Negative effects

Besides the positive effects, there are some negative effects that should be mentioned.

Close coordination

For the redesign to work, close communication between departments is inevitable. Sales engineering and SCCE have to interact for the SPO Future demand, and decision functions require close coordination between sales engineering, engineering and SCCE, and between SCCE, factories, and subcontractors.

Furthermore, SCCE and the factories have to collaborate in ordering PIs at second tier suppliers.

Factories have to stick to exact PI order quantities

The redesign only works if the factories order the exact amount of purchase items. If a factory orders more, other factories cannot receive their material on time, decreasing the material availability and performance of other factories.

IT issues

The redesign is discussed with professionals throughout the organisation and one specific issue that would result in difficulties is the IT system. In the current system, SCCE cannot order material from second tier suppliers. After initialising meetings with IT-professionals, it was concluded that it would require the implementation of new IT technologies, but that these issues can be resolved.

41 8. DETAILED INVENTORY CONTROL MODEL

In Chapter 7, a redesign is developed in which orders for items with a standard lead-time longer than the planned lead-time are placed at earlier moments, to increase the material availability. However, material unavailability can also be caused by a deviation of actual lead-time from standard lead-time given by a supplier. Iida (2015) investigated the effect of lead-time information on the performance of an inventory model, and showed that increasing lead-time information significantly improves inventory control performance. The goal of this chapter is to provide insight in this lead-time uncertainty, as it might impact the performance of the factory. Two purchase items have a standard lead-time longer than four weeks and require unknown characteristics to compute their demand (Appendix J). A small numeric analysis is performed based on data from these items, to illustrate the effect of lead-time uncertainty.

In Chapter 5, three conceptual inventory models were determined, based on sub-question 3, 4, and 5:

1. Situation 1, Local decision making and local inventory points;

2. Situation 2, Central decision making and local inventory points;

3. Situation 3, Central decision making and a single central inventory point.

Inventory control is part of OPP, and therefore centrally coordinated. For simplification, a single item, multiple variants, single component, single location and centrally coordinated inventory model is considered. This model is close to situation 3 and sub-question 5. In this chapter, first the inventory control policy is briefly introduced, next the assumptions, notation, and mathematical models are given, and finally the numberic results are discussed.

8.1 Introduction

In this section, multiple important aspects of the inventory model are explained. The first important aspect of the inventory model involves the split up of the demand: the demand in the first four weeks is deterministic, and the demand in all later weeks is stochastic. The model considers a standard lead-time of five weeks. Consequently, the demand for the first four weeks is deterministic, and for the fifth week is stochastic.

A second important aspect is that a base-stock policy is used to investigate the effect of lead-time variability on performance of the inventory model.The aim of a base-stck policy is to keep the inventory policy at a constant value (Topan, 2014). This constant value is based on the critical ratio of the newsboy model. The computation is different from the Delivery to request performance of second tier suppliers, as the Delivery to request performance would constantly be zero with a standard lead-time of five weeks.

Moreover, similar to the redesign discussed in Chapter 7, extra transportation time required to ship material from Europe to America is not considered in the inventory control model, as too little information is available about actual shipping times.

Before introducing the types of models, two key terms, as used in this model, are defined:

 Replenishment level: for a specific week, this level is the optimal quantity that meets the critical ratio for a specific demand in components.

 Base-stock level: the demand in the first four weeks plus the replenishment level of the fifth week. The base-stock level is thus computed over the demand during lead-time.

42 Four different types of models are considered

1. A model with a variable replenishment level and a constant lead-time;

2. A model with a fixed replenishment level over multiple periods and a constant lead-time;

3. A model with a variable replenishment level and stochastic lead-time;

4. A model with a fixed replenishment level over multiple periods and stochastic lead-time.

The final aspect is that a theoretical model and a simulation are developed. First, the input is used in the theoretical model to compute the replenishment level, and this replenishment level and the input are used in the simulation, resulting in final output. The relation between the theoretical model and simulation are illustrated in Figure 26. A simulation in Visual Basic for Applications in Excel is used to investigate the effect of lead-time variability.

