Eindhoven University of Technology MASTER. The design of a near optimal ABC classification at Océ. Koolen, K.H.L. Award date: 2016

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1 Eindhoven University of Technology MASTER The design of a near optimal ABC classification at Océ Koolen, K.H.L. Award date: 2016 Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 20. Nov. 2017

2 Master s Thesis THE DESIGN OF A NEAR OPTIMAL ABC CLASSIFICATION AT OCÉ KOOLEN, K.H.L SCHOOL OF INDUSTRIAL ENGINEERING EINDHOVEN UNIVERSITY OF TECHNOLOGY MARCH 2016 Supervisors Eindhoven university of technology Prof. dr. ir. G.J.J.A.N. van Houtum Dr. T. Tan Supervisors Océ Niels Houben Roger Vliegen

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4 De schrijver werd door Océ-Technologies B.V. in staat gesteld een onderzoek te verrichten dat mede aan dit rapport ten grondslag ligt. Océ-Technologies B.V. aanvaardt geen verantwoordelijkheid voor de juistheid van de in dit rapport vermelde gegevens, beschouwingen en conclusies, die geheel voor rekening van de schrijver komen.

5 ABSTRACT This thesis describes the design of a classification for spare parts inventory management. The thesis has been conducted at Océ, a leading manufacturer of printing systems that uses classification in order to manage spare parts in the supply chain. In this thesis it is shown that for an inventory model with general demand, batching, a periodic review and emergency shipment costs, classification on Demand & Price yields a performance close to the system approach, the (near) optimal approach. Furthermore, the class-sizes in a classification are shown to give a strong impact on the total cost of inventory holding. These insights have been applied on a regional distribution centre in the USA. This distribution centre uses inventory management software (GAIA) that is developed by Canon. The thesis concludes by showing that the current settings of the inventory management software can be improved and that, by changing the criteria of the classification, a big improvement in inventory management can be made. I

6 MANAGEMENT SUMMARY In 2009 Canon took over Océ to form the world s leading group in printing together. Canon and Océ offer a big variety of printing systems. The products of Océ are in general professional printing systems. These are capital goods that require a high service. In order to offer this service Océ had a service supply chain to provide spare parts to customers and its technicians. With the integration with Canon the organization became more focussed on the production of printers, the distribution is now done through the Canon organization and warehouses. The central warehouse of Océ (CSC) delivers to the regional distribution centres of Canon (RSHQs). The RSHQs then serve the warehouses and inventory downstream. In order to regain control over the supply chain Canon and Océ agreed to give Océ more control over the inventories at the RSHQs. This is in practice done through software that is called GAIA. GAIA offers Océ a way to decide the transportation mode, when the item is order and how much of the item is ordered. This is done by controlling the settings of classes of items in GAIA. Items are divided into classes by rating them in two dimensions, the demand per year and the number of months demand occurred. Océ wondered whether they, with this classification, can come close to the optimal approach. This led to the following research question: What ABC classification minimizes the sum of inventory holding cost, emergency shipment cost and order cost while ensuring a target fill rate and what ABC classification would fit for an RSHQ in the network of Océ? The scope of this research is the RSHQ in the USA, CUSA with three warehouses and two product groups. Model In order to research this, a model had to be selected from literature that included the most important features of an RSHQ. Besides that it had to be able to compute the results in a reasonable time. In order to achieve this, the model has been broken down into a grand model and a core model. In the grand model the batch size of an item is set to the EOQ, Economic Order Quantity, and a transportation mode rule is applied to decide the transportation mode of an item. In the core model the last parameter is set. This is reorder level of an item, thus when a new batch is ordered. With the reorder level, batch size and transportation mode known the fill-rate and costs are calculated using the inventory model of Äxsater (2015). Classification Using the model as described above it was possible to compare different classifications on four aspects that were based on literature. These four aspects are: the criteria of a classification, the number of classes, the class-sizes and the target setting. On every aspect several scenarios have been taken into account: Criteria: What variables are taken into account when classifying o One-dimensional: When items are rated on one dimension Demand / Price Demand / (Batch * Price) Annual Dollar Volume (Demand & Price of a product) II

7 o Two Dimensional: Demand & Price Demand & Frequency Number of classes: o One dimensional: 2,3,4,5 or 6 classes o Two dimensional: 2x2 or 3x3 classes Class-sizes have been varied by enumerating over different threshold values, the values that divides to classes. The classifications have been compared two times, once when no emergency shipments cost are involved and once with emergency shipment cost. This has been done for 100 items. The results can be summed up as follows: It is shown that without emergency shipment cost the criteria Demand/Price, Demand/Batch*Price and Demand & Price perform best, within a few percentages of the optimal solution. The Annual Dollar Volume and Demand & Frequency criteria continuously perform worse than the beforementioned criteria. With emergency shipment costs the Demand & Price classification performs best. The number of classes also has a big impact on costs. It is recommended to use three to four classes for a one-dimensional classification in order to have a near optimal solution and to keep the number of classes manageable. For a two-dimensional classification it is recommended to use 3x3 classes. Class-sizes are shown to have an big impact on the performance especially when no emergency shipment costs are applied. The difference with a setting with the best class-sizes can be over 40% of the costs for the Demand / Price classification. This can be explained by the forced presence of stock. Furthermore it is concluded that the class-sizes are greatly dependent on the characteristics of the dataset. Application at Océ First of all the possible gains at Océ have been investigated by checking the difference between the current performance and the optimal performance. In this comparison the influence of the EOQ rule on the total costs and the influence of the transportation mode on the total costs are taken into account. The application of the system approach shows that the emergency shipment costs at the RSHQ are so dominant that no optimization is needed when all items are set to their minimum cost. This means that applying a classification yields the same results as the system approach when it is assumed that the classification also with the reorder level of all items at a minimum cost level. Lastly, GAIA has been analysed, programmed and compared to the system approach. Conclusions and recommendations for Océ This led to the following recommendations and conclusions for Océ: Decide transportations modes for individual parts: The transportation of the parts is a big factor of the annual costs (around 50% for WFPS and around 10% for OIP). Applying a simple rule (Appendix D) can yield a big decrease in the costs in the supply chain (around 55% of the costs for WFPS and around 14 % for OIP). III

8 Implement the Demand X Price classification or the system approach: As shown in Section 4 the criteria used for GAIA, Demand and Frequency, performs around 20% worse than the Demand & Price classification. Set class-sizes: Class-sizes are an important factor in the cost. The optimal class-sizes are dependent on the dataset and thus have to be determined per dataset Use the insights in GAIA and the tool to reduce costs on short term in CUSA: In Section 4 is shown that the current settings in GAIA are far from the optimum in the system approach. As GAIA is already implemented in CUSA a recommendation is to use tool to optimize the target setting. Next to that it is recommended to change the class-sizes which also can result in a considerable saving. IV

9 PREFACE This master s thesis is the final work of my master Operations Management and Logistics at the University of Technology in Eindhoven. After five years of studying, in which I had the opportunity to see and do more than I ever imagined, and after finishing my last exam in Buenos Aires I had the great opportunity to finish my work at Océ Technologies B.V. During my graduation project I had the pleasure to be able to go to the department SCM Service Parts. I became well informed about the projects that are currently going on at Océ and was impressed to see the urge to improve and the insights the people had. I am glad to have been able to do this project at the department and I want to thank all the people that made this project possible. Every project has a company supervisor and I had the pleasure that Niels Houben was mine. In ups and downs Niels kept believing in me and understanding me, which I am very grateful for. With all results and questions I had, even if they were very technical, Niels wanted to know how it worked exactly and could quickly spot the difficulties and consequences. I also want to thank Roger Vliegen, the manager of the department, who made it possible for me to graduate on a project at Océ and who gave very good and accurate feedback and made some good discussions possible. I would also like to thank the employees of the department, who were very open to questions and took the time needed to explain how things worked within the organization. From the Eindhoven University of Technology I would like to thank Geert-Jan van Houtum. Geert-Jan has an incredible knowledge in the field of service logistics and helped me very well with critical questions and discussions that helped with me finding the right direction in my thesis. I would like to thank my friends, the ones I knew before coming to Eindhoven and the ones I met during my study. It was always nice to spend my time with you, whether it was in Asten, in The Villa or abroad travelling. Finally I would like to thank my parents and my brother and sister. They always supported me and I always enjoyed to come back home after a busy week and take some time to relax. Koen Koolen, March 2016 V

10 TABLE OF CONTENTS Abstract... I Management Summary... II Preface... V List of Figures... X List of Tables... XII List of Definitions... XIV 1 Introduction and Research Questions Company Background Historical context Océ a Canon Company Integration Océ and Canon The organization Spare parts at Océ The spare supply chain Order process Inventory Control at the RSHQ s CUSA Related Literature Spare Parts Environment ABC Analysis Inventory problem Problem formulation Inventory Control Research question Project objective Scope Scientific contribution Outline of the report Grand Model Assumptions and Design choices inventory model Multi-location Product Groups Batching VI

11 2.1.4 Transportation modes Emergency Shipments Review Period Demand Inventory Model Mathematical Model Costs and lead-times Cost factors Lead-times Design of an ABC Classification Design of a general classification Classification criteria Number of classes Class sizes Target setting Verification Results Classification criteria without emergency shipment costs Classification criteria with emergency shipment costs The impact of class sizes on performance Application at Océ Practical complexities The use of an R,s,S Policy Translating GAIA settings to parameters in the model (and vice versa) Dual supply System Approach Data and scenarios Cost and performance Classification for both product groups Computation times Demand & Price classification GAIA Classification criteria Classification criteria VII

12 5.1.2 Number of classes Class sizes Target setting Results GAIA Classification GAIA for a selection of SKUs Results of GAIA for the whole dataset Implementation Tool Actions to perform for using the tool Conclusions and recommendations General Conclusions Recommendations and Conclusions for Océ Recommendations for future scientific research Bibliography Appendix A. GAIA Classification Appendix B. Demand Analysis Appendix C. Batch Sizes Appendix D. Transportation Mode Appendix E. Results of Chi-Square Test Appendix F. Non-parametric distribution Appendix G. Calculation fill-rate and average inventory level Appendix H. Local minima of a class Appendix I. System Approach Appendix J. Manual calculation EOQ and Transportation mode Fill rate and cost Calculation Fill rate and respective cost for (CLMBS,1) Calculation Fill rate and respective Cost for (CLMBS, 2) System Approach Classification Appendix K. Classification with 50 emergency shipment costs Appendix L. Comparison R,s,S and R,s,Q Appendix M. System Approach Comparison Appendix N. Class size and cost VIII

13 Appendix O. Settings for GAIA IX

14 LIST OF FIGURES Figure 1.1 Organizational chart of PPP-Logistics... 2 Figure 1.2 Organizational Chart SCM Service Parts Venlo... 3 Figure 1.3 Overview Spare parts supply chain Océ... 3 Figure 1.4 The dimensions, classes and inventory control methods in GAIA... 6 Figure 1.5 A classification based on demand and price (van Wingerden et al., 2015)... 8 Figure 1.6 Characterization of the inventory to be modeled... 9 Figure 1.7 Network Scope of the assignment Figure 1.8 Parts Overview Figure 2.1 Histogram of demand per week of a fast-mover Figure 2.2 Histogram of demand per week of a medium-mover Figure 2.3 Histogram of demand per week of a slow-mover Figure 2.4 Histogram of the demand part in Columbus Figure 2.5 Simulated mean as fraction of real mean Figure 2.6 PDF of the demand during lead time (Fast mover) Figure 2.7 PDF of the lead time (Medium mover) Figure 2.8 PDF of the lead time (Slow mover) Figure 2.9 Graphic representation of the Grgrand model Figure 2.10 FOB/FCA method, Océ is responsible for leg 1, the RSHQ for leg 2& Figure 3.1 Example TrEshold values for classification Figure 3.2 Comparison Classification in percentage to system approach Figure 3.3 Comparison Classification in percentage to system approach Figure 3.4 Cost and demand percentage in class C; no emergency shipment costs Figure 3.5 Cost and demand percentage in class C; 25 emergency shipment costs Figure 4.1 cost and Aggregate fill-rate OIP normalized Figure 4.2 Total cost and Aggregate fill-rate WFPS Figure 4.3 Normalized Cost breakdown OIP Figure 4.4 Normalized Cost breakdown WFPS Figure 4.5 Inventory costs OIP Figure 4.6 Inventory costs WFPS Figure 4.7 Shipment method (red = air, blue = ocean) when applying transportation mode rule Figure 4.8 Shipment method (red = air, blue = ocean) as currently is Figure 5.1 Comparison for 100 items GAIA Figure 5.2 Results of GAIA on the WFPs Group Figure 5.3 RESULTS OF GAIA ON THE OIP Group Figure 6.1 Example of a sheet in GAIA where variables can be set Figure 6.2 Example of an outcome of the GAIA classification Figure 8.1 Settings for the WFPS group Figure 8.2 Settings for the OIP group Figure A.1 Main Classification GAIA Figure A.2 Inventory Policy Decision Tree Figure A.3 Classification of fixed point method Figure B.1 Cumulative Graph of demand per week CUSA X

15 Figure B.2 Cumulative Graph of demand per week CUSA (0-5% excluded) Figure H.1 FILL RATE OF A CLASS WITH 100 ITEMS AND ITS RESPECTIVE COSTS FROM 98% %.. 70 Figure H.2 Fill rate of a class with 100 items and its respective costs Figure K.1 COMPARISON OF CLASSIFICATION WITH THE SYSTEM APPROACH (50E EMERGENCY SHIPMENT COSTS) Figure L.1 Graphic Representation of the R,s,Q policy (Axsäter 2015) Figure L.2 Graphic Representation of the R,s,S policy (Axsäter 2015) XI

16 LIST OF TABLES Table 1 Reviewed models in literature Table 2 Characteristics Product Groups Table 3 Data Characteristics Table 4 Percentage of Chi-Square test >0.05 for 30 SKUs per class Table 5 Overview of relevant models from literature Table 6 Average cost for ocean tranport per m3 per region Table 7 Lead-times to RSHQs Table 8 Results of classification approach without emergency shipment costs (green when <5% difference from system approach) Table 9 Results of classification approach with emergency shipment costs (green when <5% difference from system approach) Table 10 Data used in analysis Océ Table 11 Scenarios compared using the system approach Table 12 Difference in shipment method WFPS group Table 13 Difference in shipment method OIP Group Table 15 Comparison GAIA with D&F (3x3) without emergency shipment costs Table 17 Frequency table part in Columbus Table 18 Table with all combinations for part in Columbus and L = Table 19 Probability density function Table 20 Products in manual calculation Table 21 Results calculated through program Table 22 Calculation of transportation mode with least cost Table 23 Emergency shipment cost Table 24 The calculation of EOQ and Optimal batch size Table 25 Master data selected parts Table 26 PDF (CLMBS, ) Table 27 PDF (CLMBS, ) Table 28 Probability Matrix for IL in leadtime Table 29 Inventory level matrix in leadtime Table 30 Probability Matrix for IL in leadtime and Review period Table 31 Inventory level matrix in leadtime and Review period Table 32 Fill rate and corresponding cost Table 33 Probability Matrix for IL in leadtime Table 34 Inventory level matrix in leadtime Table 35 Probability Matrix for IL in leadtime and Review period Table 36 Inventory level matrix in leadtime and Review period Table 37 Fill rate and corresponding cost Table 38 System Approach 25 emergency shipment cost Table 39 System Approach 0 emergency shipment cost Table 40 Enumeration over class-sizes Table items classified on D/BP criterion Table 42 Results of classification of 100 parts with 50 emergency shipment costs Table 43 Summary comparison of R,s,S - R,s,Q (S - s = Q) XII

17 Table 44 Summary comparison approximation of R,s,S - R,s,Q Table 45 Comparison R,sQ - R,s,S where S-s = Q Table 46 Comparison R,sQ - R,s,S where S-s = Q + 0.5muR Table 47 Results of System approach Table 48 Class - size and cost D/P 2 classes Table 49 Results of GAIA optmization with emergency shipment costs 0, 100 items... Error! Bookmark not defined. XIII

18 PPP OIP WFPS CP SCM Service Parts CSC RSHQ QRS Field Stock EMEA National Warehouse OEM Dealer XYZ Classification GAIA Classification GAIA Frequency SKU LIST OF DEFINITIONS Production Printing Products, Division in Canon that is operated by Océ Office Imaging Printing, product group of printers Wide Format Printing Systems, product group of printers Commercial Printers, product group of printers Supply Chain Management Service part; department at Océ Venlo that manages the service parts Corporate Supply Centre, the distribution centre of Océ in Venlo Regional Sales Headquarter, the central distribution centre of a region from Canon Quick Response Stock, an inventory location near customer sites Stocks at or near customer sites and in the cars of technician Europe, Middle East & Africa, customer region specified by Canon A distribution centre within a region that delivers to customers in a specific country Original Equipment Manufacturer, a manufacturer of printing systems or parts A party that sells Océ printers but is independent of the Canon organization ABC Classification used by Océ to manage inventory at the CSC ABC Classification used by Canon to determine inventory policies, also called GOA Code Global Allocation of parts Inventory application, information system that allows inventory management at the RSHQs The number of months in a year a spare part is demanded Stock Keeping Unit, a distinct type of item for sale XIV

19 1 INTRODUCTION AND RESEARCH QUESTIONS This chapter starts with the background of the company the master s thesis is conducted at (Section 1.1). Section 1.2 gives a description of the situation where the problem arose from, that is followed by the literature review (Section 1.3). Then the problem statement and research questions are stated (Section 1.4) followed by the scientific contribution of this report (Section 1.5) and the chapter concludes with an outline of the report (Section 1.6). 1.1 COMPANY BACKGROUND In this section a short history and an overview of the company are given. First the history of the company and the recent merger with Canon is described. Lastly the organization of today and the department the thesis is written for is described HISTORICAL CONTEXT The history of Océ starts when in 1857 when Lodewijk van der Grinten starts a pharmacy. By experimenting with chemistry Lodewijk develops a substance that colours margarine, the cheap variant of butter which is marketed in In 1920, when Lodewijk s grandson, Louis, had already taken over the company, the company started experimentation with other applications of dyes and used it to produce blueprints. In 1927 the grandsons of Lodewijk patented an easy and inexpensive method to produce the so-called diazo paper that was to be marketed as Océ, an abbreviation of the German Ohne Componente (OC). From that time on, the company focused on printers and in 1958 the company went public on the Amsterdam Stock Exchange. By 2009 the company was active in more than 80 countries and had production and research centres in several countries. However, the economic downturn in the United States and the rest of the world hit Océ hard and forced it to seek partners or buyers for the company OCÉ A CANON COMPANY This resulted in an offer from Canon to Océ in order to create the world s leading group in the printing industry. The strategic rationale for the merger between the two companies was to create a strong joint enterprise capable of long term successes by building upon each other s strengths. The Canon group operates a worldwide network for distribution, sales and marketing that can be accessed by Océ now as well. Océ has expertise in the areas of production printing and wide format printing, while Canon s expertise in printing is in the customer and office printing. Together, Océ and Canon offer complementary technologies and products in the printing industry INTEGRATION OCÉ AND CANON After buying around 80% of the stocks of Océ in 2009 it took Canon until 2011 to completely buy Océ and thus to be able to start the integration of Océ into the Canon organization. In 2013 a big part of the supply chain integration took place. The distribution and service network of Océ is now part of the Canon group. Océ delivers to the regions of the Canon organization and the products are distributed to the regional distribution centres (RSHQ s) of Canon. These regions are independent Chapter 1. Introduction and Research Questions 1

