Evaluating inventory control policies for assemble-to-order systems that serve product and component demand

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Evaluating inventory control policies for

assemble-to-order systems that serve product

and component demand

Yahmal Sybout Brown S3029891

Master thesis, MSc Technology & Operations Management University of Groningen, Faculty of Economics and Business

June 2018

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Abstract

Purpose – ATO systems that serve demand for the end product and component have different challenges to

overcome. On the one hand a replenishment policy must be set in place. On the other hand, it must be determined under which allocation policy demand can be fulfilled. Considering the fact that there are two types of demand coming in - end product and component - an allocation policy should be implemented. In case of a stock out for the end product a backorder will be considered and a stock out for the component implies lost sales. The two considered allocation policies are the first-come-first-serve and first-ready-first-served. These two prioritize orders based on the time of arrival and on the availability. The purpose of this study is to find the difference in total costs on the performance measures for the average on-hand inventory, amount of outstanding backorders, and the amount of lost sales under the allocation policies.

Methodology - For this study a discrete event simulation model was constructed. In the model, the FCFS

and FRFS allocation policy were tested under the base stock policy. For each allocation policy three cases were tested: component demand represents a significant portion of total sales, end product demand represents a significant portion of total sales, and where end product and component demand occur equally.

Findings – The results of this study show that there is a significant difference under the three cases for the

type of allocation policy. In the case where component demand represents a significant portion of total sales, the results show that a FRFS allocation policy will yield the lowest costs. In the case where the end product demand represents a significant portion of total sales, the results show that a FCFS allocation policy will yield the lowest costs. In the case of equal demand for the end product and component, the results do not show any significance and the total costs are relatively the same.

Originality/value – This study addresses the theoretical gap on how a multiple product ATO system can

cope with demand for the end product and component, where backorders are only allowed for the end product and a stock out for component demand implies lost sales. Furthermore, the results provide insights on how the allocation policies behave in the various cases under a base stock policy.

Keywords – Assemble to order, base stock model, allocation policies, first-come-first-serve,

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1. Introduction

In order for companies to offer more individualized products to their customers, they can offer their products as a configuration. Product configuration on the customer’s side has been a proven method to realize the pursuit of a more customized offering (Feng et al. 2009; Fogliatto, Da Silveira & Borenstein 2012; Ostrosi & Tié Bi 2010).

Over the past years, the shift of companies that are transforming to more customization in their product offerings is becoming noticeable (Tang, Wang & Ullah 2017). To provide more customization in their product offerings a system like Assemble to Order (ATO) could be implemented. ATO systems are known for they possibility to offer customized products while keeping lead times low (Yang et al. 2018). The ATO strategy can be seen as a mixed strategy of a pure make-to-stock (MTS) and a make-to-order (MTO) strategy. Whilst the decoupling point of products in a MTO environment is at the very beginning of the production process, the decoupling point in a MTS environment is at the end of the supply chain. The decoupling point in an ATO environment varies between companies and depends on the degree of customization of a product.

However, ATO systems that serve demand for both the end product and components, will have more aspects to consider when developing an inventory control policy (Elhafsi et al. 2015). The challenge that arises with these ATO systems is that there are separate demand streams for the end product and individual components. An example of this challenge could be a company that assembles and sells an end product XYZ and offer the individual components X, Y, and Z to the after-market. If component X is out of stock, an order for the end product XYZ cannot be fulfilled until component X is back in stock. Elhafsi et al., (2015) conducted research on this specific case and considered this unsatisfying demand to result in a lost sale. Whereas Elhafsi and Hamouda (2015) considered this unsatisfying demand to be backordered.

It is a challenge for companies, that work with ATO systems, to serve both demand for the end product and the individual components in order to prevent this occurrence of a lost sale or backorder. Needless to say, that the challenge increases when an ATO system offers multiple products.

A way of coping with these challenges is to implement an allocation policy. An allocation policy helps in determining, at the time of a customer order and at the time of component replenishment delivery, which component is allocated to which order (Lu, Song & Zhao 2010).

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6 would be a natural occurrence that the customer would move on and look for an alternative on the market, hence a lost sale. However, consider the case where a customer places an order for the end product and a stock out occurs. It would be a natural occurrence for the customer to consider the fact to wait given that the assembly will provide an added value, hence backorder, it could be very likely that the customer allows it to be backordered in the occurrence of a stock out.

Only few studies have dived into this problem in determining the allocation policy in these situations. Elhafsi et al. (2015) studied the single end product ATO system that serves two customer classes and assume that customer demands occur for the end product and the individual component. In the case of a stock out, however, the demand is considered to be a lost sale. In a similar work Elhafsi and Hamouda (2015) study an ATO system, in which the end product and individual components are also available for sale as well, but here a backorder is allowed in the occurrence of a stock out.

This paper will study a multiple product ATO system that is serving both demand for end products and components, where the components are sold in the after-sales market. The purpose of this study is to determine which inventory policy will achieve the lowest cost when considering backorders for the end product and a lost sale for the component in case of a stock out on the performance measures for the average on-hand inventory, amount of outstanding backorders, and the amount of lost sales. This study is most related to those of Elhafsi et al. (2015) and Elhafsi and Hamouda (2015), but differs in the following way. This study will allow backorders for end product demand and considers component demand to be lost in case of a stock out. This is arguably more realistic as customers may find it difficult to find an alternative supplier for customized end products, whereas components can typically be sourced from multiple suppliers. Therefore, the corresponding research question is as follows:

Which inventory policy will achieve the lowest cost for multiple product ATO systems, with end product and component demand, where backorders are allowed for the end product, but missed demand for individual components imply lost sales?