Figure 26, Relation between theoretical model and simulation

8.2 Assumptions

The proposed models are based on the folllowing assumptions:

- A single item, multiple variants, single component, single location inventory system is assumed;

- It is assumed that the inventory status is reviewed weekly;

- The assumption is made that demand in purchase items is known for the first four weeks, after that the demand is stochastic and Binomial distributed;

- Demand in components in the next two months is assumed to be deterministic in model 1 and 3, and stochastic in model 2 and 4;

- Orders are delivered after the actual lead-time;

- In model 1 and 2, it is assumed that the actual lead-time is deterministic and equal to the standard lead-time. In model 3 and 4 a stochastic actual lead-time is assumed;

- The models consider a standard lead-time of 5 weeks;

- The assumption is made that in the stochastic lead-time models, the actual lead-time can increase with one week.

- An order is received at the beginning of a week and demand happens during the week;

- Holding costs are charged over the on hand inventory;

- The minimal service level is considered as the constraint on allowable percentage of weeks at which demand in purchase items can be out of stock;

- The items that are stocked can be held across multiple weeks;

- Unfilled demand is back-ordered;

- A base-stock model is assumed, which means that the reorder (s) level is the base-stock level (S) minus one item (𝑠 = 𝑆 − 1).

43 8.3 Notation

The formal notation regarding the input is¹:

𝐼 = 𝑠𝑒𝑡 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠 𝑤𝑖𝑡ℎ 𝑖 ∈ {0,1,2, … , 𝐼}

The following variables are of importance:

𝑆_𝑗(𝑡, 𝑡 + 𝐿) = 𝑏𝑎𝑠𝑒𝑠𝑡𝑜𝑐𝑘 𝑙𝑒𝑣𝑒𝑙 𝑑𝑢𝑟𝑖𝑛𝑔 𝑙𝑒𝑎𝑑𝑡𝑖𝑚𝑒 𝑜𝑓 𝑖𝑡𝑒𝑚 𝑗

Furthermore, the notation regarding the output of the theoretical model and simulation:

𝑆̃_𝑗^∗= 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑟𝑒𝑝𝑙𝑒𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑖𝑡𝑒𝑚 𝑗, 𝑤ℎ𝑖𝑐ℎ 𝑚𝑎𝑦 𝑑𝑒𝑝𝑒𝑛𝑑 𝑜𝑛 𝑤𝑒𝑒𝑘 𝑡

∝_𝑗= 𝑎𝑐𝑡𝑢𝑎𝑙 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑖𝑡𝑒𝑚 𝑗 𝐶_𝑗(𝑆̃_𝑗^∗) = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 𝑓𝑜𝑟 𝑖𝑡𝑒𝑚 𝑗

𝑎𝑡 𝑎 𝑚𝑖𝑛𝑖𝑚𝑎𝑙 𝑟𝑒𝑝𝑙𝑒𝑛𝑖𝑠ℎ𝑚𝑒𝑛𝑡 𝑙𝑒𝑣𝑒𝑙 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡 𝑖𝑠 𝑚𝑒𝑡 𝑎𝑛𝑑 𝑐𝑜𝑠𝑡𝑠 𝑎𝑟𝑒 𝑚𝑖𝑛𝑖𝑚𝑖𝑠𝑒𝑑 8.4 Objective function and constraint

The objective of the theoretical model is to minimize the costs subject to the service level constraint.

This results in the following optimization problem:

min 𝐶_𝑗(𝑆̃_𝑗) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 ∝_𝑗≥∝_𝑗^𝑜𝑏𝑗

1This notation allows for multiple items and multiple components, however a single item in a single component is used in the computational results

44

The service level constraint is equal to the critical ratio, being the percentage of cycles during which no stockouts occur, type 1 service level (Topan, 2014). If there are no stockouts, the supplier receives 100%

performance, otherwise it receives 0% performance.

8.5 Optimal replenishment level

In the theoretical model, the optimal replenishment level is computed. First, the computation for the adjusted replenishment level of model 1 and 3 is shown, after that the fixed replenishment level for model 2 and 4 is explained.

