Eindhoven University of Technology MASTER Inventory ... · Performance indicators and objectives:...

$: Eindhoven University of Technology MASTER Inventory ... · Performance indicators and objectives: GEA Grasso BV measures its performance with a P 2 service level (fraction of demand$
Eindhoven University of Technology

MASTER

Inventory control parameter model for items with production and/or spare part demandapplication in the refrigeration compressor industry at GEA Grasso BV

den Brok, K.

Award date:2009

Link to publication

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https://research.tue.nl/en/studentthesis/inventory-control-parameter-model-for-items-with-production-andor-spare-part-demand(61def4e9-c137-41ae-be80-dc0c02a9184e).html

Eindhoven, September 2009 (form 3)

BSc Industrial Engineering and Management Science — TU/e 2007

Student identity number 0571217

in partial fulfillment of the requirements for the degree of

Master of Science

in Operations Management and Logistics

Supervisors:

dr.ir. H.P.G. van Ooijen, TU/e, OPAC

dr. T. Van Woensel, TU/e, OPAC

Inventory control parameter model for items with

production and/or spare part demand:

Application in the refrigeration compressor industry

at GEA Grasso BV.

by

Kees den Brok

ii

TUE. Department Technology Management.

Series Master Theses Operations Management and Logistics

Subject headings: spare parts, Make-to-Stock, stock control, stochastic control systems, logistics

iii

Abstract

In this Master Thesis project, research is conducted to inventory management at GEA Grasso BV, a

manufacturer of compressors for industrial refrigeration. The project concerns the products delivered

from stock used for assembling a compressor, making sub-assemblies, or as spare part. A model is

developed to support the users of the ERP-software for setting the parameters for optimal inventory

management.

An analysis is done to find the difficulties for optimal inventory management at GEA Grasso BV. The

difficulties are further researched and solutions are presented for setting the parameters optimal in their

ERP-system. This finally resulted in a model which makes use of the results from the analyses and

proposes values for the parameters of the ERP-software. Besides the model, recommendations are given

for next improvements for managing their inventory more effective.

iv

Management Summary

In this Master Thesis project, research is conducted to inventory management at GEA Grasso BV, a

manufacturer of compressors for industrial refrigeration. The Logistics department of GEA Grasso BV

thinks that they do not handle the inventories of the items kept on stock in an effective way, especially the

items with demand from production and as spare part. An ERP-software package is used to manage the

inventories, but the Logistics department does not have the possibility of arranging the settings optimal

for inventory management. One of the performance indicators of handling the inventories optimal is the

realized service level. After a rough analysis is concluded that there are no big differences between the

realized service levels of the items with different demand sources (items with demand only from

production, items with demand only as spare parts, and items with demand from production and as spare

part): For a large group of items the desired service level was not achieved, while there is also a large

group of items with a service level, much higher than the desired service level.

Based on these findings the following project description is formulated:

Develop an inventory control parameter model for items delivered from stock, for setting the

parameters of the ERP-software for optimal inventory management

The performance objective is set at a 98% P2 service level (fraction of demand directly fulfilled from

stock), while in the current situation a service level of 95% is desired. From the literature study and

interviews with employees a list of possible problem sources is drawn. The possible problem sources are

analyzed, but first an ABC-classification is made for the allocation of the results of the analyses.

The Conclusions from the Analyses to the Causes

Strategy: In the current situation only one inventory control system is used for all items, while the items

have different characteristics. For A-items and B-items a (s,Q) model is proposed, while for C-items a

(R,S) model or a Two-Bin model is advised.

Performance indicators and objectives: GEA Grasso BV measures its performance with a P2 service

level (fraction of demand directly fulfilled from stock) while for the parameter settings the P1 service

level is used.

Demand: Currently a Normal distribution is used for all items to set the inventory control parameters.

From the analyses stochastic demand is assumed, because the demand horizon is short and unstable. A

Normal and Gamma distribution are found for the monthly demand, and a Poisson distribution for the

customer order arrival process.

Lead-time: The lead-times are not constant and equal to the agreed lead-time as is currently assumed.

The lead-times follow a Normal distribution, and the average lead-time of many items (especially for

purchase items) is larger than the agreed lead-time.

Imperfect delivered orders: Two topics are merged in this subject:

• Orders which are not completely delivered: these do not have a big influence on the inventory

control results and are therefore not further used for the development of the model

• Rejection of items (items do not satisfy the requirements): orders for production items are often

partially rejected; several products of the order do not meet the quality requirements. For

purchase items, it often occurs that the complete order is rejected.

v

Replenishment Order Quantity: In the current situation the sizes of the replenishment orders are based

on the experience and expectations of the purchaser. With the developed model, optimal order quantities

are determined based on the Economic Order Quantity

ERP-software: The users of the ERP-software are not fully aware of the possibilities and behavior of the

parameters and mechanisms the software offers.

The Inventory Control Parameter Model The model is developed to set the inventory control parameters of items which are already in the system

and for new items. First a theoretical optimal model is developed and this is translated to a practical

useable model. For all production items the optimal order quantity has to be increased with the average

rejection quantity for the item. The items are grouped on their ABC-classification (based on the usage

value). The parameter settings can be used for the current inventory control mechanism with parameters

based on the historical data of the items’ characteristics, and for the start settings of the inventory control

based on forecasting.

A-items From literature a (s,Q) model is proposed with the parameter settings based on minimizing the expected

total relevant costs (ETRC) with a simultaneous approach (the optimal combination of the parameter

leading to the absolute minimum ETRC). The data for the costs parameters are not available for the items,

so an alternative formula based on the P2 service level is used for determining the parameter settings. For

the lead-time demand a Normal distribution is assumed for all A-items, because conservative initial

provisioning is advised (overstocking can be extremely expensive).

B-items For B-items also a (s,Q) model is used, comparable to the model of the A-items, and also based on the P2

service level. A group of B-items have a small average monthly demand but a high Coefficient of

Variation (CV>1). For these items a Gamma distribution is assigned to the lead-time demand (combining

a Gamma distributed demand and a Normal distributed lead-time). An approximation of the parameters is

made, because no standard formulas are found in literature. Based on the average and standard deviation

of the demand and lead-time, the Gamma distribution parameters are determined. For the other items a

Normal distribution to the lead-time demand is assigned.

C-items Two different types of C-items are distinguished: slow moving (average monthly demand smaller than

ten) and fast moving (average monthly demand larger than ten) C-items:

Slow moving C-items: a (R,S) strategy with the review period based on the combination of optimal order

quantity and the possibility of combining orders. Implementing a periodic review period in the ERP-

software is not possible. This is tried to cover with other settings of the parameters.

Fast moving C-items: A Two-Bin strategy (based on a (s,Q) strategy), in which the bin size is equal to the

order quantity based on the EOQ formula.

New items Three types of new items are discerned: replacing items, comparable items, and completely new items.

The strategy and parameters for these items are determined with the same formulas as the three categories

of items (based on the ABC-classification). As much information of the comparable or replacing items is

collected and used for determining the parameter settings and the missing information is based on

averages for the specific characteristics.

vi

Results of the Model After using the model a decrease of the average stock level and the average storage costs are expected if

the desired service level is kept on 95%. If the service level will be set at 98% an increase of the average

stock level and average storage costs are expected.

Also an indication is given of the expected average stock levels and storage costs if a service level of 98%

will be used instead of 95% both by setting the parameters with the inventory control parameter model.

The average stock level and storage costs will increase with between 10% and 20% for the items.

ABC-

classifications

new settings

(P2=95%) vs.

current settings

new settings

(P2=98%) vs.

current settings

new settings (P2= 98%)

vs.

new settings (P2= 95%)

Change of the

average stock level

A -6% +3% +10%

B -9% +4% +14%

C -10% +2% +13%

Change of the

average storage costs

A -0.8% +12% +13%

B -1.5% +16% +18%

C -10% +7,5% +20%

Table 1, results of the inventory control parameter model

Conclusions and Recommendation

• Rejection of items is an important factor for setting the parameters for optimal inventory control.

For production orders, the replenishment order quantity should be increased by the number of

expected number of products rejected. For purchase orders, which have to contend with complete

order rejections, agreements with the supplier should be made for placing rush orders in case of

complete order rejections.

• No specific settings are found for items with only demand as spare part and for items with

demand as spare part and from production. Other characteristics, like the average demand and the

criticality (ABC-analysis) are important for specific parameter settings

• To determine the optimal replenishment order quantities data for the costs parameters (storage

costs and ordering costs) are necessary. For A-items also the costs parameter for not being able to

deliver a product directly from stock is required for optimal inventory control parameter settings.

• In the developed model stochastic demand is assumed because of the short and unstable demand

horizon for all items. The ERP-software parameters assume deterministic demand, which results

in too high stock levels and service levels. The complexity of the combination of stochastic and

deterministic demand makes it very hard to find the optimal settings. A forecast of the demand is

recommended: the mechanisms of the software are suitable for forecasted demand and the

complexity of stochastic and deterministic demand can be covered.

• The use of the model is advised because:

o it is expected that the desired service levels will be achieved

o the average stock level and storage costs will decrease for the same service level

vii

Preface

This report presents the results of my research project in order to receive the Master’s Degree in Industrial

Engineering and Management Science at the Eindhoven University of Technology. This graduation

project has been carried out from September 2008 until July 2009 at the logistic department of GEA

Grasso BV, ‘s-Hertogenbosch.

The project gave me insight in the differences between theory and practice, and the content of

applicability of theory in practical situations. It has also offered me a lot of experience that will be useful,

consciously or unconsciously, for my further career.

It was very interesting talking with many people in the organization, and I would like to thank all the

colleagues for their willingness, time and effort. Especially I would like to thank my supervisors at GEA

Grasso BV: Jurgen Alessie, Frans Mulleneers and Wim van Beerendonk. The weekly discussion hours

with Jurgen and Frans were very interesting and they were, despite of their busy schedule, very helpful

and gave me useful feedback and information. Wim van Beerendonk, the Supply Chain manager and the

initiator of this project at GEA Grasso BV, was also available for feedback especially when important

decisions for the milestones had to be taken.

I would also like to thank my supervisors from the Eindhoven University of Technology, Henny van

Ooijen and Tom van Woensel. Henny van Ooijen was always available for questions and feedback, and

for the continuation of the project.

Last but not least I would like to express my thanks to my family, girlfriend, and friends for their support

and advice during my study.

viii

Table of Contents

ABSTRACT ............................................................................................................................................................. III

MANAGEMENT SUMMARY ................................................................................................................................... IV

PREFACE .............................................................................................................................................................. VII

TABLE OF CONTENTS ........................................................................................................................................... VIII

1. INTRODUCTION ............................................................................................................................................ 1

1.1 INITIAL PROJECT ................................................................................................................................................... 1

1.2 PROJECT APPROACH ............................................................................................................................................. 2 1.3 REPORT STRUCTURE .............................................................................................................................................. 3

2. COMPANY AND PRODUCT DESCRIPTION ...................................................................................................... 4

2.1 COMPANY HISTORY .............................................................................................................................................. 4 2.2 THE SUPPLY CHAIN DEPARTMENT ............................................................................................................................ 4

2.3 PRODUCTS AND KEY MARKETS ................................................................................................................................ 5

2.4 PRODUCTION AND DEMAND ................................................................................................................................... 6

3. PROBLEM DESCRIPTION ................................................................................................................................ 7

3.1 INITIAL ASSIGNMENT ............................................................................................................................................. 7

3.2 PROBLEM ANALYSIS .............................................................................................................................................. 8

3.3 CONCLUSIONS AND IDENTIFICATION OF POSSIBLE CAUSES ............................................................................................ 9

3.4 FINAL ASSIGNMENT ............................................................................................................................................ 10 3.5 RESEARCH QUESTIONS ........................................................................................................................................ 11

3.6 DEVELOPMENT PLAN .......................................................................................................................................... 12

4. ANALYSES ................................................................................................................................................... 13

4.1 ABC-CLASSIFICATION .......................................................................................................................................... 13

4.2 ANALYSES TO THE CAUSES .................................................................................................................................... 15

4.2.1 Strategy ................................................................................................................................................ 15

4.2.2 Service Level ......................................................................................................................................... 15 4.2.3 Demand Analysis .................................................................................................................................. 16

4.2.4 Lead-time Analysis ............................................................................................................................... 16

4.2.5 Imperfect Delivered Order Analysis...................................................................................................... 18 4.2.6 Order Quantity Analysis ....................................................................................................................... 19

4.2.7 ERP-Software ....................................................................................................................................... 19

4.3 CONCLUSIONS ANALYSES ..................................................................................................................................... 20

5. THEORETICAL INVENTORY CONTROL MODEL .............................................................................................. 21

5.1 INTRODUCTION .................................................................................................................................................. 21

5.2 A-ITEMS ........................................................................................................................................................... 22

5.2.1 Strategy ................................................................................................................................................ 22

5.2.2 Parameters .......................................................................................................................................... 23 5.3 B-ITEMS ........................................................................................................................................................... 24

5.3.1 Strategy ................................................................................................................................................ 24

5.3.2 Parameters .......................................................................................................................................... 24 5.4 C-ITEMS ........................................................................................................................................................... 26

5.4.1 Strategies ............................................................................................................................................. 26

5.4.2 Parameters .......................................................................................................................................... 26

5.5 NEW ITEMS ....................................................................................................................................................... 28

ix

5.5.1 Types of New Items .............................................................................................................................. 28

5.5.2 Data for New Items .............................................................................................................................. 28

6. BRIDGING THE GAP BETWEEN THEORY AND PRACTICAL DEVELOPMENT .................................................... 29

6.1 ERP-SOFTWARE ANALYSIS ................................................................................................................................... 30

6.2 STRUCTURE OF THE MODEL .................................................................................................................................. 31

6.3 A-ITEMS ........................................................................................................................................................... 32 6.4 B-ITEMS ........................................................................................................................................................... 35

6.5 C-ITEMS ........................................................................................................................................................... 37

6.6 NEW ITEMS ....................................................................................................................................................... 39

6.7 USE AND MAINTENANCE OF THE MODEL ................................................................................................................ 40 6.8 CONCLUSIONS ................................................................................................................................................... 41

7. RESULTS ...................................................................................................................................................... 42

7.1 MEASURING THE RESULTS .................................................................................................................................... 42 7.2 RESULTS A-ITEMS ............................................................................................................................................... 43

7.3 RESULTS B-ITEMS ............................................................................................................................................... 44

7.4 RESULTS C-ITEMS ............................................................................................................................................... 45

7.5 CONCLUSIONS ................................................................................................................................................... 46

8. CONCLUSIONS AND RECOMMENDATIONS.................................................................................................. 47

8.1 CONCLUSIONS RESEARCH QUESTIONS .................................................................................................................... 47

8.2 GENERAL CONCLUSIONS AND RECOMMENDATIONS ................................................................................................... 48

REFERENCES ......................................................................................................................................................... 50

APPENDICES......................................................................................................................................................... 51

APPENDIX A: OVERVIEW SUPPLY CHAIN GROUP ................................................................................................................ 52

APPENDIX B: SUMMARY LITERATURE STUDY AND RESEARCH QUESTIONS ................................................................................ 53 APPENDIX C: ABC-CLASSIFICATION ................................................................................................................................. 57

APPENDIX D: SAMPLE SIZE ............................................................................................................................................ 59

APPENDIX E: DEMAND ANALYSES ................................................................................................................................... 60

APPENDIX F: ASSUMPTIONS STANDARD FORMULAS INVENTORY CONTROL .............................................................................. 61 APPENDIX G: MICROSOFT DYNAMICS AX: AXAPTA ............................................................................................................ 62

APPENDIX H: FORMULAS PARAMETER CALCULATION .......................................................................................................... 66

APPENDIX I: ROBUSTNESS EOQ ...................................................................................................................................... 67 APPENDIX J: MINIMUM AND MAXIMUM ORDER QUANTITY ANALYSIS ................................................................................... 68

APPENDIX K: C-ITEM DEMAND ....................................................................................................................................... 69

1

1. Introduction

In this introduction the outline of the project is presented. First the initial project description is given in

paragraph 1.1, which was the starting point of the project. Based on the initial project description, a

framework for the project is created used as a guideline for the project. This framework is described in

paragraph 1.2 as the project approach. The project approach is used as the steppingstone for the structure

of the report, described in paragraph 1.3.

1.1 Initial Project

GEA Grasso BV is a manufacturer of compressors for industrial refrigeration, located in ‘s-

Hertogenbosch, the Netherlands. The compressor is made on an assemble-to-order strategy, the used

materials and products for the assembly process are held on stock. However, the products and materials

on stock are not only used for the assembly process, but also for making subassemblies and for products

used as spare part. If a customer wants to replace a part of the compressor due to wear and tear, he can

make an order for this part. So the products on stock can be used for three processes: the assembly

process of the compressor, making subassemblies, and for the spare part demand.

GEA Grasso BV thinks that they do not handle the inventories of the items kept on stock in an effective

way. They make use of an ERP-software package for managing their inventories, but do not have the

possibility for arranging the settings optimal for inventory management. Therefore, they have formulated

the following project description for a Master Thesis:

Design a decision support model for optimal inventory management

This model should be able to support the user of the ERP-software on the field of inventory management,

to set the parameters of the ERP-software optimal. Optimal inventory management should be realized

with the condition of achieving a service level of 98% for all items held on stock. The support is

concerned with setting the parameters of the current ERP-software for optimal inventory management.

