact that Model 1 has the highest total costs and inventory related costs for plant Z and PharmInc, we can conclude that the ordering policy used in PharmInc at the moment is not cost optimal for plant Z nor PharmInc. Inventory related costs PharmInc Lost sales On-hand plant Z On-hand plant X GIT Model 1 Model 3 Figure 13. Components of inventory related costs for PharmInc IMPACT OF THE TARGET IN DECEMBER To analyze the impact of the target that is put on on-hand inventory plus GIT, we compared Model 1 to Model 1 December and Model 2 to Model 2 December. Furthermore we changed the target to different values to see what the impact is of the height of the target. Impact of target on Model 1 To quantify the influence of setting a target at the end of the year on OWC in the current situation, we compared Model 1 with Model 1 December. We did this for both the performance of plant Z as the performance of PharmInc. Table 10. Performance Model 1 versus Model 1 December Model 1 Model 1 December Lost sales On-hand inventory plant Z 58, , On-hand inventory plant X 0.0 5, ,598.2 GIT 103, , Amount ordered at plant X 51, , Amount ordered at supplier S 21, , Service level Percentage of times target reached

59 The two models mainly differ in the on-hand inventory of plant Z and plant X and the percentage of times the target is reached. Surprisingly, the model where the focus lies on the inventories, Model 1 December, has a higher average on-hand inventory of kilos compared to Model 1. This means that the target on the stock height has a negative impact of the overall stock height of plant Z. This is caused by the fact that the amount of product A not ordered from plant X, will be added to the supply of the next month, January in this case. However when the order in plant X of December is not sufficient to satisfy the demand of February, also extra product A needs to be ordered locally which results in a higher on-hand inventory level. We did expect to see higher on-hand inventories in plant Z when the decision was changed in December because of the reasoning given above. Average on-hand inventory plant Z per month Model 1 Model 1 December Figure 14. Average on-hand inventory plant Z Model 1 versus Model 1 December This effect is showed in Figure 14. We shifted the months so that we are able to directly compare them. This means that the high on-hand inventory of Model 1 December shown in February actually takes place in March. The months of Model 1 have stayed the same. We would expect to see the higher inventory for Model 1 December already in March (February in the graph), but the graph shows that actually the months after March cause the higher inventory compared to Model 1. The large effect of the higher supply from plant X in December, which was caused by a lower demand from plant Y and no demand from external customers, can also be seen in February in Figure 14. This has a big impact on the average on-hand inventory of both Model 1 and Model 1 December, since it takes a long time after this high supply to get on the regular on-hand inventory level again. We did not expect the impact of this higher supply to be this large and last this long. We will further discuss this supply later in this chapter. Impact on plant Z When we look at the cost of plant Z it looks like the average total costs per year of the two models are similar (see Table 11). However there is a relatively small increase in Model 1 December of 0.004% compared to Model 1. This small increase allows them to reach their target in December 90.7% of the times instead of 2.5% of the times. We did expect the increase in costs, due to higher holding costs of the on-hand inventory. The reason that Model 1 December does not reach their target 100% of the 43

60 times is due to the fact that is it possible for the on-hand inventory plus the amount of product A ordered in plant X in November to be higher than 126,000 kilos. Since we have the minimum amount of 14,000 it is then not possible to reach the target of 140,000 kilos. We already saw that the target has a negative influence on the stock height of plant Z. In Table 11 it is also clear that is causes higher inventory related costs. Table 11. Cost and OWC of plant Z of Model 1 versus Model 1 December Model 1 Model 1 December Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 161, ,029 Impact on PharmInc The impact on PharmInc is larger than the impact of plant Z. We can see in Table 12 that the different decision in December gives relative extra total cost for PharmInc of 0.24 per year. This is mainly caused by the extra holding cost of one period in plant X over the amount that is not ordered in December. Again the target has a negative influence on the stock height. Besides the extra on-hand inventory of plant Z, we also have extra inventory at plant X. Table 12. Cost and OWC of PharmInc of Model 1 versus Model 1 December Model 1 Model 1 December Total cost per year of PharmInc Inventory related costs PharmInc Average stock height PharmInc 161, ,628 Impact of target on Model 2 Since model 2 results in a stock at plant X that is growing every period, we can only compare the impact of the target on the performance of plant Z. Impact on plant Z The impact of the target in Model 2 is much smaller than the impact in Model 1, since there is no obligation to order the supply that was not ordered in plant X in January. The largest difference we see in the on-hand inventory in plant X, but this value is skewed because of the growing inventory in plant X causing a high average number. When we look at the amount ordered at plant X it is only 10.2 kilos less than Model 1. Because there is no obligation to order from plant X, we also see that the amount that is ordered less in plant X is exactly ordered more at supplier S. The probability of reaching the target is very high in both models, with Model 2 December it is even always possible to reach the target (see Table 13). Because the average GIT of Model 2 is already quite low compared to Model 1, we can see that even without focus on the target, the target is almost always reached. 44

61 Table 13. Performance PharmInc Model 2 versus Model 2 December Model 2 Model 2 December Lost sales On-hand inventory plant Z 32, , On-hand inventory PharmInc 206,450, ,514, ,429.2 GIT 34, , Amount ordered at plant X 17, , Amount ordered at supplier S 55, , Service level Percentage of times target reached The impact of the decision in December for Model 2 is smaller than the impact we saw at Model 1. In Table 14 we can see that the inventory related costs are smaller than those of Model 2. This difference for these costs is however very small. Table 14. Cost and OWC of Model 2 versus Model 2 December Model 2 Model 2 December Total cost per year of plant Z Inventory related costs plant Z Average stock height 67,059 67,038 Because in Model 2 the target is already often met, we expected that the differences between those two models would not be that large. Changing the target We also looked at what changing the target does to the outcome of the models. To be able to compare the different targets one-on-one we used the same input data for all the targets. Because we only simulated this once we used in this one simulation 30,000 periods. We have varied the target in the model from 80,000 to 200,000, with increments of 30,000, and no target at all. Note that no target gives the same outcome as Model 1 and Model 2, with the decision the same in each period. For the costs, we will index the used target 140,000 as 100, the rest of the costs presented in the table are relative of this number. Impact on plant Z When we analyze the inventory related cost of Model 1 for plant Z, the cost first go down and then go up again (see Table 15). We saw before that Model 1 December had higher average costs than Model 1, but in this case we see that when the target is higher than 140,000, we can actually have lower cost. The same is the case with the stock height of plant Z. By choosing a higher target than 140,000 we can have lower stocks at plant Z than the situation with the current target and without a target. This means these higher targets make sure plant Z has enough product A sourced at plant X in December so that in January no extra product A is sourced externally. 45