Model 1 and 3

The replenishment level is calculated with the use of historic ratios. The sum of the historic ratios for the variants with purchase item j in it is the probability of that purchase item, referred to as 𝑝_𝑗^𝑖. Model 1 and 3 assume a variable replenishment level and Binomial distributed demand in PIs. The realization of the demand in components is 𝑑𝑖 and the stochastic demand in PIs is:

𝑋_𝑗(𝑡)~𝐵𝑖𝑛(𝑑_𝑖(𝑡), 𝑝_𝑗^𝑖)

The replenishment level of t+L can be computed with the cumulative distribution function:

𝐹 (𝑆̃_𝑗(𝑡 + 𝐿)) = 𝑃 (𝑋_𝑗(𝑡 + 𝐿) ≤ 𝑆̃_𝑗(𝑡 + 𝐿)) 𝑃 (𝑋_𝑗(𝑡 + 𝐿) ≤ 𝑆̃_𝑗(𝑡 + 𝐿)) ≥ 𝛼_𝑗^𝑜𝑏𝑗

𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑆̃(𝑡 + 𝐿) ≥ 𝐹_𝑗 ⁻¹(∝_𝑗^𝑜𝑏𝑗) Model 2 and 4

Model 2 and 4 assume the demand in components is stochastic. Therefore, a fixed and time-independent replenishment level is computed. The probability distribution function of the demand in components is approximated by calculating the mean and standard deviation of the demand given in the SPO Future demand and then fitting a theoretical discrete probability distribution. The fitting procedure developed by Adan et al. (1995) is used for this. The best fit for the demand in projects and exits was the Poisson distribution with mean 𝜆𝑖 (Appendix L). Consequently the demand in purchase items is:

𝐷_𝑖~𝑃𝑜𝑖𝑠(𝜆_𝑖) 𝑋_𝑗~𝐵𝑖𝑛(𝐷_𝑖, 𝑝_𝑗^𝑖)

A truncated distribution function is used, as the domain of the probability function is restricted with an upper boundary of the demand in components:

𝑢_𝑖= 𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑚𝑎𝑛𝑑 𝑖𝑛 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑖 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑃(𝐷_𝑖≤ 𝑢_𝑖) > 0.995 𝐹(𝑆̃_𝑗) = 𝑃(𝑋_𝑗≤ 𝑆̃_𝑗)

= 𝑃(𝑋𝑗≤ 𝑆̃_𝑗|𝐷_𝑖 = 0) ∗ 𝑃(𝐷𝑖= 0) + 𝑃(𝑋𝑗 ≤ 𝑆̃_𝑗|𝐷_𝑖 = 1)

∗ 𝑃(𝐷_𝑖 = 1)+. . +𝑃(𝑋_𝑗≤ 𝑆̃_𝑗|𝐷_𝑖 = 𝑢_𝑖) ∗ 𝑃(𝐷_𝑖= 𝑢_𝑖) 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝑆̃ ≥ 𝐹_𝑗 ⁻¹(∝_𝑗^𝑜𝑏𝑗)

45 8.6 Order of events

The order of events at week t for item j in the simulation:

1. The on hand inventory, backorders, and inventory position of week t-1 are the starting position;

2. The order placed at t-L arrives²;

3. The backorders of t-1 are, as far as possible, satisfied;

4. The actual demand for item j of week t is fulfilled as far as possible, and unmet demand is backordered;

5. The actual demand of week t+4 is known;

6. The replenishment level of week t+L is known;

7. The base-stock level at [t,t+L] is calculated;

8. The order for week t+L is calculated and placed;

9. The on hand inventory at the end of week t is calculated;

10. The inventory position at the end of week t is calculated;

11. The back orders at the end of week t are calculated.

8.7 Mathematical Model

First, model 1 is discussed in full, lateron the differences for model 2, 3, and 4 are defined. The mathematical model is discussed in the same order, as the order of events.