However, it is also a check if the current ERP-software package is apposite for optimal inventory

management for the company.

2

1.2 Project Approach

With the initial project description, a project approach can be made. The project approach is a general

framework, in which the specific steps of the project are taken.

First, a literature research is done and interviews with employees from various departments are held, to

get an overview of the company problem and possible causes of this problem. A rough problem analysis

is made based on the problem description of the company. A research proposal is made as outline of the

project carried out at GEA Grasso BV and research questions are formulated based on the literature

research. Besides the research questions also the project description is formulated in the research

proposal. These steps are the preparation of the analysis and development phases of the project

A deeper analysis is done to the problem and the possible causes are listed. These possible causes are

analyzed in more detail, and the characteristics of the problem are identified. With this information the

start is given of the development for a solution for the formulated problem and answering the research

questions.

A plan is drafted for the development of a solution for the inventory management problem of GEA

Grasso BV. First a theoretical model is build in which the theoretical optimal solutions for the items are

presented. From this theoretical model a translation is made to a practical model which can be used and is

suitable for GEA Grasso BV. With this model results are gathered and compared with the current settings.

From these results and the findings during the analyzing and development phases, conclusions are drawn

and recommendations are given.

3

1.3 Report Structure

The structure of the report is in broad outlines similar to the project approach. The first phase of the report

is an introduction to the project, after which the development part of the project is described. Finally the

results and the conclusions are presented.

The introduction to the project starts with the initial project as described by the company and the structure

of the project and report in chapter 1. Next, in chapter 2, a company and product description is given to

inform the reader of the environment in which the project is carried out. In this company and product

description the various aspects of the company are described: history, the supply chain department, the

products and markets, and the production and demand process.

After the company and product description, the problem is further researched in chapter 3. A problem

description is given, based on a problem analysis and the identification of the possible caused the final

assignment is formulated. Also the research questions and a development plan for a model, helping to

manage the inventories of GEA Grasso BV, are presented.

In chapter 4, an ABC-classification and analyses to the possible problem causes, as identified in the

problem identification in chapter 3, are carried out. From these analyses conclusions can be drawn, which

topics should be included in the development of the model.

The theoretical model for inventory management is presented in chapter 5. In this chapter the strategies

and parameters are described that are optimal for the groups of items, based on the theoretical findings. In

chapter 6 the theoretical model is translated to a practical model, which takes into account the restrictions

given by the user and/or the equipment. The model is made practicable for the user, and satisfies the

requirements that are set.

Results of the model are presented in chapter 7, and are compared to the results without the use of the

model. Conclusions are drawn based on the results and also the limitations of the interpretation and the

consequences of the results are discussed.

Finally, in the last chapter, the conclusions of the project are drawn and recommendations are given. The

conclusions are split in two parts: First the conclusions on the research questions, derived from the

literature research are drawn. The second part of the conclusions contains the general conclusions for the

company based on the development and analyses for the creation of the model. The recommendations

contain advises about the changes on inventory management and what follow-up research is

recommended.

4

2. Company and Product Description

The company description gives an overview of the environment the project is performed. In paragraph

2.1, a short summary will be presented of the development of the company from its establishment up to

now. In paragraph 2.2 the supply chain department will be described and in special the Logistics

department, which is responsible for the inventory management part. The products and the key markets

for GEA Grasso BV will be in paragraph 2.3 for classifying the company its customers and products. In

the last paragraph of this chapter, paragraph 2.4, in short the production and demand for items will be

presented.

2.1 Company History

The company is founded in 1858 in ‘s-Hertogenbosch, the Netherlands, by Willem Grasso as a forge-

workshop. After his son takes over the business (in the meanwhile the company had become a

butter/margarine machine factory), he moves the company to a larger premises at Vught. At that moment,

the company employs about 100 people. In 1913 Grasso moves back to ‘s-Hertogenbosch in a new

modern factory, stops with the production of butter/margarine machines and continues fully with the

production of compressors for industrial refrigeration. In 1937, the company is taken over by the Van

Heijst brothers from The Hague due to the economic crisis. In the Second World War, the company is

almost completely destroyed and production comes to a standstill. After the war, the company is rebuilt

and complete up-to-date machinery is installed. In 1958 during its 100 years anniversary, the company

receives the title “Royal”. New applications for industrial refrigeration industries are developed and

export is branched all over the world. The expansion continues during the coming decades until in 1992

Grasso becomes a member of GEA AG, a German multinational with 200 operating companies and

14,500 employees in 50 countries. In 1999 GEA becomes part of the MG Technologies group, and in

2005 the name changes in GEA Group. Since the first compressor left the factory, the export has been

steadily increased in volume and Grasso’s wide capacity range comprises 66 different compressor types.

2.2 The Supply Chain Department

The project is initiated by the Supply Chain manager in congruence with the Logistic manager and

Logistic engineer. The Logistic department is entrusted with the inventory management, and the project is

formulated to support the Logistic department with managing the inventories of the items. Besides the

Logistic department, the Supply Chain group also consists of the Purchasing department and the

warehouse division. In Appendix A: Supply Chain group, an organization chart of the supply chain group

is given, with the Logistic department in more detail.

5

2.3 Products and Key Markets

GEA Grasso designs and manufactures compressors for industrial refrigeration. Multiple kinds of

compressors are available, which can be subdivided in the used technique, capacity, temperature ranges,

and refrigerants. Each compressor type has its particular advantages depending on the conditions of

operation:

• Basic technique: reciprocating/Piston compressors

• Evaporating temperatures: from -65o C up to +35

o C

• Refrigeration capacities: 75 kW up to 8500 kW

• Refrigerants: NH3, CO2, and other common refrigerants (freons)

The product range of GEA Grasso BV is very wide; multiple types of compressors are available. Eight

different families of compressors can be discerned, each with multiple models. These compressors are

available as package (a compressor driven by an additional supplied motor and all other desired features)

or just as a bare compressor (only the compressor with its standard components).

The compressors made by GEA Grasso, can be used in numerous markets. Four key activities are

formulated for four types of markets:

• Food processing: Refrigeration is very important for the food processing industry; from the

production of the products until the storing of the food in cooling chambers. A broad band of

applications includes freezing processes and storage facilities of meat, fish, vegetables, etc. and

the brewery and storage of beer.

• Industrial processes: during running processes, low temperatures or varying temperatures are

required and often unique solutions are needed. All components are also available in explosion

proof execution especially for the chemical industry.

• Leisure: with the refrigeration compressors, it is possible to create wintery circumstances at any

location in the world. Grasso components have been used for ski slopes and skating surfaces in

ice rinks.

• Air conditioning: almost every building nowadays demands for an air conditioning system.

Grasso has a good reputation for their ammonia chillers, the heart of the air conditioning systems

of such large cooling capacities.

2.4 Production and Demand

As described in the previous paragraph, GEA Grasso BV offers a large range of different types of

compressors for industrial refrigeration. However, every compressor is cust

customers, and therefore unique. With this in mind, it may be obvious that it will take a long time to

completely engineer the compressor to order (ETO) or make the compressor to order (MTO)

Assemble-to-Order (ATO) strategy is followed

the place in the chain from where the product is coupled to a specific customer) is presented, with the

corresponding production strategy.

Figure 2-1, the CODP with the corresponding production strategies

To provide a lead-time, which is in conformance with the market, the subassemblies are Make

(MTS) or Buy-to-Stock (BTS). Also all the items and raw materials use

final assembly process are MTS or BTS.

The major advantage for having the items on stock is the shorter lead

compressors but also to the customer of spare parts. Items can be picked directly

them to the customer or use them for the assembly process of the compressor or the production process

for making the subassemblies.

The disadvantages of a MTS/BTS strategy are the need of storage capacity and the cost of storing and

handling the items. Another disadvantage is the production based on speculation: it is uncertain if there

will be demand for the items.

Items can be used for two different types of demand:

• Demand for an item from production: this item is used for the a

the assembly/production of a subassembly.

• Demand for an item as spare part: This item is used if a customer wants to replace a part/item of

its compressor.

6

ion and Demand


compressors for industrial refrigeration. However, every compressor is customized to the wishes of the


completely engineer the compressor to order (ETO) or make the compressor to order (MTO)

gy is followed. In figure 2.1 the customer order decoupling point (


, the CODP with the corresponding production strategies

time, which is in conformance with the market, the subassemblies are Make

Stock (BTS). Also all the items and raw materials used for the subassemblies and the

final assembly process are MTS or BTS.

The major advantage for having the items on stock is the shorter lead-time provided to the customer of

compressors but also to the customer of spare parts. Items can be picked directly from stock to deliver




wo different types of demand:

from production: this item is used for the assembly of the compressor or for

the assembly/production of a subassembly.

Demand for an item as spare part: This item is used if a customer wants to replace a part/item of


omized to the wishes of the


completely engineer the compressor to order (ETO) or make the compressor to order (MTO), so an

In figure 2.1 the customer order decoupling point (CODP,


time, which is in conformance with the market, the subassemblies are Make-to-Stock

d for the subassemblies and the

time provided to the customer of

from stock to deliver




ssembly of the compressor or for

Demand for an item as spare part: This item is used if a customer wants to replace a part/item of

7

3. Problem Description

The project is initiated by GEA Grasso BV, because they expect that there is a lot of room for

improvement on the field of inventory management. The initial assignment will be described in paragraph

3.1, including the problem brought up by GEA Grasso BV. This problem will be discussed and analyzed

in more detail in paragraph 3.2. In paragraph 3.3, the possible causes of the problem, based on interviews

and a literature study, are identified. Based on the problem analysis and the identification of possible

causes, the final assignment is presented in paragraph 3.4. Next to it, research questions based on the

literature study, are formulated in paragraph 3.5. The last paragraph describes the development plan, in

which the steps of the development of the solution for the inventory management problem are presented.

3.1 Initial Assignment

The logistic department of GEA Grasso BV thinks that it does not manage the inventory of items held on

stock optimal. Moreover, especially the items with production and spare part demand are very hard to

manage. They expect that in general too much inventory is held, just to be sure to achieve the desired

service level. However, they are not satisfied with the availability of the items on stock. Therefore the

logistic department of GEA Grasso BV formulated the Master Thesis project:

Develop a decision support model for optimal inventory management.

The current service level is set at 95%, with the service level defined as the fraction of demand for an

item that can be delivered directly from stock. If the fraction of satisfied demand is lower than this 95%

the desired service level is not met. For the new situation a service level of 98% is desired, because GEA

Grasso BV desires a higher availability of the items for the coming years.

It is also possible that the achieved service level is much higher than the desired service level. This is not

desirable because too high service levels can be an indication of holding too much inventory, which

results in high inventory costs.

Problems with managing inventories normally lead to holding too much or too less inventory, which

affects the service level and the inventory costs. For detecting the problems with the inventory, the service

level is used as a first indication of the extend of control of the inventory with the current settings. The

items are grouped based on their demand source to detect if the service levels of these groups differ from

each other. Analyzing the service levels of the items per group indicate if the problem is mainly applied

for one of the groups or for the whole range.

8

3.2 Problem Analysis

The service level of the items held on stock are analyzed for the identification of the problems with

managing the inventory. For the total set of 3085 items the service level, the fraction of demand (number

of products) that could be met directly from stock in the last four years, is determined. The service level

was set at 95%, for all items delivered from stock.

The service levels of the items are determined (the percentage of products per item that is delivered on-

time) and the items are grouped based on the demand source and their service level. The service level

categorization is based on four groups:

• a service level lower than 75%: the performance of items in this group is very low. It occurs to

often that the demand for an item cannot be delivered directly.

• a service level between 75% and 95%: the desired service level is not achieved but it is not as

disastrous as the previous group.

• a service level between 95% and 98%: the desired service level is achieved or slightly exceeded.

The parameter settings for inventory management result in the desired service level.

• a service level higher than 98%: the performance is higher than was set, which can be an

indication of holding too much inventory.

In table 3-1, the items are grouped based on their demand source and their service level.

P2 Service level spare parts production spare parts and production Total items

<75% 252 46 77 375

75%-95% 214 151 519 884

95%-98% 13 67 210 290

>98% 136 901 499 1536

Total items 615 1165 1305 3085

Table 3-1, service level per demand source

From the results presented in table 3-1 can be seen that for the total group of items, almost 50% (1536

items) have a service level higher than 98%. Next to it, 375 items have a service level of less than 75%

and 884 items a service level between 75% and 95%. This means in total 1259 items, which corresponds

to over 40% of the total number of items, do not meet the desired service level. Only a very small part of

the items, less than 10%, is categorized in the group with the acceptable service levels between 95% and

98%.

GEA Grasso BV expected to have most problems with items having demand from both sources (spare

parts demand and production demand), while from the analysis the other two groups do not seem to

perform better.

9

3.3 Conclusions and Identification of Possible Causes

From the analysis can be concluded that the problem as outlined by GEA Grasso BV is wider than

initially was expected. The problem does not only include the items with only demand from both sources,

but also the items with demand from a single source.

The problem of managing the inventory of items delivered from stock contains all items. This is an

indication that not only handling demand from multiple sources results in problems with managing the

inventory. A literature research, which is done in parallel with the problem identification, is done for

finding the possible problem sources for optimal inventory management. Also interviews with employees

from different departments are held, to get as much information from different positions in the company.

From the literature study and the interviews a list of possible problem sources are put forward:

• Strategy: are the used inventory policies appropriate for managing the inventory of the items

• Service level: how to use a service level to achieve the desired performance of the inventory

management system

• Demand: the demand from different sources leads to complicated situations, and the demand is

not constant and/or deterministic

• Lead-time: the lead-time is not constant and deterministic

• Imperfect deliveries: receiving orders with items which do not meet the quality requirements or

incomplete delivered orders, lead to problems with managing the stock levels of the items

• Order quantities: the order quantities are not based on formulas but on the experience of the

purchasers and restrictions of the supplier

• ERP-software: there are no uniform rules for setting parameters in the ERP-software and the

mechanisms of the software are not clear.

The problem of GEA Grasso BV is detected; the inventory for all types of items is not managed effective.

For a large group of items the desired service level is not achieved while for another large group of items

the height of the service level indicates too large inventories which are also not desired.

10

3.4 Final Assignment

From the problem analysis in paragraph 3.2 comes to the fore that the problem as described by GEA

Grasso BV is not complete. The problem is not specific for the items with multiple demand sources but

comprises the whole set of items delivered from stock. The service level of most of the items is lower

than desired or the stock levels are higher than desired. This is caused by the lack of competence and

capacity at GEA Grasso BV to arrange the settings optimal for managing the inventory. GEA Grasso BV

has formulated a project description to design a decision support model for optimal inventory

management. This model should support GEA Grasso BV with setting the parameters of the ERP

software optimal for managing the inventories and is a check if the ERP software is apposite for optimal

inventory management for the company.

In the previous paragraph possible causes are brought up which are indications of the need of a model,

handling the possible causes and giving GEA Grasso BV the tool for managing and controlling the

inventory more effective. The model will be developed especially for the Logistic department, and should

therefore give all and only the relevant information on the field of inventory management. The model

should advise the Logistic department with the parameter settings of the ERP-software.

The final assignment formulation:

Develop an inventory control parameter model for items delivered from stock, for setting the

parameters of the ERP-software for optimal inventory management

The model has to be able to find the optimal parameter settings with the type of input that is available and

necessary for managing the inventory. This means that the model should be able to handle the data that is

available from a database. It is not in the scope of the project to gather data not stored in a database. It can

be necessary to edit the available data to become suitable as input for the model. If data is not yet

available but can be gathered in the future, a framework should be set up for the gathered information to

use as input for the model.

The model should be useful for all items delivered from stock, based on the current information of the

items delivered from stock. The inventory of a group of items is managed with a Kan-Ban strategy and

the ERP-software does not record the specific information for these items. This group of items is not

included in the analyses. If new items are added to the range of products delivered from stock, the model

should also be able to determine optimal parameter settings for these new items.

The decision support model should result in optimal inventory management. As starting point a

theoretical optimal model will be created. This model is adapted to the possibilities and restrictions of the

ERP-software and the availability and capacity of the calculation options. This makes the model useable

and suitable for the Logistics department of GEA Grasso BV.

11

3.5 Research Questions

One of the objectives of a Master Thesis project is to contribute to the current scientific literature. A

literature study is done to find information on the field of inventory management. A contribution can be

made by doing research to a specific part of a research field. During the literature study possible causes of

GEA Grasso BV, its problems with managing their inventories are found. However, also gaps are

discovered in the scientific theory, which means not all the options on a specific field are discussed. To do

research to these gaps or as supplement of the stated theory in the literature, research questions are

formulated. Besides that doing research for the formulated research questions is supplementary for the

scientific literature, it is also directly of use for the project.

Three research questions are formulated for this project, all based on the characteristics of the final

assignment and the identified possible problem causes. The three fields on which research questions are

formulated are: items with quality issues, spare part inventory management, and inventory management

of items with demand from production and as spare part. In Appendix B the process to the research

questions is described and also the sub-questions, which are used as support for answering the research

questions, are presented.