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2. Background

2.1 Assemble-to-Order systems

A familiar example of an ATO system is Dell Computers. Dell has been a leading example in the literature on how it lets the customer configure their personal computer (PC) by selecting the various components. The number of end products, which are the total combination of options, is extensive.

Song and Zipkin (2003) define an ATO as a system that includes several components and several products, where the components are shared by several products. In an ATO system the time to assemble a product from its components is negligible. However, the time to procure or produce a component is rather significant. This results in a combination of two steps: the first one is the component procurement or production, and the second is the assembly (Atan et al. 2017). Companies that pursue an ATO system can reduce their customer response time by keeping component inventories, therefore delaying the final assembly of the end products until the arrival of customer demand (Atan et al. 2017). Figure 1 shows the customer order decoupling point for the ATO system and other production systems.

Figure 1 Customer order decoupling points (Olhager 2012)

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2.1.1 ATO system with multiple end products

Many studies have been performed for continuous review models with multiple end-products. Models with multiple end products are in general more complex in comparison to single end product models, due to the fact that they have to address component allocation and inventory replenishment policies (Atan et al. 2017). By making assumptions and looking at specific configurations of the system for the component and end product, characterizing the optimal policy becomes less difficult. The most common configurations of component and end products can be seen in figure 2.

Figure 2 Component configurations for ATO systems (Nadar, Akan & Scheller-wolf 2014)

Figure 2 shows the N-system consisting of two components and two end products. In this system one end product is assembled from two components and the other end product is produced from one of the components. The M-system shows the production of three different end products out of two components. In this system, one end product is assembled from two components and the other end products are manufactured from one component. The W-system works with three components and two end products. Here, each end product shares a common component. The nested system shows multiple components and multiple end products. In a nested system, multiple variations of end products with common components are possible (Nadar, Akan & Scheller-wolf 2014).

2.2 Inventory control policies

2.2.1 Replenishment policies

The purpose of an inventory control system is to estimate at what time an order should be placed and the amount it should be (Axsäter 2015). There are many theories on ordering policies available in the literature, where the most common are the (R, Q) policy and (s, S) policy. Under the (R, Q) policy, a batch quantity of size Q is ordered when the inventory position declines to or below the reorder point R (Axsäter 2015; Hopp & Spearman 2008). Under the (s, S) policy, the system will order up to the maximum level S when the inventory position drops to s. A variation on this policy is also called the base stock policy, where

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9 The base stock model has shown a dominant present, when looking at the replenishment policies used in research on ATO systems under a continuous review (Atan et al. 2017). Atan et al. (2017) state that optimal replenishment policy is unknown for general ATO systems. Nevertheless, these studies have achieved close to optimal results under specific assumptions.

This paper will monitor the base stock model as the replenishment policy where S denotes the base stock level, Ii(S) denotes the average on-hand inventory level (in units) for component i as a function of S, and where hi denotes the cost to carry one unit of inventory for one unit of time for component i.

Even though the base stock model is not yet considered to be the optimal replenishment policy, as stated by Atan et al. (2017), it is however an easy to use and realistic replenishment policy given that it is a common choice for studies in this area.

2.2.2 Allocation policies

When a customer demand arrives an allocation decision must be made for the customer order that should be fulfilled. In general, the most common allocation policy that is studied for ATO systems with a base stock model, is the first-come-first-served (FCFS) policy (Atan et al. 2017; Lu, Song & Zhao 2010). Another rule that is considered is the No-holdback (NHB) allocation policy first-ready-first-serve (FRFS), meaning that a backordered demand cannot reserve any available stock. The state dependent rationing level allocation policy, where allocation depends on the component inventory levels (Atan et al. 2017), is considered as well.

The FCFS allocation policy considers that demand for each component is fulfilled in exactly the same sequence as it occurs (Lu, Song & Zhao 2010). In other words when a demand arrives for the end product and one component is not available, the demand will be backordered and the available component will be allocated to that backordered demand. When a replenishment order is being delivered, it will be allocated to the oldest backordered demand with the reserved component.

The situation above describes the case of a demand that needs to be fulfilled for the end product. In the situation that a demand arrives for one of the individual components and the demand cannot be fulfilled immediately, the demand will not be backordered but considered as a lost sale.

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10 guarantees order fulfilment within a certain period of time (Lu, Song & Zhao 2010). The decision tree that illustrates the allocation rule FCFS can be found in Appendix A.

Following the NHB allocation policy FRFS, the end product demand that cannot be fulfilled immediately will be backordered. Only in this scenario the available component will not be allocated to the backordered end product demand. Therefore, demand that occurs in the meantime can be satisfied if the stock of that specific component is available. With the FRFS allocation rule, an unfulfilled component demand will be considered as a lost sale.

This process requires more information coordination in comparison to the FCFS. It is considered a drawback due to the fact that a backordered end product can only be fulfilled if both components are available at the same time. This may result in an increase of backorders of the end product as well.