At the starting position in week t, the on hand inventory of t-1, backorders of t-1, inventory position of t-1, and all orders that still had to be received in t-1 are known:

𝐼_𝑗^𝑂𝐻(𝑡 − 1), 𝐵𝑂_𝑗(𝑡 − 1), 𝐼𝑃_𝑗(𝑡 − 1),

𝐼𝑂_𝑗(𝑡 − 𝐿), 𝐼𝑂_𝑗(𝑡 − 𝐿 + 1), 𝐼𝑂_𝑗(𝑡 − 𝐿 + 2), 𝐼𝑂_𝑗(𝑡 − 𝐿 + 3), 𝐼𝑂_𝑗(𝑡 − 1)

Next, the order placed at t-L (𝐼𝑂𝑗(𝑡 − 𝐿)) arrives and, if possible, backorders of t-1 are satisfied. Actual demand (𝑥𝑗(𝑡)) at t is fulfilled and unfulfilled demand is back ordered. Moreover, the realization of demand in t+4 (𝑥𝑗(𝑡 + 4)) becomes known. The replenishment level of week t+4 is calculated by the theoretical model, and this replenishment level is used to calculate the base-stock level over [t,t+L]:

𝑆_𝑗(𝑡, 𝑡 + 𝐿) = 𝑥_𝑗(𝑡 + 1) + 𝑥_𝑗(𝑡 + 2) + 𝑥_𝑗(𝑡 + 3) + 𝑥_𝑗(𝑡 + 4) + 𝑆̃(𝑡 + 𝐿) _𝑗

Next, the order at t can be calculated and placed at the second tier supplier.

𝐼𝑂_𝑗(𝑡) = (𝑆_𝑗(𝑡, 𝑡 + 𝐿) − 𝐼𝑃_𝑗(𝑡 − 1) + 𝑥_𝑗(𝑡))⁺

After that, the on hand inventory, back-orders, and inventory position are calculated.

𝐼_𝑗^𝑂𝐻(𝑡) = (𝐼_𝑗^𝑂𝐻(𝑡 − 1) + 𝐼𝑂_𝑗(𝑡 − 𝐿) − 𝐵𝑂_𝑗(𝑡 − 1) − 𝑥_𝑗(𝑡))⁺

2In the models with lead-time uncertainty, the moment at which an order should arrive the actual lead-time of the order is known. The actual lead-time for the order ordered at week t-L can be L or L+1. If the actual lead-time is L+1, the order is received in the next week. Moreover, if the actual lead-time of the order ordered at week t-L-1 was L+t-L-1, it is received in this week.

46 replenishment level is done in the theoretical model, resulting in different input for the simulation, but no difference in calculations.

Model 3

The third model assumes a deterministic demand in components. Hence, the computations for the replenishment level and base-stock level are similar to that of model 1. The lead-time is stochastic, and there is a possibility to deliver orders at t+L+1 instead of t+L. This is known at the moment an order should be received. The Binomial distribution is used to simulate the actual lead-time. An extra input parameter is introduced in this model:

𝑃(𝐿(𝑡) = 𝐿) = 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑎𝑑 𝑡𝑖𝑚𝑒 𝑏𝑒𝑖𝑛𝑔 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑙𝑒𝑎𝑑 𝑡𝑖𝑚𝑒 Model 1 is equal to a specific setting of model 3 with P(L(t)=L)=1. The calculation for the on hand inventory and back-orders changes into:

𝐼_𝑗^𝑂𝐻(𝑡) = {(𝐼_𝑗^𝑂𝐻(𝑡 − 1) + 𝐼𝑂_𝑗(𝑡 − 𝐿) − 𝐵𝑂_𝑗(𝑡 − 1) − 𝑋_𝑗(𝑡) + 𝐼𝑂_𝑗^{𝑑𝑒𝑙𝑎𝑦𝑒𝑑}(𝑡 − 1))⁺

The calculation for the inventory position remains the same.

Model 4

Model 4 assumes a fixed replenishment level and stochastic lead-time. Therefore the calculation of the replenishment level is equal to that of model 2, and the calculations for the on hand inventory and back-orders are similar to model 3. Model 2 is again equal to a specific setting of model 4 with P(L(t)=L)=1

8.8 Average performance and costs

The output of the theoretical model consists of the average replenishment level, and the output of the simulation consists of the actual average performance and the costs.