Imperfect delivered orders As possible causes for the problem of managing the inventory effective, the quality of the products and

the incomplete delivered orders are brought up. These two topics are packed together as imperfect

delivered orders. Based on this specific topic in the literature study the following research question is

formulated:

• How to set the parameters of the inventory control system to cover also the imperfect delivered

orders.

Spare part inventory management In the inventory management literature is a lot of attention for the spare parts. However, in there is no

consensus what the best approximation is to handle the demand characteristic of the spare part demand.

The research question is formulated directly related to the project description, while the sub-questions are

derived directly from the literature gaps:

• How to set the parameters of the inventory control model for spare parts to achieve the desired

service level.

Production demand and spare part demand inventory management In contrast to the spare part demand, only scarcely information can be found for items with demand from

production and as spare part. The research question is formulated which coincides with the project:

• How to set the parameters of the inventory control model for items available as spare part and

ordered by production to achieve the desired service level.

12

3.6 Development Plan

A plan is set up for the development of the inventory control parameter model. In the project formulation

the boundaries of the project are described. For the development of the model, the problem causes have to

be analyzed. From the literature study (see Appendix B) comes to the fore that an ABC-classification can

be helpful for the analyses to the causes. The results can be allocated to the categories of the ABC-

classification.

From these analyses and based on the findings in the literature study, the theoretical optimal strategies

with the accompanying parameters are determined as well as the formulas and guidelines for determining

these parameters. The items are grouped based on the ABC-classification, with most attention to the most

important items for the company.

However, these theoretical optimal strategies and parameters should be made suitable for using them. The

theoretical optimal findings should be adapted to the used program for the model and the parameters and

mechanisms of the current ERP-software. As preparation of the development of the inventory control

parameter model, the ERP-software will be analyzed. The structure of the model will be determined to

become as close to the theoretical optimal model but suitable or the ERP-software. Important

considerations for the development of the model are the requirements set on the model, and the possibility

to approximate the theoretical optimal results.

After the development of the model, the results are presented and conclusions are drawn based on the

results. The limitations of the model and the consequences of the limitations are discussed. The last steps

of the model development process are the description of the implementation and the use of the model.

4. Analyses

In the previous chapter is described what is necessary for the development of the

parameter model. A categorization of the items is necessary for determining appropriate inventory

management strategies for the items

classification is done and presented

characteristics. The possible causes, as listed in paragraph 3.3,

paragraph 4.2. The conclusions of the analyses will be presented

4.1 ABC-Classification

With an ABC-classification can be

manage as accurate as possible and which items

already made multiple ABC-classifications base

classifications are out-dated and the characteristics of the classification are not unambiguous described

new ABC-classification is done with only the items relevant for this project.

As input for the ABC-classification, the demand and the value of the items are used. These two

characteristics are important for the

demand, more influence can be exerted with an inventory management t

represents the costs for the company. The items represent money, and the more money they represent the

more critical they are for the company.

The term used for the expression of the size of the demand in combination with its

value of the items (Silver et al., 1998

The items taken for the ABC-classification are the items delivered from stock and with at least one

demand order in the period 2005 through 2008. The total number of items used for the ABC cla

is 3085. In figure 4-1 the ABC-classification is depicted. In Appendix

classifications are presented for the different types of items, as extra information.

Figure 4-1, ABC-classification

13

In the previous chapter is described what is necessary for the development of the

model. A categorization of the items is necessary for determining appropriate inventory

management strategies for the items and for the allocation of the results of the analyses

and presented in paragraph 4.1 with the in the literature recommended

The possible causes, as listed in paragraph 3.3, will be analyzed in more detail

he conclusions of the analyses will be presented in the last paragraph.

Classification

can be determined which items are the most relevant for the company to

manage as accurate as possible and which items could have a more loosely control.

classifications based on various characteristics of the items, however these

and the characteristics of the classification are not unambiguous described

classification is done with only the items relevant for this project.

classification, the demand and the value of the items are used. These two

characteristics are important for the company on the field of inventory management. For items with high

be exerted with an inventory management tool and the value of the items

sents the costs for the company. The items represent money, and the more money they represent the

more critical they are for the company.

The term used for the expression of the size of the demand in combination with its

Silver et al., 1998).

classification are the items delivered from stock and with at least one

demand order in the period 2005 through 2008. The total number of items used for the ABC cla

classification is depicted. In Appendix C: ABC-classification, the ABC

classifications are presented for the different types of items, as extra information.

In the previous chapter is described what is necessary for the development of the inventory control

model. A categorization of the items is necessary for determining appropriate inventory

and for the allocation of the results of the analyses. An ABC-

literature recommended

analyzed in more detail in

determined which items are the most relevant for the company to

a more loosely control. GEA Grasso BV

d on various characteristics of the items, however these

and the characteristics of the classification are not unambiguous described. A

classification, the demand and the value of the items are used. These two

the field of inventory management. For items with high

ool and the value of the items

sents the costs for the company. The items represent money, and the more money they represent the

value is the usage

classification are the items delivered from stock and with at least one

demand order in the period 2005 through 2008. The total number of items used for the ABC classification

classification, the ABC-

14

The following values are found for the ABC-classification (which correspond to the percentage as

presented by Hopp and Spearman (2001), Appendix B: table B-1):

• A-items: 75% of the usage value, represented by 9% of the items

• B-items: the next 15% of the usage value, represented by 11% of the items

• C-items: the last 10% of the usage value, represented by 80% of the items

The categorization makes it possible to focus on the most important items. The C-class items are given

the less attention because of its lack of importance based on the ABC-classification. However, an item

can be classified as C-item, because of its very low demand but having a relative high value. In literature

is proposed that C-class items should be ample stored to be sure the desired service level will be achieved

against less attention from the inventory decision makers. The value of the stock is often used as an

indication of the inventory necessary for achieving a desired service level. To prevent keeping to much

stock of items with low demand but high value, the value of the item should be taken into account when

determining the parameters and attention for an item.

Price of item�

Usage value↓

A (=75% of the

sum of the prices)

B (=15% of the

sum of the prices)

C (=10% of the

sum of the prices)

Total

A (=75% of total usage value) 76 82 128 286

B (=15% of total usage value) 57 3 209 339

C (=10% of total usage value) 125 266 2069 2460

Total 258 421 2406 3085

Table 4-1, Usage value ABC vs. price ABC

In table 4-1 an overview is given with the ABC-classification as proposed based on the usage value of the

item, compared with the ABC-classification based on the item value (with the same percentage for the

price of the items as for the usage value).

From table 4-1 can be concluded that the largest part of the items is classified in the same category for the

usage values as well as for the price of the item. However, several items are not categorized in both same

classes.

We will pay extra attention to the parameter settings of the 125 C-class usage value items with an A-class

price. Ample stocking these items, which is proposed in literature for C-items, will lead to high storage

costs. So in contrast to the proposed loosely control of all the C-items, the parameters of this group C-

items have to be set very accurate.

15

4.2 Analyses to the Causes

In chapter 3, a list of possible causes for the inventory management problem is given, based on a literature

research and interviews held with employees from different departments of the company. In this

paragraph the problem causes are analyzed, to detect whether the possible problem sources actually lead

to inventory management problems for GEA Grasso. Also the characteristics and consequences of these

problem sources are determined. Per possible problem source the current situation is described, and

clarified why this problem source results in difficulties for managing inventories.

For several analyses random samples are drawn, since analyzing the whole population is too time

consuming (more information about random sampling can be found in Appendix D: random sample size).

If a random sample is drawn, the conditions are shortly described before the specific analysis. The

statistical program StatGraphics Centurion XV is used for the analyses requiring a distribution fitting.

First a Goodness-of-Fit test is done to detect possible outliers. Outliers are tracked, but Hair et al. (2006)

state that an outlier should be retained if this event fits the objectives of the research. After the Goodness-

of-Fit test, the distribution fitting analyses is carried out with the Kolmogorov-Smirnov test with a

significance level of 95%.

4.2.1 Strategy The inventories of the set of all the items relevant for this project are managed with one inventory

strategy. The current group of items managed with a Kan-Ban strategy is not in the scope of this project.

The current strategy is based on a reorder level with often a fixed order quantity, best described as a (s,Q)

model. GEA Grasso BV thinks that also a part of the set of items under research can be managed by a

Kan-Ban strategy. Besides managing the stocks based on historical data, GEA Grasso BV has (premature)

plans to forecast demand in the future, but the structure of the forecasting process is not (yet) further

elaborated.

The (s,Q) inventory strategy is widely used, and is applicable in many situation if the demand is non-

deterministic. However, to determine if this strategy is optimal for all items the characteristics of the

demand and lead-time have to be analyzed. Another important characteristic for setting the optimal

strategy is the criticality of the item, as is determined with the ABC-classification.

We think that assigning a strategy to an item should be included in the inventory control parameter model.

At this moment no distinction is made between items for their inventory control strategy, and with the

model the advice can be given for setting the appropriate strategies for the items.

4.2.2 Service Level In the problem analysis in chapter 3, the service level is determined for the items delivered from stock.

The service level was defined as the fraction of demand for an item that can be delivered directly from

stock. However, during the first interviews for the initial project description, there was not a univocal

description of the term service level.

GEA Grasso BV was not aware of the multiple types of service levels (see Appendix B), and the exact

definition of the service level. From the interviews came to the fore that the measured performance is the

P2 service level (fraction of demand satisfied directly from stock). For the calculation of the parameters

for managing the inventory, GEA Grasso BV makes use of formulas including a service level. However,

they do not know which type of service level they use. After analyzing the formulas, we conclude that

GEA Grasso BV calculates its parameters with the P1 service level. This does not coincide with the

measured service level.

16

4.2.3 Demand Analysis One of the most important factors of inventory management is the demand for the items. Several types of

demand can be distinguished: constant, deterministic and stochastic demand.

From the literature study, differences are expected for different demand sources therefore a demand

analysis based on the type of demand is performed. From the interviews held in the company is concluded

that the demand for items is not constant, which is also confirmed by the data.

The analysis, to investigate if the demand of the items is deterministic, did not result in clear-cut results.

The horizon for items with only spare parts demand is almost zero, spare parts demand has to be fulfilled

directly. For items with only production demand, the horizon is often a couple of weeks, because the

production process needs a planning, but is not fixed.

Determining the horizon for items with demand from both sources is even harder, because of the direct

delivery of spare parts and the not fixed horizon (of a couple of weeks) for production demand.

Because of the complexity of the unknown horizon of deterministic demand, we assume the demand is

stochastic and non-deterministic for all demand sources.

With the assumption of stochastic demand for all items, the demand distribution can be determined.

First demand distributions are fit on the monthly demand. If it is not possible to fit a distribution on the

monthly demand, the Poisson distribution is fitted on the interarrival time. We tried to find a group of

items with similar characteristics and the same demand distributions. The following characteristics of the

items are used for forming groups based on the findings in the literature research: demand source, ABC-

classification, size of the demand (slow-mover/fast mover) in combination with the Coefficient of

Variation (CV, the standard deviation divided by the average).

Demand analyses for items grouped on the demand sources, on the ABC-classification and on the

combination of these two (results can be found in Appendix E, respectively in table E-1, E-2, and E-3),

did not lead to satisfying results. The demand analysis for items grouped based on their CV and the size

of the demand results in the most satisfying allocation of demand distributions (see table 4-2)

CV average monthly

demand Normal Gamma

Poisson

interarrival times No fit

Total

CV≤1 >5 81 4 1 2

88

≤5 1 1 12 2

16

CV>1 >5 6 4 25 17

52

≤5 0 3 82 112

197

Total 88 12 120 133

353

Table 4-2, demand distributions vs. CV and average demand

This classification leads to quite satisfying results, especially for the items with a low CV and high

demand. For the other groups less univocal results are found, but if the items with no distribution are left

out of consideration, suitable distributions can be assigned for the groups of items.

4.2.4 Lead-time Analysis Two types of deliveries can be distinguished: items delivered after they are internally produced, and items

purchased and delivered by the supplier. After a production step in the factory, the new items are

delivered at the warehouse. If items are ordered at an external supplier, the items of the order are also

stored at the warehouse. From the 3085 items, 638 were not ordered and therefore not supplied in the last

17

four years, so these items are not included in this analysis. The remaining 2447 items can be divided in

the following groups:

• Production: 556 items are supplied after internal production

• Purchase: 1814 items are supplied by external suppliers

• Supply after production and purchase: 77 items are supplied by external suppliers as well as by

internal production the past four years (in most cases these items are purchased at the moment the

internal capacity is not sufficient)

The problem of the lead-times is that the realized lead-time often exceeds the agreed lead-time with the

supplier (production and external suppliers) and is not constant. A sample is drawn with items internally

delivered after production and items purchased at external suppliers.

First, the extend of exceeding the agreed lead-time is analyzed and the results of the analysis are

presented in table 4-3.

Average lead-time vs. agreed lead-time per item

(differences in days)

Supply source <-5 <0 0 >0 >5 total

production 29 20 2 12 15 78

purchase 10 24 2 74 136 246

Total 39 44 4 86 151 324

Table 4-3, realized lead-time vs. agreed lead-time

In the table above can be seen that especially the purchase orders are delivered later than is agreed with

the supplier. In total the average lead-time of 73% of the items is larger than agreed with the supplier.

Problems can also arise if orders are delivered earlier than agreed, which is the case of 25% of the items

of the sample. These items have an average lead-time shorter than initially determined; especially

production orders often are delivered earlier than the standard lead-time as registered in the software.

Besides deviating from the agreed lead-time also the variability of the lead-times can result in problems

with managing the inventories. For the lead-time distribution fitting, only items with at least 10 deliveries

in the past four years are included in the sample, because this guarantees in most situations the

appropriate use of the Kolmogorov-Smirnov test (Weber et al., 2006). From the sample drawn in the

previous lead-time analysis only 68 items satisfy the requirement of at least 10 deliveries. The results of

this analysis are given in table 4-4.

Probability distribution

Supply source Normal Exponential Gamma No fit Total

production 16 3 2 4 25

purchase 33 1 4 5 43

Total 49 4 6 9 68

Table 4-4, lead-time probability distributions

Most of the lead-times follow a Normal distribution (over 72%), the other distributions found are the

Exponential and Gamma distribution. For 9 items the lead-time did not follow a probability distribution.

Despite the low number of items analyzed (68), the Normal distribution seems to be the most

representative distribution for all items. For the items with less than 10 replenishments last four years, the

found distributions seem representative because we do not expect differences based on the number of

replenishments. Based on this expectation we assume a Normal distributed lead-time for all items.

18

4.2.5 Imperfect Delivered Order Analysis Quality issues and incomplete delivered orders were pointed out as possible causes for the problems with

managing the inventory. These two topics are put together under the header ‘imperfect delivered orders’.

First the influence of incomplete delivered orders is analyzed on the controllability of the inventories of

the items. No large problems arise for incomplete orders delivered by production; a new order can be start

up to fill up the previous order. Incompleteness of a purchase order often is solved by the supplier by

sending the remaining quantity right after noticing the incompleteness (with often a short lead-time).

An item has to satisfy specified requirements to be acceptable for further usage, such as selling it as spare

part, use it for the production of new compressors, or other applications. Besides the standard

characteristics as the color, length, width, and the material, also the quality of the material of the product

has to fulfill the requirements. A mismatch between required characteristics and realized characteristics

can occur at different places in the chain of supply and demand. The items with a mismatch between

requirements and realized characteristics are rejected, and cannot be used in the current form.

The items classified by the supply method, could be categorized in three groups: items with no rejections

the past four years, items for which the supplied orders contain partial rejection, and items with orders

that are completely rejected. In table 4-5 the three groups of items per supply source are presented.

Supply method no rejections partial rejections complete rejections Total

purchase 1430 25 359 1814

production 347 164 45 556

purchase and production 17 29 31 77

Total 1794 218 435 2447

Table 4-5, maximum rejection groups

The largest group of purchase items has no rejection at all and almost 20% of the purchase items have

sometimes complete order rejections, while partial rejection is uncommon for this group. For the

production items partial rejection will occur for almost 30% of the items.

Besides the categorization of the items on their type of rejection, an overview of the average rejection

percentage per item is given in table 4-6. This gives an indication for the dimension of the rejection

percentages.

average rejection percentages

Supply method <1% 1%-10% 11%-30% >30% Total

purchase 1448 225 112 29 1814

production 347 170 31 8 556

purchase and production 18 35 14 10 77

Total 1813 430 157 47 2447

Table 4-6, average rejection groups

Approximately 75% of the items did not have any rejected product the past four years. The other items

have average rejection percentages influencing the performance and the optimal parameter settings.

Therefore, we propose to use the rejection averages and the variable of the rejection groups (no rejection,

partial rejection, and complete rejection).

19

4.2.6 Order Quantity Analysis For most of the items a standard order quantity is determined, which is used if an order for this item is

placed at the supplier. However, if the Make-to-Stock Planner (see Appendix A) thinks that the order

quantity should be adapted, he is not tied at the standard order quantity. The adaptation of the order

quantity and the set standard order quantity are not based on formulas, but on the experience and

expectations of the MTS Planner. The minimum and maximum order quantity are set by the supplier, just

as the multiples (which are related to the standard package size).

GEA Grasso BV realizes that only using the experience and expectations of the purchasers are not a solid

base for optimal order quantities. However, they do not have the insight in the available formulas, how to

use the formulas, for which items and in which situations. They expect that there is a lot of improvement

possible with using formulas and guidelines for setting the order quantities.