20 entities, buying and selling Océ and Canon products. In Europe, the integration went different because traditionally the distribution centre in Venlo was the central depot for Europe. Currently, spare parts are still picked in the distribution centre in Venlo (CSC) for the car stocks throughout the European network EMEA. Administratively everything goes through Canon Europe, located in Amstelveen THE ORGANIZATION Océ is part of the Canon group, a multinational headquartered in Tokyo that employs over 200,000 individuals. Canon has two organizational entities responsible for the printing and documenting industry, Production Printing Products (PPP) and Office Imaging Printing (OIP). OIP is the production and service of office and customer printers, a market mainly served by the Canon brand of the company. PPP is the market of professional users and this is completely formed by Océ. Three categories of printers are produced by Océ, which differ in functionality, size and target group. In the first category is the Office Imaging Printing (OIP), printers that are used in general in offices and educational institutions. A second class of products are the Wide Format Printing Systems (WFPS), wide format printers for customers such as construction, architecture and engineering companies. Lastly continuous feed printers (CP) are used to print large volumes for customers as telecom companies, financial institutions and governmental institutions. There are three production locations: the latter kind of machines, CP, is produced in Poing, Germany. WFPS is produced in all locations and OIP is produced in Venlo. The Master s thesis project originates from the department SCM Service Parts in Venlo. SCM Service Parts is a department of PPP Logistics, the branch of Océ that is responsible for the inbound, warehousing and outbound transport for all the Océ locations. In Figure 1.1 the organizational chart is displayed. PPP Logistics SCM Service Parts 1 Warehouse Operations 1 Transport Services 1 SCM Service Parts 2 Warehouse Operations 2 Transport Services 2 SCE FIGURE 1.1 ORGANIZATIONAL CHART OF PPP-LOGISTICS SCM Service Parts Venlo is the department responsible for the planning and control of service parts of OIP and WFPS. The department itself is accordingly split into different functions; one group is responsible for WFPS, another group for OIP. Each group has planners that handle daily purchases and engineers that handle the exceptional cases that cannot or are not well handled using the usual statistical analysis of its information system. The third function is the customer service that is responsible for releasing orders of service parts, toner and ink to the warehouse and contact with the customer. SCM Service Parts 1 SP&E OIP SP&E WFPS Customer Service SP&E Chapter 1. Introduction and Research Questions 2

21 FIGURE 1.2 ORGANIZATIONAL CHART SCM SERVICE PARTS VENLO 1.2 SPARE PARTS AT OCÉ In this section the spare parts supply chain of Océ is discussed first (Section 1.2.1). It is followed by a description of the order process (Section 1.2.2) and we finish with a description of the current inventory management in the second echelon of Océ which is relevant to this thesis (Section and 1.2.4) THE SPARE SUPPLY CHAIN When an Océ machine breaks down it is in around 20% of the cases necessary to replace a part. These parts need to be supplied by the service parts supply chain. Two different sources provide parts to the service supply chain at Océ, internal and external suppliers. SCM Service Parts Venlo coordinates the stock and delivery of service parts from Venlo. For the service supply chain there are four relevant different types of stocking points (Figure 1.3). 1. The warehouse in Venlo, the Corporate Supply Centre (CSC), is the central warehouse. Among its suppliers are internal suppliers such as plants of Océ and external suppliers. 2. The Regional Sales Headquarters (RSHQs) are supplied by the CSC and are operated by the Canon group. There are seven RSHQs; they are located in USA, Singapore, Australia, China, South Korea, Japan and Europe. 3. National Warehouses; these supply the field stock in the respective country and are supplied by the RSHQs. 4. Field Stock is considered all the stock that is either in the technicians car or in quick response stocks: a. Quick Response Stocks (QRS); these are small warehouses near to customer sites used for sharing expensive parts between cars and stocking of more voluminous parts that do not fit in the car. b. The Car Stock; every technician has a stock of small items with high demand in their car; this can be seen as a stocking point. FIGURE 1.3 OVERVIEW SPARE PARTS SUPPLY CHAIN OCÉ Chapter 1. Introduction and Research Questions 3

22 As can be seen in Figure 1.3 there are five different ways parts can be delivered to their customer. Type 1 Type 2 Type 3 Dealer CSC Field Stock RSHQ Field Stock National Warehouse Field Stock RSHQ / CSC Dealer This represents the European network (EMEA), the network that Océ has been operating in Europe before the integration with Canon and Océ. However administratively the CSC delivers to the European RSHQ, physically the parts are still picked in the CSC in Venlo and send to the QRS and car stocks. These then deliver the parts to the customer Replenishment from the CSC to an RSHQ and then directly to the Field Stock and then to the customer. Replenishment from the RSHQ to a National Warehouse and then to the Field Stock and then to the customer. In this stream the RSHQs and National Warehouses sell printers to dealers who sell the Canon and Océ printers to their customers. The essential difference between the first three types is the responsibility of service and the ownership of service parts; in the traditional Océ model the company sells service contracts with their machines. This means the service parts are owned by Océ or the Canon Group until the part is at the user. In case of a sale to a dealer the ownership of parts and machines ends when a sale is made. OEM CSC OEM Several OEMs are delivered directly from the CSC. These OEMs often sell the printers under their own brand, as is also done by Océ for certain brands ORDER PROCESS When a request arises at a customer site from a machine delivered by Canon, mechanics from the Canon organization repair the respective machine. These mechanics have parts in their car to be able to replace broken parts immediately. When a part is used, a request to supply the car stock is sent to the next echelon upstream in the supply chain the same day. The car stocks are renewed overnight in order for the mechanics to fix the printers during the day on the way. However, it occurs that a mechanic cannot repair a machine with the parts in his car stock and thus has to return another time, causing costs for delay and downtime. The first location that is checked in this case is the Quick Response Stock. When a part is broken and the demand can be fulfilled from the Field Stock, the Field Stock orders a new part to replenish the consumed part. This can be seen as a base stock policy with a one-by-one replenishment. This order is placed at one of the National Warehouses or one of the RSHQs. These warehouses place orders at their supplier. Reordering at these locations (RSHQ, National Warehouse) is done in certain intervals (for RSHQ s once per week). This creates batched demand at the next echelon. Chapter 1. Introduction and Research Questions 4

23 When demand is not available in the Field Stock Locations, so not in the car nor in the Quick Response Stock, an emergency request is made to ship the part from the corresponding RSHQ or National Warehouse. When the RSHQ does not have it in stock either, an emergency order is placed at the CSC in Venlo. This is the last possible echelon for an emergency shipment; there are rarely shipments directly from suppliers to customers. Emergency requests cannot only be placed directly relating to a customer request, but both a National Warehouse and an RSHQ can ask for an emergency shipment at the CSC if they consider their inventory too low. Lateral transhipments, shipments between warehouses in the same echelon, occur rarely for RSHQ s. The CSC has three different ways of shipping to RSHQ s: by sea, air or express. Sea and air are the options that are used for regular transport; often the decision between sea and air depends on the RSHQ that the part will be sent to. Shipping by ocean can take several weeks, by air around one week and express shipment takes three to four days from the CSC to the RSHQ. If an emergency request arises at the RSHQ the planners at the CSC try to fulfil the demand as soon as possible using express shipment. An example of an express shipment is sending a package with a logistic service provider as FedEx INVENTORY CONTROL AT THE RSHQ S The RSHQs are the regional distribution centres of Canon, spread over the world to distribute Canon and Océ products in their region. They work as independent entities, what means that they are the owner of their own stock. Océ is their supplier and the RSHQs sell parts to the National Warehouses, QRS, Car Stocks and dealers. This in principal means that Océ does not have influence over the inventory of spare parts of Océ machines in the supply chain. RSHQs, up till now, use their own inventory control mechanisms, which can differ per RSHQ. However, in cooperation with Canon and the RSHQs, a project named GAIA is being carried out. GAIA, Global Allocation of parts Inventory Application, is the development and implementation of a software system that connects the information systems of the RSHQs to the ERP system used by Océ. Currently Océ started deploying the GAIA system. The RSHQ located in the USA is the first one that uses this system and over the course of several years the majority of the RSHQ s will use this new system. This depends on the compatibility of their systems and processes with GAIA. The main objective of GAIA is to enable Océ and the RSHQs to collaboratively manage inventory. Depending upon the settings used in GAIA it gives order proposals to the RSHQs to order items at the CSC. The RSHQ can accept these order proposals from 0% up to 120% of the order proposal. To manage inventory GAIA uses a classification which is the standard classification as used by Canon. The classification is used to have common rules for the over 8000 regular parts (see Appendix A). The parameters of this classfication can be set differently for every warehouse and for the two product groups OIP and WFPS. The goal is to eventually serve an average 95% of the demand per product group at the RSHQ from stock. This can also be referred to as a 95% aggregate fill rate per product group. The GAIA classification can be seen as a classification within a classification (Figure 1.4). The main classification is a classification based on the criteria Months of Demand (referred to as Frequency ) and Demand per year (referred to as Demand ). Ten classes are used and for every class one can set parameters in order to control the inventory. There are two different methods offered by the Chapter 1. Introduction and Research Questions 5

24 GAIA system to control inventory. The method determines the parameters that can be set. These two different methods are called in the Canon terminology order point method and fixed point method and for ease of communication these will further be referred to as the two inventory control methods. The 10 classes in the main classification each get a letter from A to J. The classes G, H, I and J use the fixed point method. All classes that have the fixed point method do not use the main classification for inventory control, but the parts in these classes fall into another classification (Figure 1.4), metaphorically speaking. For ease of communication the rest of the thesis this classification will be called the embedded classification and the first classification items fall into will be called the main classification. The embedded classification has 56 classes based on the two dimensions Demand per year and Price. Number of Months Demand Demand per 24 year Price Demand per year FIGURE 1.4 THE DIMENSIONS, CLASSES AND INVENTORY CONTROL METHODS IN GAIA For the reorder point method an order-up-to level is used per class which is expressed in a quantity of units. When the inventory position drops below this quantity new item is ordered at the next review instance (an (R,s,Q) policy with Q =1). The fixed point method uses expected demand to calculate expected inventory levels per week. This expected demand is based on average historic demand. When it detects that on hand stock will drop below a set safety stock it will propose an order date and quantity for a new batch from the CSC (an (R,s,S) policy). The expected ordering dates and quantities are then communicated to the CSC. Thus for items that are forecasted a batch size up to the order-up-to level is ordered while for the reorder point method a one-for-one replenishment policy is in place. At the moment around 88% of the items are controlled using a reorder point which represents 3% of the revenue. For more information on the inventory policies and classification in GAIA see appendix A. The inventory control method does not only determine the parameters for the inventory policy, shipping method (ocean or air) is also controlled per inventory control method. Van der Weijden (2014) developed a model to determine the optimal base-stock levels at the CSC and the RSHQs under the assumption that both Océ and the RSHQs would use a classification based on price and demand, as used at the CSC (XYZ classification). In his model a differentiation between the regular demand and the emergency demand was used. He introduced critical levels, when inventory drops under this level only emergency demands are satisfied. The outcomes of the study were that critical levels in the studied warehouses are not very effective. Furthermore, he showed that cost could be saved when different modalities of transport are considered. His model gave a lot of insight in the service supply chain of Océ; it however was not implemented. One of the main issues was that the tool of van der Weijden used a system approach at the RSHQ s which cannot be easily Chapter 1. Introduction and Research Questions 6

25 implemented in the information systems. Furthermore, the information systems are not designed for critical levels as proposed by van der Weijden CUSA At the moment, the GAIA system is already successfully implemented in the RSHQ CUSA (Canon USA). This is not a single warehouse; there are three different warehouses in different locations in the US. The main warehouse is located in Columbus, Ohio. Of the other two warehouses one is located on the west coast, in Los Angeles, California, and one on the east coast, in New Jersey. It is possible to set parameters in GAIA per location and also per product group, thus the OIP group and the WFPS group. The main warehouse has inventory for both product groups; the other two warehouses only serve customers that have OIP machines. 1.3 RELATED LITERATURE In this section the literature related to this thesis is reviewed. Firstly, the literature about the spare parts environment Océ operates in is discussed followed by literature related to ABC classification. Lastly, inventory models are discussed, initially by stating the requirements of the spare parts inventory model and then by reviewing single-echelon models SPARE PARTS ENVIRONMENT The environment of Océ can be characterized as an environment of capital goods, which is described by van Houtum & Kranenburg (2015) as an environment where machines or products are produced that are used by manufacturers to produce their end-products or that are used by service organizations to deliver their services. They require maintenance and are typically used in the primary processes of the user. The printers of Océ are an example of a capital good. A critical factor for Océ and their customers is downtime of the machines. The machines contain a high number of parts, from inexpensive screws to parts of several thousands of euros. Because of the scale of the operations and the number of different items, efficiency in the spare parts supply chain is an important factor in the company. Several models have been developed in order to try to approximate and optimize networks that distribute service parts. One way to differentiate between the models is the classification in singleand multi-item models. While in a single item model every item is optimized separately, multi-item models can take the outcome of the whole system into account. The idea behind the latter model, also called the system approach, is that customers are interested in the downtime of a machine, which is related to the availability of the parts that cause the downtime. This can be translated for the service provider into an aggregated service level of the individual parts. The constraint aggregate fill rate is currently used by Océ to determine the service level. The goal is to deliver 95% of the demand at the RSHQs from stock ABC ANALYSIS The inventory at the CSC and the RSHQs is managed using classifications. ABC classifications streamline the organization and management of inventories consisting of very large numbers of distinct SKUs. The most important reason for applying an ABC classification is that, in most practical cases, the number of different SKUs is too large to implement SKU-specific inventory control methods (Ernst & Cohen, 1990). Some companies implement SKU specific inventory control Chapter 1. Introduction and Research Questions 7

26 methods, but for many companies this is not possible due to limitations in their ERP systems or the lack of knowledge (Ernst & Cohen, 1990). On top of that, in Océ, it is used by planners to grasp the inventory levels of a part. FIGURE 1.5 A CLASSIFICATION BASED ON DEMAND AND PRICE (VAN WINGERDEN ET AL., 2015) There are four aspects that determine together the performance of an ABC classification (van Wingerden et al., 2015): the criteria, the number of classes, class sizes and the target setting. Firstly, every ABC classification uses one or more criteria to classify the SKUs. The traditional criterion for ABC classifications is annual dollar volume (Silver, et al., 1998), of which the SKUs in class A have the highest annual dollar volume and the SKUs in class C the lowest. It is easy to use, and works well for inventory management of materials that are fairly homogenous and differ from each other mainly by demand volume (Huiskonen, 2001). However, as the variety of control characteristics of SKUs increases, the one-dimensional ABC-classification is not always sufficient to segment the SKUs. Therefore, several authors suggest a classification on more dimensions (see e.g. Ramanathan (2004); Zhou & Fan (2006); Ng (2005); Hadi-Vencheh (2009)) Also Teunter et al. (2010) suggest taking more criteria into account for the classification. They research a cost criterion with a fixed service level per class and propose to use the parameters demand, holding cost, backorder cost and order quantity to classify SKUs. Besides the criteria they also go into a second aspect that determines the performance of a classification. This is the number of classes used. They recommend the use of at least six classes and provide a guideline for the cut off values between the classes. Van Wingerden et al. (2015) are the first to take four aspects into account for classification: the criteria, the number of classes, class sizes and the target setting. Their research is aimed at setting these parameters such that one comes close to the system approach. Their research follows up on the research Van Wingerden et al. (2014) who research the difference between the classification approach and the system approach when the criteria Demand and Price are used. They find that the classification approach comes close to the system approach when aggregate target service level is below 99%. Van Wingerden et al. (2015) show that for a single-echelon model the one dimensional classification based on Demand/Price yields the results closest to the system approach, followed by the two dimensional approach that uses the criteria Price and Demand. Furthermore, they show that class sizes do have a significant impact on the performance. This is tested by varying the threshold values, the values that determine the percentage of demand in every Chapter 1. Introduction and Research Questions 8

27 class. They find that the optimal values depend on the SKUs in the set. Next to that they show that the last class, with the most expensive SKUs and least demand has a big impact on performance. When this class is too big these SKUs have mandatory presence in order to reach an aggregate fill rate higher than 0%. Lastly, they find that the number of classes has an impact on the performance. For the one dimensional classification they show that four classes are enough to approximate the system approach. For a two dimensional classifications they show that a classification of two by two classes performs almost as well as three by three classes INVENTORY PROBLEM In this subsection the inventory models that can be used to model the inventory at the RSHQs as described below are discussed. First general spare parts single-echelon models that are developed for the spare parts field are discussed, followed by general models that can be applied in this particular situation. Emergency Shipments RSHQ (R,s,Q) Regular Shipment (Ocean or Air) GAIA FIGURE 1.6 CHARACTERIZATION OF THE INVENTORY TO BE MODELED The main characteristics of the inventory problem of each RSHQ are as follows: Multi-item problem One echelon, one location Regular shipments and emergency shipments from the CSC to the RSHQs Periodic review of 1 week Batching Stochastic demand Batch ordering by National Warehouses and Dealers Single item ordering from Field stock Regular orders and emergency orders from next the echelon downstream Aggregate fill-rate constraint Two possible regular transportation modes from the CSC to the RSHQ s: o Sea shipments o Air shipments Chapter 1. Introduction and Research Questions 9