Average replenishment level

The average replenishment level is 𝑆̃𝑗∗

with ∝𝑗≥∝_𝑗^𝑜𝑏𝑗. For model 1 and 3, this is the average of the weekly replenishment level, and for model 2 and 4, this is a fixed value computed by the theoretical model:

𝑓𝑜𝑟 𝑚𝑜𝑑𝑒𝑙 1 𝑎𝑛𝑑 3: 𝑆̃_𝑗^∗=∑^𝑇_𝑡=1𝑆̃_𝑗(𝑡) 𝑇 𝑓𝑜𝑟 𝑚𝑜𝑑𝑒𝑙 2 𝑎𝑛𝑑 4: 𝑆̃_𝑗^∗

47

The yearly holding costs are based on a fixed percentage of the purchase costs. The percentage includes rental costs, costs for utilities and risks. According to Durlinger (2013), the percentages that should be used are the following:

Table 8, Holding cost percentage according to Durlinger (2013)

Rental Utilities Risks Total Mechanical/Sheet

metal

18% 15% 3% 36%

Controls/Electrical 12% 10% 4% 26%

The yearly unit holding costs are therefore:

ℎ = {0.360.26

𝑖𝑓 𝑗 𝑖𝑠 𝑎 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑎𝑙 𝑖𝑡𝑒𝑚 𝑖𝑓 𝑗 𝑖𝑠 𝑎𝑛 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑖𝑡𝑒𝑚

ℎ_𝑗 = 𝑝𝑐_𝑗∗ ℎ

Calculating the average on hand inventory and multiplying this with the holding costs per item results in the yearly holding costs based on the on hand inventory for week t. The average yearly holding cost over a number of weeks can again computed:

𝐼_𝑗^{𝑂𝐻,𝑎𝑣𝑔}=∑^𝑇_𝑡=1𝐼_𝑗^𝑂𝐻(𝑡) 𝑇 𝐶_𝑗 = ℎ_𝑗∗ 𝐼_𝑗^{𝑂𝐻,𝑎𝑣𝑔}

8.9 Validation and verification

In this sub-section, the numerical examples are presented which aim to illustrate some features of the four types of models that are established in the previous sub-sections. The optimal replenishment level is found by using two theoretical models, and a simulation is performed to compute the actual average performance and costs and to investigate the effect of lead-time variation on the average performance.

Before elaborating on the results, the model is verified and validated by the model of development process in Figure 27 (Sargent, 2013).

According to Sargent (2013) there are three entities that should be considered:

 The problem entity, being the inventory setting at Vanderlande;

 The conceptual model; being the base-stock inventory model;

 The computerized model; being the simulation executed on a computer.

48

Figure 27, Simplified version of the model of development process (Sargent, 2013)

8.9.1 Conceptual model validation

The conceptual model is validated by determining that theories and assumptions of the model are correct. All assumptions can be found in section 7.1 and are based on a realistic setting at Vanderlande or at theoretical assumptions. The assumptions are discussed in Appendix C.

8.9.2 Computerized model verification

The simulated model is verified by debugging the code in VBA whenever code resulted in errors.

Furthermore, the calculations used in the mathematical model are checked by hand and only when the calculations matched the results of the model, these were used in the simulation. Consequently, it can be assured that the computer programming and implementation of the model are correct.

8.9.3 Operational validation

The validation of the model is done by first checking the behavior of the model in extreme cases. These results are presented in Appendix M. The extreme values led to expected results. Moreover, the setting of the simulation is according to the simulation method of Law (2007). The warm-up period and confidence interval are given in Appendix M. The confidence interval for the simulation is computed to check whether the number of iterations is sufficient in providing accurate output. Appendix M also elaborates on two instances with easy settings, based on real life setting of Vanderlande, which are used to validate the behavior of the models. These setting led to expected results.