4.2.7 ERP-Software As last possible problem cause, the ERP-software is named. The users of the software are not fully aware

of the possibilities of the software, and the interpretation of the information and mechanisms is not

unambiguous. The software offers a set of parameters, which can be used for determining the inventory

policy and its parameters. GEA Grasso BV does not know the underlying principles and relations between

the parameters, and does not know the consequences of the settings. By means of this report, the structure

of the ERP-software is made clear and the parameters and its interactions are appointed. The ERP-

software analysis is presented in chapter 6, in which the parameters and mechanisms of the inventory

control in the ERP-software are analyzed.

20

4.3 Conclusions Analyses

In the previous paragraph the possible problem causes are analyzed. The most important findings are

listed and consequences of these findings are shortly described.

• A (s,Q) inventory policy is used for all items. However, it is not optimal for all items to use this

inventory strategy.

• Service level: GEA Grasso BV measures its performance by the fraction of demand directly

delivered from stock, the P2 service level, while the formula used for setting the reorder level

includes only the P1 service level.

• Stochastic demand: For most items the demand horizon is short and insecure, so the demand of

all items is assumed to be stochastic. Inventory management is based on the parameters of the

stochastic demand distributions gathered from historical data.

• Demand distribution: for all items a Normal distribution is assumed for the calculation of the

parameters. From the demand analyses can be concluded that for a large group of items, the

Normal distribution does not fit the monthly demand.

• Lead-times: the used formulas for calculating the parameter settings assume constant lead-times,

as agreed with the supplier. From the analysis appears that the demand is normally distributed and

in most situations does not correspond to the agreed lead-time.

• Imperfect delivered order: the formulas do not include rejection of items, although for a group of

items this is an important issue. Incomplete delivered orders do not lead to problems for

managing the inventories.

• Order quantities: GEA Grasso BV does not make use of the opportunities to determine the

optimal order quantities in combination with minimum and maximum order quantities.

• ERP-software: the ERP-software is not used in all its opportunities, because GEA Grasso BV

does not know the behavior of all the parameters and mechanisms.

The inventory control parameter model has to support the user with setting the parameters. For

determining the parameter settings the above listed problems should be included.

21

5. Theoretical Inventory Control Model

In this chapter the theoretical inventory management model is described, which will be used as the basis

for the final model. The first paragraph of this chapter is an introduction of the model, which gives an

overview of the requirements of the model. From paragraph 5.2 until 5.4 the three categories of items,

identified with the ABC-classification in the previous chapter, with the optimal inventory management

strategies and parameters will be presented. Also is discussed how to set the parameters of new items,

which are added to the range of products. How to handle these new items and which strategy and

parameters to use, will be described in paragraph 5.5.

5.1 Introduction

In the previous chapter the possible causes leading to the problems with managing the inventories are

described. These problems are connected to specific characteristics of the items. In the literature study

multiple inventory management strategies are proposed based on the characteristics of the items. The first

characteristic used for determining the strategy is the criticality of the item, categorized by the ABC-

classification as is presented in paragraph 4.1. As the optimal strategy for the items is selected, the

corresponding parameters have to be determined. Standard formulas can be extracted from literature for

the characteristics of the items. If the standard formulas do not satisfy the requirements, alternatives have

to be considered, like approximations or derive suitable new formulas from the available formulas.

An overview of the assumptions of the standard formulas from literature is presented in Appendix F.

In this chapter the ERP-software restrictions and possibilities are not taken into account, the theoretical

optimal model is purely based on the characteristics of the items. The following characteristics of the

items are of primary interest for the optimal settings:

• Demand characteristics: stochastic demand, size of the demand, coefficient of variation, and

demand distribution

• Lead-time characteristics: lead-time distribution, actual lead-times differ from agreed lead-times

• Rejection quantities: items not satisfying the (quality) requirements

• Order Quantities: optimal order quantity, minimum and maximum order quantity, multiples

• Preferably the use of a P2 service level

22

5.2 A-Items

A-items are the most important items for the company; they are responsible for by far the largest part of

the usage value. First the strategy for A-class items will be discussed and next to it the parameters and

formulas will be presented.

5.2.1 Strategy In Silver et al. (1998) guidelines are presented for controlling the A-items:

a) Especially for expensive items, inventory records should be maintained on a perpetual basis

b) Keep the top management informed by reporting frequently

c) Estimate and influence demand and the supply of the items

d) Use conservative initial provisioning: especially for high values items, overstocking can be

extremely expensive

e) Review decision parameters frequently and determine precise values for the control parameters

f) Confront shortages as opposed to setting service levels: work with little on-hand stock and use

emergency orders and backorders to satisfy demand soon.

The above listed guidelines cannot be used as direct input for the model, but should be used as

considerations for the higher level management of A-items. Assumptions, which are inevitable for

translating a theoretical model into a practical useful model, can be influenced by the listed guidelines.

For A-items we advise continuous review because of the importance and large costs of the items. The

often proposed strategy for A-items is the (s,Q) model (see Appendix B for more information about this

inventory control model). For the parameter calculation, the A-items are divided in two groups: slow

movers (a lead-time demand smaller than ten units) and fast movers (a lead-time demand larger than

units).

Two parameters are directly involved by the (s,Q) inventory control model: the reorder level s and the

order quantity Q. Following guideline f (see above), the expected total relevant costs (ETRC) should be

used to determine the values for the parameter s and Q. The ETRC include the storage costs, the ordering

costs and the shortages costs. The optimal settings of the parameters calculated can be determined with

two strategies: a sequential approach, which optimizes the costs per inventory control parameter, or the

simultaneous approach, which optimizes the ETRC with both inventory control parameters.

The standard formulas for calculating the parameters, all assume a constant lead-time or a Normal

distributed lead-time demand. For the current project, the lead-times follow a Normal distribution. To

determine the distribution of the demand, two types of demand are analyzed: the monthly demand and the

customer order interarrival process. The monthly demands of the items follow a Normal distribution, a

Gamma distribution of no distribution at all, and a Poisson distribution is found for the interarrival

process for a group of items. De Kok (2005) presents formulas for non constant lead-times in

combination with a Normal distributed lead-time or a Poisson arrival process. In literature no formulas are

found for combining a Gamma distributed demand with a Normal distributed lead-time. Alternatives, like

approximations or derive new formulas from the available formulas, have to be developed.

To cover the rejection of items based on quality issues, Salameh and Jaber (2000) state that the

replenishment quantity should be increased with the expected rejections to receive the desired number of

good products. In case of complete batch rejection, other solutions than changing the parameters of the

inventory policy should be considered, like emergency capacity at machines or the possibility for placing

a rush order.

23

5.2.2 Parameters The following formulas are brought up in literature for determining the optimal parameter settings for a

(s,Q) model for A-items. First the formulas are presented, and directly after the formulas (formula 5-1

through 5-3), the variables are explained. To determine the values of the parameters s and Q, the Expected

Total relevant Costs have to be minimized. Use a spreadsheet to make a list of all the possible

combinations of the parameters values (within a range of at most the average demand of one year).

Slow moving A-items:

For B3 shortages costs (specified fractional charge per unit short per unit time):

��, � �� ∑ ��∑ �� |�� ∑ �� !"#$%�$"#& ��&��|��'(%�$#(%�

(formula 5-1)

For B2 shortages costs (specified fractional charge per unit short):

��, � �� 1� * +��*�� |�� ,��*��|��!"#$

$"#& -(%�

$#(%�

(formula 5-2)

The parameters of fast moving A-items can be found with the following formula, for B1 shortages costs

(specified fixed costs per stock-out occasion):

��, � �� .� 2 � 0 �� &12��&(& 3�&4 �� 0 12��&3�&!

(

(formula 5-3)

Variable Definition Variable Definition

ETRC Expected Total Relevant Costs ppo Poisson distribution

A Fixed ordering costs y Inventory position

D Demand 567 Estimated lead-time demand

r Carrying charge X Net stock position

v Unit variable costs fx Function of the net stock position Table 5-1, variable definitions A-items

The found order quantity Q has to be increased by the expected number of rejected products for the

ordered production items. For purchase items agreements with the supplier should be made to place rush

orders if purchase orders are completely rejected.

24

5.3 B-Items

B-items are not characterized as the most important items, but deserve more attention for managing the

inventories than the C-items. For A-items is holding too much inventory extremely expensive while C-

items are often ample stored, because shortages are often more expensive than holding a surplus on stock.

For B-items a compromise of these two extremes has to be found.

5.3.1 Strategy The most widely used and most extensive described inventory policy is the (s,Q) model and this is also

advised for the B-items with continuous review (Silver et al., 1998). Very important is to define the

desired cost or service objects, like the service level or the shortage costs. For A-items literature strongly

advises to use cost objectives instead of service objectives, while for B-items no special recommendations

of the objectives are given. The objective set by GEA Grasso BV is the P2 service level, so this is also

used for the strategy and formulas for setting the parameters of the B-items.

The parameters of the (s,Q) strategy are often determined with the sequence approach. First the optimal

order quantity is calculated, based on the ordering costs and the carrying costs. For the calculation of the

reorder point the type and height of the service level are used, dependent on the defined objective.

Another important issue for stochastic demand inventory control is the undershoot. De Kok (2005)

provides in his paper formulas for the undershoot. Strijbosch et al. (1998) argues to use a Gamma

distribution for the demand per customer, which is confirmed by De Kok (2005).

Also for B-items, complete order rejection and partial rejection of orders have to be taken into account

because of its influence on the inventory control performance. The optimal order quantity is the number

of products satisfying the requirements and can be used for production or sold as spare part. The actual

quantity ordered at the supplier is the optimal order quantity plus the expected number of rejected

products of the order.

5.3.2 Parameters To calculate the parameters various formulas are found, and the most relevant are presented. The variable

definitions can be found below the last formula, at the bottom of the next page.

The following formulas for calculating the parameters of the (s,Q) inventory control model based on a P2

service level, are presented by Silver et al. (1998):

First for the calculation of the order quantity the Economic Order Quantity (EOQ) formula is advised for

stationary demand. The EOQ-formula takes the ordering costs, the carrying costs, and the expected

demand into account (see formula 5-4). Initially the EOQ formula is proposed for constant and

deterministic demand, but is also appropriate for stationary stochastic demand.

�8� 9,:;<= (formula 5-4)

With the optimal order quantity, the desired service level and the standard deviation of the lead-time

demand, the safety factor k can be calculated (formula 5-5) and used for determining the reorder level s

(formula 5-6).

25

>?�@ �AB �1 � C, (formula 5-5)

� �� @D� (formula 5-6)

De Kok (2005) provides formulas to calculate if the found parameters will lead to the desired service

level. These formulas can also be used to determine the parameters s and Q. The provided formula is

suitable for every lead-time demand distribution and includes the variable undershoot:

C, 1 � �� E��FG�, G� � H�I � �F%I � J� � �E��F0, H&I � J& � �� F%I (formula 5-7)

Variable Definition

A Fixed ordering cost

D Demand (Normal distribution)

Gu(k) =L pNO�k!Q

K Safety factor

L Lead-time (constant lead-times) RSO�T A probability function of the unit normal variable

Q Reorder quantity

r Carrying charge

σL Standard deviation of the lead-time demand

s Reorder level

τ The replenishment moment

U Undershoot (difference between the reorder level s and the actual stock position at the

moment of ordering)

v Unit variable costs of the item UVL Expected lead-time demand

Table 5-2, variable definitions B-items

26

5.4 C-Items

The C-items represents a large percentage of the total range of items, but a very small fraction of the total

usage value of the company. For the C-items relatively easy inventory control models are proposed,

because sizable absolute savings in the carrying and shortage costs cannot be achieved for C-items. It is

important to keep the control costs per item quite low.

5.4.1 Strategies First has to be determined if a C-item should be stocked or just be ordered when required by the customer.

For items with a very low demand it can be favorable not to stock the items, especially in case of short

lead-times.

If the items should be directly available, two basic strategies are proposed which both will be presented in

some detail:

• (R,S) strategy: inventory of the item will be replenished to the S level every time period R.

• (s,Q) strategy: if the inventory drops at or below the level s, a replenishment order of size Q is placed.

The (R,S) strategy is useful for combining orders for multiple items: setting the period R of various items

equally or as multiple, the items can be replenished at the same time. This is especially interesting if these

items are delivered by one supplier to reduce the transportation costs, and structures the planning of

ordering and receiving C-items. Also the lead-times can be (sometimes extremely) reduced, because the

supplier knows when to deliver. The only variability is the replenishment quantity.

Furthermore the order up-to-level is suitable for items with very fluctuating demand; many periods with

no demand, and once in a while a relative large order. With the (R,S) strategy the inventory level is

brought back to the intended starting level, independent of the inventory level at the moment of ordering.

This contrasts with a (s,Q) policy which increases the stock level with a fixed quantity independent of the

inventory level.

The (s,Q) strategy for C-items is often used in the form of a Two-Bin system. If one bin is empty it will

be replenished by the supplier (bin size is replenishment quantity Q) and the other bin is used for the

demand during the replenishment (bin size is the reorder quantity s). The Two-Bin strategy is especially

useful for items with a high demand (fast-movers).

5.4.2 Parameters The parameters of the (R,S) and the (s,Q) policy can be calculated with the same underlying idea, but will

be separately presented. Both strategies are based on the performance criterion Time Between Stock-outs

(TBS, see Appendix B for more information of the service levels).

Slow movers: (R,S) Inventory policy For the (R,S) strategy two parameter have to be determined, which are based on the desired number of

replenishments per time period and the safety of having enough on stock for this period. To determine the

replenishment frequency, first the optimal review period has to be calculated with formula 5-8, which is

derived from the EOQ-formula (formula 5-4).

27

�WX� 9 ,:;<= (formula 5-8)

Based on the optimal review period, the actual review period can be determined. Generally, common time

periods are used like monthly, quarterly, half yearly, or yearly review periods. With the review period the

order up-to-level S can be calculated with the following formulas:

�?O�@ ;/Z;�[\] (formula 5-9)

^ ��Z � @DZ (formula 5-10)

First the safety factor k, is calculated with formula 5-9, based on the demand during the desired Time

Between Stock-outs (TBS) and the average order quantity (D/R). With the safety factor the S level is

calculated based on the demand during the review period and the standard deviation during this period (if

the lead-time is just marginal compared to the review period it is not necessary to include the lead-time in

the variability of the demand during the period).

Fast movers: (s,Q) Inventory policy The parameters for the (s,Q) strategy can be determined based on a comparable concept. First the optimal

order quantity has to be calculated with the EOQ-formula (formula 5-4). If the EOQ quantity does satisfy

the minimum and maximum order quantity and multiple set by the supplier, this quantity should be used.

Otherwise the nearest quantity satisfying the restrictions set by the supplier should be used.

With the order quantity the first the safety factor k can be calculated (formula 5-11) and with this safety

factor the reorder level s (formula 5-12).

�?O�@ �;�[\] (formula 5-11)

� �� @D� (formula 5-12)

Variable Definition Variable Definition

A Fixed ordering cost R Review interval

D Demand (Normal distribution) s Reorder level

Gu(k) =L pNO�k!Q S Oder up-to-level

K Safety factor TBS Time between Stock-outs

L Lead-time (constant lead-times) σi Standard deviation of the demand during i RSO�T A probability function of the unit

normal variable

v Unit variable costs of the item

Q Reorder quantity 56i Expected demand during i

r Carrying charge

Table 5-3, variable definitions C-items

28

5.5 New Items

Besides determining the parameters of items already in the database, the model should also be able to

determine the parameters of new items. First the types of new items are described and next to it the input,

strategies and parameters are discussed.

5.5.1 Types of New Items The new items can be split in two main streams:

• Items replacing items which are not longer in use, because of new requirements, a new supplier

for the item, or the supplier stops offering the item and an alternative is chosen.

• Completely new items: if a new technique for a compressor is used, a completely new item is

necessary for the production process. However, this item can often be compared with a quite

similar item with a different application. In some situations the item is not comparable to any

item; a completely new item is introduced.

So three types of new items can be discerned: replacing items, new comparable items, and new unique

items. For these three groups guidelines for the parameters are determined.

5.5.2 Data for New Items For all three groups of new items applies: which information can be used for determining the inventory

control strategy and parameter settings. The optimal strategy for the new item depends on the criticality of

the item and the demand characteristics. First an estimation of the demand should be made, based on the

historical demand of a comparable item (for replacing items and comparable items), or just on sales

expectancies (new unique items). In combination with the (expected) value of the item, the criticality can

be determined with the ABC-classification. The strategy corresponding to the ABC-classification and the

size of the demand can be found in paragraphs 5.2 through 5.4. The parameters for the strategies can be

set with the formulas for the corresponding strategy. The most difficult part is to determine the values for

the variables in the formulas. Information about the lead-time, the demand, and rejection percentages

should be gathered. Dependent on the type of new item, the information can be collected of the

replaced/comparable item, and the available data about the supplier.

The demand for the item is already estimated for determining the strategy and ABC-classification. Based

on this information the accompanying distribution and its characteristics can be assigned. The lead-time

for all the items is assumed to follow a Normal distribution, so also for the new items. The parameters can

be estimated based on information of the replacing/comparable item and information about the lead-times

of the supplier. The same method can be applied for the rejection percentages for the items. In case of no

replacing/comparable items and/or no information about the supplier, the characteristics have to be

determined by the extremes or averages of groups of items.

