Defining when and how many items to dispose in a warehouse environment

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Defining when and how many items to dispose in a

warehouse environment

A case study at Hamat B.V.

Technology and Operations Management

Master Thesis

by J.R. Surie

s1965050

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ii Date: 27 February 2018

Word count: 9279

Author

Name: Jim Richard Surie

Study: MSc Technology and Operations Management Faculty: Faculty of Economics and Business

Student number: s1965050

Email: j.r.surie@student.rug.nl

Phone: +31(0)652501748

Supervisor

Name: Dr. N.D. van Foreest

Faculty: Faculty of Economics and Business Email: n.d.van.foreest@rug.nl

Phone: 050 36 35178

Co-assessor

Name: Dr. O. A. Kilic

Faculty: Faculty of Economics and Business Email: o.a.kilic@rug.nl

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This paper attempts to research when and how many items with declining demand should be disposed to minimize costs related to keeping inventory. Little work is done which simultaneously calculates the timing and quantity of a disposal action. This paper tries to contribute via a two steps model. The first step calculates the timing of the disposal action. The second step computes the optimal quantity based on an existing disposal formula. Numerical results show that for two different items it is most beneficial to dispose everything in the first month. Sensitivity analysis visualizes the effect of different variables on the outcome. Lastly, a comparison between the proposed model and five simple disposal rules will show the relative benefits of this model. This model is limited by the assumption that no stock outs occur. Since this paper shows how the timing and quantity of a disposal action could be calculated simultaneously, this paper could be valuable from a managerial and theoretical point of view.

Keywords: excess inventory, disposal, optimal retention period, optimal disposal quantity

Acknowledgment

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2 LITERATURE REVIEW ... 2

2.1 Disposal of excess inventory ... 2

2.1.1 Optimal retention period ... 3

2.1.2 Optimal disposal quantity... 3

2.1.3 Combined disposal policies... 5

2.2 Research question ... 6

3 METHODOLOGY ... 7

3.1 Modeling and numerical analysis ... 7

3.2 Validity, verification, and reliability... 8

3.3 Data collection & analysis ... 8

3.4 Limitations ... 8

3.5 Case company ... 9

4 DISPOSAL MODEL ... 10

4.2 When to dispose ... 10

4.2.1 Argumentation of choice X and Y ... 13

4.3 How much to dispose ... 13

4.4 Relation of the model with literature ... 15

5 NUMERICAL ANALYSIS ... 17

5.1 Item selection... 17

5.2 Outcome... 18

5.3 Sensitivity analysis ... 20

5.4 Comparison with simple disposal rules ... 22

6 DISCUSSION ... 25

7 CONCLUSION ... 28

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1 INTRODUCTION

Every company with inventory may experience a scenario where there are too many or obsolete items in stock (Willoughby, 1997). This could be caused by technological development, perishability or an unforeseen shift in demand. Inventory managers should find ways to avoid such costly scenarios. One way to achieve this is to dispose excess inventory.

On the one hand, multiple authors in literature used simulation and dynamic programming to develop disposal models to understand when to dispose a certain amount of inventory (Jesse, 1976, 1986; Brounen, 2017). However, these models use simple rules to determine the disposal quantity (i.e. no exact optimal quantity). On the other hand, several authors determined the optimal disposal quantity but without an explicit statement about the timing of disposal (Hart, 1973; Rosenfield, 1989; Stulman, 1989). Finally, only a few articles define complete disposal policies by simultaneously determining when and how much a company should dispose (Fukuda, 1961; Rothkopf and Fromovitz, 1968; Teisberg, 1981).

Until today limited research addresses practical models which can be used in real life that incorporate both the timing and amount of the disposal quantity. Authors who made these models used several simplifications and limitations. This will be discussed in the literature review. Hence, an optimal disposal policy which could be used in real life to determine when and how much to dispose simultaneously is still to be made.

This research attempts to add knowledge to this literature gap by developing a model and simulate data from a real company. It provides an answer to the following research question:

‘When and how many items with declining demand should be disposed in order to minimize costs related to keeping inventory?’

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2 LITERATURE REVIEW

In order to place the problem of disposal of excess inventory in a broader context, this chapter reviews literature where similar problems are examined. It attempts to find what is done and what needs to be done in order to demonstrate the value and innovative character of this research. Literature related to the disposal of excess inventory may be classified into three different subgroups. The first group examines the optimal retention period (i.e. when to dispose). The second group is concerned with determining the optimal disposal quantity (i.e. how much to dispose). The last group formulates a model which combines the optimal retention period and the optimal disposal quantity (i.e. when and how much to dispose). Finally, the research question of this paper will be formulated based on the gap in the literature.