28 ABC Classification GENERAL SPARE PARTS MODELS Feeney and Sherbrooke (1966) developed a basic spare parts inventory model. They discussed the (S, S 1) policy, a reorder level with a batch size of one (Q = 1). They assumed compound Poisson demand and they modelled backordering and the lost sales case. Van Houtum & Kranenburg (2015) explain the multi-item model of Feeney and Sherbrooke (1966) and provide several optimization methods. The RSHQs have several characteristics that set it apart from this inventory model. First of all, batch ordering is used for 38% of the SKUs at CUSA. Secondly, the RSHQs work with a review period of one week. Thirdly, demand that is that is not satisfied by stock is sent via emergency shipment from the CSC. Lastly, demand is not necessarily approximated by a Poisson distribution, because of the mix of orders from the Field Stock and batched orders from the National Warehouses and Dealers. Models that incorporate one or several of these characteristics are discussed here. First a general spare parts model that incorporates batching will be discussed and then a general spare parts model using emergency shipments will be discussed. In most models in spare parts literature a one-for-one replenishment is assumed. The reason for this is that spare parts are generally slow moving and often demanded one by one (Wong, et al., 2007). However, upstream in the supply chain it may be more reasonable to employ batching. Parts move faster here because of accumulation of internal and external demand. The higher demand might lead to a non-negligible cost decrease when batching (Topan, et al., 2010). For the expensive SKUs the EOQ, Economic Order Quantity, goes to one, however for cheaper units batching might be more economical. Basten & van Houtum (2014) mention that, when the lead time is assumed to be deterministic, the basic single-echelon model can be adapted following Proposition 5.1 in Axsäter (2006) for using batching. Van Houtum & Kranenburg (2015) provide a basic model for emergency shipments under Poisson demand. However, they note that for a model with emergency shipments, it is less easy to incorporate batching. Emergency shipments lead to lost sales for the inventory of spare parts and, generally spoken, lost sales models are much harder to analyse than backordering models (van Houtum & Kranenburg, 2015) GENERAL LOST-SALES MODELS Bijvank and Vis (2011) provide an overview of lost sales models. Only two of the models reviewed by Bijvank and Vis (2011) are (R,s,Q) lost-sales models where a target fill rate has to be satisfied. The first one is from Johansen & Hill (2000) who assume that only one order is outstanding, which limits its applicability. The second one, from Bijvank et al. (2010), is a working paper and not available yet. Van Donselaar & Broekmeulen (2013) develop an approximation for determining the safety stocks in a lost sales model with an (R,s,nQ) policy. Due to the generality of the approximation it might also be applicable in the Océ setting of the RSHQs. They mention that the approximation is particularly suited for (medium to) fast moving spare parts. They however do not provide a cost calculation. Chapter 1. Introduction and Research Questions 10

29 Tagaras & Vlachos (2001) describe a periodic review inventory system with emergency shipments. They assume an emergency shipment of a certain batch size at the end of the cycle when a stock-out is likely. This might be applicable to the Océ network; however, the model is only based on costs, not fill-rate and next to that calculations are extensive. (R,s,Q) models are closely related to (R,s,S) models, they both take an order cost and periodic review into account (Bijvank & Vis, 2011). Bijvank & Vis (2012) provide an approximation in order to calculate the order-up-to level in an (R,s,S) model given a target service level. This approximation could serve for approximation of the order-up-to level in an (R,s,Q) model for a given fill rate BACKORDERING Although emergency orders are lost to the CSC when not satisfied immediately from stock, there are two reasons to look into backorder models as well. First of all, it is reasonable to approximate lostsales models with backorder models if the customer service level is high (Silver & Peterson, 1985). Secondly, inventory models that include lost sales are more difficult to analyse than for comparable backorder models (van Donselaar & Broekmeulen, 2013). De Kok (1991) derived an approximation for the fill rate in a (R,s,nQ) system with backordering. It assumes that demand is a continuous stochastic variable and that always an order of size Q is placed. Van Donselaar & Broekmeulen, (2011) generalized the formula for a discrete distribution and the order is not restricted to only Q but could also be a multiple of Q. Axsäter (2015) describes a model with demand following a compound Poisson distribution, a reorder level and batching. He describes one model for calculating the fill-rate and one model for optimizing both the batch size and reorder level for a backordering and emergency shipment cost situation. The properties of the models reviewed above are summarized in Table 1. TABLE 1 REVIEWED MODELS IN LITERATURE Model RSHQ Basten & van Houtum (2014) Tagaras & Vlachos (2001) Johansen & Hill (2000) Lost Sales Review Batching Demand Cost/ (CSC/RSHQ) distribution service Yes Periodic Yes General C/S No Continuous Optional Poisson C/S Yes Periodic No General C Yes Periodic Yes Normal Distributio n C Yes Periodic Yes General S Multiitem Multiitem Multiitem Singleitem Singleitem van Donselaar & Broekmeulen (2013) Singleitem Bijvank & Vis (2012) Singleitem Yes Periodic Yes General S van Houtum & Multi Yes Continuous No Poisson C/S Kranenburg (2015) item Axsäter (2015) Single- No Review Yes Compound C/S item Poisson van Donselaar & Single- No Review Yes General S Chapter 1. Introduction and Research Questions 11

30 Broekmeulen (2011) item FITTING MODELS From the reviewed models none has been found that has an exact solution to the problem presented. However, several models might be applicable to the situation at the RSHQ. The model of Basten & van Houtum uses batching which might be applicable to the fast moving SKUs at the RSHQ if the demand pattern can be estimated by a Poisson distribution. For the slow moving SKUs, the model of Kranenburg & van Houtum, that uses emergency shipments, might well be applicable. Furthermore, the model of van Donselaar & Broekmeulen (2013) seems a promising estimation for fast moving SKUs. Lastly the model of Äxsater (2015) seems to be applicable with the generality of the demand distribution. 1.4 PROBLEM FORMULATION In this section first a further elaboration on the problem is given followed by the problem statement that is used throughout the master s thesis. Using the problem statement, the research questions and project objective of this thesis are formulated INVENTORY CONTROL After the integration of the supply chain with Canon, Océ lost control of the inventory of its spare parts downstream. The RSHQs work autonomously and thus decide on their own inventory control policies. This means that every entity in the supply chain optimizes its spare parts stock. In order to regain control over the inventories downstream the project GAIA has started. GAIA should give Océ more control over and insight in the inventories downstream. GAIA uses a classification used by Canon, with 14 classes, out of which 4 are dedicated to new products (See Section 3.4 and Appendix A). The classification and inventory methods are new to Océ. Currently the parameters are quickly set in a way that gives approximately the same orders at the CSC as historically. However, the system also offers an opportunity for more efficient inventory management. The GAIA system uses the classification method also used by the Canon Group. The classification causes Océ to ask themselves how GAIA can be used to lower cost and raise service in the supply chain and what the effect is of the classification used. GAIA does not only provide the opportunity to influence the order policies at the RSHQs, it also provides the opportunity to influence the shipment method. The shipment method (ocean or air) is currently set by default and decided by the RSHQ. The cost in the supply chain might go down when shipment methods are more properly decided. GAIA also provides advance demand information from the RSHQ. Up until now this was not provided. Furthermore, GAIA has the possibility to differentiate per product group. Currently there is a differentiation between two product groups, WFPS and OIP. Due to the difference of prices in machines probably more product groups will be defined in the near future. Océ is wondering if using different settings per product group would give a lot of difference in terms of service level. Océ is thus concerned about the effect of the classification of Canon on the inventory performance. It wonders what the optimal parameter settings that would be compatible with the GAIA system would look like and what the difference would be with an optimal or near optimal approach using Chapter 1. Introduction and Research Questions 12

31 classification or the system approach. GAIA also has the possibility to manage the inventory levels per part per location, enabling the micro management of the parts and the so called system approach. However, they consider it difficult to communicate and time consuming to maintain. van Wingerden et al. (2015) already did extensive research on the impact of the aspects of ABC classification on the inventory holding cost. The model that was used by them did not include batching or emergency shipments. An extension to literature that has a practical application on Océ is the design of an ABC classification that minimizes inventory holding cost, fixed order cost and emergency shipment cost under an objective fill-rate RESEARCH QUESTION In this section the research question that is used during this thesis is stated. In this thesis we investigate which design of an ABC classification would minimize total cost when batching is used under an aggregate fill rate constraint and using emergency shipments. This can be compared to the performance of GAIA. Using the insights in classifications, Océ and other companies will be able to manage the inventory levels of their spare parts effectively. This leads to the main research question in this thesis: What ABC classification minimizes the sum of inventory holding cost, emergency shipment cost and order cost while ensuring a target fill rate and what ABC classification would fit for an RSHQ in the network of Océ? PROJECT OBJECTIVE The objective of the project is twofold. On one hand the project objective is to research the impact of classification and design of classifications for a model that includes batching and emergency shipment cost. On the other hand, the objective is to build a tool that is compatible with GAIA and can be used in order to set the inventory control parameters of spare parts at the RSHQs. This tool should set the parameters of the SKUs such that network costs are minimized while maintaining the target customer service levels. In other words: Research the design of ABC classification in order to get the lowest annual cost while ensuring a target aggregate fill-rate for a single-echelon model that includes batching, compare different designs and implement the chosen design in a tool that is compatible with GAIA SCOPE The scope of this master s thesis is described through two perspectives. Firstly, the scope of the network is described and secondly the SKUs considered in the thesis are described NETWORK The part of the network considered is the second echelon of the supply chain of Océ, the RSHQs. Océ has the possibility to gain insight in the demand, inventories and control policies of the RSHQs. On top of that the CSC can, in collaboration with the respective RSHQ, set the inventory policy of the SKUs through the setting of parameters in GAIA. It is assumed in this thesis that, if demonstrated that a certain inventory policy will save costs, the RSHQs will collaborate in setting the inventory policies as Océ recommends. This assumption holds true at the moment; GAIA is already in use at the RSHQ in the USA at the moment of writing and CUSA is well willing to collaborate in setting the parameters Chapter 1. Introduction and Research Questions 13

32 of GAIA. Since CUSA is the first and only RSHQ at the moment with respect to GAIA the scope is be limited to CUSA. However, the model and tool are built in a way that is applicable to other RSHQs. FIGURE 1.7 NETWORK SCOPE OF THE ASSIGNMENT In this thesis the dealers, National Warehouses and Field Stock are seen as the customers of an RSHQ. These customers can order a replenishment order or an emergency order. In this thesis no difference in service level is assumed to be given to the different customers and orders. The CSC in Venlo will be left out of scope and it will be assumed that the CSC can always deliver in the given lead time per transportation mode. The three transportation modes considered are air shipment or ocean shipment for regular shipment and express shipment for emergency shipment. It is assumed that all demand that cannot be fulfilled from stock is fulfilled by an emergency shipment from the CSC. Concluding, the scope of the network will include the Océ products at CUSA. The dealers, National Warehouses and the Field Stock that demand these SKUs will be seen as the customers and an aggregate fill rate at the RSHQ will have to be met ITEMS Several different classifications in SKUs are made to make the inventory control in Océ simpler and more efficient. A machine that goes into production consists of a large amount of different parts, of which only a fraction is categorized as spare part. From the parts categorized as spare parts the criticality is determined, a critical part has to be replaced because it will cause machine downtime or danger when not repaired immediately, a non-critical part does not and is not held on stock when the machine is introduced. In the thesis non-critical parts will not be considered since they do not need to FIGURE 1.8 PARTS OVERVIEW Chapter 1. Introduction and Research Questions 14

33 have the same service level as critical parts. When critical parts are introduced the demand rate and number of sales is estimated by the service department of Océ. This is used for setting a reorder point for the SKUs. An engineer regularly checks if the demand that was expected really occurs or if it is over- or underestimated. One year after the start of production the SKU is seen as predictable enough to be coordinated by software and is added to the regular parts. Machines usually have to be served seven and sometimes nine years after the last machine has been produced. Two and a half years before the last date that the machine has to be served, the part is moved to the phase out group. A phase-out can happen in multiple ways, for example a last buy can occur if the production is stopped, or the part is still being ordered with the objective to keep zero spare parts in the end. Parts that are phasing in- or phasing-out need different stock control and are left out of scope. 1.5 SCIENTIFIC CONTRIBUTION The scientific contribution of this report is twofold. First of all this report continues the research of Van Wingerden (2015) and checks if the results from his dataset are also applicable to other datasets. Secondly the model used in this thesis takes more variables into account and therefore the results of this research are applicable to more cases. First of all, it takes general demand into account instead of only Poisson demand. Taking general demand into account gives a wider range of demand distributions, making the results more generally applicable. Next to that batching is taken into account in the inventory model, which gives the opportunity to research if other classifications which include batching contribute to a better model. Lastly, the main difference is that a cost for not delivering immediately, emergency shipment cost, is taken into account. This is not yet studied in relation to the performance of the design of an ABC classification in a multi-item setting and is treated extensively in this thesis. 1.6 OUTLINE OF THE REPORT The remainder of the report is structured as follows. In chapter 2 the inventory model and the decisions made for the model are discussed, followed by the data that is used during the thesis. In chapter 3 the design of a general classification is discussed, followed by the results and discussion of results of general classifications. In chapter 4 the application at Océ is discussed, starting with the practical complexities of applying the model at Océ, followed by the theoretical gains achievable when implementing the system approach. Then the application of a general classification at Océ is discussed and finally in Chapter 5 the classification used by Canon is modelled and compared. Chapter 6 discusses the implementation of the tool at Océ and finally in chapter 7 the conclusions and recommendations for Océ and future scientific research is discussed. Chapter 1. Introduction and Research Questions 15

34 2 GRAND MODEL In this chapter the model and the data used throughout the thesis are discussed. The first section explains the assumptions and design choices, followed by the mathematical description of the model. Lastly the cost and lead-time data used in this thesis is presented. 2.1 ASSUMPTIONS AND DESIGN CHOICES INVENTORY MODEL The inventory model that will be used for the ABC classification is important in two ways. Firstly, in this thesis the research of van Wingerden et al. (2015) is generalized on two aspects. The batch size is not limited to one and demand distribution is generalized. Secondly, since this thesis is performed at Océ, the inventory model should be applicable at Océ. In order to model the situation at an RSHQ of Océ several assumptions and design choices have to be made MULTI-LOCATION The RSHQ CUSA consists of three different warehouses. In accordance with the practice at Océ it is assumed that no lateral transhipments take place between the three warehouses. However, the warehouses cannot be optimized separately because the aggregate fill rate over the SKUs in these warehouses needs to be at least higher than 95%. This could either be modelled as separate warehouses with each their individual classification or one classification for all the warehouses. During this thesis the latter is used. It is assumed that these separate warehouses can be seen as one since no lateral transhipments occur and since Océ measures the fill rate for the RSHQ as a whole. However, it is necessary to distinguish the same SKUs at different warehouses; in order to do this an extra index is used in the model. This makes it possible to optimize as if we have one inventory location with one aggregate fill rate constraint PRODUCT GROUPS Currently there are two product groups, the WFPS product group and the OIP product group. In the data set given by Océ, 1716 SKUs belong to the WFPS product group and 2430 SKUs belong to the OIP product group. During this thesis these product groups will have a target aggregate fill-rate per product group. The reason is that these product groups have different characteristics (Table 2) and have no commonality; every SKU belongs either to one product group or the other. Besides that, currently the RSHQ CUSA measures the fill-rate per product group. TABLE 2 CHARACTERISTICS PRODUCT GROUPS OIP WFPS Demand Price Demand Price Min 0.02 $ $ 0.01 Average 1.43 $ $ Max $ 11, $ 8, Chapter 2. Grand Model 16

35 2.1.3 BATCHING Océ uses batching for their warehouses in the second echelon in order to decrease fixed ordering cost. This makes variable relevant and it thus should be included in the grand model. The relevant cost in order to determine the batch size is the fixed order cost per batch. An often used method to calculate the batch size is the EOQ formula, which assumes deterministic demand and weighs the order costs against the inventory holding cost. Axsäter (2015) describes a method to optimize the reorder level and batch size simultaneously. He uses a search based on convexity to find optimal values of the reorder level and the batch size. The EOQ is an approximation for the right batch size, but Axsäter (2015) proves that even quite large deviations from the optimal order quantity will give very limited cost increase (Axsäter, 1996). In order to save computation time for the model, the EOQ will be used to determine the batch size. The largest batch size will be limited to the amount of 6 months of demand. This will be done to avoid very large batch sizes. Very large batch sizes in an uncertain environment may contribute to obsoleteness of SKUs when the demand of SKUs changes. For the mathematical expression see Appendix C TRANSPORTATION MODES At the RSHQ there are two methods for shipping regular SKUs, shipment by air or ocean. On top of that there is an emergency shipment method. In this thesis air and ocean are the only modes considered for regular supply and every SKU has one regular transportation mode, as is the practice at Océ. Literature provides extensive research on the topic of optimizing shipment in combination with inventory (e.g. see (Minner, 2003)). These models however introduce a lot of complexity in the model. Van der Weijden (2014) observes that the transportation mode has a significant impact on the total cost for an RSHQ. This is caused by the cost for the inventory that is in transit to the RSHQ. In order to construct a general model and to keep the model computationally efficient, lead-times are decided outside the optimization procedure of the core model. A rule of thumb is used based on the observations of van der Weijden (2014). The rule of thumb is introduced as following: when the expected inventory holding cost during the extra lead time by ocean exceeds the extra cost to ship by air the SKU is set to air shipment. For the mathematical expression see Appendix D. This rule is referred to in this thesis as the transportation mode rule. It is assumed that the lead-times are constant. In reality they may vary several days due to uncertainty in the shipment times and handling times at the ports; however overall these differences are quite small EMERGENCY SHIPMENTS As described in Section 1, emergency shipments are used in order to fulfil customer demands that cannot be fulfilled directly from stock. Emergency shipment costs are a significant cost in the network of Océ and will thus be accounted for in the model. Chapter 2. Grand Model 17

36 Emergency orders influence the customer side and the supply side at a warehouse. At the customer side of an RSHQ there are regular and emergency orders. Océ does currently not use a different fillrate for emergency shipments at the RSHQs and regular orders. There is also no trustworthy data available in order to estimate the percentage of the demand that is emergency orders. Lastly, RSHQs order emergency shipments at the CSC for both regular and emergency orders. Because of the reasons mentioned above, it is assumed that for both streams emergency shipments are ordered when an item is out of stock. Thus in the model both streams are seen as if they were of equal importance for the RSHQ and no difference is made in fill rate for the emergency orders or the regular orders. If there is a stock out at the RSHQ it is assumed that an emergency order is placed at the CSC, independent of whether the stock out is for an emergency order or for a regular order. On the supply side it is possible to estimate the amount of emergency shipments via the fill rate at the RSHQ. The part that cannot be fulfilled directly from stock can be seen as the part of the stream that has to be supplied from the CSC in Venlo. As described in the literature review in Section 1 emergency shipments lead to lost-sales, which influence the fill rate of the system. However, in order to use a model that incorporates batching, the choice is made to assume a backordering policy in the model. This is done because there are no models that include both lostsales and batching. On top of that the aggregate fill rate is high and thus the emergency shipments will be a small fraction, leading to a small deviation from the real fill-rate. The estimation will be slightly conservative since a similar fill-rate in the backorder policy leads to a higher reorder level than in the lost-sales case (van Donselaar & Broekmeulen, 2013). However a backorder model is used, which relates to penalty costs per backorder, throughout the thesis the term emergency shipment costs will be used, because this is what the penalty costs represent for Océ REVIEW PERIOD The review period at all the RSHQs is currently one week. This is 17% or 50% of the lead-time (depending on the transportation mode). Assuming continuous review while a review period is in place will have a negative influence on the safety stock. Taking a review period into account for a continuous model is possible, for example by adding half the review period to the real lead-time as done by van der Weijden (2014). A continuous review model could thus approximate the situation; however, a periodic review model is preferred when possible DEMAND In order to determine the demand distributions, historic demand data of 104 weeks (2 years) is gathered to analyse the demand distribution. Only SKUs that have demand in both two years are selected in order to exclude SKUs with a change in part number. Besides that, only parts that have a part number in GAIA are selected in order to exclude dangerous goods and Canon parts. Firstly, the demand rates are checked (Appendix B, Figure B.1). As expected, the demand rates of the SKUs are hugely different, ranging from a demand of 1300 per week to 0.03 per week. For evaluation purposes SKUs are placed in three classes: fast-, medium- and slow- movers. The threshold values are set on 5% and 40% based on inspection of the cumulative demand graphs (Appendix B, Figure B.1, Figure B.2). Chapter 2. Grand Model 18