The advantages are that the total on-hand inventory will be minimized compared to FCFS. This will result in a decrease of the total on-hand inventory I(S). It is also stated by Lu et al. (2010) that the FRFS allocation rule will minimize the average number of back orders B(S). The decision tree that illustrates the allocation policy FRFS can be found in Appendix A.

This paper will focus on the FCFS rule and the NHB allocation rule FRFS. These policies are chosen due to the fact that they are regularly seen in practice (Kapuscinski et al. 2004; Xu, Allgor & Graves 2009). However, these allocation policies have not been tested under the circumstances of a base stock model that serves demand for both the component and end product with backorders and lost sales.

Under these allocation policies, the average number of outstanding backorders and average number of lost sales for component i per time unit will be monitored, denoted by B(S) and Ci(S) respectively. For each

occurrence a penalty will be assigned, where b denotes the cost to carry one unit of backorder for one unit of time, and ci denotes the cost for not fulfilling one unit of demand for component i.

2.3 Conceptual model

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11 The conceptual model shows the direct of the allocation decision on the total costs. The relationship between the type of allocation decision and costs were tested by performing a simulation study.

ATO systems with end product and component demand

Allocation decision

Total costs Leads to

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3. Methodology

This section gives an overview of the steps needed to execute this research and provides a structure within which the research is conducted. Furthermore, it will describe the type of research required to obtain the information, which information is required to answer the research question, and how the data will be analysed.

3.1 Research method

The purpose of this study is to find the difference in total costs on the performance measures for the average on-hand inventory, amount of outstanding backorders, and the amount of lost sales under the FCFS and FRFS allocation policies for ATO systems that serve demand for the end product and component. In order to achieve this goal, the proposed methodology is simulation. Computer simulation is the chosen research method, as this study will deal with several scientific models to compare the results with, increasing the complexity of this study (Karlsson 2016). Furthermore, performing a simulation model can help predict the system performance and compare alternative system designs in order to determine the effect of certain policies on the system, due to the different type of customer demands and the accessory variability (Robinson 2014). This study will use Siemens’ Tecnomatix Plant Simulation 12 to build and run the simulation model. This software is chosen due to its availability and free access that is being provided by the University of Groningen.

3.2 Model design

This study will consider an ATO system with three end products and three components. The inventory for the three components is controlled under a base stock model and continuously reviewed. Demand is considered for the end product and the individual components. Backorders are only allowed for the end product and unfulfilled demand for the individual components are considered as lost sales.

For this study, the base stock model will be considered as the replenishment policy for the individual components. Regarding the allocation of stock to fulfil demand the FCFS and FRFS allocation policies are considered, as described in the previous chapter. The study is based on the following assumptions.

1. Supplier lead times for the components are constant.

2. Unfulfilled demand for the end product is backordered and a penalty cost per time unit is incurred. 3. Unfulfilled demand for the individual component is lost and a penalty cost per lost sale is incurred. 4. Assembly of the end product is instantaneous. This is motivated by the fact that the supplier lead times are often much longer then the assembly time (Elhafsi & Hamouda 2015; Kapuscinski et al. 2004).

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13 6. Demands for the end product and individual components occur continuously over time according

to independent Poisson streams.

The performance of the FCFS and FRFS allocation policies under the base stock model will be measured with the above described assumptions. The on-hand inventory level, backorder level, and the lost sales level will be monitored, and used to determine the total cost (per time unit). The total cost function is given by:

𝑌(𝑆) = ℎ𝑖𝐼𝑖(𝑆) + 𝑏𝐵(𝑆) + 𝑐𝑖𝐶𝑖(𝑆)

Y(S) = cost function of the average inventory holding costs, back order costs, and lost sales costs per time unit

Ii(S) = average on-hand inventory level (in units) for component i as a function of S

B(S) = average number of outstanding backorders for the end product as function of S

Ci(S) = average number of lost sales for component i per time unit as a function of S

S = Base stock level (in units)

S – 1 = reorder point (in units), which represents inventory level that triggers a replenishment order

hi = cost to carry one unit of inventory for one unit of time for component i

b = cost to carry one unit of backorder for one unit of time

ci = cost for not fulfilling one unit of demand for component i

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14 The simulation model will monitor three performance measures. The first one is the average on-hand inventory level of the three warehouses of the components. In this study a fixed base stock level of S

= 10 units will be considered. The reason for not considering the base stock level as a variable is due to the

fact that this study is focused on the performance of the FCFS and FRFS allocation policy are under a base stock model. The base stock level was set at S = 10 units due to the fact that it results in a minimum service level of 0.99 for the different cases where demands shift. In appendix B the base stock level and service level calculations are explained. The second performance measure is the average number of outstanding backorders for the end product. The simulation model has a separate buffer that keeps track on the amount of incoming backorders and stores them until they can be fulfilled. The third performance measure is the average number of lost sales for component demand, it was monitored how many lost sales occurred per time unit.

An example of Hopp and Spearman (2008 p. 86) is used for the costs analysis. According to this example a company has a unit cost per part of €150 with an annual interest rate of 20 percent. The holding costs will be:

ℎ = €150 × 0.2 = €30 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟

Since this costs analysis is done per month, the holding costs will be set at:

ℎ =€30

12 = €2.50 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ

The costs for a backorder is set at €8.33 per month for the backorders. Regarding the lost sales for the components, the penalty will be €3.33 per lost sale.