2.1 Disposal of excess inventory

One of the problems faced by inventory managers is an excess amount of stock (Rosenfield, 1989; Willoughby, 1997). According to Tersine & Toelle (1984, page 246). Excess stock can be seen as ‘dead weight’ which uses storage space, blocks opportunities, raises holding costs, and reduces the return on investment. This phenomenon can be found in, for example, manufacturing businesses (Silver and Willoughby, 1999), the army (Simpson, 1955; Mohan and Garg, 1961), and the oil industry (Teisberg, 1981).

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look at how long each individual item is kept in stock. Based on that knowledge, the items which are kept in stock for the longest time or everything that will be in stock for more than a certain time could be disposed. Although these models are very practical, they neglect related costs and benefits such as holding costs and salvage value. To understand the value of these simple rules compared to the following models, this paper will compare the financial costs and benefits of the proposed model with these simple rules. How this is done will be explained in the methodology.

2.1.1 Optimal retention period

First of all, there are several authors who demonstrated how an optimal retention period can be computed. Brounen (2017) used simulation to compare the relative net benefits of retention and disposal to determine when a company should dispose. A critical limitation in his work is that there is no option to dispose single items but only the entire stock. The net benefit of disposing is computed by multiplying the entire stock by a certain salvage value. The net benefit of not dispose any items are the expected sales minus holding costs plus the expected sales in the future. Jesse (1976) determined the optimal retention period mathematically by comparing the costs as well, but with the assumption of uncertainty about the timing of future reorders. Here, deterministic reorder quantities are used. In a later paper, Jesse (1986) developed a similar model, but incorporated stochastic reorder quantities. Although these models are accurate and have managerial value they do not investigate the optimal disposal quantity, but only state that all inventory should be disposed or to use a simple rule to determine the quantity. In contrast to the aforementioned articles, the following authors did research the optimal disposal quantity.

2.1.2 Optimal disposal quantity

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procedure, which calculates all costs for all retention levels. An assumption here is that demand is predictable. Others incorporated stochastic demand with perishability (Rosenfield, 1989) or without perishability (Stulman, 1989; Silver and Willoughby, 1999) in their mathematical optimization model. An original model is developed by Tersine and Toelle (1984) since they also modelled the minimum economic salvage value and used this to understand the role of the disposal price. According to them, companies must not dispose anything if the salvage value is not high enough. This statement is evaluated and confirmed by Wee and Cung (2005) as well. Additionally, George (1987) showed that if the disposal price was 80 percent or more of the normal selling price the entire inventory should be disposed immediately. The optimal disposal quantity is also modelled in very specific situations. For instance, an integrated buying and disposal model when there is a temporary chance to receive a purchasing discount (Chen and Min, 1995). Other environments are large-scale projects with expensive items and demand uncertainty (Willoughby, 2001) or integrated vendor-buyer relations (Chung and Wee, 2008). More examples of determining the optimal disposal quantity can be found in Yang and Wee (2001) and Karimi et al. (2012).

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be logic to execute the disposal action directly after computation. However, it might also be valuable to spread the disposal action over time due to an uncertain demand distribution, stock-out probability and variable salvage values (e.g. art, classic cars, certain technology etc.)

The explicit lack of information about timing appears to be true, since these models do not compute a variable related to time but only the amount to dispose or retain. In other words, these models cannot be used to know when items should be disposed. A model which combines both knowledge about the amount as well as the timing might be valuable for inventory managers. Therefore, the following paragraph looks into combined disposal policies.

2.1.3 Combined disposal policies

Perhaps the first author who modelled the ‘how much’ and ‘when to’ question simultaneously did this by developing acquisition and disposal policies at the same time (Fukuda, 1961). This was developed in a multiperiod inventory system with three options at the beginning of each period; order, dispose or do nothing. Variables such as salvage value, back ordering costs and holding costs were incorporated. Combining acquisition and disposal policies simultaneously is also done within the U.S. oil market (Teisberg, 1981). Here, a multiperiod stochastic programming tool is used to define the disposal and acquisition policies. However, the model is based on economics (i.e. supply and demand function of the oil market) rather than pure costs or benefits. Rothkopf and Fromotivz (1968) discussed an optimal disposal policy (e.g. how much and when to dispose) in an environment with bulk material brought in containers. Here, the rental of containers to store the material could be stopped by bringing back the container. However, the entire value of all bulk material inside that container must be discarded. So, it seems that it is not possible to compute the exact amount of bulk to be disposed. Alternatively, Waddell (1983) developed a dynamic programming algorithm that computed the timing and exact amount of tractors to be disposed for Philips.