37 TABLE 3 DATA CHARACTERISTICS Fast (5%) Medium (35%) Slow (60%) Demand per week Price($) Demand per week Price($) Demand per week Price($) Min Average Max These three different datasets have different characteristics as can be seen in Table 3. It is noticeable the average price of fast movers is far lower than that of slow movers. However, there are also expensive SKUs in the dataset of the fast movers. One can see that the tail of the demand is quite long thus implying more variance than the Poisson distribution (Figure 2.1, 2.2, 2.3). On top of that there are some SKUs with many weeks without demand and some weeks with a big demand, which is caused by batching downstream. In order to forecast the demand well, a distribution has to be designated to the parts. There are several ways to do this. Mostly demand is simplified to a parametric demand distribution e.g. normal or Poisson (Willemain, et al., 2004). Advantages of parametric distribution are the convenience, efficiency and that they are easier to interpret. Another way is to construct a non-parametric distribution or empirical distribution. The advantages of non-parametric distributions are that no suitable parametric model has to be found, which is usually hard, they are less sensitive to outliers and parameters cannot be specified wrongly (Castro, 2013). In this section firstly parametric distributions are tested for their significance and it is concluded with the relevance of using a non-parametric distribution FIGURE 2.1 HISTOGRAM OF DEMAND PER WEEK OF A FAST-MOVER FIGURE 2.2 HISTOGRAM OF DEMAND PER WEEK OF A MEDIUM-MOVER FIGURE 2.3 HISTOGRAM OF DEMAND PER WEEK OF A SLOW-MOVER Based on Axsäter (2015) four demand distributions have been selected that might fit the demand. These are the Poisson and compound Poisson as discrete distributions. Poisson is an often used distribution for service parts and might well be applicable on slow-moving parts. A compound Poisson distribution is selected because it can take the effect of batching downstream into account. To simplify calculations, the orders for the compound Poisson distribution are assumed to follow a logarithmic distribution. With this assumption the compound Poisson distribution can be simplified Chapter 2. Grand Model 19

38 to a binomial distribution (Axsäter, 2015). This compound Poisson distribution requires the coefficient of variation to be larger than 1. As continuous distributions the normal distribution and the gamma distribution are chosen. These distributions might be more applicable on fast-movers. The central limit theorem (CLT) states that given certain conditions the mean of sufficiently large number of counts of a distribution will be approximately normally distributed. The gamma distribution is an alternative to the normal distribution that is always non-negative. TABLE 4 PERCENTAGE OF CHI-SQUARE TEST >0.05 FOR 30 SKUS PER CLASS Poisson Negative Binomial Gamma Normal Slow 90% 31% 66% 0% Medium 17% 59% 10% 0% Fast 7% 0% 41% 17% The fit is tested using a chi-square distribution for 30 SKUs per class. For every distribution the respective mean and standard deviation is used to calculate the parameters of the respective distribution. The results per SKU can be found in Appendix E. Table 4 shows that per class a different distribution constitutes the best fit. For most slow movers the hypothesis that the demand follows a Poisson process cannot be rejected. Poisson is usually a good estimation for a distribution for slowmoving SKUs with much variance. For medium movers the negative Binomial distribution is a better estimation, but one can already see that not all SKUs can be assumed to be negative binomial distributed. A closer look in the data shows that many medium movers do not have much demand occasions but orders often arrive in batches, which is reflected by the negative binomial distribution. For fast-movers the gamma distribution appears to be the best fit; however, 59% of the SKUs in this class cannot be reflected by the Gamma distribution Histogram Frequency Bin FIGURE 2.4 HISTOGRAM OF THE DEMAND PART IN COLUMBUS Thus for many parts, especially medium and fast movers, no suitable distribution can be found. An example of a part where it is difficult to display a distribution can be found in Figure 2.4. This figure Chapter 2. Grand Model 20

39 shows that the demand is intermittent, a lot of weeks without demand. However, when demand occurs it can range from 1 to 400. This highly fluctuating demand pattern is not possible to catch in standard distributions. That is the main reason to look into non-parametric distributions. The advantages of non-parametric distributions are that no suitable parametric model has to be found, which is hard for the intermittent and batched demand that many SKUs in the dataset of Océ have. Thus the empirical distribution is used throughout this thesis. Twelve months of demand are available for estimating the distribution. The demand in the dataset provided is expressed in daily demand. For estimation of the fill-rate and costs the distribution of the demand during lead time should be specified. A way to estimate the distribution during the lead time is dividing the demand of the year into pieces of the length of the lead time. This would however result in a small sample size (especially when an SKU is shipped per ocean) and a loss of information (Strijbosch & Heuts, 1994). Strijbosch & Heuts (1994) research three different methods to construct the distribution for lead time demand. The first method is that of Lau & Zhao (1989) that construct all possible combinations of demand during lead-time, referred to in this thesis as the combinations method. A second method is contruction of the distribution of lead time demand using simulation and the third method is a parametric estimate. They show that by using the non parametric distribution, as proposed by Lau & Zhao (1989), inventory cost are minimal. However, they also acknowledge that the computation times can easily get big. An estimation of the time it would take to build a lead time distribution for every SKU in the dataset of Océ is 17 hours. This is mainly caused by the 7% of the SKUs that have many different demand quantities per week. A different approach for these SKUs that could be used is simulation. Willemain et al. (2004) use simulation for constructing lead-time demand for SKUs with intermittent demand. The approach they use is called bootstrapping. A difference is between Strijbosch & Heuts (1998) and Willemain et al. is that the latter use jittering for the demand, which means that not only values from historical demand are chosen but also a normal distribution around these demands (for more information see Appendix F). Furthermore they introduce the concept of a possible autocorrelation, which means that one order can lead to more orders in the next periods (or vice-versa). Willemain et al. (2014) test their distribution on several datasets and compare it to Croston s method and Exponential Smoothing, other widely used concepts for constructing non-parametric distributions. They find that their method outperforms the other two methods. One objection for using the model could be that the auto-correlation that is introduced in the model of Willemain et al. (2014) can just be seen in a few SKUs in the dataset of Océ. The model does however not demand autocorrelation, the autocorrelation specified depends on the parameters that are used in the Markov chain (Appendix F). In order to model demand a combination of the method of Strijbosch & Heuts (1994) and the method of Willemain et al. (2014) is used. This combination is done for several reasons. The method of Strijbosch & Heuts costs a lot of time for fast-movers, but is really fast for slow movers and takes every combination into account thus no simulation is needed. On top of that the jittering used in Willemain et al. (2014) is not necessary for slow movers, since these demands are demand quantities of one or two. The jittering algorithm bounds the demand to zero and replaces negative demands by the mean which might result in a higher average for slow-movers. For the fast(er) Chapter 2. Grand Model 21

40 movers Willemain et al. (2014) is far more efficient and the jittering on bigger demand quantities results in a smoother distribution, which is closer to reality. As can be seen in Figure 2.6 after simulations the deviation in expected demand is less than 0.2%. Thus, this amount of simulation will be taken for bootstrapping. FIGURE 2.5 SIMULATED MEAN AS FRACTION OF REAL MEAN FIGURE 2.6 PDF OF THE DEMAND DURING LEAD TIME (FAST MOVER) FIGURE 2.7 PDF OF THE LEAD TIME (MEDIUM MOVER) FIGURE 2.8 PDF OF THE LEAD TIME (SLOW MOVER) INVENTORY MODEL As explained in the section above several characteristics are important to include in the inventory model that will be used. The relevant models discussed in Section 1, Table 1 can be found in Table 5. As can be seen none of the models found in literature have all characteristics as described except for the model of van Donselaar & Broekmeulen. Their model however only applies to fast-movers and requires a lot of computations, which makes it unsuitable. As mentioned batching is an important characteristic of the RSHQ. This leaves us with two models, the first model of van Houtum & Kranenburg (2015) and the model of Axsäter (2015). Because the latter model, with a little adaption, can take general distribution and periodic review into account, this model is chosen as inventory model in this thesis. Chapter 2. Grand Model 22

41 TABLE 5 OVERVIEW OF RELEVANT MODELS FROM LITERATURE Model Emergency shipments Review Batching (CSC/RSHQ) Arrival distribution Cost/ service RSHQ Yes Periodic Yes General C/S van Houtum & No Continuous Yes Poisson C/S Kranenburg(2015) model 1 van Donselaar & Yes Periodic Yes General S Broekmeulen (2013) van Houtum & Yes Continuous No Poisson C/S Kranenburg(2015) model 2 Axsäter (2015) No Periodic Yes General C/S 2.2 MATHEMATICAL MODEL We consider multiple warehouses in which multiple SKUs are kept on stock. Whenever an SKU is requested, it is immediately delivered from stock on hand. Demand is backordered if there is no stock on hand causing a emergency shipment cost. The set of SKUs is denoted by I and the set of warehouses is denoted by J; the number of SKUs is I ( N {1,2, }); the number of warehouses is J ( N {1,2, }). For notational convenience, the SKUs are numbered 1,, I and the warehouses are numbered 1,.., J. For each SKU i at warehouse j the stock is controlled by a policy with a reorder level s i,j, a batch size Q i,j and review period R in years. The average demand per year is μ i,j and all SKUs follow a non-parametric distribution. The total demand per year for all SKUs is denoted by Μ = i I j J μ ii. The replenishment lead-time of SKU i at warehouse j is L i,j (T i,j ), where T i,j is the transportation mode. The replenishment lead-time is assumed to be constant and a multiple of R. There are four types of costs that are considered in the model. First of all, one has cost for transportation. The cost c t i,j (T i,j ) is applied per unit every time an SKU i is shipped to warehouse j and is dependent on the transportation mode T i,j. The average annual transportation cost for an SKU at a warehouse equals μ i,j c t i,j (T i,j ). Secondly one has costs for holding inventory. The inventory holding costs are c h i per unit per year. This is calculated by multiplying of the holding rate c h and the purchase price of an SKU c a i. The holding costs are calculated over expected net stock II + ii for SKU i at the warehouse j and the average pipeline stock. The pipeline stock is the average demand during lead-time corrected with the fill-rate, β i,j s i,j, Q i,j, T i,j μ i,j L i,j (T i,j ). The correction of the fill-rate is used because the units are flown by emergency shipment in a short period of time, which means they are not in transit for a period of a lead time. Thirdly one has emergency shipment costs. Each time an order cannot be fulfilled from stock a cost of c ee ii is applied. The fill rate for SKU i at warehouse j in steady state is denoted by β i,j s i,j, Q i,j, T i,j. The quantity that has to be shipped depends on the fraction that cannot be Chapter 2. Grand Model 23

42 delivered directly from stock (1 β i,j s i,j, Q i,j, T i,j ). The average emergency shipment costs per SKU per year are equal to μ i,j 1 β i,j s i,j, Q i,j, T i,j c ii ee. Lastly one has fixed order cost every time an order is placed. c k is used to denote the fixed order cost per order. The fixed order costs per year for SKU i at warehouse j are equal to μ i,j c k. Q i,j Then the total average costs per year per SKU i at warehouse j are equal to C i,j s i,j, Q i,j, T i,j = (2.1) μ i,j c t i,j T i,j + c h i,j II + ii + β i,j s, Q i,j, T i,j μ i,j L i,j T i,j +μ i,j (1 β i,j s, Q i,j, T i,j c ii ee + μ i,j Q i,j c k And the total average costs over all SKUs and warehouses are equal to: C(s, Q, T) = i I C i,j s i,j, Q i,j, T i,j j J where s = s 1,1,, s I, J, Q = Q 1,1,, Q I, J, T = T 1,1,, T I, J. As described in the section above, Q and T are calculated outside the core model following the procedure as described in Appendix C and Appendix D. This leaves us with a simplified average cost formula to use in the optimization procedure: C i,j s i,j = c h i,j II + ii + β i,j s i,j μ i,j L i,j + μ i,j 1 β i,j s i,j c ee (2.2) and the total average costs are equal to C(s) = i I j J C i,j s i,j. The target aggregate fill is given by β ooo. The objective is to minimize the average total cost subject to an aggregate fill rate constraint. In mathematical terms the optimization problem P is as follows: (P) Min C(s) subject to β(s) β ooo i I, j J, Where β(s) = i I β i,j s i,j μ ii j J. The fill rate β M i,j s i,j and expected inventory level II + ii are calculated using the model of Axsäter (2015). See Appendix G for the calculations. Although assumptions are made on the distribution of demand and inventory control policy this approach can be easily applied with other demand distributions and inventory control policies. Chapter 2. Grand Model 24

43 Concluding, from the three parameters in the grand model, the batch quantity, the transportation mode and the reorder levels, two of those are set by applying a rule. The reorder level is set in the core model. The outcome of system are the aggregate fill-rate of a product group and the corresponding costs: the transportation costs, the fixed order cost, the inventory holding cost and the emergency shipment cost. FIGURE 2.9 GRAPHIC REPRESENTATION OF THE GRGRAND MODEL 2.3 COSTS AND LEAD-TIMES In this chapter the derivation of the costs, lead-times and weights and volumes are discussed COST FACTORS Three different kind of relevant costs can be distinguished that are relevant for the model. These are the inventory holding cost, the transportation cost and the fixed order cost. In a recent thesis of van der Weijden (2014) the inventory holding and transportation cost have been researched. The results of this research will be used to estimate costs in this thesis. Three relevant cost factors are discussed first: Inventory holding cost Transportation cost Emergency shipment Fixed order cost INVENTORY HOLDING COST Holding cost is money in order to keep the spare parts in the supply chain. Notice that this is counted over the pipeline stock and the SKUs in a warehouse. Factors that influence holding cost are space, equipment, labour, insurance, interest and other expenses. Another factor is that the SKUs that are stored may become obsolete. This last factor is especially relevant in the field of spare parts, since demand of most parts is unpredictable and machines have an end of service date, after which a machine is not serviced anymore. Chapter 2. Grand Model 25

44 For Océ two factors are taken in order to determine the inventory holding cost. The first factor is the cost of capital. There are two sources of capital for a company in general, equity and debt. For a listed company the cost of capital for equity can be calculated by determining the dividend per share. Océ is however not listed anymore thus this makes estimation difficult. The cost of debt is the interest paid for the debt. The cost of capital can then be determined by the weighted average cost of capital (WACC). The second factor that is taken into account is the risk of obsolescence. The risk of obsolescence depends on the months until the end of service. Van der Weijden (2014) calculated both factors and determined a cost of capital of 7% and a cost of obsoleteness of 13%. Since the cost of Océ did not change significantly over this time this cost of capital, 20%, is taken for this thesis as well. This cost of capital is multiplied by the expected value of the inventory. The value of the inventory is calculated by summing the inventory value of the items. The inventory value of the items based on the price that a region pays when buying a part from the CSC TRANSPORTATION COST Transportation costs in the organization of Océ are quite complex and thus difficult to estimate. This is due to several causes. The main reason is that Océ is part of a bigger organization, the Canon group, which uses FOB/FCA in order to allocate cost to the separate entities in the organization. FOB/FCA means that the supplier within the organization is responsible and cost accountable until the (air)port and the internal customer pays for the shipment from the (air)port until its destination (Figure 2.10). As a result, Océ only has insight in the part of the trip until the (air)port. A second reason is that the Canon group tries to consolidate shipments from its organizations in order to gain purchasing power and economies of scale. Thirdly prices can fluctuate heavily, especially for air transportation. The same transportation costs are used in this thesis as van der Weijden (2014) since cost did not change significantly according to a specialist at Océ. WH Set status shipment -> Goods in Transit Post Goods Issue Customer WH Set status shipment -> Goods in Transit Post Goods Issue Customer Leg 1 Port of departu re Leg 2 & 3 Port of arrival FIGURE 2.10 FOB/FCA METHOD, OCÉ IS RESPONSIBLE FOR LEG 1, THE RSHQ FOR LEG 2&3 The method used by van der Weijden (2014) to estimate the cost for shipment is to use the average utilization of a container, which is around 35%, and the costs for a container. These numbers are Chapter 2. Grand Model 26

45 used to calculate the cost per cubic meter. The results are shown in Table 6. For the air shipments a cost of 4.50 per kilo is estimated. TABLE 6 AVERAGE COST FOR OCEAN TRANPORT PER M3 PER REGION Shipment to Average cost per m3 CUSA 137 CCN 69 CSPL 69 CMJ 137 C Oceania 163 CKBS 163 For emergency shipments, express shipments are used which take 3-4 days from door-to-door. An employee in the logistics department estimates that the express shipment costs are on average 25 per shipment WEIGHT AND VOLUME In order to calculate the cost of transportation by air or by ocean the weight and volumes of the SKUs should be known. This data is retrieved from the SAP database of Océ. In order to make the data consistent the volumes and weights have translated into one unit of measurement. This is due to several different units of measurements that are used to describe the dimensions of an SKU. On top of that, there is quite some data missing, especially for the criterion volume. In order to be able to do calculations with the data, the missing data is filled with the mean of the dimension FIXED ORDER COST Fixed order costs are the cost that occur per order line and do not change with the quantity of the SKU per order line. The costs can be separated into several parts. First of all, an order line has to be accepted by the planners, secondly the order has to be picked and lastly it has to be packed in the sending warehouse. Then in the receiving warehouse the items have to be received and put into the warehouse again. An expert in SCM Service Parts estimates that the fixed order costs are 5 per order line LEAD-TIMES In this thesis the scope is the RSHQ in the USA, however data for all RSHQs will be presented since the tool that should be developed has to be used for more RSHQs. The lead-times are based on the thesis of van der Weijden (2014) and expert opinion on these lead-times. The estimates of the lead-times are presented below (Table 7). For both air and ocean shipments transportation times are estimated. The lead-time is estimated by adding the expected days for picking & packing, security check and transportation to and from the port. For ocean shipments this means another 17 days are added to the transportation time. For air shipments a standard lead-time of two weeks is taken for every RSHQ. Chapter 2. Grand Model 27