62 For Model 2 December we see that the inventory related cost and the average inventories go up until they are on the level of the model without a target. Table 15. Influence of changing the target on KPIs of plant Z Model 1 December Model 2 December Target Inventory related costs plant Z Stock height plant Z Inventory related costs plant Z Stock height plant Z 80, , , , , , , , , , , , , , ,037 No target , ,037 Impact on PharmInc For PharmInc we could only look at Model 1, since we do not have a different decision in December for Model 3 and Model 2 gives higher cost and inventories with each added period. We can see in Table 16 that having no target on OWC results in the lowest costs and the lowest stock for PharmInc. Since we knew that any target would cause higher stock in plant X and plant Z than having no target, this result was expected. Table 16. Influence of changing the target on KPIs of PharmInc Target Inventory related costs PharmInc Stock height PharmInc 80, , , , , , , , , ,026 No target ,569 When we look at where this decrease in inventory related costs comes from, it is mainly the on-hand inventory of plant Z and plant X (Figure 15). We saw before when comparing Model 1 to Model 1 December that the target of 140,000 causes higher on-hand inventory in plant Z. This effect is even larger with a lower target, since the order at the external supplier in January will be higher in order to fulfill the demand in February. A lower target naturally also causes higher on-hand inventory in plant X, since less product A will be ordered in December. 46

63 Inventory related costs PharmInc per target Lost sales On-hand plant Z On-hand plant X GIT No target 7.6. FOCUS ON OWC Figure 15. Components of inventory related costs of PharmInc per target Furthermore we analyzed what happens when plant Z and PharmInc would focus on the OWC throughout the whole year instead of only in December MODEL 1 The focus on OWC in Model 1 means that the decision is made in every month to stay under the target of 140,000 kilos. This is also in line with the objective of the target, which is a healthy inventory level in every month and not only at the end of the year. When the decision in every month is made according to Formula (5. 11), there is a large stock build up at plant X. Since we have an average on-hand inventory per month of plant Z of 58,437 kilos in the regular Model 1 and an average supply from plant X of 51,665, the average on-hand inventory plus GIT is 161,767. This is far above the target, so it was expected that the decision to stay under target every month causes large stock build-ups at plant X MODEL 2 With Model 2 we can analyze what happens when plant Z focuses on optimizing their OWC the whole year. Since GIT account for a large part in their OWC, they try to source as little as possible from plant X. This means that they will only order the minimum amount in plant X, so Q t XZ = m XZ. We will call this model Model 2 OWC. The results of this in comparison to Model 2 are shown in Table 17. Here we can see that focusing on OWC causes higher total cost for plant Z, but indeed lowers the inventory related costs and the average stock height. The inventory related costs are reduced with 8.71%, which is mostly due to the lower amount of GIT. This can be seen too in the decrease of average stock height of 6,492 kilos. The total costs rise with 0.02%, because product A from supplier S is more expensive than product A from plant X. It is logical that the total costs will rise when focusing on OWC, since the decisions in Model 2 are made to optimize the total costs. 47

64 Table 17. Cost and OWC plant Z of Model 2 versus Model 2 OWC Model 2 Model 2 OWC Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 67,059 60,567-6, MODEL 3 When we look at model 3 and try to optimize the OWC of PharmInc, we want the probability of sourcing externally to be as close to zero as possible. This results in a maximum order in plant X, so always order the supply: Q t XZ = S t XZ. The decision of Q t SZ stays the same. We will call this model Model 3 OWC When PharmInc focuses on OWC this results in a small decrease of the average stock height of PharmInc of 201 kilos per month (see Table 18). However, when we look at the total costs and inventory related costs, we see an increase of respectively 0.02% and 0.08%. This means that although the average stock height is lower, the costs for the inventories are higher. This is due to the fact that it is cheaper to hold inventories in plant X than when they are in transit or plant Z, because of the import duties that have to be paid when shipping product A to plant Z. Table 18. Cost and OWC PharmInc of Model 3 versus Model 3 OWC Model 3 Model 3 OWC Total cost per year of PharmInc Inventory related costs PharmInc Average stock height PharmInc 157, , The impact for plant Z, shown in Table 19, is nonetheless much larger. The average on-hand inventory in plant X of Model 3 is now added to the on-hand inventory of plant Z. Besides the higher on-hand inventory of 5,317, the total costs and inventory related costs also rise with respectively 0.09 and This was expected, since the on-hand inventory of plant Z will rise with the decision to always order the full supply from plant X. Table 19. Cost and OWC plant Z of Model 3 versus Model 3 OWC Model 3 Model 3 OWC Total cost per year of plant Z Inventory related costs plant Z Average stock height plant Z 151, ,959 5,317 Impact for plant Z of ordering full supply Since the decision on Q t SZ is the same in Model 2 and Model 3, Model 3 OWC is essentially Model 2 with a forced supply from plant X in every period. Therefore it is interesting to compare Model 2 to Model 3 in order to see the impact for plant Z of having to order the full supply from plant X. 48

65 In Table 20 we see that the forced supply from plant X costs plant Z 0.29% per year relative from the total yearly cost they have in Model 2. In terms of the inventory related costs, the difference is much larger: %. Also the average stock height for plant Z is 89,900 kilos higher when they have to order product A that is supplied from plant X. Table 20. Cost and OWC plant Z of Model 2 versus Model 3 OWC Model 2 Model 3 OWC Total cost per year of plant Z Inventory related costs plant Z Average stock height 67, ,959 89,900 Impact for PharmInc of external sourcing strategy We saw that PharmInc currently orders product A at supplier S in order to reach an on-hand inventory in plant Z of 29,400 kilos in the period after. In Model 1, they do not take the stochastic nature of the demand into account. This is reasonable in real life, because there they have much more influence over the demand for product A, since this is a result of their production schedule. From the used parameters we can see that on average there is an over-forecast of the demand for product A. One month before the actual demand, the forecast is on average 7,872 kilos higher than the actual demand. Therefore we expect a decrease in costs and stock height when having an ordering policy that takes the stochastic nature of the demand into account. With Model 3 OWC having the same decision for Q t XZ as Model 1, namely Q t XZ = S t XZ, we can compare the external sourcing strategy of these two models. We did so by comparing the performance in terms of costs and average stock height, as seen in Table 21. We can conclude from this table that when it comes to ordering Q t SZ the external sourcing strategy of Model 3 is indeed beneficial for PharmInc. It gives lower total cost, lower inventory related cost and a lower average stock height. The external sourcing strategy orders less from the supplier S, which caused the average on-hand inventory to be lower than that of Model 1. The average GIT is the same, so the decrease of average stock height of 4,867 kilos is due to the on-hand inventory in plant Z. Table 21. Cost and OWC PharmInc of Model 1 versus Model 3 OWC Model 1 Model 3 OWC Total cost per year PharmInc Inventory related costs PharmInc Average stock height PharmInc 161, ,959-4, STEADY SUPPLY FROM PLANT X We saw before that a higher supply from plant X in December has quite some impact, especially on the on-hand inventory of Model 1 and Model 1 December. We therefore also considered the situation where the supply of December is the same as in every other month. Note that steady supply does not mean that the supply is exactly the same every month, only the probability distribution is the same every month. 49