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disposal quantity (i.e. only entire containers). Therefore, this study will focus on developing a disposal policy which combines knowledge about the timing and quantity of the disposal action and not takes into account other policies (e.g. acquisition policy, reorder policy).

2.2 Research question

In order to develop an additional model which can be used by organizations to understand when they have to dispose and if so, how much they need to dispose, the remainder of this paper attempts to demonstrate how this can be done. Therefore, the research question of this paper is:

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3 METHODOLOGY

This chapter explains the methodology that will be used to answer the research question. First, arguments will be provided why and how the method is suitable. Then, it is explained how the validation and reliability are ensured. Thirdly, a description of the data analysis and collection is given. Finally, a brief description of the company will be given which will be used to provide numerical examples.

3.1 Modeling and numerical analysis

A quantitative model may be used to build an object model which explains the behaviour of reality (Karlsson, 2009). An advantage of quantitative modeling is that future scenario, which fit the assumptions of the model can be predicted objectively and with rigor. On the contrary, everything outside the model is very ambiguous. According to this definition, a quantitative model will be used in order to answer the research question. How this proposed model works will be elaborated in chapter four.

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3.2 Validity, verification, and reliability

To validate and verify the model, numerous experiments of the model will be performed (Karlsson 2009). First of all, certain parameter values for which theoretical results are available will be used. Secondly, causal relations will be investigated to verify if the effect on individual changes of one variable while keeping the others equal will lead to a likely decrease or increase in another variable. How this is done can be found in the appendices.

3.3 Data collection & analysis

The data which will be used to perform the numerical analysis is primary data collected by the case company. The goal is to collect data generated in the year 2016 and 2017 from different products with different characteristics. These products are slow-moving items with a declining demand. This is done, because Hamat B.V. has a very large product range and the difference between items regarding demand frequency, ordering prices and selling prices is significant. The collected data entails holding costs, selling prices, salvage prices, inventory levels, and demand levels.

A sensitivity analysis will be performed to understand the individual effect of each variable on the outcome of the model (Powell and Baker, 2010). Each variable will be changed by multiplying the base case with 10 while holding the other variables constant to test for the effect that each variable has on the model. By choosing a large multiplier, knowledge over a large range of numbers could be derived. Finally, the results of the model will be compared with five simple disposal rules. How this is done and a description of the rules can be found in chapter five.

3.4 Limitations

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3.5 Case company

The company which will be used to calculate different outcomes of the proposed model is Hamat Mattenfabriek B.V. This company is suitable for this paper since data covering all required variables are available. Additionally, Hamat has slow-runners and end-of-life items with declining demand in stock. Furthermore, Hamat does not have a clear disposal policy. Hamat offers a comprehensive range of indoor and outdoor floor mats, runners, carpets, and rugs. The manufacturing is done by Avimat Coating B.V. The only buyer of Avimat is Hamat. Hamat uses a fully automated warehouse with high stock levels in order to retain a high service level. However, currently, there is no disposal policy. Hamat delivers internationally and since they accommodate specific customer needs the number of different items in their warehouse is very high. Recently, Hamat built a new warehouse. Due to this new warehouse, the total inventory capacity has increased by 40%. The inventory increase is an opportunity and a pitfall at the same time since it is now possible to stack a large number of items even though the items may not be sold in the near future. In order to utilize the new warehouse in an economically viable manner without lowering their service level, a disposal policy could be an outcome.

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4 DISPOSAL MODEL

In this chapter, it is explained why this model is used and how the proposed disposal works. A step by step explanation will describe the development of the model. Additionally, a relation with previous disposal models in literature will be given to understand the similarities and differences between the model in this paper and previous models.

This paper attempts to make a contribution to the field of disposal models. There appears to be an extensive set of models which could be used to determine the timing or quantity of a disposal decision. As elaborated in the literature review, there are many disposal models which compute the quantity. However, an explicit integration of the exact timing of this decision remains absent most of the times. Hence, this model tries to do both simultaneously.

This is done by combining formulas about the timing and quantity in two sequential steps. The first step is to determine when to dispose and the second step is to calculate how much to dispose. With this sequential procedure, this paper attempts to define a disposal policy in order to minimize costs related to keeping inventory.