46 TABLE 7 LEAD-TIMES TO RSHQS Shipment Ocean Air to Transportation time (days) Lead-time (days) Transportation time (days) Lead-time (days) CUSA CCN CSPL CMJ C Oceania CKBS Chapter 2. Grand Model 28

47 3 DESIGN OF AN ABC CLASSIFICATION In this section the design of ABC classifications is discussed. This will be structured following the paper of van Wingerden et al. (2015) who considers four different aspects of a classification. As the four different aspects cannot be considered separately, each combination will be evaluated according to their holding cost and emergency shipment cost. Transportation cost and ordering cost will be left out of scope in comparing the classifications. In this section first the four aspects and the decisions on these criteria for general classifications will be explained. The verification of the model built is discussed. The chapter concludes with a discussion of the results. 3.1 DESIGN OF A GENERAL CLASSIFICATION From the four aspects the classification criteria are considered first in this section. Then the number of classes considered for each of the classifications is explained. Thirdly the class sizes are explained and lastly the target setting is described CLASSIFICATION CRITERIA An important aspect of an ABC classification is the criteria that enable the user to rank the SKUs. Ideally the criteria are chosen in such a way that the costs involved are minimized. Many different classification criteria are proposed in literature (Section 1.3.2). Traditionally the annual dollar volume (ADV) is used, which is the demand volume per SKU times the price of an SKU. However, van Wingerden (2015) shows that this is not an efficient criterion for his model. This criterion will be taken into account to see how it performs when batching, emergency shipment costen and a general distribution is involved. Van Wingerden et al. (2015) show that the performance of the one-dimensional criteria Demand/Price is the best for their inventory model. The reasoning behind this is that, as in the system approach, parts with a high demand and/or low price will be given a higher service level while parts with low demand and/or a high price. This classification is based on Teunter et al. (2010) who proposed a classification with a one-dimensional criterion that takes demand, price, batch size and emergency shipment cost into account. Since the latter two, batch size and emergency shipment cost, are not considered in the model used by van Wingerden et al. (2015) they do not take these cost into account for their criteria. Batch sizes are taken into account in the form of the EOQ in the model used in this thesis. An interesting extension on the research of van Wingerden et al. (2015) would be to see if taking batch sizes into account in the criterion for classification would result in a better performance. Furthermore, there are two more criteria that are interesting to look further into. Firstly, it would be interesting to see how the two-dimensional classification criterion demand and frequency performs. The reason is that the criteria of main classification in GAIA is demand and frequency. Lastly the twodimensional criterion demand and price will be taken into the comparison. However shown not the best classification by van Wingerden et al. (2015), it is widely used by companies (van Wingerden et al., 2015). The CSC in Venlo currently uses this criterion in order to manage inventory at the CSC. Chapter 3. Design of an ABC Classification 29

48 Concluding, the following criteria are compared in this thesis: 1. Demand /(Batch size * Price) (D/PB) (one-dimensional) This criterion is based on the criterion of Teunter et al. (2010). The SKUs are classified based on their demand rate divided by their price multiplied by batch size. They are then ranked in descending order, where the first SKUs, consisting of fast moving and cheap SKUs, are considered class A, which gets the highest service level. As the emergency shipment cost in the dataset at Océ are the same for all SKUs emergency shipment costs would not add value in this criterion. 2. Demand / Price (D/P) (one-dimensional) This criterion is shown by van Wingerden et al. (2015) to be the best for their inventory model. The SKUs are classified based on their demand rate divided by their price. They are then ranked in descending order, where the first SKUs, consisting of fast moving and cheap SKUs, are considered class A, which gets the highest service level. 3. Annual Dollar Volume (ADV) (one-dimensional) This is the most common criteria for classification (Silver, et al., 1998). In this classification each SKU is classified based on Price multiplied by Demand per year. The SKUs that score highest fall in the first class and the lowest scoring SKUs fall in the lowest class. 4. Demand and Frequency (D&F) (two-dimensional) This criterion is based on the classification currently used at the RSHQ where each SKU is classified on both the demand per year and the months of demand per year. In the GAIA classification 9 classes are used for items that have demand in the last 12 months. There are differences between this classification and GAIA which are explained in Section Price and Demand (P&D) (two-dimensional) This classification is often found in practice (van Wingerden et al. 2015) and is also used at the CSC in Venlo. Each SKU is classified on both price and demand. At the CSC nine classes are used. Furthermore, van Wingerden et al (2014, 2015) show that it comes close to the system approach NUMBER OF CLASSES ABC classification often refers to a classification with three classes, class A, class B and class C. However, van Wingerden et al. (2015) and Teunter et al. (2010) show that more classes give a better performance. The reasoning behind using fewer classes is that it reduces complexity of the problem. More classes will lead to better results because more options are available at the cost of a higher complexity of the problem. It is thus a trade-off between manageability and performance. When manageability would not be a problem in a company, the system approach could be used which leads to (near) optimal results. This could be compared to having one class for every item. The maximum used number of classes in the research of van Wingerden et al. (2015) is six. They show that up to four classes the performance increase is big. For more than four classes the additional cost savings are limited. In this thesis for the one-dimensional classifications two to six classes are tested. Chapter 3. Design of an ABC Classification 30

49 For two-dimensional classifications a matrix approach is used. Here two by two matrices and three by three matrices are tested. Four by four matrices would make 16 classes which becomes computationally large and more difficult to manage. This means in total 19 different combinations of criteria and class numbers are used CLASS SIZES For every combination mentioned above it has to be decided which SKU falls in which class. This can be done by deciding on the class sizes. Teunter et al. (2010) mention that usually in literature a rule of thumb is used where 20% of the demand fall in class A, 30% of the demand falls in class B and the remaining 50% in class C. When more classes are added Teunter et al. (2010) extrapolate the class sizes. Van Wingerden et al. (2015) found that these standard class-sizes are not always the best. They show that the optimal class sizes have a big effect, and they especially refer to the size of class C. They explain it as following: In the best solutions there is always a class consisting of the expensive and infrequently requested SKUs for which SKUs are not stocked. These SKUs have a big impact on the total inventory costs. When the percentage of demand within this class becomes larger than the percentage of total demand that is allowed not to be satisfied directly from stock on hand, we always need to stock these SKUs. They call it a forced presence of these SKUs. In the model used in the thesis there is however another cost that is taken into account: emergency shipment cost. This might cause that the SKUs should have presence in order to reduce the cost related to emergency shipments. To find out what the effect is for an inventory model with emergency shipment costs and because van Wingerden et al. (2015) show the importance of the class sizes the optimal class sizes will be determined for every combination. To do this, threshold values are used to determine which class each SKU falls into. A threshold value is the cut-off point between two classes. This means that for every dimension if the number of classes for that dimension is x, the number of threshold values is x 1. The SKUs that rank higher than the value of largest threshold value fall in class x, the ones which rank lower than the lowest threshold value fall in class 1. Parts that fall in between threshold values fall into the corresponding class following the same logic. As used in van Wingerden et al. (2015) enumeration over the threshold values is used to determine the optimal class sizes. The threshold values are set equal to the y-th percentile with y {Δ, 2Δ,, 100/Δ Δ}. Using the threshold values the class of SKU i at warehouse j, k ii, can be determined. Threshold 1 Threshold 2 A B C FIGURE 3.1 EXAMPLE TRESHOLD VALUES FOR CLASSIFICATION Chapter 3. Design of an ABC Classification 31

50 Note that threshold values cannot be the same because this creates an empty class. Furthermore, the value of threshold i has to be higher threshold than the value of threshold i 1 to avoid overlapping classes TARGET SETTING In the literature review two different algorithms have been mentioned to optimize the base-stock levels using classification, both developed by Van Wingerden (2015). The first algorithm developed by van Wingerden firstly decouples the classes and considers them separately. For every class the algorithm calculates the cost for a range of fill rates. The results of all classes are then enumerated to find an efficient solution (for more information see van Wingerden (2015)). The second algorithm proposed is a greedy algorithm that iteratively increases the fill rate for the class that gives the biggest bang for the buck until the objective aggregate fill rate is reached. Van Wingerden (2015) mentions calculation time increases rapidly when the number of classes is increasing. The greedy algorithm obtains a calculation time saving of around factor 20 for an aggregate fill rate of 90% and 5 classes and the savings increase for a higher fill rate. Despite that the greedy algorithm is not optimal it is accurate and gives an average cost increase of less than two percent when using more than three classes. There is no difference in reason to assume that the greedy algorithm gives different results for classification when the model of this thesis is used. In order to keep computation times reasonable the greedy algorithm is used. Van Wingerden et al. (2015) mention that there are many ways to manage inventory of each SKU in a class, however to be able to compare the results with the results of van Wingerden et al (2015) the same method to set targets is used. Every SKU i I of warehouse j J belongs to one class out of the set of classes K, denoted by k ii. A class k K is managed through setting service targets per class, θ k. The fill rate of an SKU i at warehouse j has to be greater than or equal to the target fill rate θ k for the class k ii. A difference between the model used in the thesis and the model of van Wingerden (2015) is the use of emergency shipment costs. As a consequence, the reorder-level with the minimum cost is not always minus 1 (no inventory on stock). To account for this the reorder level all SKUs have to be equal to or higher than the reorder level where costs are minimal (s i,j,mmm ). In other words: for every SKU i I at warehouse j J s ii is set equal to the lowest integer value that satisfies the target fill rate of its class θ kii if this is higher than the s i,j,mmm, otherwise it is set to s i,j,mmm. The problem Q can then be formulated as follows: (Q) min C(s) subject to β(s) β ooo s ii = max s i,j,mmm, mmm x β ii (x) θ kii, x N 0 i I, j J θ k [0,1] k K k i {1,2,, K} Chapter 3. Design of an ABC Classification 32

51 To solve this problem, the greedy algorithm as proposed by van Wingerden et al. (2014) will be used. As explained there is also a cost minimum, where inventory cost and emergency shipment cost combined are minimal. So firstly for an SKU in every class the minimum has to be found that will serve as a starting point for the greedy algorithm. The greedy algorithm is based on the idea of getting the biggest bang for the buck. The fill rate is increased of the class θ k where the biggest increase in aggregate fill rate per euro invested can be gained. To do this θ k is increased with a small step, θ ssss for the class where we get the biggest Γ k, the ratio between the increase in aggregate fill rate and cost increase. The algorithm is as follows: 1. Set s i,j = s i,j,mmm fff aaa i I aaa j J s = (s 11,mmm, s 12,mmm s II,mmm ) For all k K set θ k min(β ii (s): i I, j J, k ii = k Compute C(s)aaa β(s) 2. For all k K (a) For all i I and j J If k ii = k: v ii = min {x β ii (x) θ kkk + θ ssss, x N 0 } s ii Else, v ii = 0 (b) v k = (v 11, v 12,, v II ) Γ k β(s+v k ) β(s) C(s+v k ) C(s) 3. m = arg max{γ k : k K} S = S + v k θ k min β ii (S): i I, j J, k ii = k for all k K 4. Compute C(S) and β(s) If β(s) β ooo then stop else go to step VERIFICATION Verification in this thesis means that the models as described are correctly translated and implemented in the coding language. Several different ways to verifify the program have been used. First of all, the program has been coded in separate functions for each part of the models. These are building blocks that together form the program. Every function has been thoroughly checked to verify if the input corresponds with the output and it has been debugged when necessary. Secondly the models have been run with 100 SKUs and the outcomes of the total program and some functions have been interpreted by people in the department of SCM Service Parts. The outcomes have been checked to verify whether they are based on proper calculations and can be explained and/or compared to the real outcomes. The third method used is manual calculation. For two parts the calculation of EOQ and transportation mode, fill rate and cost calculation and the application of the system approach have been checked (Appendix J). For the classification approach the boundary setting and enumeration over scenarios have been checked manually (Appendix J). Chapter 3. Design of an ABC Classification 33

52 3.3 RESULTS In this chapter the findings regarding the inventory investment costs and emergency shipment costs for the different classifications are presented. This is done with a smaller dataset to in order to keep computation times reasonable. The dataset consisted of 100 SKUs randomly selected from the WFPS product group. The algorithm has been applied with several target aggregate fill rates (90%, 95% and 98%) and the emergency shipment costs per SKU have been differed with 0, 25 and 50. The scenarios with 0 and 25 emergency shipment cost are treated in this section. The results of 50 emergency shipment cost can be found in Appendix K and are not treated because the emergency shipment cost are that high that the classification does not or only slightly impact performance. The threshold-values steps are set at a Δ of The θ step for the greedy algorithm has been set to 0.1% CLASSIFICATION CRITERIA WITHOUT EMERGENCY SHIPMENT COSTS For every combination, emergency shipment cost and fill rate the cost are calculated. The minimum cost have been taken to compare the different combinations (Table 8). This has been compared to the system approach in order to evaluate the performance of the combination. To calculate the costs for the system approach the method of Appendix I is followed. These costs are the (near) optimal costs as the system approach takes the number of classes equal to the number of SKUs. TABLE 8 RESULTS OF CLASSIFICATION APPROACH WITHOUT EMERGENCY SHIPMENT COSTS (GREEN WHEN <5% DIFFERENCE FROM SYSTEM APPROACH) Classes 90% 95% 98% Demand / 2 $12, $20, $27, (Batch * Price) 3 $11, $19, $26, $11, $19, $26, $11, $18, $26, $11, $18, $26, Demand / Price 2 $12, $20, $27, $11, $19, $26, $11, $18, $26, $10, $18, $26, $10, $18, $26, Annual Dollar Volume 2 $15, $21, $29, $15, $21, $28, $14, $21, $28, $14, $21, $28, $14, $21, $28, Demand & Price 2 x 2 $12, $19, $27, x 3 $11, $18, $26, Demand & Frequency 2 x 2 $21, $29, $33, x 3 $19, $27, $33, Item approach $27, $32, $36, System approach $10, $17, $25, Chapter 3. Design of an ABC Classification 34

53 The results found about the Annual Dollar Volume are in line with the results found by Teunter et al (2010) and van Wingerden et al. (2015). It gives continuously worse results than other criteria. The ADV gives poor results because it classifies expensive SKUs in the same class as the SKUs with high demand. From a cost perspective it is more interesting to stock less expensive SKUs over expensive SKUs and from a fill rate perspective it is more interesting to stock fast moving SKUs over slow moving SKUs because of their higher contribution to the fill rate. One can see in the results that the first class, with the highest demand and the expensive units is given a lower target fill rate than the class with the cheaper and slow moving SKUs (Appendix J). 200% 180% 160% 140% 120% 100% FIGURE 3.2 COMPARISON CLASSIFICATION IN PERCENTAGE TO SYSTEM APPROACH It is noticeable is that the difference between ADV classification and the item approach is relatively bigger than the differences found by van Wingerden et al. (2015) and on the other hand the difference between the system approach and the item approach is smaller than the difference found by van Wingerden et al(2015). Both differences can be attributed to the differences in the dataset. In the dataset of Océ many SKUs have a low price and on top of that some of the higher priced SKUs are fast-movers. The most important reason however is that there are only 100 SKUs in the dataset. With more items in a dataset the differences in items can be exploited better. Next to that brings less items in a dataset the SKUs per class down making the classification approach come closer to the system approach, that has one class per SKU. The Demand & Frequency yields the worst results overall, with up to 80% more costs than the system approach when the target aggregate is fill-rate 90%. Adding classes yields substantial savings, but with 9 classes the results are far off from other classifications. It is just slightly better than the item approach. This can be explained by the fact that the dimension frequency is highly related to the dimension demand. Both dimensions do not take the price of an SKU in account, while price is one of the main influencers in the holding costs. The classifications that yields the best results and are within 5% of the system approach are the classifications D&P, D/BP and D/P. The differences with the system approach are within a few percent. Even after close inspection of the data, no explanation could why the difference between D/P, D/BP and the system approach with 95% target aggregate fill rate is bigger than with 98% or 90% target aggregate fill rate. The criteria D/P and D/BP are overall close to each other; however the D/P criterion performs slightly better. When looking closer into the data (Appendix J) one can see that setting the Q to the EOQ gives a correlation between the batch size and the demand. Thus the extra demand which might bring the SKU to a higher class gets divided by a higher batch size. This might be a reason why including batching, despite the findings of Teunter et al. (2010) does not give a better classification criterion. Chapter 3. Design of an ABC Classification 35

54 These three criteria, D/P, D/BP and D&P, catch an important feature in inventory management. They catch the trade off in extra fill rate and price. This is also the trade-off that is used when applying the greedy algorithm in the system approach. Noticable is that the D & P classification performs better than found by van Wingerden et al. (2015). A possible explanation is that there are some fast-moving items with a high price, which can be set apart by a two-dimensional structure and not a onedimensional structure as D/P. The results show that the number of classes has a significant impact on the costs of the classification. When changing from 2x2 to 3x3 classes for the D&P criterion significant improvement can be gained. For the D/P and D/BP criteria a similar results can be found. Changing from two to three classes gives a significant gain. However, increasing the number of classes further gives a smaller to minimal gain. One can derive that three or four classes are enough to get near optimal results CLASSIFICATION CRITERIA WITH EMERGENCY SHIPMENT COSTS In the former section no emergency shipment costs are taken into account, however in some cases in the spare parts industry a emergency shipment cost is applied when not being able to deliver directly from inventory. In this section 25 emergency shipment costs per backorder are applied. The results are shown in Table 9. TABLE 9 RESULTS OF CLASSIFICATION APPROACH WITH EMERGENCY SHIPMENT COSTS (GREEN WHEN <5% DIFFERENCE FROM SYSTEM APPROACH) Classes 90% 95% 98% Demand / 2 $17, $21, $28, (Batch * Price) 3 $16, $21, $27, $16, $21, $27, $16, $21, $27, $16, $21, $27, Demand / Price 2 $17, $21, $27, $16, $21, $27, $16, $21, $27, $16, $21, $27, $16, $21, $27, Annual Dollar Volume 2 $17, $23, $30, $16, $22, $29, $16, $22, $29, $16, $22, $28, $16, $21, $28, Demand & Price 2 x 2 $16, $21, $28, x 3 $16, $21, $27, Demand & Frequency 2 x 2 $16, $22, $30, x 3 $16, $22, $29, Item approach $29, $29, $37, System $16, $20, $26, Chapter 3. Design of an ABC Classification 36