66 When we look at Figure 16 we can see the impact of the different decision of December in Model 1 December more clearly with the steady supply. Here the average on-hand inventory of plant Z is shown per month. We scaled the y-axis in order to show the increase better, so note that it does not start at 0. We see that the average on-hand inventory of Model 1 is approximately the same in every period, the small differences are caused by the stochastic nature of the supply and demand. In Model 1 December we see a decrease in average on-hand inventory in February and an increase in March, where the onhand inventory becomes higher than that of Model 1. This difference with Model 1 becomes smaller every period, but does last until January. This lasting difference leads to an overall higher average onhand inventory for Model 1 December compared to Model Average on-hand inventory plant Z per month Model 1 Model 1 December Figure 16. On-hand inventory plant Z of Model 1 versus Model 1 December with steady supply The impact of the decision is December gets significantly smaller when there is a steady supply. We see the impact of the higher supply in December clearly in Table 22, where the change in inventory related costs for PharmInc and average stock height of PharmInc especially stands out. The differences in costs are presented in a percentage of Model 1. Table 22. Comparison of basic model and steady supply for Model 1 and Model 1 December Basic model Steady supply Difference between Model 1 and Model 1 December Difference between Model 1 and Model 1 December Average stock height plant Z Average stock height PharmInc 5,802 1,177 Inventory related costs plant Z Inventory related costs PharmInc Total cost per year of plant Z Total cost per year of PharmInc

67 Besides the differences between Model 1 and Model 1 December, we also see that the on-hand inventory of Model 1 is now steady. In the basic Model 1 with a higher supply in December we had a higher on-hand inventory in February that slowly decreased over the months. The absence of the peak in on-hand inventory in February with the steady supply gives a decrease in inventory related costs of 13.23% (see Table 23). Remember that we only used the cost of transportation for product A from plant X, since we assumed that the production cannot be lowered. Because plant Z has to order more from the external supplier S now, the total costs of PharmInc will naturally get higher because of the large cost difference between product A from plant X and supplier S. We see the same happing for Model 3, see Table 24. Since Model 2 almost never orders the full supply from plant X the impact of steady supply on Model 2 is negligible and therefore omitted here. Table 23. Comparison of basic model and steady supply model Model 1 Basic model Steady supply Total costs per year of plant Z Total costs per year of PharmInc Inventory related costs plant Z Inventory related costs PharmInc Table 24. Comparison of basic model and steady supply model Model 3 Basic model Steady supply Total costs per year of plant Z Total costs per year of PharmInc Inventory related costs plant Z Inventory related costs PharmInc SENSITIVITY ANALYSIS Because the holding cost rate was estimated, we performed a sensitivity analysis on the holding cost rate. We have used the same input data for every holding cost rate and simulated for 30,000 periods. Details of the impact of the various holding costs rates on the on-hand inventories and lost sales are shown in Appendix Q. We will limit this section to discussing the inventory related costs of the various holding cost rates. The total cost per year show approximately the same increase as the inventory related cost, so these are omitted here and shown in Appendix Q. Impact on inventory related costs of plant Z The overall cost structure for plant Z stays the same, in terms of which model has less inventory related costs for plant Z and PharmInc (see Table 25). We see that the costs of Model 1 and 3 rise faster than Model 2. Besides the lower relative increase of Model 2, we also saw before that the inventory related costs were approximately half of those of Model 1 and 3. This means that in absolute terms the inventory related costs of Model 2 rise even less than those of Model 1 and 3. This is mainly due to the 51

68 fact that Model 1 and 3 have more GIT which also become more expensive. So when having higher holding cost it is even less attractive for plant Z to order more at plant X. Table 25. Sensitivity analysis H, inventory related costs plant Z H Model 1 Model 2 Model Impact of inventory related costs of PharmInc The inventory related costs of Model 3 rise faster than the costs of Model 1. We saw before that Model 1 has on average a higher inventory level than Model 3. This is because Model 3 can optimize their costs given the new holding cost rate, where the decision making of Model 1 is not influenced by the changing holding cost rate. Table 26. Sensitivity analysis H, inventory related costs PharmInc H Model 1 Model As a result we can conclude that the results of the models are quite robust against a changing holding cost rate. This is due to the fact that the overall cost structure - in terms of which model has the lowest costs for plant Z or PharmInc - stays the same. Though, the absolute differences between the models are increasing. Mainly the differences with Model 1 are increasing, because in this model the decisions do not take the higher holding cost into account. 52

69 8. CONCLUSIONS AND RECOMMENDATIONS This chapter describes the conclusions and recommendations based on the results of the simulations. It will also describe the academic relevance and will provide suggestions for further research CONCLUSIONS & RECOMMENDATIONS Our main research question, as defined in Chapter 3, is the following: What is the impact of local decision making within the product A supply chain on the performance of the business units and the whole company, as measured by the key performance indicators, and in which ways can this impact be mitigated? We will give answers to this question in this section. We examined two decisions that can be considered to be local. The first is the decision to order less product A from plant X at the end of the year in order to reach the target for the stock height in December. The second local decision is based on plant Z fully focusing on the optimization of their own KPIs and disregarding any consequences for PharmInc IMPACT OF DECISIONS BASED ON REACHING THE TARGET OF DECEMBER A striking conclusion that can be drawn from the results in chapter 7 is that the target on stock height actually has a counterproductive effect. The target results in a higher average stock height for both plant Z and PharmInc. Considering the impact on plant Z of this decision in the as-is situation, we saw that the costs and stock height went up when the decision was changed in December in order to reach the target. It did however cause an improvement of reaching the stock height target in December from 2.5% to 90.7%, with only a small increase in the costs. Since personal premiums are tied to the targets, it can be considered rational for plant Z to change their decision in December in order to reach the target. For PharmInc the impact is much larger, the target on stock height causes higher costs because of the extra stock in plant X for one period. The impact of the decisions to reach the target in December when plant Z optimizes their own KPIs, so in Model 2, is much smaller. This is because they are able to reach the target already quite often when they do not make their decisions based on this target. By changing the target we can change the impact of these decisions. The higher the target is, the lower the impact of the decision since the decisions come closer to the situation where the costs are optimized in every period. For PharmInc we get the lowest costs and average stock height when there is no target on stock height in plant Z IMPACT OF DECISIONS TO OPTIMIZE KPIS OF PLANT Z When plant Z would only consider their own KPIs, they would order less than a quarter of their demand for product A at plant X and the rest at the external supplier S. This results in a large stock being build up at plant X, so it causes extremely high costs and inventories for PharmInc. This is mostly due to the 53