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Table 1 Experimental settings for the simulation model

Parameter Experimental setting

Type of components A; B; C Type of products AB; AC; BC Supplier lead times 10 days

Replenishment policy Base stock model (S = 10)

Variable

Order arrival rates component/end product 6 days/24 days; 24 days/6 days; 15 days/15 days Allocation policy FCFS; FRFS

Performance measures

Average on-hand inventory level Amount of backorders Amount of lost sales

Costs measures

hi €2.50

b €8.33

ci €3.33

3.3 Experimental design

The initial data that the simulation model generates will generally not be valid. According to Robinson (2014), a simulation will be valid as soon as the model is in the steady state. In order to determine the steady state of the simulation model the average throughput per day of the customer orders have been examined with the Welch method. The Welch method calculates the moving average and graphically shows the steady state of the simulation model. The graph concerning the warmup time can be found in appendix D. This graph shows that the simulation model reaches the steady state at approximately 120 days.

The run length of the simulation has been set at 1300 days. According to Robinson (2014), a rule of thumb is that the run length is at least ten times the warm up time. With this rule of thumb, the run length of the simulation is valid.

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16 amount of replications has been chosen as the replication rate for the total simulation model. Appendix E shows the confidence interval method and replication rates per order type. It shows that the order for the end product AC takes a fairly long time for the graph to be stable. However, the deviation rate is well below 5%. In order to come up with useable data, safe this study will perform 40 replications per experiment. Table 2 summarizes the settings of the simulation model.

Table 2 Experimental design parameters

Parameter Number

Warmup time 120 days Run time 1300 days Simulation time (run time + warmup) 1420 days Replications 40

3.4 Data analysis

Three performance indicators were measured during the simulation run, in order to measure the performance of the FCFS and FRFS allocation policy with the base stock model as replenishment policy. Firstly, the average on-hand inventory level (in units) for component i. Secondly the average number of outstanding backorders for the end products per time unit. And lastly, the average number of lost sales for component i per time unit. The output results were statistically analysed to justify the conclusions of this research. The MANOVA test has been performed, as this simulation used an independent random stream and is used to determine which allocation policy will yield the best result based on the total costs.

The MANOVA test has been performed with the program SPSS. The MANOVA test analysed whether the two allocation policies differ from each other based on several variables. Before testing, a few assumptions had to be met first. The first was the normality test. The output of data showed for several performance indicators normality in the data, but not for all. However, due to the high number of replications it could be assumed by the central limit theorem that the data were valid (Stein 1972).

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Table 3 Durbin-Watson test results

R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson

.770a _0.593 _0.581 _12.516 _1.305

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4. Results

This chapter describes the results of the behaviour of the performance measures under the FCFS and FRFS allocation policy during the simulation. The first part describes the output data generated by the simulation model for the average on-hand inventor level under the FCFS and FRFS allocation policy and their significant differences. The second part describes the output data generated by the simulation model for the number of backorders under the FCFS and FRFS allocation policy and their significant differences. The third part describes the output data generated by the simulation model for the amount of lost sales under the FCFS and FRFS allocation policy and their significant differences. This chapter will conclude with an overview of the total costs of the performance measures under the FCFS and FRFS allocation policy.

4.1 Average on-hand inventory

Three warehouses were monitored during the simulation runs, according to thee component system. The average amount of components in the respective warehouses, with base stock level S=10, were measured. In table 4 the average on-hand inventory levels of the warehouses are given.

Table 4 Average on-hand inventory of component A, B and C per month

Allocation policy Experiment Average Inventory level component A Average Inventory level component B Average Inventory level component C

FCFS 1. Demand components > Demand end products 0.26 0.82 0.50 2. Demand components < Demand end products 0.20 0.20 0.20 3. Demand components = Demand end products 0.70 0.50 0.36 FRFS 4. Demand components > Demand end products 0.20 0.20 0.20 5. Demand components < Demand end products 0.44 0.45 0.44 6. Demand components = Demand end products 0.43 0.44 0.37

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Figure 4 Average on-hand inventory of component A, B and C per month

The results of the MANOVA test need to be analysed to determine if the differences under the FCFS and FRFS allocation policy are also significant. Table 5 shows the MANOVA results.

Table 5 Significance levels for the average on-hand inventory level

Experiment (FCFS vs FRFS) Inventory A Inventory B Inventory C

Demand component > Demand end product 0.998 0.006* 0.000* Demand component < Demand end product 0.552 0.689 0.001* Demand component = Demand end product 0.402 0.999 1.000 *p < 0.05

The table shows that the average inventory level for A remains fairly the same without any significance (p > 0.05), if the component demand is more frequent than the end product demand. Figure 3 suggests the same. With respect to the average inventory level for B and C, the MANOVA test shows a significant difference under the FCFS and FRFS allocation policy (p < 0.05). Figure 3 suggests that this difference is in favour of the FRFS allocation policy.

Furthermore, figure 3 shows that the average inventory level for all components under a FCFS allocation policy will be lower in comparison to the FRFS allocation policy, in the case where demand for the end product is more frequent than the individual component. However, this effect is only significant for component C (p < 0.05) and not significant for component A and B (p > 0.05).