55 The first thing that stands out is that the difference of all combinations compared with the system approach is significantly smaller. The explanation is that, by setting the reorder levels to the value with the minimum cost, a certain aggregate fill-rate is already reached. If the objective aggregate fillrate is close to the aggregate fill-rate with the minimum cost, not many reorder levels will have to be changed. Thus the difference with the system approach is smaller. One can derive this also from the results. Namely, the higher the objective fill-rate, the larger the difference is between the classifications, which was not the case when no emergency shipment costs were applied. The results also show that the best performing criteria stay the same criteria. In this case Demand & Price yields the best results in most cases. Similar to the scenario without emergency shipment cost, savings can be realized when adding classes. When changing from 2x2 to 3x3 classes for the D&P criterion significant improvement can be gained. For the D/P and D/BP criteria a similar result can be found. Changing from two to three classes gives a significant gain. However, increasing the number of classes further gives a smaller to minimal gain. 120% 115% 110% 105% 100% FIGURE 3.3 COMPARISON CLASSIFICATION IN PERCENTAGE TO SYSTEM APPROACH THE IMPACT OF CLASS SIZES ON PERFORMANCE In the previous section only the scenarios with the lowest cost were considered. Van Wingerden et al. (2015) showed that in their case the class-sizes values have a big impact on the cost. The classsizes commonly proposed is to have around 20% of the SKUs in class A, 30% in class B and 50% in class C (Teunter et al., 2010). Van Wingerden et al. (2015) found that there are large inventory investment cost differences when changing the percentage in each class. To analyze the impact in this thesis the D/P criterion with two classes is taken and the class-sizes are varied. One can find the impact of changing the class-sizes in Figure 3.4 and Figure 3.5. Contrary to the findings of van Wingerden et al. (2015) in none of the solutions the SKUs are not stocked. This can be caused by two things: first of all, if the batch size is bigger than one, the fill-rate is higher than zero and secondly, the dataset used is different. Still we can see that when the class C gets too big, the forced presence of these SKUs raises the costs significantly. In order to reach the objective aggregate fill-rate the class has to have a certain aggregate fill rate, giving a forced presence to the SKUs in that class. Setting the threshold values well can save up to 47% of the cost with an objective aggregate fill-rate of 90%. Forced presence works two ways, when class C is too small the expensive SKUs also fall into the class with the cheaper SKUs giving a higher inventory holding cost. After inspection of the dataset, can be concluded that the best settings of the classsizes depend highly on the SKUs in the dataset (Appendix J). Chapter 3. Design of an ABC Classification 37

56 Thousands $ 40 $ 35 $ 30 $ 25 $ 20 $ 15 $ 10 Thousands $ 35 $ 30 $ 25 $ 20 $ 15 $ 10 $ 5 $ 5 $ - 0% 20% 40% 60% 80% 100% $ - 0% 20% 40% 60% 80% 100% 90% 95% 98% 90% 95% 98% FIGURE 3.4 COST AND DEMAND PERCENTAGE IN CLASS C; NO EMERGENCY SHIPMENT COSTS FIGURE 3.5 COST AND DEMAND PERCENTAGE IN CLASS C; 25 EMERGENCY SHIPMENT COSTS The impact of class-sizes gets smaller when emergency shipment costs are introduced. This can be explained by the fact that the fill rates of the classes do not have to be raised that much since they already start at the minimum reorder level. One can see, as could be seen in the previous section, that a higher objective aggregate fill-rate also raises the impact of class-sizes on costs. Chapter 3. Design of an ABC Classification 38

57 4 APPLICATION AT OCÉ In this chapter the insights of the previous chapters will be used for the application on Océ. First of all the most important practical issues that have been found in order to compare the situation of Océ to the model are listed. Then the results of applying the system approach are presented together with the impact of the choice for the EOQ and the transportation mode. These results are the theoretical gains that can be achieved for Océ. Then results of applying the DxP classification on both product groups is analysed. 4.1 PRACTICAL COMPLEXITIES Comparing the model to practice brought along several complications. The most important ones are listed here and their impact on the validity of the model is discussed. These are the use of an R,s,S policy, the translation of the settings of GAIA into the model and dual transportation THE USE OF AN R,S,S POLICY After close inspection the GAIA software batch sizes appeared to vary. This is because GAIA does not use a standard batch size for reordering; it uses an order-up-to-level S, which means that when the inventory position reaches s it is raised up to S. In an inventory policy with continuous review and batches of one the R,s,Q and R,s,S policies are exactly the same. In this case Q = S s (Axsäter, 2015). Océ, however, uses a periodic review and a significant part of the SKUs are ordered in batches. The R,s,Q policy thus cannot be used without consideration to draw conclusions about a system with an R,s,S policy. The batch size an RSHQ orders is thus not only S s, but because of periodic review it includes the demand during review period under the reorder point. This is also referred to as the undershoot. To check the effect of the use of R,s,Q policy in the model it is compared to an R,s,S policy in Appendix L. From the comparison it can be concluded that there is a difference between the two policies. However, one can approximate the actual situation by applying Equation (4.1). This gives an approximate difference of 0.03% of the fill rate and 1.33% of difference in the expected inventory level. Q ii + μ iir 2 = S ii s ii (4.1) TRANSLATING GAIA SETTINGS TO PARAMETERS IN THE MODEL (AND VICE VERSA) The GAIA interface uses different terminology than the terminology used in this thesis and common logistic literature. In order to make meaningful statements about the performance of GAIA and in order to generate output that is meaningful it is important that the terminology from GAIA is translated into the thesis terminology. In this section the two inventory control methods and their translation to parameters in the model are discussed. Chapter 4. Application at Océ 39

58 FIXED POINT METHOD In the fixed point method, the inventory position after review is always equal to the set level, γ ii. This means that SKUs that have this inventory control method have the following characteristics: Q ii = 1 (4.2) s ii (γ ii ) = γ ii 1 (4.3) REORDER POINT METHOD In the reorder point method the target per class is set by a Weeks of Stock (WWS ii ). This weeks of stock is a measure of the demand per week of an SKU i at a warehouse j. When the net inventory level is expected to drop below the set WWS ii within the lead time and one week a new batch is ordered. It can thus be seen as the safety stock. This can be translated to a reorder level as followed: s ii (WWS ii ) = 7 WWS ii L 365 ii μ ii (4.4) The order up to level is determined through a parameter called Order Cycle Weeks, OOW ii. This is the difference between the order up to level and the reorder level in weeks of demand. There has to be a minimum difference of one between the reorder level and the order-up-to-level. S ii = s ii (WWS ii ) + max rrrrr 7OOW ii 365 μ ii, 1 (4.5) Then, using Equation (4.1), the batch size is calculated DUAL SUPPLY An assumption in the model (Section 2.) is that the products have one transportation mode: via air or ocean. However, GAIA has the possibility to ship through another transportation mode when inventory drops below a pre-determined level. This means that SKUs that usually are transported via ocean can be transported via air. It reduces the lead-time from six weeks to only two weeks. This can have a significant effect on the aggregate fill rate and inventory levels since SKUs arrive quicker when a stock-out is likely to happen. The RSHQ in the USA does ship most SKUs of one product group (OIP) by air, and SKUs of the WFPS product group mainly by sea. Because the lead-time of air shipped SKUs cannot be shorter by another mode of transportation (except for emergency shipments) the dual transportation does barely affect the current results of the WFPS group. For the OIP group the difference can be significant. For this group one can still compare the inventory levels and the corresponding aggregate fill to check if the current settings come close to optimal settings. On top of that one can use the tool and aim for a lower target aggregate fill rate to adjust for dual supply. Chapter 4. Application at Océ 40

59 4.2 SYSTEM APPROACH In this section the application of the system approach on the whole dataset of Océ is analysed. This is done to see what the possible gains would be for Océ and to check the implication of the choice for the EOQ as batch size and the transportation mode rule for the transportation mode. First the data and different scenarios are discussed, followed by a discussion about the cost breakdown and a further analysis on the transportation cost DATA AND SCENARIOS For this analysis the dataset as described in Section is used which has the characteristics as displayed in Table 10. TABLE 10 DATA USED IN ANALYSIS OCÉ OIP 2430 SKUs in warehouses WFPS 1716 SKUs in warehouses Demand per week per SKU Price Demand per week per SKU Price Min 0.02 $ $ 0.01 Average 1.43 $ $ Max $ 11, $ 8, As discussed in Section 2. the batch sizes are set to the EOQ and the lead-times are dependent on the transportation mode rule in Appendix D. To research the impact of this decision 5 different scenarios have been taken to compare the effect of these decisions. In four of the scenarios the transportation mode and batch size determination have been varied. In these scenarios the core model is optimized using the system approach following Appendix I. The last scenario is the performance of the current settings in GAIA according to the grand model. TABLE 11 SCENARIOS COMPARED USING THE SYSTEM APPROACH Scenario Abbreviation Batch size Transportation mode Reorder levels 1 Current As currently set As currently set As currently set 2 (Cur,Cur) As currently set As currently set System Approach 3 (EOQ,Cur) EOQ As currently set System Approach 4 (Cur,TR) As currently set Transportation mode rule System approach 5 (EOQ,TR) EOQ Transportation mode rule System Approach COST AND PERFORMANCE The cost and fill rate of the five scenarios are displayed in Figure 4.1 and Figure 4.2 (detailed results can be found in Appendix M). Figure 4.3 and Figure 4.4 show the cost breakdown into the four different costs. First the effect of the transportation mode rule and the EOQ are discussed, followed by a comparison with the current performance and concluding with a deeper analysis of the transportation costs THE EFFECT OF TRANSPORTATION AND BATCHING The differences between the scenarios with the reorder levels set by system approach (scenario 2-5) comes purely from the manner of setting batch size and transportation mode. These scenarios can thus explain the effect of applying these rules. Chapter 4. Application at Océ 41

60 To analyse the effect of the transportation mode rule the scenarios 2 and 4 can be compared. The difference when using the transportation mode rule can be mainly found in a decrease of transportation costs for the OIP product group. This decrease is 77.1% in transportation cost for this product group and on top of that a 1.8% saving in inventory holding cost. This is a combined saving of 54.7% in total costs of this product group that can be attributed to using the transportation mode rule. For this group the transportation costs are also dominant; even when the transportation mode rule is applied they take up as much as 34.7% of the total cost in this part of the supply chain. At the moment a significant part is set to air, a mode that is generally costly. A side note is that the transportation costs are based on an estimation and can fluctuate. The general conclusion however, is that there is a lot of room of improvement, as also shown in Section ,00 100,00 80,00 60,00 40,00 20,00 0,00 94% 95% 96% 97% 98% 99% 1 (EOQ,TR) 2 (Cur,Cur) 3 (EOQ, Cur) 4 (Cur, TR) 5 Current FIGURE 4.1 COST AND AGGREGATE FILL-RATE OIP NORMALIZED 120,00 100,00 80,00 60,00 40,00 20,00 0,00 91% 92% 93% 94% 95% 96% 1 (EOQ,TR) 2 (Cur,Cur) 3 (EOQ, Cur) 4 (Cur, TR) 5 Current FIGURE 4.2 TOTAL COST AND AGGREGATE FILL-RATE WFPS 120,00 100,00 80,00 60,00 40,00 20,00 0,00 120,00 100,00 80,00 60,00 40,00 20,00 0,00 Emergency Inventory Order Transporation FIGURE 4.3 NORMALIZED COST BREAKDOWN OIP Emergency Inventory Order Transporation FIGURE 4.4 NORMALIZED COST BREAKDOWN WFPS For the WFPS group the gain in transportation costs is less significant. This can be explained by the fact that now the parts are shipped by ocean, an inherent cheap way of transportation. Here a decrease of 6.3% of the transportation costs are realized when the transportation mode rule is applied. The savings for transportation in this group are mainly achievable by a decrease in emergency shipment costs of 13.8% and a decrease inventory costs of 15.9%. This gives a combined costs saving of 12.4% of the total costs. Chapter 4. Application at Océ 42

61 The effect of applying the EOQ rule to the batch size appears to be less significant. To analyse the effect the scenarios 5 and 4 are compared. For the WFPS a combined saving of 6.4% on the total cost and for the OIP group a combined saving of 5.9% can be realized according to the model. This can be explained by a decrease of the fixed order cost with 44.4% and 36.7% for the WFPS and OIP group respectively. This can be attributed to bigger batch sizes. This also means that the inventory costs are higher, but the increase is insignificant (<0.4%). On top of that the emergency shipment costs are lower due to a lower probability of a stock out with bigger batch sizes COMPARISON WITH THE CURRENT SETTINGS In the first scenario the current settings in GAIA have been uploaded into the model. The first observation is that at the OIP group the current scenario has an aggregate fill rate of 95.1% which is around what the RSHQ reports. For the OIP group the performance according to the model is 91.5%, while in reality the performance is around 95%. This can explained by the fact that in this group dual transportation is used. The default is ocean; however when the net inventory drops below a predetermined level an air shipment is ordered. Still, if we do not consider emergency shipments because these are higher in the model than in reality, one can make statements about the performance in the current situation. First of all, when looking at the WFPS group a cost reduction of 22.3% can be attained by only applying the system approach (comparison scenario 2 and 5). When leaving transportation costs and order costs out of scope the savings are as much as 51.1% of the costs while a similar aggregate fillrate can be reached. This proves that the inventory control using classification can very probably be improved. 35,00 30,00 25,00 20,00 15,00 10,00 5,00 0,00 94% 95% 96% 97% 98% 99% 1 (EOQ,TR) 2 (Cur,Cur) 3 (EOQ, Cur) 4 (Cur, TR) 5 Current Figure 4.5 Inventory costs OIP 60,00 50,00 40,00 30,00 20,00 10,00 0,00 91,00% 92,00% 93,00% 94,00% 95,00% 96,00% 1 (EOQ,TR) 2 (Cur,Cur) 3 (EOQ, Cur) 4 (Cur, TR) 5 Current Figure 4.6 Inventory costs WFPS When transportation mode rule is applied and the EOQ is used as batch size the theoretical costs savings are as much as 67% (comparison scenario 1 and 5). For the OIP group the inventory costs are the main driver, consisting of 74.5% of the current costs when emergency shipment costs are excluded. This could be explained by the fact that the SKUs in the OIP group are more expensive than the SKUs of the WFPS group on average. From Figure 4.6 one can deduct that, even though dual shipment is used, the inventory can be managed more cost efficient while increasing the aggregate Chapter 4. Application at Océ 43

62 fill-rate significantly. With an inventory holding cost decrease of 54.7% an aggregate fill rate of 95.1% can be met instead of 91.4% (comparing scenario 1 and 5). With the use of dual supply the aggregate fill rate can even be higher TRANSPORTATION COSTS In this section the difference in transportation costs is analysed. There are five variables that are taken into account when applying the transportation mode rule, the difference in lead time, the price of a part, the costs per transportation mode, the weight of the part and the volume. After close inspection of one hundred parts of the WFPS group price and weight appear to be the leading variables in the decision for the transportation mode (Figure 4.7). When price increases a higher weight of an SKU is accepted to fly the SKU, because the inventory costs get linearly higher with the price. Figure 4.8 shows that currently this distinction is not made and nor the weight nor the price of an SKU is taken into account ,01 0, , Weight (Kg) 0,1 0,01 Weight (Kg) 0,1 0,01 0,001 Price ($) 0,001 Price ($) FIGURE 4.7 SHIPMENT METHOD (RED = AIR, BLUE = OCEAN) WHEN APPLYING TRANSPORTATION MODE RULE FIGURE 4.8 SHIPMENT METHOD (RED = AIR, BLUE = OCEAN) AS CURRENTLY IS As shown in Table 12 and Table 13 the transportation mode rule sets for both product groups a higher percentage of the demand to air, especially in the OIP group. This does not mean more SKUs are transported through the air, but that the different SKUs are set on air. One can see that the average price increases when applying the rule and the average weight decreases. TABLE 12 DIFFERENCE IN SHIPMENT METHOD WFPS GROUP Currently Transportation mode rule Demand % Item % Avg Price Avg Weight Demand % Item % Avg Price Avg Weight Air 21.7% 58.4% $ Kg 45.7% 47.3% $ Kg Ocean 78.3% 41.6% $ Kg 54.3% 52.7% $ Kg TABLE 13 DIFFERENCE IN SHIPMENT METHOD OIP GROUP Currently Transportation mode rule Demand % Item % Avg Price Avg Weight Demand % Item % Avg Price Avg Weight Air 4.5% 51.9% $ Kg 50.8% 52.2% $ Kg Ocean 95.5% 48.1% $ Kg 59.2% 47.7% $ Kg Chapter 4. Application at Océ 44

63 4.3 CLASSIFICATION FOR BOTH PRODUCT GROUPS First the impact of the computation times on classification for both product groups are explained. Then the Demand & Price classification is applied for the current settings and the results are explained COMPUTATION TIMES In this thesis several decisions have been made in order to reduce computation times. Still, the computation times in order to search for the bes settings for class-sizes are very large, especially if the number of classes increases. In this subsection this problem is broken down and explained. The times mentioned are for a laptop with Intel Core i5-6200u Processor and 8 GB RAM. The computation time for making the empirical distribution for all 4149 SKUs is around 30 minutes, which is acceptable. Computation times for calculating the system approach are around 60 minutes per product group. This can be explained by the fact that for that the inventory model uses a sum in a sum, making the calculation of some fast-moving parts very computationally intensive. This can still be seen as a feasible computation time. The computation time for target setting for classification also takes around 60 minutes product group when the class-sizes are given. Because intermediate results are cached, the reorder level with its corresponding fill-rate and expected inventory level, this can be brought down to 15 minutes per product group. There are 1296 different scenarios to calculate for a two-dimensional classification with 3x3 classes and Δ of the class-sizes of 0.1. This brings the total calculation time to around 2 weeks for only one classification. Therefore only one classification is chosen to apply to the whole dataset DEMAND & PRICE CLASSIFICATION Only one criterion is chosen because computation times are very large, so a comparison with other criteria is not possible. Based on the results in Section and the usage of a Demand & Price classification at the CSC the Demand & Price 3x3 is chosen. With the estimated emergency shipment cost and a 95% fill rate per product group the Demand & Price gives the same results as the system approach. This can be explained by the fact that the emergency shipment cost are relatively high compared to the costs of most parts, so the reorder level with the minimum cost is already high. This makes the aggregate fill rate of reorder levels with the minimum cost for both product groups already higher than 95%. Concluding, for this dataset en these settings one can already find the minimum cost and desired aggregate fill-rate by setting all items to the reorder level with the minimum cost. Chapter 4. Application at Océ 45