70 relative small difference between the price of product A sourced internally and externally and the long transportation time for the internally sourced product A, making it unattractive to order product A from plant X. However, focusing on their own KPIs is by far the most optimal option for plant Z. This results in reducing their inventory related costs and average stock height by more than half when comparing it to the other ways of decision making. We can also look at this the other way around: it is costing plant Z more than double to make their decisions based on the KPIs of PharmInc. Besides the huge benefits cost wise and stock wise, focusing on the KPIs of plant Z also makes it possible to always reach the target on stock height, to which a personal incentive for the employees of plant Z is linked to. We have to note that only the cost factors influenced the decision making of plant Z in this study. We did not incorporate other preferences for product A from plant X or the external supplier. In reality product A from plant X is made with a more sustainable process than product A from supplier S. This can be a factor that influences the decision making at plant Z, for example when the more sustainable product A results in better brand perception or higher product value RECOMMENDATIONS TO MITIGATE IMPACT In this section the recommendations to mitigate the impact of the local decisions are given. We recommend to remove the target which is currently used and instead put a target on the on-hand inventory of the externally sourced product A. Therewith we also recommend to evaluate the supply from plant X to plant Z. Remove target on on-hand inventory + GIT of plant Z We found that the current target on stock height is causing higher costs and inventory for both plant Z and PharmInc. The lowest achievable costs and OWC for PharmInc in the different models is by removing the target. This leads plant Z to not base their decisions at the end of the year on the target. Even a target which is set only on the on-hand inventory is hard to reach. We saw that Model 1 and 3 have on average a much higher on-hand inventory level than Model 2 because of the forced ordering at plant X. Thereby literature contributes that incentives of divisions should be based on something they can influence. When a reward is based on something a division can hardly influence, it does not motivate them to improve their performance (Hyde & Choe, 2005). Therefore we propose to remove the target on the end of year stock height of plant Z. This will change the decision making in December, resulting in lower costs and lower inventories for both plant Z and PharmInc. Focus on external sourcing strategy It is however useful to have some target or assessment of performance to ensure that people are striving to optimize company results. Thus we propose to put more emphasis on the local sourcing strategy and look whether they made right decisions with the external sourcing, considering they have to order the supply from plant X. 54

71 One way of focusing more on the external sourcing strategy is to measure the performance of plant Z on the on-hand inventory that consists of the locally sourced product A. The inventories of product A from plant X and from supplier S are already tracked separately, so it is easy to get this information. Further research within PharmInc could be conducted to find the optimal value of the target on the part of onhand inventory that is externally sourced. Evaluate the supply from plant X to plant Z We recommend to provide a more steady supply to plant Z. This mitigates the impact of the decision in December and the impact of decisions to optimize the KPIs of plant Z. Do not always send full supply available We saw that at the moment there is an agreement within PharmInc that plant Z has to order everything that plant X has available for them. From the results of the optimization of plant Z s own KPIs, we can conclude that it is very disadvantageous for plant Z to order this full supply. We have even proven that it is disadvantageous in terms of costs for PharmInc to always let plant Z order the full supply, although this disadvantage is small. When plant Z has a very high on-hand inventory and plant X wants to send a large amount of product A, it is beneficial for PharmInc to keep the stock one period longer in plant X. This results in a later payment of transportation costs and import duties and gives PharmInc more flexibility to sell or ship product A from plant X to other parties. What those exact values are of a too large supply, is influenced by the forecasted demand of product A for the next two periods. We would suggest an evaluation of the amount to be sent to plant Z with the global planner of product A and the planner of plant Z in order to decide on the optimal amount. This is especially advantageous for plant Z, but also gives plant X the flexibility to respond to a change in the demand of external customers or plant Y. Lower the supply available for plant Z The supply available from plant X to plant Z is dependent on the production, the demand of plant Y and the demand of external customers. The production is already on full capacity and we want to keep it this way, so we are going to focus on the demand of plant Y and external customers. The lower the available supply to plant Z is, the lower the stock height of all the product A in the network is, because of the large decrease of GIT. The higher average supply in December is caused by an on average lower supply to plant Y and no demand from external customers. Because we only have two data points for the supply to plant Y in December we cannot prove that there is a deliberate lower supply to plant Y in December. We do know that also plant Y, just as plant Z, has their own target on on-hand inventory plus GIT. A same mechanism could be in place for the external customers, for example when they have targets on purchasing costs. The higher supply in December leads to a more extreme reaction of plant Z in December. It also has a long lasting effect on the on-hand inventory of plant Z. Based on the benefits for both PharmInc and plant Z we suggest to further investigate the supply to plant Y, especially in December. It should not be the case that plant Z gets their higher inventory because plant Y wants to meet their target. 55

72 In general we advise to sell more to external customers. This would result in a higher profit for PharmInc because of the higher profit margin, lower costs for plant Z and an overall lower stock level. When we look at the amount plant Z would source on average per period in order to optimize only their own KPIs, there is 34,453 kilos per month left that can be sold extra to external customers. This would result in a combined inventory level of plant X, plant Z and GIT of 67,059 kilos product A on average per month. Use different transfer price for managerial evaluation One obvious way to make it more beneficial for plant Z to order product A from plant X is by reducing the price. However, the transfer pricing within companies is watched closely by tax authorities and not easily altered. One possibility also found in literature is to have a transfer price for tax purposes, which is authorized by the tax authorities and one internal transfer price only used to assess the performance of the business units (Shunko, Debo, & Gavirneni, 2014). By using an internal transfer price for managerial evaluation of c T h X, which is what PharmInc pays for every kilo shipped from plant X to plant Z, we can mimic the optimal strategy for PharmInc. We do have to note that this causes an extra administrational burden because there are two different administrations that have to be kept up with. Another option is to use this lower price c T h X when plant Z makes their business cases regarding product A. This already happens with other products of PharmInc that are sold internally. This means it is not necessary to have a double bookkeeping and they will regard the costs of product A from plant X the same as the costs for PharmInc when basing their decisions on a business case. Carry over inventories from plant X later in time At the moment the GIT from plant X to plant Z are immediately counted as stock of plant Z. This causes that ordering product A at plant X has a negative influence on stock height and inventory related costs for plant Z. When the inventories are carried over one month later or when product A arrives at country Z, this negative impact is mitigated for plant Z. This will cause the local decision making to be closer to the central decision making, because it is more beneficial than before to order from plant X. However, the cost benefit of ordering product A from plant X rather than supplier S will still be small ACADEMIC RELEVANCE In the researched literature we have not found evidence that there exists literature that studies decision making within a two-supplier model with one internal and one external supplier. In this research we have tried to fill that gap by using a practical case study from a pharmaceutical company and developing a mathematical model. Despite the models being made to fit a certain situation, we are confident that it can be used in other situations by changing the parameters or relax the assumptions. There are more companies that have both internal and external suppliers. When the internal supplier and buyer belong to different divisions with their own targets and profit and loss statements, it is possible to encounter a similar situation as described within PharmInc. Therefore the model can be generalized to situations where there exists local decision making with one internal and one external supplier. We have to note that because we use a myopic model, our model is not suitable in situations where the stock remains for a long period on-hand. 56