4.2 When to dispose

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To solve the question the following variables are defined: It = Inventory at the end of month t

Dt = Demandin month t

Dz = Annual demand in year z

St = Sales in month t

Rt = Value in month t

X = Decision to retain the entire stock

Y = Decision to dispose a unit and retain remaining stock C = Holding cost per unit per month

P = Standard selling price per unit Vt = Salvage value per unit in month t

Note that no ordering costs are incorporated due to the assumption that no reordering will take place. Additionally, note that choice Y incorporates the disposal of one item instead of the optimal disposal quantity. This is because this step is only used to determine whether to dispose a certain amount. In other words, it says when to dispose but not how much to dispose.

The goal here is to make the decision (i.e. Y or X) which will generate the highest expected value in a certain month (i.e. Rt). First of all, consider option X. To compute the value, the

expected sales, holding costs, and the expected value of the remaining inventory for the next month are needed.

Sales are equal to the demand unless the inventory level is not sufficient (i.e. Dt > It-1).

Future demand will have the same demand distribution as the given past demand. If there is not enough stock to fulfill demand, items cannot be sold so there will be lost sales. Hence, the expected sales in month t when choice X is made is:

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The inventory level in month t after the choice of X can be computed by taking the inventory in month t-1 minus the expected sales in month t.

Therefore, the inventory level in month t by option X is:

I

t

(X)

(Y)

= min {D

t ,

I

t-1

– 1, 0}

The inventory level is calculated differently because one unit is disposed. Namely:

I

t

(Y) = max {I

t-1

– S

t

– 1, 0}

, Y) }

Lastly, the value of the remaining inventory for the next month (i.e. Rt+1(It)) can be

computed via backward induction. To do this, first, you need to know the optimal expected value of the inventory of the final month, Rn(In), of the finite horizon. Once that

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the remaining inventory will be disposed since in this model there is a finite horizon and no demand will occur after the last month.

Hence, the value of the last month is:

R

n

= V

n

* I

n

Via this step, it can be determined when it is beneficial to dispose one item instead of retaining everything.

4.2.1 Argumentation of choice X and Y

Thetwo choices involve different costs and benefits. If everything is retained (i.e. choice X), there are holding costs, expected sales value in that month and the expected value of the future which is influenced by the choice of that month (i.e. disposal decreases inventory, so the demand could be higher than the inventory). If one item is disposed and the rest is retained (i.e. choice Y) this will result in a salvage value, less holding costs than the choice of X, and the expected sales value of that month and the future. If the inventory is high enough to fulfill future demand with the choice of Y, the expected sales value in a certain month and the future will be the same for the choices X and Y. Here, the future demand will be based on the past demand distribution. So, the only difference lies in the holding costs and salvage value. If the salvage value of one item is higher than the holding cost of one item it is evident that, according to this model, it is more beneficial to salvage one item. If, for example, the salvage value per item is lower than the holding cost per item or the inventory level is not sufficient to fulfil demand after disposing one item the outcome could differ and result in a more beneficial choice of X in month t. The main point here is to first determine if it is rational to dispose or not, and then determine how much this should be.

4.3 How much to dispose

In the previous chapter a model is proposed which can be used to determine when the disposal of one item is beneficial. However, disposing one item instead of another amount will probably not be the optimal case. Therefore, it is necessary to compute the optimal disposal quantity.

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with a high chance of a stock out. In his basic model (i.e. without the role of perishability) he developed a formula that computes the optimum level of items to retain. Here, optimum means the amount where the sales value and salvage value minus the holding costs have a maximum value (Rosenfield, 1989). In a later paper, Rosenfield (1992) showed that the quantity in his formula is also optimal when there are disposal opportunities in the future. This is interesting since his findings imply that although one might want to dispose an amount in the future, it stills remains optimal to dispose an amount for a single time directly and nothing in the future. Rosenfield’s model is suitable for the numerical analysis in this paper since demand follows a Poisson distribution, there is excess inventory, the item under investigation has a declining demand, and it is assumed that no stockouts will occur. Additionally, all variables used in his formula are provided by Hamat B.V. Therefore, in this paper, the formula of Rosenfield (1992) will be used instead of developing a new model that has the same goal.

The optimal retention quantity K* is the largest integer less than (Rosenfield, 1992):

𝐾 =

𝑙𝑜𝑔

𝑉 +

𝐶

𝑖

𝐴 + 𝐶𝑖

𝑙𝑜𝑔 𝜆

_{𝜆 + 𝑖}

Where i is the discount rate, λ is the average demand per month, V is the salvage value and A is the average selling price per unit. V, C, and A are denoted as a percentage of the current value of the item. For example, if an item normally sells for €50 and the holding costs are €1 per item, C is 0,02. Obviously, the optimal disposal quantity (i.e. everything which is not retained) can easily be computed by extracting the retention quantity from the inventory level. Note that it is assumed that there is no discount rate in this paper, thus the discount value is always set on 1.