64 5 GAIA 5.1 CLASSIFICATION CRITERIA The classification used in GAIA has several features that set it apart from a general classification as described in Section 3. The reader is referred to Section and Appendix A for a detailed description and all the parameters in the classification in GAIA. In this section the optimization of the classification that is used in GAIA is described. This is done using the aspects as used by van Wingerden et al. (2015) CLASSIFICATION CRITERIA Océ is currently obliged to use the GAIA classification as it is; it is already programmed and used all over the Canon organization. The classification criteria used in GAIA are fixed and thus these will be used in this thesis for determining the performance of GAIA NUMBER OF CLASSES The number of classes is currently 10 in the main classification and 56 in the embedded classification. However, for the main classification the four classes that have the reorder point method as inventory control method are not considered since the SKUs in these classes are managed using the embedded classification. This brings the number of classes in the main classification to 6. In the embedded classification seven classes are dedicated to SKUs without demand. Those classes are not considered bringing the number of classes in this classification to 49. The number of classes of the embedded classification is hardcoded in the GAIA information system and this number thus will not be changed throughout this thesis. The number of classes in the main classification has a maximum of 26 classes (A-Z). Some of these classes are reserved for other purposes. To reduce complexity the number of classes in the main classification is kept CLASS SIZES The class-sizes, whether in the main classification or the embedded classification, are variable in GAIA. Van Wingerden et al. (2015) demonstrate that the class-sizes are important in the performance of the classifications. In order to try to get close to the system approach these should thus be consider. The main classification in GAIA has eleven threshold values on each dimension, giving 104 cells. On top of that it has an embedded classification with seven threshold values on both dimensions. Enumeration over all these possibilities would result in vast computation times. To set class-sizes the insights gained in the Demand & Frequency 3x3 classification in Section are used. The classsizes that were best for this classification are also set for GAIA to see if they yield a performance increase TARGET SETTING As mentioned in Section two methods have been developed for target setting. Due to the amount of classes and in order to keep the computation time reasonable, the greedy algorithm is used to minimize cost against a given service level. The greedy algorithm obtains a calculation time Chapter 5. GAIA 46

65 saving, especially when class sizes increase compared to the first algorithm proposed by van Wingerden et al. (2015). Every SKU i I of warehouse j J belongs to one class out of the set of classes K, denoted by k ii. The set K consists of two subsets, the subset G K that contains the classes that belong to the main classification and the subset H K that fall into the embedded classification. For both subsets the target setting is different. For the classes k G the Weeks of stock (WOS) is the unit for the safety stock per class. Weeks of stock is the average demand over one week for the last year. For every class k G thus a WWW has to be set, denoted by WWW k. For an SKU i I at a warehouse j J in class k G the WWW has to be greater than or equal to the target WWW for the class, which is denoted by WWS kii. The reorder level will be calculated using the logic in GAIA. This is done following Equation (4.4). The classes k H are managed by an order up to level. For every class thus an order up to level has to be set, denoted by γ k. This is translated to a reorder level following Equation (4.3).For every SKU i I at warehouse j J in a class k H γ ii is set equal to the target reorder level of the class, denoted as γ kii. The problem Q can then be formulated as follows: (Q) min C(s) subject to β(s) β ooo s ii = min {x s ii (x) WWS kii ), x N 0 } i I, j J, k G s ii = γ kii 1, γ kii N 0 i I, j J, k H WWW k [0, ) fff k G γ k N 0 k H H = {k 1.. k H }, G = {k H +1.. k K }, k i {1,2,, K }, H G = K, H G = To solve this problem the greedy algorithm as proposed by van Wingerden et al. (2014) will be used. As explained in Section there is also a cost minimum, where inventory cost and emergency shipment cost combined are minimal. This cannot be done on SKU level because SKUs can only be managed per class in GAIA. So firstly for every class the minimum has to be found. Let WWW k,mmm be the WWS k where C k (s) for k Gis minimal and γ k,mmm be the γ k where C k (s) for k H is minimal. We may exclude the solutions with WWS k < WWW k,mmm and γ k < γ k,mmm. The greedy algorithm is based on the idea of getting the biggest bang for the buck. WWS k or γ k is increased with a small step size, respectively WWS ssss and γ ssss, where the biggest increase in aggregate fill rate per euro invested can be gained. This ratio, denoted as Γ k is the difference in aggregate fill rate divided by the difference in investment costs when class k G is increased with WWS ssss or class k H is increased with γ ssss. Chapter 5. GAIA 47

66 The algorithm is as follows: 1. For all k G set WWS k =: WWW k,mmm For all k H set γ k =: γ k,mmm For all k G For all i I and j J calculate s ii (WWS kii ) For all k H For all i I and j J calculate s ii (γ kii ) s = (s 11, s 12,, s II ) ℇ s Compute C(s) and β(s) 2. For all k K (a) For all i I and j J If k ii = k k G : v ii = s ii (WWS k + WWS ssss ) s ii (WWS k ) Else if k ii = k k H : v ii = s ii γ ii + γ ssss s ii (γ ii ) Else v ii = 0 (b) v k = v 11, v 12, v II Γ k = Δβ(s+v k) ΔC(S+v k ) 3. m arg max{γ k k K} S = S + v k If k G WWS k = WWS k + WWS ssss Else: γ k = γ k + γ ssss Compute C(S) and β(s) If β(s) β ooo stop else go to step RESULTS GAIA CLASSIFICATION In Section the GAIA classification is applied on a selection of SKUs in order to compare the results with the results of general classification in Section 3. In Section the GAIA classification is applied on the whole dataset provided by Océ. For the objective fill-rate 95% is taken and the emergency shipment cost per unit is set to GAIA FOR A SELECTION OF SKUS In order to compare the GAIA with the classifications in Section 3 the 100 SKUs as used in Section 3 are also used in this section. Chapter 5. GAIA 48

67 Thousands $35 $30 $25 $20 $15 $10 $5 $0 GAIA Current Boudaries Item approach GAIA Classsizes as DxF 3x3 DxF 3x3 DxP 3x3 System Approach FIGURE 5.1 COMPARISON FOR 100 ITEMS GAIA As can be seen in the results the GAIA classification with the current boundaries yields high costs compared to the Demand & Frequency 3x3 classification, even higher than the item approach. This can be attributed to several differences: the class-sizes, the minimum cost per item, and the target setting. These factors are treated one by one in the following paragraphs: CLASS-SIZES As explained in Section 5.1.3, computation times do not allow to find the best class-sizes. One can however conclude from Figure 5.1 that changing the class-sizes for the current settings to the settings as in the best Demand & Frequency 3x3 classification yields a cost decrease of 11.1%. As discussed in Section also with emergency shipment costs the class-sizes are of influence MINIMUM COST PER ITEM In the core model two types of costs are influencing the total cost, the emergency shipment cost and the inventory holding cost. In the general classifications discussed in Section 3 this is taken into account by first setting all items to their reorder level with minimum cost. This is, however, not possible in GAIA, thus the class is set to its minimum costs. As a consequence some items in start with a higher reorder level than that of the minimum cost and some start with a lower reorder level. This can be accounted for when comparing the classification D&F 3x3, which is similar to GAIA, and GAIA itself when no emergency shipment costs are applied. The difference between both classifications (Table 14) is 8.1% of the cost in this case, far lower than when emergency shipment costs are included. Without the emergency shipment costs, the difference with the item approach is also a lot bigger. A big part can thus be explained by the impossibility to set the reorder level per SKU to the level with the minimum cost. TABLE 14 COMPARISON GAIA WITH D&F (3X3) WITHOUT EMERGENCY SHIPMENT COSTS Classfication Threshold values P2 Cost DxF 3x3 Best 95.1% $22, GAIA Class-sizes as DxF 3x3 As D&F 95.2% $23, Item Approach 95.0% $32, TARGET SETTING The remaining difference between GAIA and the general classifications can be explained by the fact that the target setting per class is different in GAIA. Classes are managed on a target fill-rate per class, while classes and thus the SKUs in GAIA are managed on their average demand (in the main Chapter 5. GAIA 49

68 classification) or their exact reorder-level. This means no distribution of the demand is taken into account CONCLUSION GAIA performs badly because of several characteristics. First of all D&F is shown to be a bad criteria. Secondly the class-sizes are not set in a way to yield a cost minimum. Thirdly one cannot set items to their minimum cost level and fourthly no distribution is taken into account when translating targets for a class to reorder levels of items RESULTS OF GAIA FOR THE WHOLE DATASET Lastly, it is checked what applying the logic of GAIA on the whole dataset yields. For this, the current settings of the batch size and the transportation mode are taken. This is done to be able to compare the result of setting the targets of the classes and the current settings. Next to this it is compared to the system approach. As explained in Section 0 a general classification is equal to the system approach due to the relatively high emergency shipment cost at Océ. The results of these comparisons can be found in Figure 5.2 and Figure 5.3. One can clearly see that only by setting the targets of the classes better a big increase in performance can be gained. However, one can also see that it performs badly compared to the system approach. WFPS OIP $120,00 $120,00 $100,00 $100,00 $80,00 $80,00 $60,00 $60,00 $40,00 $40,00 $20,00 $20,00 $- Current Settings GAIA System Approach $- Current Settings GAIA System Approach Inventory Emergency Inventory Emergency FIGURE 5.2 RESULTS OF GAIA ON THE WFPS GROUP FIGURE 5.3 RESULTS OF GAIA ON THE OIP GROUP Chapter 5. GAIA 50

69 6 IMPLEMENTATION In this section a short explanation on the tool developed to support Océ on the decision making on their classification is given. Then, shortly, the actions that have to be taken in order to use the tool are stated. 6.1 TOOL To support Océ with the setting of reorder levels, deciding the transportation mode and deciding the batch size a tool was developed. This tool uses the python program that is used throughout the thesis to generate results. The front-end of the program is an Excel workbook that can be easily interpreted by the engineers at the SCM Service parts department. An Excel front-end and python backend is chosen to combine the power of python programs and the ease of building an understandable front-end in Excel. The tool is designed in such a way that it can handle the introduction or change in product groups, as is planned by Océ. Next to that it is flexible in location, which means that the tool can be applied to other RSHQs as well. To use the tool three different sheets need to be downloaded from the ERP systems of Océ / Canon. The demand data is needed, the parts information from GAIA and the volumes and weights of the parts. These three are then combined to one single table with all parts that had demand in the past year and are SKUs in the GAIA system. FIGURE 6.1 EXAMPLE OF A SHEET IN GAIA WHERE VARIABLES CAN BE SET The next step is to set the variables as lead-times, costs and an objective fill-rate per product group. As in this thesis, one can choose between a batch size as currently in GAIA or a batch size equal to the EOQ. Likewise, the transportation mode rule can be applied or the current transportation modes can be chosen. There are two ways one can set the reorder levels in the tool. The first method is using the system approach. The second method is to use the GAIA classification. The first one is chosen because this Chapter 6. Implementation 51

70 gives Océ insight in how far from optimal they currently are. The latter is chosen because this can give immediate benefits to Océ as stated in Section The results of the system approach are displayed in a summary sheet with the costs and fill-rate per product group and a details sheet with the cost, fill-rate and variables. When one chooses to use GAIA one can determine the class-sizes and the inventory control method. The tool will then calculate the optimal levels per classes and give an output of the settings per product group and detailed settings per SKU. FIGURE 6.2 EXAMPLE OF AN OUTCOME OF THE GAIA CLASSIFICATION 6.2 ACTIONS TO PERFORM FOR USING THE TOOL The tool can support the planners and engineers on decisions on the settings of the SKUs through the classification or the system approach. The added value of this tool is that it proposes parameters based a greedy algorithm, which balances the added cost and fill-rate of an item. However, to be able to use the tool it is important that engineers and planners, of both Océ and the RSHQs of Canon, understand the logic behind the tool and understand how the tool should be used. A presentation has already been given for the engineers at Océ. However, CUSA has up until now not been involved in the project. Their cooperation and understanding is vital for the successful us of the tool. The step after creating awareness is training in the use of the tool. It is important that the right input is uploaded into the tool, that the variables are set in a correct manner and lastly that the output is interpreted correctly. To support this a manual has been written. Lastly, it is important that the tool is used for every RSHQ and product group once in every three months. Because demand and prices of parts can change it is important to keep the settings of the SKUs and / or the classification up to date. Chapter 6. Implementation 52

71 7 CONCLUSIONS AND RECOMMENDATIONS In this chapter first the general conclusions are described that are drawn from the research about classification, followed by the conclusion and recommendations for Océ about spare parts inventory management in their second echelon. Section 7.3 contains some opportunities for future research that have arisen from this research. 7.1 GENERAL CONCLUSIONS In Section the project objective of this thesis is described as follows: Research the design of ABC classification in order to get the lowest annual cost while ensuring a target aggregate fill-rate for a single-echelon model that includes batching, compare different designs and implement the chosen design in a tool that is compatible with GAIA. To research the design of an ABC classification the four aspects for the cost performance of a classification as introduced by van Wingerden et al. (20515) are used. These four aspects are the classification criteria, number of classes, class sizes and target fill-rates per class. The inventory model was a more general than the one used by van Wingerden (2015), with the inclusion of batching, a general demand and effect of emergency shipment costs. In Section 3.3 is shown that without emergency shipment cost the criteria Demand/Price, Demand/Batch*Price and Demand & Price perform best, within a few percentages of the optimal solution. The addition of the batch size in the Demand/ Batch * Price did not give better results, which could be related to the application of the EOQ to the batch size. The D&P performs relatively better than in the research of van Wingerden et al. (2015) which can most probably be attributed to the items in the dataset, especially the fast-moving expensive items. The Annual Dollar Volume and Demand & Frequency criteria continuously perform worse than the beforementioned criteria. The number of classes also has a big impact on costs. For the criteria Demand / Price and Demand / Batch * Price a significant improvent can be seen when using 3 classes instead of two. The improvent, however, gets smaller when more classes are added. It is recommended to use three to four classes for these one-dimensional classification in order to have a near optimal solution and to keep the number of classes manageable. For the Demand x Price classification a significant improvent is found when using 3x3 classes instead of 2x2 classes. Furthermore the class-sizes are shown to have an impact on the performance. The difference with a setting with the best class-sizes can be over 40% of the costs for the Demand / Price classification. This can be explained by the forced presence of stock. Furthermore it is concluded that the classsizes are greatly dependent on the characteristics of the dataset. When significant emergency shipment costs are applied (i.e. 25 in this case) the Demand & Price performs better than the other criteria, but the Demand/Price and Demand/Batch*Price also perform within a few percentages of the system approach. The main difference when applying emergency shipment costs is that the difference between the classifications and system approach is smaller. This difference gets bigger if the objective aggregate fill rate is higher. Chapter 7. Conclusions and recommendations 53

72 Next to that the impact of the class sizes on performance is smaller when applying emergency shipment costs. This can be explained by the fact that if the objective aggregate fill-rate is close to the aggregate fil-rate with the minimum cost not many reorder levels have to be changed. 7.2 RECOMMENDATIONS AND CONCLUSIONS FOR OCÉ Several conclusions and recommendations can be drawn that can be of practical use for Océ. First the recommendations that result from this thesis are stated followed by recommendations for further improvement. Decide transportations modes for individual parts: The transportation of the parts is a big factor of the annual costs (around 50% for WFPS and around 10% for OIP). Applying a simple rule (Appendix D) can yield a big decrease in the costs in the supply chain (around 55% of the costs for WFPS and around 14 % for OIP). In order to make effective use of the rule it is recommended that the dimensions of all parts are stored in the database and the relevant cost factors are communicated well within the Canon organization. Implement the Demand & Price classification or the system approach: As shown in Section 4 the criteria used for GAIA, Demand and Frequency, performs around 20% worse than the Demand x Price classification. This can be explained by the fact that the dimension Price is an important factor for inventory costs and the dimension Frequency is similar to demand. Next to that GAIA does target setting on the basis of a mean per class while a fill rate per class takes the distribution into account. The rest of the difference can be explained by the impossibility to set SKUs to the reorder level where the emergency shipment costs and inventory holding costs are minimal. Furthermore in Section 3 is shown that the D&P classification comes within a few percentages of the system approach. Set class-sizes: As show in Section 3 the class-sizes are an important factor in the cost. The optimal class-sizes are dependent on the dataset and thus have to be determined per dataset. It is thus recommended that Océ sets the right class-sizes for every product group and for every different region. Use the insights in GAIA and the tool to reduce costs on short term in CUSA: In Section 4 is shown that the current settings in GAIA are far from the optimum in the system approach. As GAIA is already implemented in CUSA a recommendation is to use tool to optimize the target setting. Next to that it is recommended to change the class-sizes which also can result in a considerable saving. The change has to be discussed well with the region as this will have a significant impact on the inventory. To be able to implement this it is recommend to share the results of this thesis and to stress the importance of classification on inventory management with the regions and their responsible managers. Recommendations for further improvement: Expand GAIA to other regions and DCs in order to gain control over inventories downstream: GAIA is at the moment only in use for the region USA. The project is currently running for the region Singapore as well and there are plans to expand GAIA to more regions. As shown in this thesis good inventory management can have significant impact on the costs and performance of the organization. Therefore it is recommendable too use GAIA in all regions and try to implement a supply chain management tool as GAIA in the next echelon(s). Chapter 7. Conclusions and recommendations 54

73 Research the effect of classification in a multi-echelon setting: This research was focused on one echelon. However, the service supply chain of Océ consists of more echelons. A It is recommended to get insight into the effects of classification in a multi-echelon setting. Include trends and lifecycle information in forecasts: In this thesis an assumption is made that demand is constant over time. However, SKUs, especially in the beginning and end of their lifecycle, show increase and decline in demand. An interesting topic for research would be to include life-cycles or trends in the forecast of demand. Research the impact of dual-transportation on cost and performance of inventory: In this thesis it is assumed that every SKU has one transportation mode. However, SKUs that are shipped by ocean have the possibility to be shipped by air when net inventory levels are getting low. An interesting topic for research would be the effect of dual-transportation modes and the corresponding optimal parameters. 7.3 RECOMMENDATIONS FOR FUTURE SCIENTIFIC RESEARCH An interesting topic for future research is to see how classification in multiple-echelons could be modelled. Especially target setting and the impact of class-sizes make this an interesting but also complex topic. Furthermore the setting of batch-sizes will probably be different than the EOQ. Furthermore enumeration was used in this thesis to get the best class-sizes. This is a very time intensive process and an interesting research would be to see if there are other possibilities to reach (near) optimal class-sizes. A possibility would be to see if the information from the system approach can be used for this. Next to that it would be interesting to see if a transportation mode per class would get close to optimal settings. A last interesting topic for future research would be the combination of lost-sales and batching in an inventory model. Currently one or the other is there (Kranenburg & van Houtum, 2015) but a combination is not yet there. Chapter 7. Conclusions and recommendations 55