73 8.3. SUGGESTIONS FOR FURTHER RESEARCH We have used assumptions in order to be able to scope the problem. Further research could be based on what happens when we relax these assumptions, in order to be able to generalize the models more. We have already found that a lot of out assumptions when relaxed give approximately the same overall costs structures in terms of which model is more beneficial in a certain situation. For an overview of these assumptions, see Appendix D. There are two assumptions that we expect to have a large impact on the outcome of the models. The first is the assumption that the supply from plant Z is unlimited. One suggestion therefore is to research how the decisions change when this is not the case anymore. This will probably have the biggest impact in Model 2, since they did not use the full supply of plant X there yet. Furthermore the assumption that all the demand for product A of external customers is already fulfilled when deciding on the available supply from plant X to plant Z can have a large impact. This can cause the available supply to be significantly smaller due to the uncertainty of the demand of external customers. We would also suggest making a complete model of supply chain under investigation, so include the decision making of plant Y and the production of product B into the models. We saw some evidence that also plant Y alters their decision in December, which could be a result of the target that is put on their on-hand inventory plus GIT. By including this decision making, we get a more complete picture of the local decision making within the supply chain. The inclusion of the production of product B in the model would require a model that is able to suggest a certain optimal production schedule of plant Y and plant Z within the restrictions of the capacity. The demand of product B is then used as external variable in the model. This allows for more realistic demand for product A and possibilities to influence the needed product A. 57

74 BIBLIOGRAPHY Barankin, E. W. (1961). A delivery-lag inventory model with an emergency provision. Naval Research Logistics Quarterly, Bertrand, J. W., & Fransoo, J. C. (2002). Operations management research methodologies using quantitative modeling. Operations Management Research, 22(2), Cohen, M. A., & Mallik, S. (1997). Global supply chains: Research and applications. Production and Operations Management, 6(3), Field, A. (2009). Discovering statistics usings SPSS (3th ed.). London: SAGE Publications Ltd. Goetschalckx, M., & Fleischmann, B. (2005). Strategic Network Planning. In H. Stadtler, & C. Kilger (Eds.), Supply chain management and advanced planning (3rd ed., pp ). Berlin, Heidelberg: Springer. Hyde, C. E., & Choe, C. (2005). Keeping two sets of books: The relationship between tax and incentive transfer prices. Journal of Economics & Management Strategy, 14(1), Laínez, J. M., Schaefer, E., & Reklaitis, G. V. (2012). Challenges and opportunities in enterprise-wide optimization in the pharmaceutical industry. Computers and Chemical Engineering, 47, Lee, H., & Whang, S. (1999). Decentralized multi-echelon supply chains: Incentives and information. Management Science, 45(5), Minner, S. (2003). Multiple-supplier inventory models in supply chain management: A review. International Journal of Production Economics, Narayana, S. A., Pati, R. K., & Vrat, P. (2012). Research on management issues in the pharmaceutical industry: a literature review. International Journal of Pharmaceutical and Healthcare Marketing, 6(4), Narayana, S. A., Pati, R. K., & Vrat, P. (2014). Managerial research on the pharmaceutical supply chain - A critical review and some insights for future directions. Journal of Purchasing & Supply Management, 20, Sargent, R. G. (2013). Verification and validation of simulation models. Journal of Simulation, 7, Schmidt, G., & Wilhelm, W. E. (2000). Strategic, tactical and operational decisions in multi-national logistics networks: a review and discussion of modeling issues. International Journal of Production Research, 38(7), Sethi, S. P., Yan, H., & Zhang, H. (2003). Inventory models with fixed costs, forecast updates, and two delivery modes. Operations Research, 51(2),

75 Shah, N. (2004). Pharmaceutical supply chains: key issues and strategies for optimisation. Computers and Chemical Engineering, 28, Shunko, M., Debo, L., & Gavirneni, S. (2014). Transfer pricing and sourcing strategies for multinational firms. Production and Operations Management, Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory management and production planning and scheduling (3th ed.). New York: John Wiley & Sons. van Schijndel, E. (2014). Optimization and coordination of global pharmaceutical supply chains. Literature review: Eindhoven University of Technology. Van Strien, P. J. (1997). Towards a methodology of psychological practice. Theory and Psychology, 7, Vidal, C. J., & Goetschalckx, M. (1997). Strategic production-distribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research, 98, Whang, S. (1995). Coordination in operations: A taxanomy. Journal of Operations Management, 12,

76 APPENDIX A: LIST OF ABBREVIATIONS Abbreviation Meaning API Active Pharmaceutical Ingredient BU Business unit EBITDA Earnings before interest, taxes, depreciation and amortization GIT Goods in transit KPI Key performance indicator OWC Operating working capital WACC Weighted average cost of capital 60

77 APPENDIX B: LIST OF FIGURES Figure 1. Supply Chain product A... III Figure 2. Average on-hand inventory of Model 1 versus Model 1 December with steady supply... VI Figure 3. Supply Chain product A... 2 Figure 4. Forecasted and actual demand of product A in plant Z over Figure 5. Stock development of product A in plant Z over Figure 6. Stock development of product A in plant X over Figure 7. Model of Mitroff for research design (1974)... 7 Figure 8. Part of the product A supply chain under investigation Figure 9. Timeline and legend of events in plant Z Figure 10. Forecast updates Figure 11. Framework validation and verification (Sargent, 2013) Figure 12. Components of inventory related costs for plant Z Figure 13. Components of inventory related costs for PharmInc Figure 14. Average on-hand inventory plant Z Model 1 versus Model 1 December Figure 15. Components of inventory related costs of PharmInc per target Figure 16. On-hand inventory plant Z of Model 1 versus Model 1 December with steady supply

78 APPENDIX C: LIST OF TABLES Table 1. Cost and OWC plant Z of Model 1 versus Model 2 versus Model 3... V Table 2. Cost and OWC PharmInc of Model 1 versus Model 2 versus Model 3... V Table 3. Cost and OWC plant Z of Model 1 versus Model 1 December... V Table 4. Cost and OWC PharmInc of Model 1 versus Model 1 December... VI Table 5. Overview of locations and products... 1 Table 6. Notation Table 7. Performance Model 1 versus Model 2 versus Model Table 8. Cost and OWC plant Z of Model 1 versus Model 2 versus Model Table 9. Cost and OWC PharmInc of Model 1 versus Model 2 versus Model Table 10. Performance Model 1 versus Model 1 December Table 11. Cost and OWC of plant Z of Model 1 versus Model 1 December Table 12. Cost and OWC of PharmInc of Model 1 versus Model 1 December Table 13. Performance PharmInc Model 2 versus Model 2 December Table 14. Cost and OWC of Model 2 versus Model 2 December Table 15. Influence of changing the target on KPIs of plant Z Table 16. Influence of changing the target on KPIs of PharmInc Table 17. Cost and OWC plant Z of Model 2 versus Model 2 OWC Table 18. Cost and OWC PharmInc of Model 3 versus Model 3 OWC Table 19. Cost and OWC plant Z of Model 3 versus Model 3 OWC Table 20. Cost and OWC plant Z of Model 2 versus Model 3 OWC Table 21. Cost and OWC PharmInc of Model 1 versus Model 3 OWC Table 22. Comparison of basic model and steady supply for Model 1 and Model 1 December Table 23. Comparison of basic model and steady supply model Model Table 24. Comparison of basic model and steady supply model Model Table 25. Sensitivity analysis H, inventory related costs plant Z Table 26. Sensitivity analysis H, inventory related costs PharmInc Table 27. Shapiro-Wilk test of normality for demand from plant Y Table 28. Shapiro-Wilk test of normality for transformed demand from plant Y Table 29. Shapiro-Wilk test of normality for demand of external customers Table 30. Shapiro-Wilk test of normality for demand parameters plant Z Table 31. Correlation between forecast updates Table 32. Overview of specified parameters Table 33. Outcomes for zero supply from plant X Table 34. Outcomes for extreme demand in plant Z Table 35. Results deterministic demand Table 36. Performance of Model 1 under different holding cost rates Table 37. Performance of Model 2 under different holding cost rates Table 38. Performance of Model 3 under different holding cost rates Table 39. Sensitivity analysis H, total costs plant Z Table 40. Sensitivity analysis H, total costs PharmInc