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The last step in his article is to define the optimum quantity to retain by assuming that there is a uniform batch size of one.

So, the proposed disposal model works with two sequential steps. In summary:

Step 1: Determine the optimal retention period. If Rt(Y) > Rt(X), go to step 2.

If Rt(Y) < Rt(X), retain everything and repeat step one in month t+1.

Step 2: Determine the optimal retention quantity K

Via the two steps, it is explained how this paper attempts to answer the research question and via which model this is done. Also, a short motivation to choose Hamat B.V. as a case is given. Via data of Hamat, an example will show how the methodology combined with the disposal model could answer the research question. In the following chapter, the actual results will be given. But first, it will be explained how the proposed model is related to existing disposal models.

4.4 Relation of the model with literature

According to the literature review in this paper, there are only a few authors who made a model which combined the ‘how much' and ‘when to' question. In that sense, this model could be added to their work. However, via this model, an entire inventory could be evaluated instead of one unit (e.g. the single tractor evaluation of Waddell (1983)). The model of Waddell (1983) is less applicable for larger batches due to the characteristics of his formula. Additionally, this model computes an exact number for the disposal quantity whereas Rothkopf and Fromofitz (1968) made a model for entire containers with bulk material. The difference between this model and the model of Fukuda (1961) is the intertwined acquisition policy. Fukuda modeled acquisition (i.e. reordering), but this model does not. Since ordering policies lies beyond the scope of this research it is decided not to incorporate these decisions and since perishability is not included reordering is not very logic to incorporate since items should be disposed.

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5 NUMERICAL ANALYSIS

This chapter gives an overview of the actual results. The outcomes are based on the mathematical model and real data from Hamat of the year 2016 and 2017. The validation of the model can be found in the appendix. First, a description of the item selection will be given. Secondly, the outcomes are presented. Multiple scenarios will be used to show the results. Thirdly, a sensitivity analysis will show how multiple variables are related to the eventual outcome of the model. Lastly, a comparison between this model and simple disposal rules will determine if it is beneficial to use this model instead of simple disposal rules.

5.1 Item selection

There are over 1000 different items stored in the warehouse of the case company. Each item has their own specifications regarding demand distribution, selling price, inventory levels, and production costs. This paper deals with the disposal of items with a declining demand in order to minimize the costs related to inventory. It is necessary to choose items which can be related to the goal of this paper. Therefore, items with a high inventory level and low demand are useful. Table 5.1 gives an overview of the needed data of the items. The data from the year 2016 and 2017 are used to extract this data. Note that the salvage value is 50% of the selling price. The selling price of Jamaican Lover is an interpretation of the data of Hamat since no factual data is given about the selling price per item, but only the selling value per a certain unknown quantity is available. The holding cost per pallet per week is known. The holding cost per item per month is an estimation, based on the assumption of 600 items per pallet. No data is available about the discount rate. Therefore, it is assumed that there is no discount rate which will affect the outcome. However, Rosenfield (1992) integrated a discount value in his model. To cope with this, this number will be always 1.

Item Bombay Floors Jamaican Lover

Average demand per month 0 0,273

Selling price per item € 5,07 € 9,79

Salvage value € 2,54 € 4,89

Holding cost per month € 0,01 €0,01

Inventory level start 804 33

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5.2 Outcome

When the predefined values, which can be found in table 5,1, are put into the disposal model the outcome will follow automatically. This works in the following way. The first step of the model indicates when it is beneficial to dispose one item instead of retaining everything. This happens when Rt(It, X) < Rt(It, Y). Then, the formula in chapter 4.3

* 1

R

1

(I

1

, Y) = € 5,07 * 0 – (~€0,01803) +€46.685,84 + €2,54 1 =

€46,688.39

The difference is the result of the lower holding costs and a salvage value for one item. Note that the holding costs per item per month is computed from the holding costs per pallet per week (i.e. €1,50) by assuming that there are 600 items on one pallet. Since the value of disposing one items appears to be higher than retaining everything, the optimal retention quantity can be calculated (Rosenfield, 1992). Namely:

𝐾 =

𝑙𝑜𝑔

0,5 + 0,002136752

1 1 + 0,002136752

₁

𝑙𝑜𝑔 0,043478261

_{0,043478261 + 1}

= 0 𝑢𝑛𝑖𝑡𝑠

Therefore, the optimal disposal quantity is 804 (i.e. inventory level minus retention quantity). To indicate the difference between retaining everything and disposing the optimal disposal quantity one could use formula R1(I1, Y), but take a salvage value of 804

instead of 1. The difference expressed in a percentage is:

𝑅1(𝐼1, 𝑌) − 𝑅1(𝐼1, 𝑋)

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Thus, 804 items of Bombay floors should be disposed in the first month. This will result in value increase of 4,39%. These results can also be found in table 5.2.