For A-items overstocking is extremely expensive, so the characteristics should be set for optimistic lead-

times and rejection percentages (agreed lead-time is the average lead-time with a small standard deviation

and no rejection is expected).

For the C-items no shortages are desired because shortages are often far more expensive than

overstocking so a pessimistic estimate for the lead-times and rejection quantity should be used as input.

For the B-items the average lead-time exceeding and the average rejection percentages should be used.

29

6. Bridging the Gap between Theory and Practical Development

In this chapter the theoretical model as described in the previous chapter is converted to a practical

useable model. For A-items and B-items a (s,Q) strategy is proposed, but the parameter settings have to

be determined with different performance objectives. For A-items the Expected Total Relevant Costs are

advised, while for B-items the P2 service level can be used. For C-items is a distinction made between fast

movers, for which a Two-Bin strategy is very useful, and slow movers, for which (R,S) policy is advised.

The model should also be able to set parameters of new items, which are split in three groups based on the

already available information for the parameters: replacing items, comparable items, and completely new

items. For the completely new items, the user has to give a lot of input, while for replacing and

comparable items information can be collected from the a database. In this chapter the translation has to

be made of these theoretical guidelines and formulas into a practical useable model. A gap is expected

between theory and practice, caused by the available information (data), formulas, and parameters.

It is important to formulate accurately the considerations and assumptions during the development of the

practical model, to know the limitations of the results and the consequences for the use of the model.

In the first paragraph the ERP-software is analyzed, because the model should be able to support the user

with setting the parameters of the software. In paragraph 6.2 the structure of the model is presented,

including the conditions the model should satisfy. In the paragraphs 6.3 through 6.6, the theoretical

models as described in the previous chapter, are made applicable for the practical use. The practical use

depends on the parameters of the ERP-software and the restrictions of the data and requirements. The

translation from a theoretical inventory model to a practical model will be presented per category items,

based on the ABC-classification, and for new items. In paragraph 6.7 the use of the model and the

refreshment of data and other maintenance to the model will be described. The last paragraph is the

conclusion of the development of the practical model. This chapter contains an overview of the most

important restrictions, adaptations and consequences of the development from a theoretical to a practical

model.

30

6.1 ERP-Software Analysis

The ERP-software, Microsoft Dynamics AX, is used for all the processes through the company, so also

for the inventory management part. In this paragraph the most important parameters and mechanisms are

described, more extensive information can be found in Appendix G.

The software offers two ‘ordering strategies’ supporting the user with managing the inventories. Both

strategies make use of a minimum stock level to determine when to place a replenishment order:

• Period: if the minimum stock is reached, the demand during the set period after reaching the

minimum stock, is at least covered with the replenishment order.

• Min/Max: if the minimum stock is reached, an order is placed to bring the stock level back to the

maximum level.

The minimum stock level can be calculated by the software with a standard formula which includes the

demand, lead-time, and the desired service level (see formula 6-1).

_�`�_a_ �cde@ ��f�ghi j W�� @ j D��f�ghi j 9W�� (formula 6-1)

Variable Definition

E Expectation

D Demand

L Lead-time

k Safety factor

σ Standard deviation

Table 6-1, variable definitions ERP-software

This formula assumes that the monthly demand follows a Normal distribution, and uses the average and

standard deviation of the monthly demand. Furthermore is assumed that the lead-time is constant, and that

a P1 service level is desired for setting the minimum stock level.

If the ordering strategy Min/Max is chosen also a maximum stock can be set, which have to be done

manually.

A replenishment order is proposed if the software notices that the stock level will reach/reaches the

minimum stock level. The proposed ordering data for the replenishment order is set to receive the order at

the moment the stock level will reach the minimum stock. However, this is only possible if the demand

during the lead-time is completely known.

With the option ‘reach minimum’ can be regulated what should be done if the stock level drops below the

minimum. Two options are available:

• ‘Date today + lead-time’: as long as the stock level does not become negative, the replenishment

order does not have to come earlier

• ‘Date today’: if the stock level drops below the minimum stock, everything should be done to get

the replenishment order earlier to prevent the stock level drops further

For setting the order quantities a standard order quantity, a maximum order quantity, a minimum order

quantity, and a multiple can be filled in. These options can be used as restrictions set by the supplier, but

also to support the user for ordering optimal quantities.

31

6.2 Structure of the Model

The intention of the development of the inventory control parameter model is to approximate the optimal

situation as outlined in the previous chapter. However, the model has to be harmonized with the ERP-

software and the formulas have to be feasible for the items under control. First, the program used to

develop the model is determined and next the structure of the model is outlined. In the next paragraphs

the strategies and parameters implemented in the model are described in detail.

First is analyzed if it possible to develop the inventory control parameter model in/with the ERP-software.

The direct options in the ERP-software appeared to be very limited (changes in the structure of the

software are needed to make analyzes possible, which is not feasible for this project), so an alternative has

to be found. Microsoft Excel is chosen because this program is widely used and available, the structure

and formulas are well known (by the developer and the users), and has a clear interface. The acquaintance

of the users with Excel can turn out be a very important advantage: if adaptations are necessary in the

course of time, they are not restricted by the structure of the program and the structure of the formulas.

The disadvantage is the limited availability of standard formulas and the size of the files if multiple

formulas and tables are included.

The model will be developed to support the Logistics department and in special the make-to-stock

planners for setting the parameters of the MTS items. They are not interested to see which transitional

stages are between the input and the outcome. The input of the user for the model has to be minimized

and the input data should be easily implementable. The output, the parameter values, has to be presented

in the same format as the list of parameters in the software, to prevent making mistakes. The results from

the model have to be copied by hand as long the model is not integrated in the ERP-software.

From the analyses presented in chapter 4 and the theoretical model in chapter 5, is known which

characteristics of the items are necessary for the calculations and the parameter settings. Based on the

ABC-classification and the average demand a strategy is assigned to the item. Based on this strategy the

accompanying parameters are calculated with the information about the demand, lead-time, the rejection,

and the desired service level for the item.

This list of information necessary for the parameter settings means that this information should be

gathered from a database and the appropriate assumptions and distributions have to be assigned. With this

data for each characteristic of the item, the formulas for the parameter settings can be filled. The results of

the formulas will present the parameter settings for the analyzed item(s).

Besides analyzing the items, which are already in the database, the model also has to be able to set

parameters of new items. Therefore also an interface has to be created for the user to give information

about this new item. Furthermore, GEA Grasso BV also wants be able to change the service level. In the

assignment a P2 service level of 98% for all items is desired, however if the desired service level will be

increased/decreased in the near future, the user has to be able to easily change this.

The model has to be able to determine the parameters based on the historical data. However, the model

should also be able to include parameters for a forecasting strategy. A forecasting is recommended for A-

items, the ERP-software mechanisms are based on deterministic demand, which can be simulated with a

forecasting demand, and GEA Grasso BV considers the use of forecasting in the near future. The settings

of the parameters for a forecasting model are based on the accuracy of the forecasting instead of the

characteristics of the stochastic distributions of the demand and the lead-time. However, the model can be

used as a starting point when the forecasting strategy will be implemented.

32

6.3 A-items

For the most important items of the company a (s,Q) strategy is proposed, for which the parameters

should be determined precisely and frequently. It is important to use conservative provisioning because

overstocking can be very expensive. The parameters should be determined based on cost objectives

instead of service levels, because of the very expensive stocking costs of these items (using emergency

orders and backorders are often less costly). However, GEA Grasso BV does not have any information

about backordering costs and the consequences of not having the item on stock. Therefore, the P2 service

level will be used for determining the optimal parameter settings. Another guideline for managing the A-

items is to influence and estimate the demand and supply of items (for example a demand forecast).

Item characteristics and parameters For determining optimal parameter values for A-items, the theoretical model provides a formula which

makes use of cost performance objectives and a simultaneous approach. However, the cost objectives are

not specified by GEA Grasso BV and not in the scope of the project to collect the data for these cost

objectives. Therefore, the formula of De Kok (2005) is used for determining the s level and the EOQ

formula for the optimal Q for the items, as is proposed for B-items.

C, 1 � �� E��FG�, G� � H�I � �F%I � J� � �E��F0, H&I � J& � �� F%I (formula 6-2)

The following characteristics of the items are determined which are necessary for calculating the values

of the parameters:

• Demand: the demand source(s), per demand source the average and standard deviation of the

demand per month and the coefficient of variation (CV), the average customer order quantity and

the standard deviation of the customer order quantity

• Lead-time: the supply source, average lead-time and the standard deviation

• Rejection percentage: supply source, the average rejection percentage and the maximum rejection

percentage

• Value of the item, the minimum, maximum and standard order quantity and the multiples of the

item (as registered in the database)

Based on the demand characteristics, average demand per month and the CV, a demand distribution is

assigned based on the results of the demand analysis (paragraph 4.2.3). The following distributions are

assigned to the demand characteristics:

Distribution Demand characteristics

Normal distribution monthly demand Average monthly demand >5, and CV≤1

Poisson customer order arrival process Average monthly demand ≤5, or CV>1

Table 6-2, A-items demand distributions

The Gamma distribution is not taken into account for A-items because only a very small number of A-

items have a demand following a Gamma distribution (see Appendix E) and a conservative demand

distribution is advised to prevent overstocking. A Poisson interarrival process of the demand leads to a

slightly more conservative lead-time demand than a Gamma distribution for the monthly demand.

For the lead-time a Normal distribution is assumed: the average and standard deviation for the analyzed

item is determined with the lead-time data from the database.

The average rejection percentage and the maximum rejection percentage are calculated for the item.

33

First the optimal order quantity has to be determined with the EOQ-formula. The EOQ formula is based

on the ordering and storage costs for the items. At this moment GEA Grasso BV does not have the

information about the ordering and storage costs available. However, the EOQ-formula is implemented in

model, because rules of thumb and estimations of the costs can already be very useful. A rule of thumb is

to use the percentage of 25% per year of the value of the item as storage costs (Beerens, 2006).

Estimations and rules of thumb can be used as a first step for determining the optimal order quantity,

because the EOQ-formula is quite robust. A miscalculation of a variable or a deviation of the variable of

20% results in a deviation of the order quantity of approximately 10% and 1% increase in costs

(Durlinger, 1998). More detailed information about the robustness can be found in Appendix I.

For the values of the variables of formula 6-2, the parameters and distribution for the lead-time demand

have to be determined. The lead-time and the demand are analyzed independently of each other, and no

distribution is tried to fit on the lead-time demand, because more demand data is available if the analyses

are performed separately. For the lead-time demand for A-items we assume a Normal distribution, based

on the parameters of the demand and the lead-time. In Appendix H are the formulas presented for

combining a Normal distributed lead-time with a Normal distributed demand or a Poisson distributed

arrival process.

A Normal distributed lead-time demand is assumed because the lead-time already following a Normal

distribution, just as the demand for a large group of A-items. For the group of items with a Poisson arrival

process, a Normal distribution approximates the Poisson distributed arrival process in case of at least five

arrivals (Silver et al., 1998).

The undershoot (the formulas to calculate the parameters of the undershoot are presented in Appendix H)

is added to the lead-time demand, and for the combined variable the distribution of the lead-time demand

is taken.

Now all the variables of the formula are determined to calculate the reorder level s:

• P2 service level of 98% (which can be manually adapted before making the calculations)

• Q: the order quantity, calculated with the EOQ formula or the standard order quantity is taken,

and if necessary is the rejection percentage used to compensate for the items not meeting the

quality requirements

• The lead-time demand plus the undershoot with its distribution and parameters

ERP-software parameters The parameters of the (s,Q) model are determined, and these need to be translated to the ERP-software

parameters. For the A-items it is advised to estimate the future demand, for example with a forecast. This

is also in line with the ERP-software parameter ‘reach minimum’ which also expects to know the demand

during the lead-time. However, we assumed that the demand is non-deterministic and GEA Grasso BV

currently does not make use of a forecasting strategy. Therefore the option Date today+lead-time is

useful, which only warns the user if the stock level runs the risk of becoming negative. In case of

choosing the option Date today, the user will be warned continually during the lead-time, because the

minimum stock level is already reached.

Assuming non-deterministic demand has also consequences for the setting of the minimum stock level: the

minimum stock level can be set equal to the formulated reorder level s.

The (s,Q) strategy can best be approximated with the ordering strategy Period. Originally, the strategy

determines the minimum order quantity by the demand during the set period. However, the demand in the

set period is not known and the standard order quantity can be used as the replenishment size. The

alternative option was to use the Min/Max strategy, but this strategy increases the inventory level not with

34

the optimal order quantity but with a variable quantity to bring the inventory level back to the maximum

level.

The standard order quantity is set equal to the calculated value for Q determined with the EOQ formula,

which is based on stable demand. Besides the setting of the standard order quantity, also the minimum and

maximum order quantity have to be set. The purchaser can use the minimum or maximum order quantity

to quickly react on the fluctuation of the expected demand. From the analyses to the optimal settings for

the minimum and maximum order quantity (see Appendix J for the results) is concluded:

�f"g �8�/√2 (formula 6-3)

�fl2 �8� j √2 (formula 6-4)

However, if the minimum and/or maximum order quantity are more closely restricted by the supplier, the

suppliers restrictions have to be used just as the option multiple. If the expected demand decreases or

increases over a longer period, a new optimal order quantity has to be determined

Conclusions A-items Better settings for the A-items can be determined, if the shortage costs are used as the performance

objective instead of using a P2 service level. Besides, determining the shortage costs also the storage and

ordering costs have to be determined, for a more precise calculation of the optimal order quantity. We

also propose the use of a forecast for the demand for A-items: forecasting the demand makes it possible to

manage the inventory more effective and there is also a better match with the ERP-software parameters

settings. The parameters (excluding the minimum stock formula in the software) all assume deterministic

demand; with a forecast the demand is not made deterministic but can be assumed deterministic and

safety stock or safety times can be used to cover the forecast errors. With the current strategy based on

stochastic demand and the developed model, many assumptions are made for the lead-time demand and

the optimal strategy could not be used because of the limitation of the performance objective and the

limited availability of the ordering, storage and shortages costs.

35

6.4 B-items For B-items also a (s,Q) inventory control model is proposed and, in contrast with the formulas for the A-

items, formulas to use a P2 service level are provided in literature. These formulas are already used for the

control of the A-items, because the P2 service level is set as performance indicator and at the moment no

information about the shortage costs is available. Therefore, the parameter settings for the B-items are

quite similar to the settings of the A-items.

Item characteristics and parameters For the B-items the following demand distributions are used for the demand characteristics:

Demand

characteristics

Average monthly

demand

Coefficient

of Variation Demand Distribution

Lead time

demand distributions

>5 ≤1 Normal distribution monthly demand Normal distribution

≤5 ≤1 Poisson customer order arrival process Normal distribution

>5 >1 Poisson customer order arrival process Normal distribution

≤5 >1 Gamma distribution monthly demand Gamma distribution

Table 6-3, B-items demand distributions and lead-time distribution

For B-items the Gamma demand distribution is included, because the costs for overstocking B-items are

not as expensive as for A-items. For the lead-time a Normal distribution is assumed for all items, with the

average and standard deviation as parameters.

For A-items a Normal distributed lead-time demand is assumed. For B-items two probability functions

are provided for the lead-time demand:

For the items with a Normal distributed demand, a Normal distribution is assumed for the lead-time

demand. Combining the Normal distributed demand with the Normal distribution of the lead-time, a new

Normal distribution is found for the lead-time demand.

For the items for which a Poisson arrival process was fit to the demand also a Normal distributed lead-

time demand is assumed. In case of at least five orders, a Normal distribution is a good approximation of

the Poisson arrival process (Silver et al., 1998). For the group with less than five orders per month also a

Normal distribution for the lead-time demand is assumed, because this group contains a lot of items with

a relatively high value and a low demand (see table 4-1 ABC-classification, 57 B-items are classified as a

A-items based on only the value). For these items overestimating the lead-time demand can lead to high

overstocking costs. With a Normal distribution for the lead-time demand a more conservative reorder

level is calculated.

The last group of items contains the items with a demand following a Gamma distribution. In the

scientific literature no standard formulas are presented for combining a Normal distributed lead-time with

a Gamma distributed demand. Several possibilities for combing these distributions are analyzed, and a

simulation is done to find a quite simple method for determining parameters. A Gamma distribution is

assumed for the lead-time demand and the parameters are determined by first calculating the average and

standard deviation of the lead-time demand (see Appendix H: formulas H-1 and H-2), and then transform

them to the corresponding standard Gamma parameters (see Appendix H: formulas H-9 and H-10). This

approach is chosen because it requires just a few formulas and resulting in parameters which overestimate

36

the lead-time demand just slightly. Other methods include large data sets and dozens of formulas which

require a lot of computation power which affects the performance of the model.

An overview of the formulas for calculating the parameters for the lead-time demand are listed in

appendix H. The calculation of the order quantity is similar to the A-items, with the EOQ formula the

optimal order quantity is calculated. The optimal order quantity is increased by the expected rejections in

case of production orders and the optimal order quantity is ordered for the purchase items.