79 APPENDIX D: LIST OF ASSUMPTIONS Suppliers are reliable We have assumed that everything that is ordered will be delivered on time in full, for simplicity of the model. The supply from plant X is reliable in terms of quantities, since plant X decides themselves how much they can supply to plant Z. With the actual lead time no serious disruptions were mentioned in the supply from plant X to plant Z. We made the lead time in the model two weeks longer, so the impact of this assumption for the supply from plant X will be small to non-existent. For plant Z we assumed an unlimited supply within one month. However, we do not have insights in the maximum supply per year of the supplier S. Also the negotiations for the supply from supplier S usually start usually some time before the order is placed. We assumed here that the order can be placed directly and the lead time is one month from first contact. In our model we therefore assume supplier S to be more reliable and faster than they are in reality. This can have a large impact on the outcomes of the models. Minimum supply from plant X is constant We considered the minimum supply from plant X to be able to make product B2 and B3 to be constant at 14,000. When in one month there is still some product A left that is supplied from plant X, it is not necessary to order again a minimum of 14,000 kilos from plant X. However, we assumed that the minimum amount is always 14,000. Because of the volatility of the demand, we do not know for sure how much product A from plant X is going to be on-hand in two periods and we want to be sure to be able to produce these products for cost reasons. Only a constant minimum order from plant X will ensure that there is enough product A from plant X on-hand to produce products B2 and B3. We also do not add extra costs for the case when S t XZ < m XZ. The only model where we could be in trouble because of too little product A from plant X on-hand is Model 2, since we have very low order from plant X there. But because the low orders, the supply gets high very quick and we do not have to worry about a too small supply. In Model 1 and Model 3 we usually have a high order from plant X, so we can expect that there is still enough product A from plant X on-hand in order to produce B2 and B3 when the supply is smaller than 14,000. Only in 2.3% and 2.0% of the periods the supply is lower than 14,000 for respectively Model 1 and Model 3. Therefore we do not expect a large impact of this assumption on the outcome of the models. Lost sales We assumed all demand of product A that cannot be fulfilled to be lost sales. Since product A is used in a next production step to produce product B, this is only the case when plant Z is not able to produce product B in another period. Therefore the production utilization should be maximum. In the first three quarters of the year this is usually the case, however in the last quarter the production of product B is usually not at full capacity. The impact of this assumption is that the penalty cost are estimated higher 63

80 than with backorders and the average on-hand inventory is larger, since we do not need to fulfill the demand in a later period. We also assumed that the lost sales would not result in less demand in future periods. Since product B1, B2 and B3 that are produced in plant Z from product A are mostly sold on the spot market without fixed contracts, we can assume this is the case. In order to calculate the optimal value for Q t XZ in Model 2 and Model 3 we have assumed that the lost sales are negligible. For the model that has the highest lost sales, Model 2, the lost sales are 0.45% of the total demand. Therefore we can expect the lost sales indeed to be negligible. When we run the models and allow for back orders instead of lost sales, the results are very close to the models with lost sales. The average on-hand inventory of plant Z is only 0.59% lower when having backorders than when having lost sales. The overall outcome of the models stays the same when we relax this assumption so we do not expect a large impact of this assumption on the outcomes. Order plant Y and external customers We assumed that the order from plant Y and external customers are always smaller than the supply. This means everything that plant Z does not order in one period is added to the next period. Since we are working with normal distributions, it is possible that the demand of plant Y and external customers is higher than the production in plant X. However, we have made a restriction during the simulation that when this is the case, the resulting supply for plant Z will be zero. We also saw within PharmInc that there was never a period with zero supply. This makes it reasonable that the order of plant Y and external customers is never more than the production in plant X. Another assumption is that the demand for external customers is already fulfilled when plant X decides on the maximum supply for plant Z. In reality this demand is very uncertain. To account for this uncertainty plant X has to have some safety stock. Because the profit margin for external customers is very high compared to selling it to plant Z, this can have a big impact on the supply to plant Z. A smaller supplier causes the models to be closer together, since the outcomes of Model 1 and 3 will be closer to Model 2. Target on OWC is reached in December The target on OWC is measured four times a year, at the end of each quarter. We do see the consideration to reach the target is especially present in December, when also the personal premiums will be paid soon. Therefore we decided to focus on this measurement of the target and assume that the target is reached when it is reached in December. We saw that when the decision is made every month to reach the target, there is a high stock build-up at plant X. This assumption therefore does have a big impact, especially on the decision making of Model 1. However we did not find evidence that there is local decision making at the end of the other months or quarters, making this a correct representation of the reality. 64

81 On-hand inventories for maximum one period This assumption affects Model 2 and Model 3 since it is there used to determine the order quantity at supplier S. After running the simulation we saw how often the demand of a certain period is less than the on-hand inventory of the previous period, which indicates that the on-hand inventory is there for longer than one period. The percentage of periods where this is the case is 15.2% and 28.3% for Model 2 and Model 3 respectively. This means we have in these periods product A on-hand for more than one period, therefore resulting in higher costs that we do not take into account and higher orders at supplier S than what would be optimal. In Model 3 this also includes the on-hand inventories at plant X, where we assume that they are onhand for one period. When we test this assumption we saw that in 3.0% percent of the periods the stock at plant X is there for more than 1 period. This causes the order from plant X in Model 3 to be lower in our myopic model than what it should be to be cost optimal. We did see with the higher holding cost, that the costs went up, but the same conclusions could be drawn from the differences between the models. Therefore we expect that this assumption does not have a big impact on our conclusions. Full production plant X PharmInc produces product A on full capacity in plant X, because they have fairly high fixed costs compared to their variable cost. Besides, product A is made via a process that is very difficult and expensive to stop. Price is constant We assumed the price is constant for simplicity and tractability of the model. When the price at supplier S goes up, the difference between the costs of sourcing product A at supplier S and plant X will become smaller. This means that it is more likely that more is ordered at supplier S. At some point it is even more expensive to order from plant X than from supplier S When the price gets lower, the difference gets larger, causing plant Z to order more from plant X. Because the transfer price is based on the price paid at the external customers, the differences will never be marginal. We therefore expect that this assumption does not affect the outcomes of the models a lot. 65