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1. Demand components > Demand end products 2. Demand components < Demand end products 3. Demand components = Demand end products 4. Demand components > Demand end products 5. Demand components < Demand end products 6. Demand components = Demand end products FCFS FRFS Av era ge o n -h an d in ve n to ry with S = 10

Average on-hand inventory levels (per month)

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20 In the case where demand for the component and end product are equal, the average inventory levels under a FCFS allocation policy are, however, more scattered in comparison to the average inventory levels under a FRFS allocation policy. However, this effect is not significant for any component (p > 0.05).

4.2 Average amount of backorders

In the occurrence that an end product demand could not be fulfilled, the demand would be backordered. In table 6 the average amount of backorders per month under the FCFS and FRFS allocation policy is given.

Table 6 Average amount of backorders per month

Allocation policy Experiment Average amount of backorders

FCFS 1. Demand components > Demand end products 3.118846154 2. Demand components < Demand end products 3.684807692 3. Demand components = Demand end products 3.409038462 FRFS 4. Demand components > Demand end products 3.684807692 5. Demand components < Demand end products 14.40692308 6. Demand components = Demand end products 5.682692308

Table 6 suggests that the FCFS allocation policy will yield a lower average of backorders in every type of demand distribution. Figure 4 shows these results in a chart.

Figure 5 Average amount of backorders per month

0 2 4 6 8 10 12 14 16 1. Demand components > Demand end products 2. Demand components < Demand end products 3. Demand components = Demand end products 4. Demand components > Demand end products 5. Demand components < Demand end products 6. Demand components = Demand end products FCFS FRFS N u m b er o f b ack o rd ers

Average amount of backorders (per month)

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21 The results of the MANOVA test need to be analysed to determine if the differences under the FCFS and FRFS allocation policy are also significant. The MANOVA test results are given in table 7.

Table 7 Significance levels on the average amount of backorders

Experiment (FCFS vs FRFS) Backorder

Demand component > Demand end product 0.000* Demand component < Demand end product 0.000* Demand component = Demand end product 0.000*

Figure 4 shows that a lower average amount of backorders is measured under a FCFS allocation policy when the demand for the components is more frequent than the end product. This difference in average amount of backorders appears to be significant when looking at table 7 (p < 0.05).

In the case of demand for the end product being more frequent than the component demand, figure 4 shows that a much lower average amount of backorders is achieved under a FCFS allocation policy. Table 7 suggests that this difference is significant (p < 0.05).

Figure 4 suggests that a lower average amount of backorders is achieved under a FCFS allocation policy, when demand for the component and end product is equal. Table 7 shows this difference is significant (p < 0.05).

4.3 Average amount of lost sales

The component demand was considered to be lost in the occurrence that an individual component demand could not be fulfilled due to a stock out. In table 8 the amount of lost sales per month are given.

Table 8 Average amount of lost sales for component A, B and C per month

Allocation policy Experiment Average amount of lost sales A

Average amount of lost sales B

Average amount of lost sales C

FCFS 1. Demand components > Demand end products 2.667115385 2.728846154 2.610576923 2. Demand components < Demand end products 4.033269231 4.133653846 4.056346154 3. Demand components = Demand end products 1.281346154 1.273269231 1.231153846 FRFS 4. Demand components > Demand end products 4.033269231 4.133653846 4.056346154 5. Demand components < Demand end products 0.882115385 0.895961538 0.887884615 6. Demand components = Demand end products 1.416346154 1.375961538 1.475769231

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22 sales when the component demand is more frequent. Whereas in case of more frequent component demand, the FRFS allocation policy will yield a lower average amount of lost sales. Figure 5 shows these results in a chart.

Figure 6 Average amount of lost sales for component A, B and C per month

Again, the results of the MANOVA test need to be analysed to determine the significance of the differences under the FCFS and FRFS allocation policy. The MANOVA results are given in table 9.

Table 9 Significance levels for average amount of lost sales

Experiment (FCFS vs FRFS) Lost sale A Lost sale B Lost sale C

Demand component > Demand end product 0.000* 0.000* 0.000* Demand component < Demand end product 0.000* 0.000 0.000* Demand component = Demand end product 0.942 0.972 0.528 *p < 0.05

Figure 5 suggests that the FCFS allocation policy yields a lower average of lost sales in comparison to the FRFS allocation policy for all components when the demand for the component is more frequent than the demand for the end product. Table 9 shows that this a significant difference (p < 0.05).

Furthermore, the figure shows that the FCFS allocation policy yields an average of lost sales almost five times larger in comparison to the FRFS allocation policy, when the demand for the end product is more frequent than the demand for the component. Table 9 shows a significant difference in average lost sales for all components (p < 0.05). 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 1. Demand components > Demand end products 2. Demand components < Demand end products 3. Demand components = Demand end products 4. Demand components > Demand end products 5. Demand components < Demand end products 6. Demand components = Demand end products FCFS FRFS N u m b er o f lo st sales

Average amount of lost sales for (per month)

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23 The case where the demand for the component and the demand for the end product are equal, figure 5 shows that there is a slight difference between the FCFS and FRFS allocation policy. It appears that there is a higher average amount of lost sales under the FRFS allocation policy. However, table 9 shows that this difference is not a significant one (p < 0.05).