The outcome of the actual situation is compared to the outcome of four hypothetical situations to understand what will happen to the disposal decision when the situation changes. The three hypothetical situations are to change one variable while keeping all other variables the same. Namely, lower the salvage value by 80 percent, increase the holding costs by 300 percent, and double the average demand per month. The first number represents the month of the disposal decision, while the second number indicates the optimal disposal quantity. Note that this number must lay between zero and the inventory level. Therefore, constraints are used in Excel to avoid that the outcome would be unrealistic. The last number indicates the financial benefit related to the disposal action in percentages. In other words, the financial change when the optimal disposal quantity is taken in comparison with no disposal at all.

Bombay floors Jamaican Lover

Current situation 1; 804; 4,39% 1; 33; 4,37%

Salvage value -80% 1; 804; 4,52% 1; 32; 4,38%

Holding costs +300% 1; 804; 4,46% 1; 33; 4,40%

Average demand +100% 1; 804; 4,39% 1; 33; 4,35%

Table 5.2: Disposal decisions for two items with the current situation and four hypothetical situations. The first number indicates the timing, the second number represents the quantity, and the last number stands for the percentage of change in expected value of the inventory.

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5.3 Sensitivity analysis

In order to understand how each variable will affect the outcome of the model, a sensitivity analysis could be used to visualize the effect of each individual variable on the outcome. The outcome can be measured by the last two numbers of table 5.2. That is the percentage of change between Rt(X) and Rt(Y) and the optimal disposal quantity. Where

t appears to be always 1. The percentage indicates the change in expected value when the choice Y is made instead of choice X on day t. In figures 5.1-3the relationship between different variables and the outcome are visualized. The variables under investigation are holding costs, the ratio between salvage value and selling price, discount value, inventory level, and average demand.

Figure 5.1: The Sensitivity analysis for the average demand per month, related to the percentage of change between the expected value for choice X and choice Y (i.e. Rt(X) and Rt(Y)).

Figure 5.2: Sensitivity analysis for the holding costs per item per month, related to the percentage of change between the expected value for choice X and choice Y (i.e. Rt(X) and Rt(Y)).

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Figure 5.3: Sensitivity analysis for ratio salvage value to selling price per item, related to the percentage of change between the expected value for choice X and choice Y (i.e. Rt(X) and Rt(Y)).

Figure 5.4: Sensitivity analysis for the inventory level at start, related to the percentage of change between the expected value for choice X and choice Y (i.e. Rt(X) and Rt(Y)).

Again, the figures show the individual effect of one variable on the outcome of the model. Figure 5.1 indicates that the outcome of the Bombay Floors remains quite stable. On the contrary, the measured outcome of the Jamaican Lover decreases more even though the same multiplier rules are applied. This could be explained via the ratio between the inventory level at start and the average demand rate which are given in table 5.1. For the computation, the average demand in the base case of Bombay floors is set to 1, because multiplying 0 has no effect. The same explanation can be applied to understand figure 5.2. Here, the increase in outcome is steeper for Bombay Floor than for Jamaican Lover since there is more inventory and therefore a relatively higher value for holding costs. Figure

0 1 2 3 4 5 6 7 8 *10 *20 *30 *40 *50 *60 % C h an ge ex p ect ed v al u e Multiplier

Salvage value

Bombay Flower Jamaica Liver 4,36 4,365 4,37 4,375 4,38 4,385 4,39 4,395 *10 *20 *30 *40 *50 *60 % C h an ge ex p ect ed v al u e Multiplier

Start inventory level

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5.3 shows that the effect of changing the salvage value has almost identical effects on the outcome as changing the holding costs. The only difference between the two variables is that the optimal disposal quantity remains constant if the holding costs are changed, but decreases slightly when the salvage value is changed. Figure 5.4 tells that the height of the inventory level at start has no effect on the outcome of the model. Also, the inventory level is not incorporated into the formula of the optimal disposal quantity. This might be related to the assumption that no stockouts will occur and thus the inventory level is not relevant. Moreover, the outcome is the difference of the expected outcomes between the two choices and since increasing the inventory level results in an equal increase for both choices the percentage of change between the choices remains indifferent.