82 APPENDIX E: FINDING THE MINIMUM OF COST FUNCTION Q t XZ The following cost function is used in Model 2 to decide on Q t XZ : E[Cost t (Q XZ t )] = Q XZ t c XZ + E[Q t+1 SZ ] c SZ We have to find the value of Q t XZ that minimizes the above cost function. We can find the minimum of a function by setting the first derivative of the cost function Cost t (Q t XZ ) to 0 and later check whether this is truly the minimum by finding the value of the second derivative. Step 1. 1 ( pz For simplicity we denote G t+2 p Z +h Z) OH t+1 as x with an at the moment unknown probability distribution function f(x) and cumulative probability distribution function F(y) = P{x y}. E[Cost t (Q XZ t )] = Q XZ t c XZ + E[Q t+1 SZ ] c SZ E[Cost t (Q t XZ )] = Q t XZ c XZ + c SZ With Leibniz s Rule we can find the first derivative of c SZ Leibniz s Rule: a d 2 (y) dy h(x, y)dx = a 1 (y) a 2 (y) a 1 (y) dh(x, y) dx dy Q t XZ QXZ t (x Q t XZ )f(x)dx (x Q t XZ )f(x)dx + h(a 2 (y), y) da 2(y) h(a dy 1 (y), y) da 1(y) dy When we apply Leibniz s Rule to (x Q XZ t )f(x)dx QXZ we get the following. t dcost t (Q XZ t ) DC = c XZ + c SZ [ ( 1)f(x)dx + ( Q XZ dq t )f( )(0) (Q XZ t Q XZ t )f(q XZ t )(1)] t Q t XZ dcost t (Q XZ t ) XZ = c XZ + c SZ f(x)dx dq t Q t XZ dcost t (Q XZ t ) XZ = c XZ c SZ f(x)dx dq t Q t XZ dcost t (Q t XZ ) dq t XZ = c XZ c SZ (1 F(Q t XZ )) F(Q XZ SZ t ) represents the cumulative probability that Q t+1 is zero, since we denoted G t+2 1 ( pz p Z +h Z) XZ OH t+1 as x and F(y) = P{x y}. At the moment that x Q t the local order of the next period (Q t+1 will be zero. So 1 F(Q XZ t ) SZ is the probability that the order of Q t+1 is greater than zero. SZ ) 66

83 dcost t (Q t XZ ) dq t XZ = c XZ c SZ P{x Q t XZ > 0} = 0 P{x Q t XZ > 0} = cxz c SZ Step 2. To be sure this is the minimum, we perform a convexity check with the second derivative of the cost function. dcost t (Q t XZ ) dq t XZ = c XZ c SZ (1 F(Q t XZ )) = c XZ c SZ + c SZ F(Q t XZ ) d 2 Cost t (Q t XZ ) d 2 Q t XZ = c SZ f(q t XZ ) Since the cost c SZ are positive and the probability distribution function can only take values between 0 and 1, the second derivative is always greater than or equal to 0. This means the cost function is convex and we have a minimum at the specified Q t XZ. Step 3. 1 ( Now we insert G t+2 pz p Z +h Z) OH t+1 again instead of x. P {G t+2 1 ( pz p Z + h Z) OH t+1 Q XZ t > 0} = cxz c SZ 67

84 APPENDIX F: DISTRIBUTION OF D t,t+1 AND G t+2 1 ( D t,t+1 pz p Z +h Z) For D t,t+1 the only unknown variable is the realization of period t+1 of R 2, which is normally distributed with mean μ R 2 and standard deviation σ R 2. Therefore we know the distribution of D t,t+1 to be the following: G t+2 1 ( pz p Z + h Z) 1 D t,t+1 ~N(f t+1 + r t+1 + μ R 2, σ R 2) Of G t+2 1 ( pz p Z +h Z)we only know f t+2 at time t. We will first analyze G t+2 and know the variables that are known at time t+1. At time t+1 G t+2 1 ( pz p Z +h 1 ( pz p Z +h 1 f t+2 + r t+2 + R 2 1 ~N(f t+2 + r t+2 + μ R 2, σ R 2) pz G t+2 (x) = P{d t+2 x} = p Z + h Z Z) as if we are at time t+1 Z) is just a number. G 1 t+2 ( pz p Z + hz) = x 1 P{f t+2 + r t+2 + R 2 x} = pz p Z + h Z 1 Since f t+2 and r t+2 are constants and known at time t+1, we can also subtract them from the value x on 1 the other side of the equation. We set x f t+2 r t+2 equal to a value z. 1 P{f t+2 + r t+2 + R 2 x} = P{R 2 x f t+2 r 1 t+2 } = P{R 2 z} The probability that R 2 is smaller or equal to z is still decided by the ratio denoted by the cumulative distribution function Z(z) of R 2. Z(z) = P{R 2 z} = p Z + h Z To calculate the value of z we can use the inverse function of Z(z). pz pz Z 1 ( p Z + h Z) = z = x f t+2 r t+2 1 x = z + f t+2 + r t+2 1 p Z p Z +h Z. This probability is 68

85 Since we do not get more information about R 2 SZ at time t+1 when Q t+1 is decided, the value of z will not change at time t+1 compared to time t. Therefore z is a constant in every period of t and only depends on μ R 2 and σ R 2. The only value that is unknown at time t and known at time t+1 is r 1 t+2. We do know the distribution of R 1, so we can use this distribution to define the distribution of G t+2 1 ( pz p Z +h Z). G t+2 1 ( pz p Z + h Z) = z + f t+2 + R 1 ~N(z + f t+2 + μ R 1, σ R 1) 69

86 APPENDIX G: DEMAND DATA FROM PLANT Y Due to confidentiality this appendix is left out. 70

87 APPENDIX H: NORMALITY TESTS DEMAND FROM PLANT Y Table 27. Shapiro-Wilk test of normality for demand from plant Y Table 28. Shapiro-Wilk test of normality for transformed demand from plant Y 71

88 APPENDIX I: DEMAND DATA EXTERNAL CUSTOMERS Due to confidentiality this appendix is left out. 72

89 APPENDIX J: NORMALITY TESTS DEMAND EXTERNAL CUSTOMERS Table 29. Shapiro-Wilk test of normality for demand of external customers 73