8.9.4 Data validity

The input data used in the theoretical model and simulation is based on actual data of Vanderlande. The actual demand in components in week 3 to 27 of 2017 is used to fit a distribution function and determine the parameters of the function. The distribution function is used as input for the simulation.

Furthermore, the service level constraint is based on the actual average performance level Vanderlande and its suppliers strive for, and the lead-time of 5 weeks is the standard lead-time of items of the SPO.

The probability of an item j in component i is calculated with historic ratios based on actual data.

Moreover, the holding cost rate is based on literature.

49

8.10 Results

Two items that are part of the group with unknown characteristics and that have a lead-time longer than four weeks are considered:

 Item 1, which is part of component (B);

 Item 2, which is part of component (C).

First, the input parameters of the items are defined. Next, the output of the model is discussed.

8.10.1 Input parameters

The input parameters consist of the demand in components, demand in purchase items, standard lead-time, holding costs and purchase costs, service level constraint, and the probability of an item j required for component i. Moreover, in model 3 and 4 the stochastic lead-time is added to the model. The input parameters for a specific item in a component are similar for every type of model, in order to compare them. The input data³ is displayed in Table 9.

Table 9, Input values, item 1 and item 2

Input parameters Values for item 1 Values for item 2

𝑪𝒐𝒎𝒑𝒐𝒏𝒆𝒏𝒕 (𝐵) (𝐶)

The output that is generated by the theoretical model and simulation is the following:

 Average replenishment level;

 Average actual performance;

 Average costs.

To analyse the impact of a possibility on an actual time of one week longer than the standard lead-time, the four models are compared.

Item 1

First, the replenishment level of the models is computed. The cumulative probability 𝑃(𝐷_𝑖≤ 8) >

0.995 , therefore the upper boundary of the truncated demand is 8. The replenishment levels for the models as computed in the theoretical model are displayed in Table 10.

3It should be mentioned that the costs for both items are similar. The reason for this could be that the items are similar with for example a different angle, but therefore resulting in a similar price. Furthermore, both items are mechanical.

50

Table 10, Replenishment levels, item 1

Output Theoretical model Model 1 and 3 Model 2 and 4

𝐒̃_𝟏^∗ 2.36 3

The results of the simulation of model 1 and 3 are given in Table 11. The average performance of model 1 is with 99.71% well above the 98% constraint, However, a probability of 0.9 on a lead-time of 5 weeks decreases the performance with 2.14% to 97.57%. A decrease of the probability with 0.1, results in an average decrease of the performance of 3.12%, an average decrease of the on hand inventory of 0.12 items, and a decrease in the costs of on average €0.61.

Table 11, Results of model 1 and 3, item 1

Table 12 displays the results for item 1 in model 2 and 4. Model 2 meets the service level constraint, but a decrease of 0.1 on the probability of a lead-time of 5 weeks, results in an average decrease of the performance of 1.28%, an average decrease of the on hand inventory of 0.08 items, and a decrease in the costs of on average €0.42. Again, little uncertainty, P(L(t)=L)=0.9, results in a performance level under the service level constraint.

Table 12, Results of model 2 and 4, item 1

A comparison of the models with adjusted and with a fixed replenishment level is illustrated in Graph 7.

A decrease in the probability on a lead-time of 5 weeks has a bigger impact in the model with an adjusted replenishment level than it has on the model with a fixed replenishment level. Model 1 performs slightly better than model 2, but model 4 performs better than model 3. The decrease of the performance of the models with an adjusted replenishment level is on average 2.98%, and the decrease of the models with a fixed replenishment level is on average 1.28%. The costs of the models with an adjusted

A decrease in the probability on a lead-time of 5 weeks has a bigger impact in the model with an adjusted replenishment level than it has on the model with a fixed replenishment level. Model 1 performs slightly better than model 2, but model 4 performs better than model 3. The decrease of the performance of the models with an adjusted replenishment level is on average 2.98%, and the decrease of the models with a fixed replenishment level is on average 1.28%. The costs of the models with an adjusted

In document Eindhoven University of Technology MASTER Redesign of the control structure and inventory control at Vanderlande Gubbels, P.M. (pagina 57-0)