5.4 Comparison with simple disposal rules

The goal of the proposed model is to minimize costs related to keeping inventory by disposing excess items. Literature has shown that there are also simple rules to do this (Pattinson, 1974; Brown, 1978; Silver, Pyke and Peterson, 1998). However, these simple ways might be less beneficial than the proposed model.

In order to understand the relative value of the proposed disposal model compared to simple disposal rules, it is valuable to make a comparison. Brounen (2017) did this as well. Namely, dispose an item after it is more than a certain time in stock or dispose an item after it has no demand for a certain time.

The type of simple disposal rules, used by Brounen (2017) can also be used in this paper because the characteristics of his model are to a certain extent similar to the characteristics of the model formulated in chapter four. Additionally, the answer to the research question must be related to the timing and quantity of a disposal decision. Simple disposal rules used by Brounen (2017) could provide such an answer.

Tables 5.3 and 5.4 give an overview of the outcomes for the two selected items generated according to multiple simple disposal rules. The meaning of the sequence of numbers is identical to table 5.2. However, the percentage equals:

Rt(simple) − Rt(It, Y)

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23 The disposal rules are:

1) If an item lays more than one year in stock, dispose it 2) If some item lays more than two years in stock, dispose it 3) If there is no demand for more than one month, dispose it 4) If there is no demand for more than four months, dispose it 5) If there is no demand for more than twelve months, dispose it Rule Current Salvage -80% Holding costs

+300% Average +100% demand 1 13; 804; -5,25% 13; 804; -25,75% 13; 804; -15,5% 13; 804; -5,37% 2 25; 804; -9,52% 25; 804; -47,09% 25; 804; -28,3% 25; 803; -9,63% 3 2; 804; -0,42% 2; 804; -2,14% 2; 804; -1,28% 2; 804; -0,43% 4 5; 804; -1,71% 5; 804; -8,55% 5; 804; -5.13% 5; 804; -1,71% 5 13; 804; -5,25% 13; 804; -25,75% 13; 804; -15,5% 13; 804; -5,37%

Table 5.3: Disposal decision based on 5 different disposal rules for Bombay floors. The first number indicates when to dispose (i.e. first month = 1, second month is 2), the second number is the number of items to dispose, and the third number is the percentage of change in value between the optimal outcome of the proposed model and the value of the simple rule.

Rule Current Salvage Holding costs Average demand

1 13; 30; -11,65% 13; 30; -21,88% 13; 30; -16,76% 13; 30; -20,59% 2 25; 30; -13,66% 25; 30; -31,94% 25; 30; -22,79% 25; 30; -22,45% 3 2; 33; -0,22% 2; 33; -1,11% 2; 33; -0,67% 2; 33; -0,22% 4 5; 33; -0,89% 5; 33; -4,43% 5: 33; 2,66% 5: 33; -0,89% 5 13; 30; -11,65% 13; 30; -21,88% 13; 30; -16,76% 13; 30; -20,59%

Table 5.4: Disposal decision based on 5 different disposal rules for Jamaican Lover. The first number indicates when to dispose (i.e. first month = 1, second month is 2), the second number is the number of items to dispose, and the third number is the percentage of change in value between the optimal outcome of the proposed model and the value of the simple rule.

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the meanwhile, holding costs must be paid. Therefore, in this environment with the predefined set of assumptions and the characteristics of the chosen items the expected value decreases over time. Another remarkable point is that the outcome of rule one and five are similar for both items. That is because those rules have the same meaning. For mathematical purposes, the demand for Bombay floors is set on 0,04 instead of 0, otherwise, no difference can be found in the situation of increasing demand.

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6 DISCUSSION

In the previous chapter, the numerical results were developed. In this chapter, a discussion of the research will be stated. This is done in the following way. First, the main findings will be summarised and the implications for the research question will be given and discussed. Then, any deficiencies or practical difficulties will be evaluated. Furthermore, how the findings of this paper support or challenge the theoretical background will be discussed. Lastly, alternative approaches to answer the research question will be formulated.

As shown in the numerical analysis, all items should be disposed in the first month according to the two steps model stated in chapter four. The research question is:

Hence, the research question is answered. Note that this implies that three items of Jamaican Lover could not be sold since there is no inventory after the disposal decision. However, a few characteristics are quite urgent. First of all, this answer only applies to items with limited demand. Secondly, the optimal disposal quantity is calculated with the assumptions that no stockouts will occur. Moreover, the formula of Rosenfield (1992) does not take the inventory level into account but looks to the average demand per unit of time. In the specific cases of the items that have been taken into consideration, this might be applicable. However, when the inventory might not fulfill the total demand the proposed model may be less valuable. The following example illustrates this. If the total demand in two years is 100 units while there are 33 items in stock, the model gives an optimal disposal quantity of 30. That is, keep 3 items in stock. Following this rule, sales will be only 3 items. When the sales value is significantly higher than the salvage value and holding cost, disposing 30 items may not be optimal. Hence, the model might not work for items where there is a change of stock out.