ERP-software parameters The settings of the ERP-software for the B-items are comparable with the A-item settings: the ordering

strategy Period should be used, and the minimum stock level is set equal to the calculated s level. For the

standard order quantity the calculated optimal order quantity (including the expected number of rejected

products) can be used and for the minimum and maximum order quantity respectively formula 6-3 and

formula 6-4 are proposed. For the parameters ‘reach minimum’ the option Date today+lead-time is

advised because also for B-items the demand is not deterministic or forecasted.

Conclusions B-items Just as for the A-items, also for the B-items a forecast is desired to set the ERP-software parameters

optimal. The formulas for the calculation of the optimal order quantity include cost factors which are not

determined at the moment. If the ordering and storage costs for the (groups of) items are gathered, it is

possible to determine the optimal order quantity more accurate.

37

6.5 C-items

Two types of C-items can be distinguished: low valued items with a large demand, and items with small

demand. For items with high demand, the fast movers, a (s,Q) policy is proposed, while for the slow

movers a (R,S) policy is advised. In literature no standards are set for making a classification for C-items

as slow or as fast mover, but an often used cutoff value is an average lead time demand of ten units. An

analysis to the average lead-times shows a very large group (74%) of C-items with an average lead-time

between 3 and 6 weeks. Therefore, we classify items with an average monthly demand of at least ten units

a fast mover, and less than ten units a slow mover.

Fast movers The (s,Q) model for fast moving C-items can be implemented as a Two-Bin strategy: if one bin is empty

it will be replenished, and in the meantime the other bin is used for the lead-time demand. The sizes of the

bins can be based on two different principles:

• Equal bin sizes: both bins can be used as reorder level and as replenishment quantity, so the

reorder level is equal to the replenishment quantity.

• Dissimilar bin sizes/multiple refill bins: one bin is used as the reorder level while the other(s)

is/are of the size of the replenishment quantity.

The advantage of the first method is the simplicity of the strategy and practical use, while the

disadvantage is the less optimal settings.

For the items first the optimal order quantity is determined based on the EOQ-formula:

�8� 9,:;<= (formula 6-5)

A Normal distribution is found for the demand of items with a CV≤1, and a Poisson distribution for items

with a CV>1 (which can be approximated with a Normal distribution is the number of customer arrivals is

larger than five (Silver et al., 1998)). For the combination of a Normal distributed demand and a Normal

distributed lead-time, a Normal distributed lead-time demand is assumed. The formulas for calculating the

values of the parameters can be found in Appendix H.

The standard used performance objective of C-items is the ‘Time Between Stock-outs’ (TBS), which is

not defined by the Logistics department as the performance objective. The importance of the items is

underlined by the Logistics department: If these items are not directly available it will cause a delay for

almost all compressors in production, because of their wide use in the company. A very high availability

of this item is assured with setting the safety factor k=3 (which corresponds to a TBS of 92 years if the

item is replenished 8 times per year, and a P1 service level of 99.86% for items with a Normal distributed

lead-time demand).

For the reorder level the standard formula is used: � �� @D� (formula 6-6)

If the calculated EOQ is larger than the reorder level s, the optimal bin size is equal to the reorder quantity

Q. If the optimal order quantity is smaller than the reorder level, the reorder level is used as bin size. If the

optimal order quantity is very large compared to the reorder level and the bins are physically very large,

also can be chosen to use two different sizes of bins or multiple bins. This inventory control strategy does

not have to be supported with ERP-software settings, but physically handled between the supplier and the

receiver of the item.

38

Slow movers For the slow movers a (R,S) strategy is proposed. A time period has to be set and after each period the

stock level is reviewed and replenished to the order up-to-level S. The time periods should be regulated to

the groups of items per supplier, which can decrease the transportation costs. The review period R can be

determined based on the optimal order quantity and the expected demand. This is presented in formula 6-

7:

�WX� 9 ,:;<= (formula 6-7)

The actual review period should be determined in combination with other items of the same supplier.

With the R, now the other parameter, the order up-to-level S, can be calculated. This level should be able

to fulfill the demand during the review period. The formula for the S level is based on the average

demand during the review period plus a safety stock.

^ ��Z � @DZ (formula 6-8)

Most of the slow-moving C-items have a Gamma distributed demand, and a Normal distributed lead-time.

First the average and standard deviation of the lead-time demand is determined with the following

formulas:

�m��0, HIn �E�I j �EHI (formula 6-9)

D,o��0, HIn �EHI j D,�� D,EHI j �,E�I (formula 6-10)

A distinction is made between items with a high value (A-items based on value) and low valued items (B-

items and C-items based on value). For the low valued items a Gamma distribution is assumed for the

lead-time demand, and a Normal distribution for the high valued items. A Normal distribution will results

in a lower reorder level which is desired for high valued items because of the high stocking costs. For the

low valued items a Gamma distribution is used, because the stocking costs are low and shortage costs are

often higher. The used k value depends on the lead-time distribution, the TBS, and the expected number

of replenishments during the TBS.

In contrast with the fast movers, the slow moving C-items have to be managed with the ERP-software.

However, the exact (R,S) policy is not implementable, because no parameters are available for setting a

review period, so with other settings this policy has to be approximated. The S level is comparable with

the maximum stock level, which can be used if the Min/Max ordering strategy is applied. However, this

strategy implies the use of a minimum stock level. This minimum stock level is determined with formula

6-9:

� �� @D� (formula 6-11)

Because the review is continuous and not periodically in the ERP-software, formula 6-8 has to be

replaced by the following formula:

^ � � ��Z (formula 6-12)

This is the best approximation of the (R,S) strategy with the available parameters: the demand during the

determined review period brings the stock-level to the minimum stock level. A replenishment order brings

the stock back to the maximum stock level.

39

6.6 New Items Three different types of new items can be classified: replacing items, comparable items, and completely

new items. Assigning a strategy and the corresponding parameters are based on the same principles as for

the items already in the database, as described in the previous paragraphs.

Replacing items Replacing items take over the position of the replaced items. For these items no changes in demand

patterns are expected so the historical demand data of the replaced item can be used. Also the lead-time

and rejection information of the replaced item is used, if the item is delivered by the same supplier.

Otherwise, an average of this information and information of the new supplier is taken for setting these

parameters. Depending on the value of the new item, the same optimal order quantity and minimum and

maximum order quantity are set. So the only user input required for the model is the replaced item

number (and its value) and the supplier of the new item.

Comparable items For comparable items also the new item number, the value of the item and the supplier are necessary user

input. With this information the expected lead-time and rejection quantities are calculated. Also the

demand prognosis is asked for the new item, because this can vary from the comparable item. With this

information first the criticality will be determined. Next to it, a strategy can be assigned based on the

criticality and the demand prognosis, and the parameters can be calculated.

Completely new items For the completely new items it is very difficult to set parameters, because just little information is

known. The user is asked to give input for the demand, the agreed lead-time, the supplier and the value of

the item. With the demand prognosis and the value of the item, the criticality can be determined with an

ABC-classification. With the criticality and demand prognosis an appropriate inventory control strategy

can be assigned to the item. For the other characteristics averages of items in the same categories (based

on the ABC-classification and average demand) are used and the corresponding probability distributions.

40

6.7 Use and Maintenance of the Model

The model is developed to analyze each item individually. The used formulas are based on assumptions

which are described in the previous paragraphs and historical data available from a database. The results

of the model are therefore dependent on the made assumptions and data for the analyzed characteristics of

the items. To be sure that the assumptions and conclusions are not getting out dated, the analyses to the

characteristics have to be repeated every four years (when completely new data is available). Another

important issue is the consistent use of the ERP-software and giving adequate input to the software: the

results of the inventory control parameter model depend on the data from the database, registered via the

ERP-software. Input mistakes can be made, which can have a large influence on the results of the

inventory control model. If remarkable changes are found in the results compared to the previous results,

the individual characteristics should be checked in the model. If the mistake is caused by unlikely results

in the database, it has to be changed in the database. It is also possible that the mistake is caused by the

structure, assumptions, or formulas in the model. A manual is written for the model, which includes

information about how to use and structure of the model and also a description (of the structure) of the

formulas.

Besides repeating the analyses of the characteristics for checking the classification and assumptions, also

the database of the model has to be refreshed. The database of the model is not permanent linked to the

database of the ERP-software. The refreshment period of the model database should go hand in hand with

the desired refreshment of the parameters in the ERP-software. A refreshment period shorter than six

months is not advised, because the influence of this new data on a four year data set is very limited. For

A-items is advised to refresh the parameters every year, because small parameter changes can have large

influence on the inventory control costs. While for C-items the absolute savings are very low and the

controlling costs should counterbalance the absolute savings. A refreshment of these parameters of more

than once every two year is not advised, except if changes of the characteristics are observed or expected.

For B-items a middle course should be taken. For example the parameters of the A-items can be refreshed

every year while for B-items and C-items just by turns.

41

6.8 Conclusions

In this paragraph conclusions are drawn based on the findings of translating the theoretical model into a

practical useable model. This includes the limitations of the used assumptions and formulas, requirements

set by GEA Grasso BV, and the restrictions of the ERP-software.

The results from the analyses of the characteristics of the items are used for assigning distributions,

strategies and formulas to the items. Generalizations are necessary because not every individual item can

be analyzed for all its characteristics. Most of the assumptions are based on generalization, and some are

based on qualitative arguments. For A-items conservative estimates and assumptions for the demand are

made, to prevent overstocking, while for C-items shortages are not desirable so more positive lead-time

demands are assumed. This will have its effect on the service levels of the items: the service level of the

A-items will be slightly lower than expected and for the C-items a higher service level is expected..

Values for the cost parameters for the EOQ formula are not available so the optimal order quantity cannot

be calculated. However, this option is built in so GEA Grasso BV can make use of it when this

information is available.

For A-items it was not possible to transform the optimal theoretical inventory control strategy to ERP-

software input parameters: the performance settings by GEA Grasso BV did not correspond to the

proposed performance indicator. The strategy of the slow moving C-items could not be implemented

because the ERP software did not have the parameters for periodic review. The proposed strategy is tried

to approach with available parameters but the specific advantage of periodic reviewing (combining

orders) could not be assured. For fast moving C-items and for B-items no large strategy implementing

problems were discovered.

The parameters offered by the ERP-software all assume deterministic demand (except the minimum stock

level), and can therefore not optimally used in case of (partial) stochastic demand.

The demand for items at GEA Grasso BV is non-deterministic, because the demand horizon is short and

unstable. In the software a forecasting model can be implemented, to consider the forecasted demand as

deterministic, for optimal use of the parameters. The developed model provides the starting parameter

settings for a forecasting strategy. Generally, forecast errors have to be covered by safety stocks or safety

time. At the start of the forecasting no forecast errors are known, so the parameter settings can be set

based on the historical data. When the forecast error information is collected, these data should be used

for the safety stock and/or safety time settings.

With the current settings a higher than necessary reorder level is set, because we assumed no future

demand is known while in practice a (small) part of the future demand is known several weeks in

advance. A replenishment order is earlier placed and received than necessary, which will have its

consequence for the service level and average stock level.

42

7. Results

The decision support model is developed to support GEA Grasso BV with managing their inventory. To

get an indication of the performance of the model, the new parameter settings are used for the calculation

of the expected service level and the average stock levels of the items. In the first paragraph the types of

outcomes are discussed and the restrictions of (comparing) the outcomes that have to be kept in mind. In

paragraph 7.2, the results of the A-items after using the model are compared to the results with the

current. The same is done for the B-items in paragraph 7.3 and C-items in paragraph 7.4. In paragraph

7.5, conclusions are drawn based on the results and the (impact of the) limitations of the results are

discussed.

7.1 Measuring the Results

The results before using the model are displayed in chapter 3, in which the problem description is made.

From the problem analysis is concluded that the service level was for a large group too low: the desired

service level was not achieved. However, there was also a large group with a service level much higher

than the desired service level of 95%. After using the model, we expect that the service level of a very

large group will be close to the desired service level.

The new service level is set at 98%, which is higher than the original set service level. This makes it hard

to compare directly the results without using the model and after using the model. To compare the results,

first the parameter settings are determined for a service level of 95%. Next to it, also the difference

between the results with the current settings is compared with the results after using the model with a

desired service level of 98%.

As extra reference material also the expected service level with the current settings are calculated. So the

realized service level can be compared with the expected service level under the same settings. And both

service levels can be compared to the new expected service level. If there will be found large differences

between the realized and expected service level without using the model, also differences between the

expected and realized service level can be expected for the new settings.

For optimal use of the developed model, more information has to be collected for determining the values

of the cost factors (like the ordering costs and the carrying charge/storage costs). To compare the average

inventories before and after using the model also the optimal order quantities should be calculated.

However, the values of the cost parameters are not available, so the order quantities as already registered

in the ERP-software are used. The average inventory position depends on the reorder level and the order

quantity, while the reorder level depends on the order quantity and the service level. So without the

calculation of the order quantity, the model is not used optimal, and the found average stock levels are not

optimized. For the calculation of the storage costs a fixed percentage (25%) of the value for the item is

used (rule of thumb provided by Beerens (2006)).

For the group of C-items for which a Two-Bin strategy is proposed, the standard order quantities are used

for the calculation of the service level and the stock levels. For the other group of C-items, which make

use of an inventory control system derived from the (R,S) strategy, the review period corresponding to the

standard order quantity is used.

7.2 Results A-items

The results of the A-items after using the inventory control parameter model are compared with the

results of the current settings. The realized service levels of the A

service level with the current settings, and these are compared to the expected service level

service level of 95%) after using the inventory control parameter model. The

in table 7-1.

Results current settings

service level Realized P2 service level

<75% 3

75%-95% 19

95%-98% 9

>98% 42

sum 73

Table 7-1, comparison P2 service level A-items

The realized service levels for A-items are generally higher than the expected service level.

explanations of this finding is based on the assumption made for the demand. For this project and the

calculations is assumed that all demand is stochastic and non

demand is non-deterministic and the s

results in earlier replenishment orders, but has as negative side effect the higher average inventories.

After comparing the new expected service level with the current expected service le

that only for a very small group of items a high service level (P

have relatively large demand and a high reorder level, which makes it possible to approximate the desired

service level. The consequences of the new reorder levels for the alteration of the average stock levels are

displayed in table 7-2.

Table 7-2, current vs. new average stock A

As explained above, the exact calculations for

influence of the deterministic demand. Nevertheless

with the new levels because the same influence of deterministic demand is expected after usin

model. Four items will have an increase of more than 100%,

minimum stock level of zero. In total a decrease of 6% of the average inventory level is expected

A-items with new settings if the servic

level, also a small decrease of 0.8% is expected for the average storage costs

The required service level is set at 98% for all items delivered from stock.

increasing the service level from 95% to 98%

stock level and an increase of 12% of the storage costs.

43

items after using the inventory control parameter model are compared with the

The realized service levels of the A-items are compared to the expected

service level with the current settings, and these are compared to the expected service level

after using the inventory control parameter model. The service levels are presented

Results current settings Results new settings

service level Expected P2 service level Expected P2 service level

8 0

20 0

16 69

29 4

73 73

items

items are generally higher than the expected service level.


calculations is assumed that all demand is stochastic and non-deterministic. However, in practice not all

deterministic and the software is able to use the information of the future demand.


After comparing the new expected service level with the current expected service level, can be concluded

that only for a very small group of items a high service level (P2>98%) is expected. Most of the A


equences of the new reorder levels for the alteration of the average stock levels are

new average stock A-items

s explained above, the exact calculations for the average stock levels are hard to define because of the

influence of the deterministic demand. Nevertheless, it is possible to compare this average stock level

with the new levels because the same influence of deterministic demand is expected after usin

Four items will have an increase of more than 100%, in which is included the items with a current

In total a decrease of 6% of the average inventory level is expected

items with new settings if the service level is set at 95%. Besides the decrease of the average stock

level, also a small decrease of 0.8% is expected for the average storage costs.

The required service level is set at 98% for all items delivered from stock. The consequence

the service level from 95% to 98% and using the model are an increase of 3% of the average

stock level and an increase of 12% of the storage costs.

items after using the inventory control parameter model are compared with the

items are compared to the expected

service level with the current settings, and these are compared to the expected service level (desired

service levels are presented

Results new settings

service level

0

0

69

4

73

items are generally higher than the expected service level. One of the


deterministic. However, in practice not all

oftware is able to use the information of the future demand. This


vel, can be concluded

>98%) is expected. Most of the A-items


equences of the new reorder levels for the alteration of the average stock levels are

hard to define because of the

it is possible to compare this average stock level

with the new levels because the same influence of deterministic demand is expected after using the

in which is included the items with a current

In total a decrease of 6% of the average inventory level is expected for the

Besides the decrease of the average stock

The consequences of

increase of 3% of the average

44

7.3 Results B-items

In this paragraph the results of the B-items are presented and shortly discussed. First, the new service

level (based on a desired service level of 95%) is compared to the realized and expected service level of

the current settings, which are displayed in table 7-3.


service level Realized P2 service level Expected P2 service level Expected P2 service level

<75% 5 7 0

75%-95% 19 15 0

95%-98% 17 17 63

>98% 35 37 13

sum 76 76 76

Table 7-3, comparison P2 service level B-items

The groups for the realized and expected service levels for the current settings are of comparable size.