4.4 Total costs behaviour under a FCFS and FRFS allocation policy

The results of the performance measures have been observed in the previous paragraphs, suggesting which performance measures give rise to a significant difference when changing the allocation policy. However, this paper researches how the total costs will behave under the FCFS and FRFS allocation policy.

Below the total costs function, as described in chapter 3, is given. This formula will be used to identify how the total costs will behave under a numerical experiment.

𝑌(𝑆) = ℎ𝑖𝐼𝑖(𝑆) + 𝑏𝐵(𝑆) + 𝑐𝑖𝐶𝑖(𝑆)

Y(S) = cost function of the average inventory holding costs, back order costs, and lost sales costs per time unit

Ii(S) = average on-hand inventory level (in units) for component i as a function of S

B(S) = average number of outstanding backorders for the end product as function of S

Ci(S) = average number of lost sales for component i per time unit as a function of S

S = Base stock level (in units)

S – 1 = reorder point (in units), which represents inventory level that triggers a replenishment order

hi = cost to carry one unit of inventory for one unit of time for component i

b = cost to carry one unit of backorder for one unit of time

ci = cost for not fulfilling one unit of demand for component i

Table 10 provides an overview of the costs for the performance measures to determine the total costs under the FCFS and FRFS allocation policy.

Table 10 Numerical data for the total costs

Element Notation Value

Holding costs hi €2.50 per month

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24 The total costs function is filled in with the results provided in the previous paragraphs. Table 11 and figure 6 provide an overview of the totals costs for each performance measure under the respective allocation policy.

Table 11 Total costs for all performance measures

Allocation policy Experiment Inventory costs A Inventory costs B Inventory costs C Backorde r costs Lost sales costs A Lost sales costs B Lost sales costs C Total costs FCFS 1. Demand components

> Demand end products € 19.23 € 61.21 € 37.61 € 25.98 € 8.88 € 9.09 € 8.69 € 170.70 2. Demand components

< Demand end products € 14.75 € 14.77 € 15.31 € 30.69 € 13.43 € 13.77 € 13.51 € 116.24 3. Demand components

= Demand end products € 52.36 € 37.33 € 27.11 € 28.40 € 4.27 € 4.24 € 4.10 € 157.80 FRFS

4. Demand components

> Demand end products € 14.75 € 14.77 € 15.31 € 30.69 € 13.43 € 13.77 € 13.51 € 116.24 5. Demand components

< Demand end products € 32.73 € 33.91 € 33.06 € 120.01 € 2.94 € 2.98 € 2.96 € 228.59

6. Demand components

= Demand end products € 31.88 € 32.86 € 27.79 € 47.34 € 4.72 € 4.58 € 4.91 € 154.09

Table 11 shows that the FRFS allocation policy outperforms the FCFS allocation policy, in the case where end product demand occurs more frequent in comparison to the component demand. When looking at figure 6, it shows that the cost difference is mainly due to the holding costs.

However, the FRFS allocation policy will yield a lower cost per month according to table 11 if the component demand occurs more frequent than the end product demand. Figure 6 suggests that the large costs difference resides in the holding costs and backorder costs. Regarding the lost sales costs, the figure suggests that the FRFS allocation policy generates lower lost sales.

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Figure 7 Total costs per month for each allocation policy

€ ,000 € 50,000 € 100,000 € 150,000 € 200,000 € 250,000 1. Demand components > Demand end products 2. Demand components < Demand end products 3. Demand components = Demand end products 4. Demand components > Demand end products 5. Demand components < Demand end products 6. Demand components = Demand end products FCFS FRFS To ta l co sts in €

Total costs per month

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5. Discussion

The purpose of this study is to find the difference in total costs on the performance measures for the average on-hand inventory, amount of outstanding backorders, and the amount of lost sales under the FCFS and FRFS allocation policies for ATO systems that serve demand for the end product and component. Where in the case of a stock out an end product demand will be backordered but the individual component demand will be considered as a lost sale. The research question of this study is:

Which inventory policy will achieve the lowest cost for multiple product ATO systems, with end product and component demand, where backorders are allowed for the end product, but missed demand for individual components imply lost sales?

The base stock model has been chosen as the inventory replenishment policy. Regarding inventory allocation, the FCFS and FRFS were considered. A simulation model has been designed to simulate the behaviour of the FCFS and FRFS allocation policies in combination with the base stock model. The performance of the allocation policies was measured by monitoring the average inventory level, the amount of backorders and the amount of lost sales. The output of the performance measures was checked on their significant differences and the difference in total costs.

This chapter summarizes and discusses the results that were gained from the simulation by comparing results from similar studies. Moreover, the theoretical and practical implications of this study will be discussed. This chapter will conclude with limitations and future research proposals.

5.1 Key results

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27 be reasoned less lost sales will be made when more components are available, knowingly that the average inventory levels are higher under a FCFS allocation policy. A more in-depth analysis should be made of this relation in order to provide a profound reasoning on this argument.