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time frame, and then dispose another amount. This cannot be done via the proposed model.

A limitation of this paper is the scope of the numerical analysis. Mainly due to time constraint, it was not possible to demonstrate the outcome of the model for more items with other product characteristics like the average demand. By using a limited set of items, it is also possible to show numerical results of the model, understand how each variable influences the result, and see what the outcome is. The previous chapter attempted to demonstrate how this could be done.

During the development of this paper two main practical difficulties where encountered. First of all, data of the case company could not be used directly and essential data related to the sales price was missing. Namely, the sales price per item for Bombay floors was given but for Jamaican Lover, only the sales value for an unknown quantity was given. Therefore, an estimation of the sales value per item must be made. Secondly, the outcome of the sensitivity analysis based on a changing salvage value could be interpreted as dissatisfying. Since multiplying the salvage value by 60 only gives a small increase in the percentage of change between the base case and the ‘what-if' scenario. This is due to the fact that the percentage is based on the difference of the value of choice X and Y, and both choices incorporate the optimal value of the next day. Therefore, a higher salvage value leads not only to a higher choice Y but also to a higher value of choice X due to the increasing optimal value of the day after which is added to both choice Y and X.

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7 CONCLUSION

This paper attempted to demonstrate when and how much items with declining demand should be disposed in order to minimize costs related to keeping inventory. Two items from the case company Hamat B.V. were researched in order to design a disposal decision. For both items, it appeared to be most beneficial (i.e. minimal costs or maximum value) to dispose the entire stock in the first month. In this way, the salvage value would be maximized and the holding costs would be minimized. To compute this outcome, this paper suggested a disposal model with two subsequent steps. First, determine when it is beneficial to dispose one item instead of nothing. Then, determine how much the optimal disposal quantity would be at that moment. It is assumed that no stockouts will occur by defining the disposal quantity. According to this assumption, there will be no lost sales. This assumption is also the limitation of this paper since if the inventory level appears to be insufficient to fulfil demand after the disposal decision there might be lost sales. A way to cope with this, is to always keep a certain base level of inventory which is related to the probability function of demand. The height depends on the desired service level of a company as well.

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Rosenfield, D. B. (1992) ‘Optimality of Myopic Policies in Disposing Excess Inventory’, Operations Research, 40(4), pp. 800–803. Available at:

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9 APPENDICES

The appendices show how the design in Excel works and how the model is validated.

9.1 Design

Based on the formulas in chapter 4, a model in Excel helps to make the numerical analysis in this paper. The model uses two sheets. One to determine when to dispose and one two define the optimal disposal quantity. Note that figure 9.1 is made with random numbers and an incomplete time frame. However, the formulas and the interconnectedness between the two tabs remain the same.

Figure 9.1: Overview of the two related tabs in Excel. The first tab determines when to dispose, the second compute how much to dispose based on the model of Rosenfield (1992).

These are the descriptions of each column of tab ‘when’:

- Column B: Expected demand per month.

- Column C: Inventory level per month. Inventory – actual sales.

- Column D: Actual sales per month. If demand < inventory, sales = demand. If demand > inventory, sales = inventory.

- Column E: Selling price.

- Column F: Holdings costs per month. Inventory * holding costs per month per item. - Column G: Salvage value. Calculates the salvage value of the optimal disposal

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- Column H: Expected value of option X. Sales value – holding costs + optimal value of the next month.

- Column I: Expected value of option Y. Sales value – holding costs + salvage value + optimal value of the next month + savings holding costs (i.e. optimal disposal quantity * holding costs)

- Column J: Expected optimal value of the month. Highest value of X and Y. - Column K: Optimal choice for the month. Linked to column J.

The optimal value of the ‘end’ month is to dispose all inventory since it is assumed that no demand will occur after the time frame.

The calculation behind the sheet ‘how much’ is based on Rosenfield (1992). The values in the box ‘given data by Hamat’ are linked. So, if something changes in the first sheet it automatically results in the outcome of the second sheet. Note that the optimal retention quantity in cell D1 cannot be higher than the inventory level at start in cell O4. Therefore, a ‘MIN(..)’ function is used.

9.2 Validation

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Figure 9.2: Validation of demand for optimal choice. Zero demand leads to option X. If demand equals start inventory, option Y is optimal.

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