However, analyzing them individually results in large differences between realized and expected service

levels for the individual items. For 37 items a service level of more than 98% was expected, and for a

large part of this group the reorder level can be decreased. Besides the decrease of the reorder level also a

group of 22 items need an increase of the reorder level. This resulted in a group of 63 items for which a

service level between 95% and 98% is expected after the use if the model. Next to it, there is a group of

13 items with an expected service level of more than 98%. This is caused by the relative low lead-time

demand, which makes it impossible to set the reorder level exactly at the level to expect achieving the

desired service level (increasing the reorder level with one unit has already a large influence on the

expected service level for these items).

The average stock levels of the items after using the model, with the service level set at 95%, is decreased

with 9%. A decrease of the average stock level was expected because the group of very high service level

is larger than the group of low service levels for the current settings (see table 7-3). Furthermore, an

increase of a service level from 75% to 95% can be obtained in many situations with a smaller increase of

products, than the decrease of the service level of items from 98% to 95%. The decrease of 9% of the sum

of the average stock level is coupled with a decrease of only 1.5% of the stocking costs.

Increasing the service level from 95% to 98% and making use of the model with the new set service level,

will results in an increase of the average stock level of 4% and the average stocking costs will increase

with 16%.

45

7.4 Results C-items

The last group of items for which the service level and stock levels are compared is for the C-items. For

this group first the service levels and subsequently the stock levels and stock values are compared.


service level Realized P2 service level Expected P2 service level Expected P2 service level

<75% 18 8 0

75%-95% 21 22 0

95%-98% 10 13 62

>98% 44 50 31

sum 93 93 93

Table 7-4, comparison P2 service level C-items

The realized service levels of most of the C-items are lower than the expected service level. This is

remarkable because for most of the C-items the lead-time demand is overestimated, so the realized service

level is expected to be higher than the expected service level based on the calculations.

The results for the new settings (based on a desired service level of 95%) show a large group of items for

which a service level of more than 98% is expected. This is caused by the large group of slow-moving C-

items: the reorder level cannot be set to approximate the desired service level. The reorder level is low

and a small increase of the reorder level will have large influence on the service level.

The average stock level of the C-items, using the model compared to the current settings, is expected to

decrease with 10% and the average storage value will decrease with 10%.

An increase of the service level from 95% to 98% and using the model in the new situation, heavily

influences the average stock level and the average storage value. The sum of the average number on stock

will increase with more than 2% and the average storage costs even with 7.5%.

46

7.5 Conclusions

The current parameter settings are based on a P1 service level of 95%, and the desired service level of

GEA Grasso BV was at that moment a P2 of 95%. Measuring the realized performance as the P2 service,

give an overview of the diverse performance of the items: a large group with a very low performance, and

a large group with a performance higher than desired. The realized service level did not correspond to the

expected P2 service level, for which two explanations can be given:

• The assumption of stochastic demand, used for the calculations for the expected service level, do

not hold for all the items: some have a partial deterministic lead-time demand, which leads to

higher service levels than expected

• The rejection of items, especially the rejection of complete orders, can lead to lower service

levels.

Besides these assumptions and item characteristics, also the influence of the user of the system should not

be underestimated: the user can still ignore the proposed replenishment orders or change the settings of

the software. This also influences the performance of the items.

In the next table an overview of the influences of the model and the increase of the service level from

95% to 98% is given.

ABC-

classifications

new settings

(P2=95%) vs.

current settings

new settings

(P2=98%) vs.

current settings

new settings (98%)

vs.

new settings (95%)

Change of the

average stock level

A -6% +3% +10%

B -9% +4% +14%

C -10% +2% +13%

Change of the

average storage costs

A -0.8% +12% +13%

B -1.5% +16% +18%

C -10% +7,5% +20%

Table 7-5, overview stock level changes and storage costs changes

After using the model a decrease of the average stock level and the average storage costs are expected if

the desired service level is kept on 95%. If the service level will be set at 98% an increase of the average

stock level and average storage costs are expected. Interesting is the difference of the percentage of the

average stock levels and the percentage of the average storage costs: if the service level is kept at 95% a

decrease of especially the lower valued items is proposed, while for increasing the service level to 98%,

especially more higher valued items have to be kept on stock.

Also an indication is given of the expected average stock levels and storage costs if a service level of 98%

will be used instead of 95% both by setting the parameters with the inventory control parameter model.

The average stock level and storage costs will increase with between 10% and 20% for the items.

In the calculations of the results after using the model the current order quantities are used, because

insufficient information is available for the cost factors for calculating optimal order quantities.

Making use of the model will lead to service levels closer to the desired service levels and also will lower

the inventory level and costs, if continuing the current service level. Besides these positive effects, also

the ordering costs can be decreased, if the cost information is gathered, which also can lead to substantial

cost savings.

47

8. Conclusions and Recommendations

In this chapter the conclusions based on the findings are presented. First the conclusions directly related

to each of the three research questions (as formulated in paragraph 4.2) are discussed. Subsequently, in

paragraph 8.2, the general conclusions and recommendations are presented, based on the findings, results

and limitations of the analysis and development of the model.

8.1 Conclusions Research Questions

The first reach question is related to the imperfect delivered orders:

• How to set the parameters of the inventory control system to cover also the imperfect delivered

orders.

From the analysis to the imperfect delivered orders is concluded that partial delivered orders do not

influence the performance of the inventory control. Therefore, this is also not used for the parameter

settings for the items. The rejection of the items, based on the requirements of the items, have influence

on the performance of the inventory control so the parameter settings have deal with the rejection

quantity:

Complete order rejection for purchase items do not have to be covered by parameter settings, agreements

with the supplier should be made about rush orders in case of completely rejected orders. The group with

partial purchase order rejection is small and is not taken into account.

For production orders the partial rejection is taken into account by increasing the order at the supplier

with the expected number of rejected products. Complete rejected also orders have to be covered with

rush orders and not with inventory control parameters settings.

The second research question is especially focused on spare parts:

• How to set the parameters of the inventory control model for spare parts to achieve the desired

service level.

No particular settings are found which should be specifically applied to spare parts. The parameter

settings are not based on the type of demand, but especially on the usage value of time (ABC-

classification). The size and coefficient of variation of the demand did not deviate significantly from the

other items, to manage the spare parts different and with other parameter settings. The general proposed

strategies are also used for the inventory control of the spare parts.

The last formulated research question is focused on the items with a combined demand:

• How to set the parameters of the inventory control model for items available as spare part and

ordered by production to achieve the desired service level.

From the demand analysis is concluded that no difference should be made based on the demand source.

Besides this, the demand for an item as spare part and the demand from production are completely

independent from each other. Combining the demands for these items leads to lower stock levels than

determine the safety stock levels for both demand sources separately.

48

8.2 General Conclusions and Recommendations

Besides the conclusions specific to the research questions also more general conclusions can be drawn

based on this project. The general conclusions are split in two parts: first the conclusions based on the

analyses and item characteristics will be presented. Next to it, the conclusions based on the ERP-software

and the parameter settings will be discussed.

Analyses and items characteristics Currently for all items one strategy is used to manage the inventories. This is not desirable because the

items have different characteristics and based on the characteristics an appropriate strategy has to be set.

A (s,Q) strategy for A-items and B-items, a Two-Bin strategy for fast moving C-items, and a (R,S)

strategy for slow moving C-items.

With the average monthly demand and the coefficient of variation of the demand, can be determined

which probability function fits best (a Normal, Gamma, or a Poisson distribution). Currently the

parameter settings are based on a Normal distribution for the demand of all items.

The lead-time is not constant as currently assumed for all items, but a Normal distribution as a more

appropriate approximation. For purchase items also turns out that the agreed lead-time is often exceeded;

the average lead-time is larger than is agreed with the supplier.

The rejection of items (the order contains products not meeting the requirements) is currently not taken

into account. In the developed model, the average rejection quantity is integrated for items with

production as supply source. With the supplier should be arranged to place a rush order in case of

complete batch rejections.

An important factor for inventory control is the performance indicator. Currently GEA Grasso BV

measures its performance with a P2 service level, while in the ERP-software a P1 service level is set for

the parameter settings. For optimal inventory control for A-items no service level but backordering or

shortages costs should be used, for B-items a P2 service level is suitable, and for C-items the Time

Between Stock-outs is the generally proposed performance objective.

ERP-software and parameter settings For the optimal settings of the order quantity the EOQ formula is used, which calculates the order

quantity based on the storage and ordering costs. At the moment GEA Grasso BV does not have the

information of these costs variables. This makes it difficult to determine the optimal order quantities;

therefore we recommend to collect information of the cost parameters.

The ERP-software offers parameters, which are intended for deterministic demand, while we assume

stochastic demand for the items. The actual situation is a combination of these two types of demand, but

the uncertainty of the deterministic demand horizon makes it not useable for calculations. This will

influence the service level and average stock level: the reorder level is based on pure stochastic demand,

while a part of the demand is known in advance. The software places replenishment order taken the

deterministic demand into account while the reorder level does not.

Making use of the model and keeping the service level at 95%, a decrease of the average stock level and

the storage costs are expected. Setting the service level at 98% and make use of the model, will result in

an increase of the average stock level and storage costs. As is described above the theoretical optimal

settings for the items are not all based on a P2 service level. GEA Grasso BV should consider to change

49

the performance objectives for different types of items and also which performance level is desired. An

increase of the service level will heavily influence the average stock levels and storage costs, if the

parameter settings are based on the inventory control parameter model results in both situations.

For optimal use of the parameters and to combine stochastic and deterministic demand, the demand can

be forecasted. The forecasted demand can be used for the ordering strategy and with setting safety stocks

or safety times, the forecast errors can be covered. If the demand will not be forecasted, and the parameter

settings are completely based on stochastic demand, the mechanisms of the parameters should be changed

to prevent overstocking the items.

The use of the developed model is advised because the parameter settings are improved:

• It is expected that the desired service level will be achieved

• The average stock level and storage costs will decrease if the service level is kept on 95%

The model can be used for the current inventory control mechanism based on historical data of the items’

characteristics and as starting point for a forecasting strategy.

50

References

Beerens, H. 2006. Componenten die de voorraadkosten bepalen.

http://www.logistiek.nl/dossierartikelen/id334-Componenten_die_de_voorraadkosten_bepalen.html

Durlinger, P.P.J. 1998. Effectief voorraadbeheer, een stappenplan, First Edition, The Netherlands:

Kluwer.

Hair, J.F.Jr., Black, W.C., Babin, B.J., Anderson, R.E., and Tatham, R.L. 2006. Multivariate Data

Analysis. Sixth Edition. New Jersey: Pearson Education.

Hopp, W.J., and Spearman, M., 2001. Factory Physics. Second Edition. New York: McGraw-Hill.

Kok, de, A.G., 2005. Analysis of stock control models for one location with one product. Technical

University Eindhoven, College Logistiek 1 (1CC10) April 2005.

Salameh, M.K. and Jaber, M.Y., 2000. Economic production quantity model for items with imperfect

quality. International Journal of Production Economics, Vol. 64, 2002, pp. 59-64.

Silver, E.A., Pyke, D.F., and Peterson, R., 1998. Inventory Management and Production Planning and

Scheduling. Third Edition. New York: Wiley.

Strijbosch, L.W.G., Heuts, R.M.J., and Schoot van der, E.H.M., 1998. Improved spare parts inventory

management: a case study. Discussion paper provided by Tilburg University, Center for Economic

Research.

Weber, M.D., Leemis, L.M., and Kincaid, R.K. 2006. Minimum Kolmogorov-Smirnov test statistic

parameter estimates. Journal of Statistical Computation and Simulation, Vol. 76, No. 3, March 2006. Pp.

195-206.

51

Appendices

Appendix A: Overview Supply Chain Group

Figure A-1, Organization chart Supply Chain department

52

erview Supply Chain Group

Organization chart Supply Chain department

53

Appendix B: Summary Literature Study and Research Questions

A literature study is done for identifying the possibilities and problems of inventory management for

GEA Grasso BV. First a general introduction to inventory management is given in paragraph 4.1. From

this general introduction, the service level (paragraph 4.2), safety stock (paragraph 4.3) and the order

quantity (paragraph 4.4) are discussed. In paragraph 4.3, the demand and lead-time problems are shortly

described and also the imperfect delivered orders. In the next paragraphs (paragraph 4.5, 4.6 and 4.7) the

literature research is focussed on the specific types of demand for the items. During the literature study

research questions are formulated. The research questions are based on a mix of lack of information in the

literature and the possible problems identified at GEA Grasso BV. The last paragraph presents a

conclusion and some remarks of the literature research.

Inventory Management in General Silver (2008) and Vollmann et al. (1992) stated that inventory management attempts to answer three key

questions:

• How often should the inventory status be determined, that is, what is the review interval?

• When should a replenishment order be placed?

• How large should the replenishment be?

To answer these questions several methods and models are developed to provide inventory management

with support. Inventory management makes use of specific inventory control models based on the

collection of factors and constraints for making decisions. Silver et al. (1998) framed four questions to

systematically establish inventory policies:

• How important is the item? This indicates the criticality of the product for the company. This can

be determined with the use of a ABC-classification.

• Can or should the stock status be reviewed continuously or periodically? Is it necessary to

evaluate the stock status continues or is it desirable to do this after a specified time interval?

• What form should the inventory policy take? There are multiple inventory policies, and the form

primary depends on the demand characteristics.

• What specific cost or service objectives should be set? To manage the inventory it is important to

set the appropriate objective.

ABC-Classification In table B-1 the standard percentages of an ABC-classification based on the annual usage value is

presented from three different scientific sources.

Items Class A Class B Class C

Authors

% of all

items

% of the

total value

% of all

items

% of the

total value

% of all

items

% of the

total value

Silver et al. (1998) 20% 80% 30% 15% 50% 5%

Hopp and Spearman (2001) 5-10% 75-80% 10-15% 10-15% 80% 10%

Vollmann et al. (1992) 20% 65% 30% 25% 50% 10% Table B-1, ABC-Classification

Service Level There are multiple options for wanting to be able to deliver products to the customer (Silver et al., 1998).

These options can be categorized as based on cost optimization, customer service or a combination of

54

these two. We focus on the customer service objective, based on the project description formulated by the

company. Four different kinds of customer service levels can be distinguished:

• The probability (P1) of not going stock-out during a replenishment cycle (cycle service level)

• the fraction (P2) of demand to be satisfied routinely from the shelf (fill rate)

• the fraction of time (P3) during which net-stock is positive (ready rate)

• the average time (TBS) between stock-out occasions

Safety Stock If uncertainty is present in at least one of the factors influencing the inventory, some kind of safety is

necessary to be able to satisfy the desired service level. The most frequent uncertainties described in

literature are the demand for products, the lead-time of products, and the quality. If demand is not

deterministic and therefore not exactly known in advance, a probability function is fit. This demand

probability function gives the probabilities of a demand quantity. The same principle can be done for the

lead-time and the quality, a probability function is fitted on the length of the lead-time and on the number

of items (not) satisfying the quality requirements.

In literature, the demand distributions and its influences on the safety stock are frequently described. In

addition, the influence of the lead-time is investigated for many probability distributions. However, how

to combine a demand distribution and a lead-time distribution is not as extensively described as these two

independent from each other. How to handle with quality problems for a (part of an) order is even harder

to find. The term imperfect delivered orders is used as the collective noun for the items with quality

problems and for orders which are delivered only partial (due to miscommunication or problems at the

supplier). Therefore, a research question with sub-questions is formulated about this topic:

How to set the parameters of the inventory control system to cover also the imperfect delivered orders. -on which types of items have the imperfect delivered orders a significant effect on the

service level?

-what are the probabilities of imperfect delivered orders for different types of items?

-what is the impact of imperfect delivered orders for setting the parameters of the inventory

control system for these items?

The term imperfect delivered orders is chosen which covers all the orders for items, which are not

fulfilling all the requirements set. The requirements can be the quality, sizes, weight etc. of the items or

the number of delivered products, which deviates from the ordered quantity.

Order Quantity Besides determining the moment of ordering, also the quantity that should be ordered has to be

determined. Silver et al. (1998) distinguishes two different types of demand, deterministic and non-

deterministic demand. In the case of deterministic demand (demand is exactly known in advance), Silver

et al (1998) proposed to use the EOQ-formula in case of ‘constant’ demand (coefficient of variation is

smaller than 0.2) or heuristics when demand is not constant.

Three often proposed heuristics:

• Lot-for-Lot: for every demand, an order has to be placed to cover the specific demand.

• Silver-Meal: minimizes the Total Relevant Costs per unit time based on the carrying and setup

costs.

• Wagner-Within: minimizes the Total Relevant Costs over the complete horizon based on the

carrying and setup costs.

If demand is non-deterministic, the Economic Order Quantity formula (EOQ-formula) is advised. , if

demand is stochastic (demand quantity events happen with probabilities, which are distributed following a

55

probability distribution function). Products with a stochastic demand can be ordered best with the EOQ-

formula. The economic order quantity can be calculated with the following formula:

�8� p2��

With A= setup costs (€/setup)

D=demand rate per unit time (products/year)

v=variable costs per unit (€/product)

r= carrying costs per monetary unit per time unit (€/€/year)

The EOQ-formula can be adapted to include multiple conditions like inflation, discounts, and limitations

on order sizes.