The results show that a FCFS allocation policy will yield lower total costs if the demand for the end product represents a significant portion of the total sales. This difference in costs remains for the most part in the total amount of backorders, which are around four times higher under a FRFS allocation policy. This occurrence is expected, considering the fact that there are no reservations made for components when a product demand is backordered under a FRFS allocation policy. This results in an allocation of the component towards a possible individual component demand after a replenishment is done and cannot immediately fulfil the backordered end product. This reasoning is also supported by Lu, Song and Zhao (2010), as they state that a policy that reserves inventory of products may perform better if the objective of a given base stock policy is to reduce the total number of backorders. An unexpected finding is that the total inventory costs appear to be higher under the FRFS allocation policy. It was expected that this would be lower, considering the fact that no reservations of components are made. An explanation for this result can be found in a study conducted by Lu, Song and Zhao (2010). They state that the FRFS may not always outperform other rules in terms of minimizing total inventory or number of backorders when products differ in the number of components. They recommend a policy that reserves inventory for products requiring the largest amount of components. The study of Lu, Song and Zhao (2010) explains the result contrary to the hypothesis (?), as end product demand represented a large portion of total demand in this case.

Regarding the case of equal demand for the component and end product, the results show that there is not a large difference in the total costs. However, there is a noticeable difference for the inventory costs and backorder costs. Under a FCFS allocation policy, the inventory costs are relatively higher compared to the FRFS allocation policy. This can be explained due to the reservations of components under a FCFS allocation policy. Regarding the backorder costs the FRFS allocation policy yields a higher backorder costs, which can be explained by the fact that a FRFS allocation policy is a NHB rule. Therefore, it may occur that the average level of backorders is larger per time unit. This reasoning is also supported by Lu, Song and Zhao (2010), as they state that a policy that reserves inventory of products may perform better if the objective of a given base stock policy is to reduce the total number of backorders.

5.2 Theoretical implications

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28 of total sales, the inventory levels will be higher for the FRFS allocation policy in comparison to the FCFS allocation policy. This result implies that there is also a dependency on how the demand between the end product and component is divided relatively to the total sales.

The second theoretical implication that can be drawn from this study is one that builds upon the first theoretical implication. The results of this study show that performance of the FCFS and FRFS allocation policy significantly differ when the demand for the end product and component represent different portions of the total sales. Within the literature there were a few studies that showed similarity. E.g., ElHafsi (2009) studied different demand classes with variability in deman and order size. However, they assumed order sizes to be larger than one and therefore allowed orders to be partially satisfied. Other studies like the ones conducted by Elhafsi and Hamouda (2015) and Elhafsi et al. (2015) looked at different scenarios under which their heuristics perform, but did not analyse their results in different portions of end product and component demand relative to total sales.

The third theoretical implication of this study is that unfulfilled demand for the end product is to be backordered and unfulfilled demand for the component is to be considered lost. Most of the literature found considered unfulfilled demand to be lost (Elhafsi et al. 2015) or allowed a backorder (Elhafsi & Hamouda 2015). Few studies have considered both backorders and lost sales (Bušić, Vliegen & Scheller-Wolf 2012; Dayanik, Song & Xu 2003; Gao, Shen & Cheng 2010). However, these were applied to demand for the end product and component. This study looked at the specific case where it would reflect the situation where customers are willing to accept a delayed delivery for the end product and would rather look for an alternative on the market in case a component could not be delivered.

5.3 Practical implications

The practical implications that can be extracted from this study is that implementing an allocation policy in an ATO system with multiple end products that also serve component demand, can generate different outcomes when it comes to the total costs. It is interesting for these ATO systems that work with a base stock policy and receive more frequent demand for the component in comparison to the end product, to implement a FRFS allocation policy. In case the demand for the end product occurs more often in comparison to the component demand, a FCFS allocation policy will achieve lower costs.

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5.4 Limitations and future research

The research findings in this study have a few limitations. Firstly, the tested allocation policies were only limited to two. Within the theory there are many more allocation policies that could have been considered. Secondly, the cost of a backorder or lost sale were not considered in the allocation policies as other studies have done (Elhafsi et al. 2015; Elhafsi & Hamouda 2015). If an allocation policy with costs/future profit would have been considered, a different result may have occurred. Thirdly, the scope of this research was limited to the allocation policies, meaning that different levels for the base stock were not considered and therefore the service level was also limited. Fourthly, this study did not consider a time window in when a backorder needs to fulfilled, which could yield different results (Lu, Song & Zhao 2010). Therefore, it is assumed that customers are willing to wait for an unspecified time in the case of a back order for the end product. Finally, the numerical example that was given for determining the total costs under the FCFS and FRFS allocation policy was limited to one example.

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6. Conclusion

The purpose of this study was to find the difference in total costs on the performance measures for the average on-hand inventory, amount of outstanding backorders, and the amount of lost sales under the FCFS and FRFS allocation policies for ATO systems that serve demand for the end product and component.

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Appendix A: Allocation policy decision trees

Appendix A-1: FCFS decision tree

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Appendix A-2: FRFS decision tree

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Appendix B: Service level calculation

The base stock level for component A, B and C has been set at S = 10. The service level has been

calculated with the calculations described in the addendum of Chapter 2 Hopp and Spearman (2008). The order arrival rate and supplier lead times are given in table 13.