90 APPENDIX K: DATA MINIMUM SUPPLY FROM PLANT X Due to confidentiality this appendix is left out. 74

91 APPENDIX L: HISTORICAL COSTS OF EXTERNALLY SOURCED PRODUCT A Due to confidentiality this appendix is left out. 75

92 APPENDIX M: HISTORICAL DATA PRODUCT A DEMAND IN PLANT Z Due to confidentiality this appendix is left out. 76

93 APPENDIX N: NORMALITY TESTS DEMAND PARAMETERS PLANT Z Table 30. Shapiro-Wilk test of normality for demand parameters plant Z Table 31. Correlation between forecast updates 77

94 APPENDIX O: OVERVIEW PARAMETERS Table 32. Overview of specified parameters Parameter Description Value c SZ Marginal cost of buying one kilo extra from supplier S c T Transportation cost per kilo product A from plant X to plant Z c XZ Marginal cost of buying one kilo extra at plant X F Two-month forecast of the demand in ~ N( ; ) plant Z h X Holding cost per kilo product A in plant X h Z Holding cost per kilo product A in plant Z m XZ Minimum supply from plant X to plant Z 14,000 p SZ Price of one kilo product A bought at supplier S p XZ Price of one kilo product A bought at plant X p Z Penalty cost per kilo product A for which demand cannot be fulfilled. XE Q t Demand at plant X from external ~N( , ) t = 1,,11 customers 0 t = 12 XY Q t Demand at plant X from plant Y 127,202 (TQ XY t ) 2 t = 1,,11 ~N( ; ) t = 12 R 1 First forecast update, made one period ~N( ; ) before the demand is realized R 2 Second forecast update, reveals the actual ~ N( ; ) demand XZ S t Available supply from plant X to plant Z 189,000 Q XE XY t Q t 78

95 APPENDIX P: OPERATIONAL VALIDATION For the operational validation we will test extreme cases, such as zero supply from plant X, extreme high demand in plant Z and deterministic demand. Zero supply from plant X We will look at what happens when the supply from plant X is zero. To do so we assume that there is no minimum amount anymore that plant Z has to source from plant X. Because no product A can be ordered in plant X, it means that the service level in plant Z of Model 2 and 3 is only dependent on the amount that is sourced from plant Z. Since we order the amount of plant Z to be on a service level of the critical ratio p Z p Z +h Z = , which means we have enough on stock to fulfill the demand completely in 95.6% of the periods. We can check whether the simulated service level has this value. We ran the models seven times, which resulted in an average service level of (see Table 33). The 95%-confidence level of the service level is ( ; ), which includes the actual service level of We have to note however that the average simulated demand is higher than the average demand that the model uses to calculate the choices, because we do not allow for negative demand. This would result in a lower service level than indicated with the critical ratio. Table 33. Outcomes for zero supply from plant X Model 1 Model 2 & 3 Lost sales On-hand inventory plant Z 37, ,675.1 On-hand inventory plant X GIT Amount ordered at plant X Amount ordered at supplier S 72, ,530.4 Service level Percentage of times target reached Extreme high demand Now we model what happens when there is an extreme high demand in plant Z for product A. We changed the two-month forecast F to 829,669. The maximum supply from plant X will still be the same, which means we know for sure that we always have to order extra at supplier S. Now in every model the complete supply is ordered at plant X for the months January till November. Only with the models that have a different decision in December we see that the supply is not always ordered. This means only in the month December the actual order is lower than the supply. Again, since the quantity from plant X is never enough to fulfill the demand, the service level is completely decided by the local sourcing for model 2 and 3. After seven simulations we have an average service level of , where the critical ratio was The 95%-confidence interval of the service level is ( ; ), therefore including the real mean. 79

96 Table 34. Outcomes for extreme demand in plant Z Model 1 Model 2 & 3 Lost sales On-hand inventory plant Z 37, ,607.9 On-hand inventory plant X GIT 103, ,411.2 Amount ordered at plant X 51, ,704.4 Amount ordered at supplier S 767, ,172.2 Service level Percentage of times target reached Deterministic demand We assume now that the demand is deterministic and constant, with 70,000 kilos per month. This means that the two month forecast is 70,000 and the two forecast updates are 0. In order to be able use the formulas we have defined in Chapter 5, it is important to still define the forecast and the forecast updates as random variables. Therefore we give them a standard deviation of This causes model 2 and 3 to never order more than 70,000 kilos from plant X. Since we can be so certain that the demand is 70,000 kilos, the probability of having a positive order from supplier S the next period is 1 until 70,000 is ordered in plant X and 0 from 70,000 kilos ordered in plant X. P(Q t+1 SZ > 0) = { 1 if Q t XZ < 70,000 0 if Q XZ t 70,000 Because the demand is deterministic we do not need any safety stock and the on-hand inventory of model 2 and 3 will be zero in all periods. For model 1, where plant Z is obliged to take the amount of product A supplied from plant X, we have a much higher inventory position. We can see the results in Table 35. Table 35. Results deterministic demand Model 1 Model 2 & 3 Lost sales On-hand inventory plant Z 38, On-hand inventory plant X 0.0 9,010.9 GIT 103, ,452.6 Amount ordered at plant X 51, ,724.2 Amount ordered at supplier S 18, ,272.4 Service level Percentage of times target reached

97 APPENDIX Q: SENSITIVITY ANALYSIS HOLDING COST RATE Because the holding cost rate was estimated, we did a sensitivity analysis on the holding cost rate. We have used the same input data for every holding cost rate and simulated for 30,000 periods. Impact on outcomes models For model 1 we do not see any changes in the outcomes, since Model 1 do not take the holding cost into account when the decisions are made (see Table 36) Table 36. Performance of Model 1 under different holding cost rates H Lost sales On-hand inventory Amount ordered Service level plant Z supplier S ,781 21, For Model 2 we see in Table 37 increasing lost sales and decreasing on-hand inventory, which leads to a lower service level. Also the amount that is ordered at the external supplier will get less, since the critical ratio of the decision gets smaller with higher holding costs. Table 37. Performance of Model 2 under different holding cost rates H Lost sales On-hand inventory Amount ordered Service level plant Z supplier S ,881 55, ,693 55, ,662 55, ,752 55, ,939 55, For Model 3 we see in Table 38 the same increasing and decreasing values as we saw in Model 2. Here we also added the on-hand inventory in plant X. With the increase of the holding cost rate, also the holding cost in plant X get more expensive which leads to higher orders from plant X. Table 38. Performance of Model 3 under different holding cost rates H Lost sales On-hand inventory plant Z On-hand inventory plant X Amount ordered supplier S Service level ,988 6,149 21, ,859 6,067 21, ,886 5,986 21, ,034 5,905 21, ,278 5,826 21,

98 Impact on total costs models The total costs of all models increase with an increasing holding cost rate (see Table 39 and Table 40). Model 1 does rise faster than the other models, which we already saw with the inventory related costs of the models. Table 39. Sensitivity analysis H, total costs plant Z H Model 1 Model 2 Model Table 40. Sensitivity analysis H, total costs PharmInc H Model 1 Model

99