Inventory Management for Items with Production Demand In literature many items describe inventory models for deterministic and stochastic demand. Because the

company makes use of a make-to-stock (MTS) or buy-to-stock (BTS) policy for most of the items,

demand for products is not deterministic. For these products statistical inventory management models are

proposed. A short overview of these models is given:

• (s,Q): when the inventory position drops down to/under the reorder level s an order of size Q is

placed.

• (s,S): when the inventory position drops down to/under the reorder level s, an order is placed to

bring the inventory position to the order up-to-level S.

• (R,S): after every period of R time units, and order is placed to bring the inventory position back

to the order up-to-level S

• (R,s,Q): after every period of R time units, the inventory position is determined and if the

inventory is at/below the reorder level s, and order of size Q is placed.

• (R,s,S): after every period of R time units, the inventory position is determined and if the

inventory is at/below the reorder level s, and order is placed to bring the inventory position back

to the order up-to-level S.

Inventory Management for Items with Spare Part Demand Another field of research about inventory management is how to handle spare parts. A lot of scientific

information can be found about inventory management and spare parts. One of the characteristics of spare

parts is the lumpy demand for it: periods with low/zero demand alternated with peaks for a specified part.

The spare parts can be categorized as slow movers or as fast movers. Slow movers are often the expensive

and recoverable/repairable spare parts, while the fast movers are the inexpensive and expendable spare

parts (Razi, 1999). The proposed strategy for handling the inventory of spare parts is often the (s,Q)

strategy. This strategy can also be used as the starting point of the statistical inventory system of the ERP-

software. However, to set the parameters of this strategy the demand characteristics is very important. In

literature is no consensus what the best approximation is to handle the demand characteristic. Many

probability distributions (especially the Normal, Exponential, Gamma, and Weibull distribution are

extensively described) are fitted to calculate the appropriate reorder point s. Therefore, the following

research question and sub-questions are formulated which are in line with the project description as stated

by GEA Grasso BV:

How to set the parameters of the (s,Q) model of spare parts to achieve the desired service level. -what is the demand distribution of the spare parts

-what is the influence of the lead-time on inventory management of spare parts

56

Inventory Management: Items with Combined Demand The last group of items, which is investigated, are the items with demand from production and have

demand for it as spare part as well. In contrast with items with production or spare part demand, there is

not many information available about how to handle items with demand from both production and as

spare part.

The point of departure of this research is a (s,Q) statistical inventory control model because of its wide

use in scientific literature and the current approach of the company (which is restricted by the ERP

software, see also paragraph 2.4 Inventory management and ERP-software).

Three kinds of situations are described which can be used for the design of a decision support model:

• A situation with demand from two sources: one source with deterministic demand and a source

with non-deterministic demand.

• A situation with demand from multiple sources with all the same demand patterns.

• A situation where priority is given to one of the demand sources and an extra parameter is

included to handle with these different priorities.

A research question with sub-questions is formulated which coincides with the project description:

How to set the parameters of the (s,Q) model of the items available as spare part and ordered by

production to achieve the desired service level. -what are the demand patterns of these items?

-should the items be handled as two separate types of items (spare part item and production item)

or is it desirable to handle these items as one type item?

-what is the influence of the demand (size and distribution) and the lead-time (length and

distribution) on the parameters of the inventory control model?

Conclusion and Remarks The three research questions are formulated based on the (lack of) information from scientific literature in

combination with the project description of the company, the environment of the company (including the

ERP-software), and interviews with employees. The major disadvantage of a literature research based on

company information is the use of assumptions already made or subconscious assumptions made by

gathering the information of the company. However, this also brings the advantage of finding information

in literature that is more relevant and practical usable. The research questions are therefore framed with a

combination of assumptions made and nevertheless an open-minded attitude.

References

Hopp, W.J., and Spearman, M., 2001. Factory Physics. Second Edition. New York: McGraw-Hill.

Razi, M.A., 1999. Periodic review inventory control models for slow moving spare parts. Scription for the

degree of Doctor of Philosophy at Virginia Commonwealth University.

Silver, E.A. 2008. Inventory management: an overview, Canadian publications, practical applications and

suggestions for further research. INFOR, Vol. 46, No. 1, February 2008, pp.15-28.

Silver, E.A., Pyke, D.F., and Peterson, R., 1998. Inventory Management and Production Planning and

Scheduling. Third Edition. New York: Wiley.

Vollmann, T.E., Berry, W.L., and Whybark, D.C., 1992. Manufacturing Planning and Control Systems.

Third Edition. Homewood: Business One Irwin.

57

Appendix C: ABC-classification

Figure C-1: items with only spare part demand

Figure C-2: items with only production demand

0%

20%

40%

60%

80%

100%

120%

% Usage Value

% Usage Value

0%

20%

40%

60%

80%

100%

120%

0%

10

%

20

%

30

%

40

%

50

%

60

%

70

%

80

%

90

%

10

0%

% Usage Value

% Usage Value

58

Figure C-3, items with demand from production and as spare part

0%

20%

40%

60%

80%

100%

120%

% Usage Value

% Usage Value

59

Appendix D: Sample Size

With the following formulae the sample size can be determined:

^^��`1�`�cq �d�arsc�d` tuj��j��v�wx (formula D-1)

^^�1�`�cq �d�arsc�d` ]]�"gy"g"hz ��?{lh"�g�%||�}~�}~}�� }�~��}�� }�~ (formula D-2)

With:

Z = Z-value for the corresponding confidence level

p = percentage of picking a choice (=0.5 for a sample size)

CI= Confidence interval

60

Appendix E: Demand Analyses

demand

source sample size

Monthly demand

distribution

Interarrival

distribution

Normal Gamma Poisson no-fit total

spare parts 84 5 0 42 37 84

production 89 13 1 24 51 89

both sources 90 40 3 32 15 90

total 263 58 4 98 103 263

Table E-1, demand distribution vs. demand source

ABC

classification sample size

Monthly demand

distribution

Interarrival

distribution


A 73 34 3 29 7 73

B 76 15 2 26 33 76

C 93 3 0 25 65 93

total 242 52 5 80 105 242

Table E-2, demand distribution vs. ABC-classification

demand source ABC-

classification

Monthly demand

distribution

Interarrival

distribution


spare parts A 3 1 2 5 11

B 1 2 5 13 21

C 2 0 35 32 69

production A 20 1 12 8 41

B 5 1 7 8 21

C 7 0 18 35 60

both sources A 10 1 8 3 22

B 19 0 6 10 35

C 21 3 27 22 73

total

88 9 120 136 353

Table E-3, demand distribution vs. demand source/ABC-classification

61

Appendix F: Assumptions Standard Formulas Inventory Control

Assumptions:

(1) The demand has a normal distribution with expectation µ and variance σ2

(2) No restriction on order sizes and the entire order quantity is delivered at the same time

(3) Delivery is immediately

(4) Long planning horizon with constant parameter values

(5) Fixed setup costs and unit variable cost does not depend on the replenishment quantity

(6) The products can be treated entirely independent of other items

(7) All demand which cannot be met immediately from stock is backordered

(8) The net inventory after arrival of an order is positive

(9) Delivery times are constant and equal to L

(10) Subsequent orders cannot overtake each other

Table F-1, assumptions standard fromulas inventory control

62

Appendix G: Microsoft Dynamics AX: Axapta

One of the important characteristics of a decision support system is its relation to the subject to support

and the mechanism this subject is controlled. For the design of a decision support model for optimal

inventory management, the decision support model has to support decisions for inventory management.

The decisions that have to be made are related to the mechanism used for inventory management. The

ERP-software Axapta, used for managing the inventory, is a combination of standard inventory control

models and extra parameters to span the gap between the theoretical inventory models and practice.

The theoretical inventory control models are explained in chapter 3, where a summary of the literature

study is described. In paragraph 2.3 a general description of the ERP-software, Microsoft Dynamics

Axapta is given. This chapter presents the variables and relations between variables available in Axapta to

manage the inventory. First the basic strategies are presented and shortly described. The second paragraph

is about the possibilities for setting parameters for a group of articles, while the third paragraph is aimed

at the parameters for individual articles.

Basic strategies There are three basic strategies for inventory management:

Completely manual The inventory of articles can be managed manual, without the help of the software. However, this does

not necessarily mean that the used strategy is just based on intuition. The used strategy can be a “two-bin”

strategy, for which the bin-sizes are determined once. This strategy does not need any further continuing

administrative navigation; the supplier takes care of the replenishment.

Lot-for-Lot Every time there is demand for an article, this article will be ordered at the supplier if the current stock

position is not large enough for fulfilling the order. The quantity of the replenishment order is just enough

to serve the customer, and brings the inventory back to zero.

Minimum stock The software makes use of the term minimum stock, which can be explained as the reorder-level or the

safety stock for an article. The use of the minimum stock depends on the circumstances (other parameter

options) and the calculations. The term minimum stock will be used for the parameter value, while the

terms safety stock and reorder level are used for the explanation of the calculations for the minimum

stock.

A reorder level is the level at which a replenishment order should be placed to replenish the inventory of

the article. The reorder level is set to cover the demand during the time between the replenishment order

is placed and the article is replenished with this order. This level is not dynamic; it does not change

continuous. The safety stock is the stock that only will be used in case of unexpected events, like large

demands or longer lead-times. A replenishment order should be placed the time it takes to replenish the

stock of an article before the stock of the article reaches the safety stock.

Parameters for groups of articles There are several parameters available, which can be set for a group of articles. The parameters are listed

in table 9.1 with their options and their description.

63

Parameter Options Description

Order method Period Order the quantity as needed in the specified

period

Lot-for-Lot Replenishment order is equal to the demand

Min-Max Replenishment order brings the stock back to

the specified Max. level

Manual Ordering without suggestions from Axapta

Demand Period Fill the time period in

working days

When the stock level drops under the

minimum stock level, an order of the size of

all the demand during this period is proposed. Table G-1, parameters for group of articles

The first parameter is the ‘order method: it determines the strategy of ordering. These are described in the

previous paragraph, however in this table there is made a distinction in the order strategy in case of the

use of the minimum stock. With the ‘Min/Max’ option, Axapta proposes every time the minimum stock is

reached (‘Min’), a replenishment order is placed with the size to bring the stock to the defined level

(‘Max’). If the option ‘Period’ is chosen, a replenishment order is created when the minimum stock is

reached, and the size of this order is equal to the total demand during this period, starting from the

moment the minimum stock is reached. This option is only of use in case the demand in the (near) future

is known/predicted with a forecast.

The parameter ‘Demand Period’ can be used if ‘Period’ is the used order method. With the demand period

the replenishment order frequency and replenishment order size can be influenced. It summarizes all the

demands that are already in the system for the specified period, starting from the moment the minimum

stock is reached.

This option can be used in this parameter group to regulate the order frequencies for a group of articles.

For example, if there is chosen to replenish a group of articles of the same supplier every month, the

option Demand Period can be set at a month. The replenishment quantity satisfies all the demands that are

in the system already for the coming month. To be sure that exactly the demand during this month is

covered, all the demand during this period should be deterministic.

Parameters articles individually

In the previous paragraph the parameters for groups of articles can be set. It is also possible and necessary

to set some parameters for articles individually. In table 9.2 the parameter with its options and a

description are given.

Parameter Options Description

Order method Period Order the quantity as needed in the specified

period

Lot-for-Lot Replenishment order is equal to the demand

Min-Max Replenishment order brings the stock back to

the specified Max. level

Manual Ordering without suggestions from Axapta

Demand Period Fill the time period in

working days

When the stock level drops under the

minimum stock level, an order of the size of

all the demand during this period is proposed.

Minimum stock Number of products

for the minimum stock

If the minimum stock is/will be reached, a

replenishment order is proposed.

Maximum stock Order up-to-level, in When the minimum stock is reached,, the

64

number of products stock will be refilled up to the maximum stock

Reach minimum Date of today There is checked if every day (from today),

there is at least the number of products on

stock as defined as minimum stock

Date of today + lead-

time

There is checked if at every day (from the day:

today + lead-time), there is at least the

number of products on stock as defined as

minimum stock

Standard

replenishment order

size

Number of products The number of products that will be used in

case of manually managed inventory

Minimum

replenishment order

size

Number of products The minimum number of products that should

be ordered

Maximum

replenishment order

size

Number of products The maximum number of products that should

be ordered

Multiples Number of products A multiple of this number of products should

be ordered Table G-2, article specific parameters

The ‘order method’ and ‘demand period’ are the same as the order methods as described in the previous

paragraph. The minimum stock is the level of stock Axapta is trying to avoid: there is tried to receive a

replenishment order when the stock drops down to the minimum stock. This is only possible if there is

information available of demand in the future. Otherwise, a replenishment order is created at the time the

stock level drops down the minimum stock, and the replenishment order is received after the lead-time

length in days. Maximum stock is the level, which is tried to reach when a replenishment order is

received. The size of the replenishment order is the number of products to order to bring the stock to this

maximum level. This option is only available of the ‘Min/Max’ order method. The minimum are the

levels of minimum stock that are defined for specified periods. This makes it possible to work with

different levels during the year that only needs to be defined once.

The next parameter is about when the minimum stock should be reached. The first option is ‘Date today’,

every day the stock level should be at least the minimum stock level. If this is not the case, there is a

replenishment order created to bring the stock at least to the minimum stock level. The same is true for

‘Date today + lead-time’, but the difference between these options is that ‘Date today’ does not take into

account the lead-time. It gives the announcement that there should be tried to get the replenishment order

at the date the stock drops below the minimum stock (even this is within the lead-time). ‘Date today +

lead-time’ does not want to get the replenishment order in at the date of the stock level is below the

minimum stock if this is not possible. The replenishment order should be received at the date of ordering

plus the lead-time. Only if the stock drops below zero, it gives an announcement of trying to get it in

when the stock drops below zero (even if this is within the lead-time).

The ‘standard replenishment order size’, is used if the inventory is managed manually, and for the cost

price calculations. The ‘minimum replenishment order size’ and ‘maximum replenishment order size

restrict the order size with a minimum and maximum quantity. The last parameter of interest for this

project is ‘multiples’. The replenishment order size should be a multiplication of this multiple.

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Formulas and calculations Axapta

Axapta offers some tools to support the user for determining the minimum stock. It provides two options:

• Using a safety factor based on the desired service level

• Using the average demand during the lead time plus the average demand during the margin for

the lead-times (with the possibility of multiplying this value with a factor)

The assumptions made for determining the minimum stock based on a service level:

� Normal distributed lead time demand

� Constant and deterministic lead-time

� There is no undershoot

In Axapta the service level is defined as: “the percentage of time during which there is no stock out”.

However, this is not in line with the standard calculations and descriptions of the corresponding service

level. The service level that corresponds with this data information is the P1 service level: the probability

of not going stock out during a replenishment cycle. The standard calculation used by Axapta for

determining the minimum stock:

_�`�_a_ �cde@ �o��_d`c�� j �W�� @ j Do��H_d`c�� j 9 � � (formula G-1)

With E=expectation

D=demand

L=Lead-time

k=safety factor

σ=standard deviation

The calculation is based on monthly demand, with 31 calendar days per months. The safety factor is the

factor that corresponds with the cumulative probability function of a normal distribution.

With this formula the reorder level of a statistical inventory model with a continuous review can be

calculated. When the inventory position drops to/under this level, a replenishment order should be placed,

and this order is expected to be delivered a lead-time period later. However, the software does not

propose to place a replenishment order when the reorder level is reached, but proposes to receive the

replenishment order at that moment. This results in receiving the replenishment order too early, caused by

the known demand in the near future. A part of the demand is known in advance (as explained in chapter

4) so Axapta is able to schedule replenishment orders, based on the known demand in the future. This

makes the use of the formula in combination with the replenishment method not appropriate.

The use of a safety time (the second option Axapta provides for the regulation of the minimum stock

level) is based on the lead-time. With this safety time (the margin that has to be set), there is tried to cover

the demand if the lead-time becomes longer than expected. Besides a time margin, a multiplier can be

used to cover demand that is larger than the expected demand. Axapta does not provide any relation

between a service level and these two tools.

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Appendix H: Formulas Parameter Calculation

Lead-time demand distributions

Normal distribution:

�m��0, HIn �E�I j �E�I (formula H-1)

D,o��0, HIn �E�I j D,�� D,E�I j �,E�I (formula H-2)

Poisson distribution:

�m��0, HIn ��EHI�E��I (formula H-3)

D,m��0, HIn ��EHI�E��,I � �,D,EHI�,E��I (formula H-4)

Undershoot Gamma distribution:

� WuE;�IAu�;� (formula H-5)

� �WE;�I (formula H-6)

�EJI ��%�,� (formula H-7)

�EJ,I ��%��%, �u (formula H-8)

Gamma distributed lead-time demand:

� ��A �⁄ u (formula H-9)

� ��A �⁄ u (formula H-10)

Appendix I: Robustness EOQ

Table I-1, robustness EOQ

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Appendix I: Robustness EOQ

Appendix J: Minimum and Maximum Order

Table J-1, minimum and maximum order quantity analysis

68

Appendix J: Minimum and Maximum Order Quantity Analysis

1, minimum and maximum order quantity analysis

Appendix K: C-item demand

Table K-1, C-item demand

69

item demand

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