Table 12 Order arrival rates and supplier lead times

Demand component > demand end product

Demand component = demand end product

Order A 6 days 24 days 15 days

Order B 6 days 24 days 15 days

Order C 6 days 24 days 15 days

Order AB 24 days 6 days 15 days

Order AC 24 days 6 days 15 days

Order BC 24 days 6 days 15 days

Supplier lead times

10 days 10 days 10 days

The first step is to determine the daily demand. In the first case where component demand occurs more frequent than end product demand. The demand for each component occurs every 6 days and two times every 24 days. 𝐷𝑎𝑖𝑙𝑦 𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 1 6+ 1 24+ 1 24= 0.25 𝑢𝑛𝑖𝑡𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 The second step is to calculate the mean demand during replenishment lead times. Knowing that the replenishment lead times are 10 days. The mean demand during replenishment lead time can be calculated as follow:

𝑀𝑒𝑎𝑛 𝑑𝑒𝑚𝑎𝑛𝑑 𝑑𝑢𝑟𝑖𝑛𝑔 𝑟𝑒𝑝𝑙𝑒𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 𝑙𝑒𝑎𝑑 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 10 × 0.25 = 2.5 𝑢𝑛𝑖𝑡𝑠 Knowing that demand is modelled using the Poisson distribution, he Poisson distribution of Excel can be used with POISSON.DIST(x;mean;cdf), where x represents the reorder level (S – 1). This results into the following service level.

𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 (9) = 0.999722648

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36 𝐷𝑎𝑖𝑙𝑦 𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 1 24+ 1 6+ 1 6= 0.375 𝑢𝑛𝑖𝑡𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦 𝑀𝑒𝑎𝑛 𝑑𝑒𝑚𝑎𝑛𝑑 𝑑𝑢𝑟𝑖𝑛𝑔 𝑟𝑒𝑝𝑙𝑒𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 𝑙𝑒𝑎𝑑 𝑡𝑖𝑚𝑒 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 10 × 0.375 = 3.75 𝑢𝑛𝑖𝑡𝑠 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 (9) = 0.994692826

In the case where component demand equals the end product demand, the demand for each component occurs every 15 days.

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Appendix C: Screenshot simulation model

In figure the simulation model that has been developed in order to perform this study is given. Orders arrive according to different inter-arrival times which are defined in “TypeDemand” and are called by the global variables “DemandA” until “DemandBC”. These global variables indicate which type of order inter-arrival time should be used from the table file “TypeDemand”.

The method “OrderAllocation” and “BackorderAllocation” determine which allocation policy FCFS or FRFS is used. This is based on the global variable “AllocationVar”.

In the occurrence of a backorder for the end product, the backorder will be stored in “BufferBackorder” and remains there until it can be satisfied. Lost sales for the components are immediately transferred to the “BufferLostA”, “BufferLostB” and “BufferLostC”.

The results of the performance measures are stored in the table files “Exp1” till “Exp6” for each experiment.

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Appendix D: Warmup period

The initial data that the simulation model generates will generally not be valid. According to Robinson (2014), a simulation will be valid as soon as the model is in the steady state. In order to determine the steady state of the simulation model, the average throughput per day of the customer orders have been examined with the Welch method. The Welch method calculates the moving average and graphically shows the steady state of the simulation model. This graph shows that the simulation model reaches the steady state at approximately 120 days. 0 200000 400000 600000 800000 1000000 1200000 1400000 1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 M ov ing a v e ra ge Periods

Welch's Method

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Appendix E: Replications

The confidence interval method as has been described by (Robinson 2014), has been used to determine the number of replications that the simulation model should use. The average throughput per day per order type (components and end products) were used as the input for the confidence interval method. In the end, 60 replications have been performed in total. The data of these 60 replications have been entered in the confidence interval method calculations, which showed the minimum amount of replications that should be performed with a significance level of 5%. Due to the fact that this was given per order type, the order that required the highest amount of replications has been chosen as the replication rate for the total simulation model. The figures below show that the order for the end product AC takes a fairly long time for the graph to be stable. However, taking into account the deviation, it is well below the 5%. In order to come up with useable date this study will perform 40 replications per experiment.

0,00 0,01 0,02 0,03 0,04 0,05 0,06 2 7 12 17 22 27 32 37 42 47 52 57

Cum

u

lative

m

ean

ave

rage

Number of replications

Order A

0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 2 7 12 17 22 27 32 37 42 47 52 57

Cum

u

lative

m

ean

ave

rage

Number of replications

Order B

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40

Figure 14 Confidence interval method for C

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Figure 136 Confidence interval method for AC

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Appendix F: Levene’s test

Table 12 shows the results of the Levene’s test that determines the homogeneity of the output data According to the assumption the homogeneity had to be equal for all experiments, are independent and contain the same number of replications. The performed Levene’s tests showed that the equality of variances was not equally distributed, with p < 0.05 for all dependent variables. However, the experiments of the simulation model were independent and had equal number of replications. Therefore, the assumptions for the MANOVA test were all acceptable.

Table 13 Levene's test of linearity

Model Sum of Squares df Mean Square F Sig. Regression 52998.848 7 7571.264 48.335 .000b Residual 36341.135 232 156.643 Total 89339.983 239

a. Dependent Variable: Total orders

b. Predictors: (Constant),

WarehouseA Average on-hand inventory, WarehouseB Average on-hand inventory, WarehouseC Average on-hand inventory, Amount of Backorder,

Lost A per month, Lost B per month,

Evaluating inventory control policies for assemble-to-order systems that serve product and component demand