74 8 BIBLIOGRAPHY Axsäter, S., Using the Deterministic EOQ Formula in Stochastic Inventory Control. Management Science, 6(42), pp Axsäter, S., Inventory Control. New York,NY: Springer. Axsäter, S., Inventory Control. 3rd ed. Lund: Springer. Baganha, M. P. & Pyke, D. F., The undershoot of the reorder point: tests of an approximation. International Journal of Production Economics, 45(1), pp Basten, R. & van Houtum, G., System-oriented invenotry models for spare parts. Surveys in Operations Research and Management Science, Volume 19, pp Bijvank, M., Bhulai, S. & Huh, W., Lost-sales Inventory Systems with Fixed Order Costs. Working Paper, pp. Department of Computer Science and Operational Research, University of Montreal. Bijvank, M. & Vis, I. F., Lost-sales inventory theory: A review. European Journal of Operational Research, Volume 215, pp Bijvank, M. & Vis, I. F., Lost-sales inventory systems with a service level criterion. European Journal of Operational Research, Volume 220, pp Castro, R., Introduction and the Empirical CDF. [Online] Available at: [Accessed ]. de Kok, A., Basics of inventory management models, Research reports FEW Tilburg, The Netherlands: Department of Economics, Tilburg University. Ernst, R. & Cohen, M. A., Operations related groups (ORGs): a clustering procedure for production/inventory systems. Journal of Operations Management, pp Feeney, G. & Sherbrooke, G., The (s-1,s) inventory policy under compound poisson demand. Management Science, Volume 19, pp Hadi-Vencheh, A., An improvement to multiple criteria ABC inventory classification. European Journal of Operations Research, pp Huiskonen, J., Maintenance spare parts logistics: Special characteristics. Int. J. Production Economics, Volume 71, pp Johansen, S. & Hill, R., The (r,q) control of a periodic-review inventory system with continuous demand and lost sales. International Journal of, Volume 68, pp Lau, H. & Zhao, L., An efficient computer procedure for constructing the compound lead-timedemand distribution. Computers Industrial Engineering, 16(3), pp Minner, S., Multiple-supplier inventory models in supply chain management: A Review. Int. J. Production Economics, Volume 81-82, pp Chapter 8. Bibliography 56

75 Ng, W. L., A simple classifier for multiple criteria ABC analysis. European Jounal of Operational Research, pp Ramanathan, R., ABC inventory classification with multiple-criteria using. Computers & Operations Research, Issue 33, pp Silver, E. & Peterson, R., Decision Systems for Inventory Management and Production Planning. 2nd ed. New York: John Wiley & Sons. Silver, E., Pyke, D. & Peterson, R., Inventory management and production planning and scheduling. s.l.:john Wiley & Sons. Strijbosch, L. & Heuts, R., Investigating several alternatives for estimating the lead time demand distribution in a continuous review inventory model. Reprint series / CentER for Economic Research, Volume 160. Tagaras, G. & Vlachos, D., A Periodic Review Inventory System with Emergency Replenishments. Management Science, Volume 47, pp Teunter, R. H., Babai, Z. M. & Syntetos, A. A., ABC Classification: Service Levels and Inventory Costs. Production and Operations Management, pp Topan, E., Bayindir, Z. & Tan, T., An exact solution procedure for multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse. Operations Research Letters, Volume 38, pp van der Weijden, N., Spare parts inventory control at Océ, Eindhoven: Eindhoven University of Technology. van Donselaar, K. H. & Broekmeulen, R. A., Fill rate approximations for a perishable inventory system with positive lead time and fixed case pack size using a modified (R,s,nQ)-replenishment policy in a lost sales environment. Available at SSRN: / van Donselaar, K. H. & Broekmeulen, R. A., Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate. Int. J.ProductionEconomics, Volume 143., pp van Houtum, G. & Kranenburg, B., Spare Parts Inventory Control under System Availability Constraints. Eindhoven: Springer. van Wingerden, E., Tan, T. & Van Houtum, G., Design of a near-optimal generalized ABC classification for a multi-item inventory control problem. Working paper. van Wingerden, E., van Houtum, G. & Tan, T., Combining a classification for spare parts with a greedy algorithm coming close to the result of a system approach. Woking paper. Willemain, T. R., Smart, C. N. & Schwarz, H., A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting, Issue 20, pp Chapter 8. Bibliography 57

76 Wong, H., Kranenburg, D., Van Houtum, G. & Cattrysse, D., Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time contraint per local warehouse. OR Spectrum, Volume 29, pp Zhou, P. & Fan, L., A note on multi-criteria ABC inventory classification using weighted linear optimization. European Journal of Operational Research, Issue 182, p Interviews with employees of Océ Internal website Compass Chapter 8. Bibliography 58

77 Appendix A. GAIA Classification As shown in Figure A.1 there are 144 different fields, 12 by 12, that can be assigned to ten different classes named A to J. One of the dimensions is the months of orders and the received order quantity over a year. Months of Demand Received Order QTY ,000-99,999,999 A A A D D D D D G G G G J A A A D D D D D G G G G J B B B D D D D D G G G G J B B B D D D D D G G G G J B B B D D D D D G G G G J C C C E E E E E G G G G J C C C E E E E E G G G G J 6-11 C C C F F F F F H H H H J 3-5 C C C F F F F F H H H H J 2-2 C C C F F F F F I I I I J 1-1 C C C F F F F F I I I I J 0-0 J J J J J J J J J J J J J FIGURE A.1 MAIN CLASSIFICATION GAIA For every location and product group the settings of the classes can be set. In Figure A.2 the decision tree per class can be found. These decisions can be taken: Ordering Point Method: it predicts the demand based on the average historic demand and places orders at the CSC according to that predicted demand. Several parameters can be set with this method: o Safety Stock Weeks on Stock (Standard): This is the number of items, based on the weekly demand, which is used to cover variance in the demand during the leadtime. Orders are placed at the CSC the lead-time before the inventory level is expected to drop under the safety stock. Weeks on Stock (Urgent): When stock is expected to drop below this level of stock, also denoted in weeks of demand, a different transportation mode could be used for the order placed at the CSC. o Forecast Method Average demand: This forecast method uses the average demand of the set time period and predicts the same average. Trend: This method discovers a trend in the demand of the set period and uses this trend in its predictions. Manual o Order Cycle Setup: Per price level, the difference between reorder level and orderup-to-level can be determined, denoted in weeks of demand o Time period: The historic time period on which the forecast is based. Fixed point method o Method: As shown Figure A.3 in the reorder point can be set per price and quantity, a classification that contains 42 classes for which the cut-off values can be set as well Maximum Reorder point: The maximum demand of the past set time period as reorder point Appendix A. GAIA Classification 59

78 o Average Reorder point: The average demand as reorder point Fixed Reorder point: A manual number as reorder point. Time period: The historic time period on which the reorder points are based. FIGURE A.2 INVENTORY POLICY DECISION TREE FIGURE A.3 CLASSIFICATION OF FIXED POINT METHOD Appendix A. GAIA Classification 60

79 Appendix B. Demand Analysis Units of Demand per week Demand per week ,00% 50,00% 100,00% FIGURE B.1 CUMULATIVE GRAPH OF DEMAND PER WEEK CUSA Units of Demand per week Demand per week 5-100% 0 0,00% 50,00% 100,00% FIGURE B.2 CUMULATIVE GRAPH OF DEMAND PER WEEK CUSA (0-5% EXCLUDED) Appendix B. Demand Analysis 61

80 Appendix C. Batch Sizes The determination of the batch size is as following. Firstly the EOQ for item i at warehouse j with yearly demand μ i,j, price c a i,j, fixed order cost c k and holding cost c h i,j can be calculated. EEQ i,j = 2 μ i,jc k h c i,j (8.1) The EOQ is usually not an integer and thus the integer that is rounded up and down from the batch size calculated with the EOQ formula have to be tested. This is done using the total cost formula expressed in equation (8.2). TT(Q i,j ) = c a i,j μ i,j + μ i,jc k Q i,j + c i,j h Q i,j 2 (8.2) if TT rrrrrrrrr EEQ i,j < TT rrrrrrr EEQ i,j thee Q i,j = rrrrrrrrr EEQ i,j eeee: Q i,j = rrrrrrr EEQ i,j The maximum batch size is half year of demand. Q i,j = min (Q i,j, 0,5 μ ii ) (8.3) Appendix C. Batch Sizes 62

81 Appendix D. Transportation Mode The transportation mode T i,j of SKU i at warehouse j is determined before the calculation. Two transport methods are possible: air and ocean. Two variables in our model depend on the decision in t transportation mode, the cost of transportation c i,j and the lead time L i,j. The cost for transportation can be divided into two cost factors, firstly the inventory cost during the extra lead-time and secondly the extra cost for the shipment method. The extra lead-time L eee is the lead-time for shipment by ocean L o minus the lead-time by air L t. L e = L o L a (8.4) The expected demand for item i at warehouse j during this lead time can be expressed as the fill rate β i,j of the item times the demand during the extra lead-time β i,j μ i,j L e. The extra transport cost for air shipment can be expressed as the cost for air shipment c tt i,j minus the cost for ocean shipment c tt i,j. c tt i,j can be calculated using the weight (ω i ) of the object times the price per kilo and the price per kilo c ω for air transport. c tt ω i,j = ω i c j (8.5) The cost for ocean transport can be calculated using a similar manner; however for ocean shipment volume (V i ) is the driving cost factor. c tt V i,j = V i c j (8.6) To calculate the extra inventory holding cost the demand during the extra lead-time has to be multiplied by the holding cost (c h i,j ). Then the transportation method can be determined and thus the lead-time for the item. ii c h i,j μ i,j L e > c tt i,j c tt i,j t thee T i,j = aaa, c i,j = c tt i,j aaa L i,j = L a eeee: T i,j = ooooo, t c i,j = c tt i,j aaa L i,j = L o Appendix D. Transportation Mode 63

82 Appendix E. Results of Chi-Square Test Part Number Category Chi-square Poisson Chi-square N-Binomial Chi-square Gamma 1 Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Slow Medium Slow Medium Medium Medium Slow Medium Medium Medium Slow Slow Medium Medium Medium Medium Medium Slow Medium Medium Medium Chi-square Normal Appendix E. Results of Chi-Square Test 64

83 44 Medium Medium Medium Fast Slow Medium Fast Medium Fast Fast Medium Medium Fast Medium Medium Fast Fast Medium Fast Fast Medium Fast Fast Fast Fast Fast Medium Fast Fast Medium Medium Fast Fast Fast Fast Fast Fast Fast Fast Fast Fast Fast Fast Appendix E. Results of Chi-Square Test 65

84 Appendix F. Non-parametric distribution To calculate P{D i,j (X) = x} the empirical distribution is used. This distribution is created either by following Strijbosch & Heuts (1994) or from Willemain (2004) et al. When the number of combination, NN, as expressed in Equation (8.7), exceeds 2000 the method of Willemain et al. (2004) is chosen, otherwise the method of Strijbosch & Heuts (1994). n + r 1 NN = r (8.7) Where n is the number of different demand quantities and r the amount drawn from the demand quantities. This amount is equal to the lead-time in weeks. Strijbosch & Heuts (1994) generate the probability density function as follows. This explanation will be done by example of the demand of a part for a lead-time of 3 weeks. First of all they construct a frequency table as in Table 15. TABLE 15 FREQUENCY TABLE PART IN COLUMBUS Count Frequency Probability Then all different combinations are listed of the demand during lead-time. Each combination can be ordered differently. To correct for this the number of permutations per combination is calculated. With the number of permutations and the probability on each demand the probability of the combination can be constructed as displayed in Table 16. TABLE 16 TABLE WITH ALL COMBINATIONS FOR PART IN COLUMBUS AND L =3 Demands Sum No of Permutations Probability 0,0, x0.92x0.92x0.92 0,0, x0.92x0.92x0.04 0,0, x0.92x0.92x0.04 0,1, x0.92x0.04x0.04 0,1, x0.92x0.04x0.04 0,2, x0.92x0.04x0.04 1,1, x0.04x0.04x0.04 1,1, x0.04x0.04x0.04 1,2, x0.04x0.04x0.04 2,2, x0.04x0.04x0.04 Appendix F. Non-parametric distribution 66

85 Using the probabilities of each combination and the respective demand during the lead-time a lead time demand distribution can be created as displayed in Table 17. TABLE 17 PROBABILITY DENSITY FUNCTION Warehouse Product P(X=0) P(X=1) P(X=2) P(X=3) P(X=4) P(X=5) P(X=6) nr. CLMBS When the number of combinations is more than 2000 the simulation method of Willemain et al. (2004) is used. They use the following algorithm to construct the probability density function: Step 0 Step 1 Step 2 Step 3 Step 4 Obtain historical demand data in chosen time buckets (weeks) Estimate transition probabilities for two-state Markov model (zero demand vs. non-zero demand) Use Markov model to generate a sequence of zero/nonzero values over the lead-time period Replace every nonzero state marker with a numerical value sampled at random with replacement from the set of observed nonzero demands Jitter the nonzero demand values. This is done the following way. Let X be an observed nonzero demand and Z be a standard normal random deviate: JJtttttt = rrrrr(x + Z X) ii JJJJJJJJ < 1 Thee JJJJJJJJ = X It is chosen to only Jitter values higher than 4, since a deviation from the average demand can be seen when values lower than 5 are jittered. This is due to a high probability of jittered demands less than 1 that are set to the mean. Step 5 Step 6 Sum the forecast values over the lead time Repeat step times and construct a PDF. Appendix F. Non-parametric distribution 67

86 Appendix G. Calculation fill-rate and average inventory level Axsäter (2015) describes how to calculate the fill-rate for an item when backordering, discrete demand, batching and a periodic review period is used. For SKU i at warehouse j we consider the interval between the two times t + L i,j and t + L i,j + R where L ii is the lead-time and R is the review period. The expected demand during this period is μ i,j R. We consider the part of the demand in this interval that cannot be met from stock. This part of demand is backordered. It can be determined as the difference between the expected backorders after lead-time, E(IL ) i,j, and the expected backorders after lead-time and review period, E(IL ) i,j. This means that the fill rate can be determined following equation 5.79 in Axsäter (2015): β i,j (s ii, Q ii ) = 1 E(IL ) i,j E(IL ) i,j μ i,j R (8.8) Axsäter (2015) points out that using equation (8.9), as given below, is usually most practical to calculate the expected backorders E(II). This formula uses the expected net inventory E(II) + and expected inventory position E(II) to calculate the expected backorders. It is an exact formula and it is used becausee(ii) + cannot be higher than S i,j + Q i,j while E(II) can go to infinity. Equation (8.9) can be used to calculate E(II ) ii and E(II ) ii. E(II) = E(II) + E(II) (8.9) E(IL ) ii = s ii + Q i,j + 1 μ 2 i,j L i,j E(IL ) ii = s ii + Q i,j μ i,j L i,j + R (8.10) (8.11) To calculate the net inventory E(II) + Equation (5.78) from Axsäter (2015) is used as expression for the probability that after a period of demand the net inventory level II is b. s i,j +Q i,j P(IL ii = b) = 1 P{D Q i,j (X) = k b} i,j k=max [s i,j +1,b] (8.12) D i,j (X) is the demand of SKU i at warehouse j during a time period X. P{X = x} depends on the distribution of demand during lead-time or the distribution of demand during lead time and review period. The distributions can be looked up in the probability density function as created in Appendix F. Using Equation (8.13) the net inventory level can be calculated, since the net inventory can range from 0 to s ii + Q ii. s i,j +Q i,j s i,j +Q i,j 1 E(II) + ii = b P{D Q i,j (X) = k b} i,j b=0 k=max [S i,j,b] (8.13) Appendix G. Calculation fill-rate and average inventory level 68

87 Concluding, in order to calculate the fill rate of an SKU, β ii (s ii, Q ii ) one can follow the formula as given above in Equation (8.8). In this equation the expected backorders after lead-time, E(II ) i,j, and the expected backorders after lead-time and review period, E(IL ) i,j, are used. In order to calculate these Equation (8.9),(8.10),(8.11),(8.12) and Equation (8.13) are used. These are summarized in Equation (8.14) and (8.15). s i,j +Q i,j s i,j +Q i,j 1 E(IL ) i,j = b P{D Q i,j (L ii + R) = k b} i,j b=0 k=max [S i,j,b] s i,j +Q i,j s i,j +Q i,j 1 E(II ) i,j = b P{D Q i,j (L ii ) = k b} i,j b=0 k=max [S i,j,b] s ii + Q i,j + 1 μ 2 i,j L i,j + R s ii + Q i,j + 1 μ 2 i,j L i,j (8.14) (8.15) Besides calculating the fill rate of an SKU at a warehouse the results of the formula can also be used to calculate the average net inventory. The average net inventory II + is the average inventory in a review period, thus the average over the inventory at the start of the review period and the end of the review period: II + = E(IL ) + + E(IL ) + 2 (8.16) Appendix G. Calculation fill-rate and average inventory level 69

88 Appendix H. Local minima of a class When finding the fill-rate with the lowest cost of a class one cannot just raise the part with the lowest fill rate until cost increases. As can be seen in Figure H.1, the costs steadily drop and the lowest cost can be found near a fill-rate of 100% (this is a scenario with 50 emergency shipment costs). In Figure Y we can however see that there are many local minima, and the global minimum can only be found by looking further than the local minima. $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $ ,00 $50.000,00 $- 0,0% 20,0% 40,0% 60,0% 80,0% 100,0% Fill rate FIGURE H.2 FILL RATE OF A CLASS WITH 100 ITEMS AND ITS RESPECTIVE COSTS $66.000,00 $65.500,00 $65.000,00 $64.500,00 $64.000,00 $63.500,00 $63.000,00 $62.500,00 97,5% 98,0% 98,5% 99,0% 99,5% 100,0% Fill rate FIGURE H.1 FILL RATE OF A CLASS WITH 100 ITEMS AND ITS RESPECTIVE COSTS FROM 98% % Appendix H. Local minima of a class 70

89 Appendix I. System Approach The system approach is taken from Houtum & Kranenburg (2015). First the parameters are stated: I J β ii s ii E(II) i,j The set of SKU s {1,2,, I} with I ε N The set of warehouses {1,2,.. J} with J N The fill rate for part i ε I at warehouse j J calculated as in Appendix G The expected net inventory level for part i ε I at warehouse j J calculated as in Appendix G M Average total demand i I j J μ ii μ ii Average of demand for part i ε I at warehouse j J s ii Reorder level of part i ε I at warehouse j J c h Holding cost rate C ii s ii Total cost per year of part i ε I at warehouse j J C(S) C(S) = C i (S i ) i I = c a i S i I i, the total investment cost β(s) Aggregate fill rate i I j J β ii s ii ee c ii Penalty cost for part i ε I at warehouse j J for a backorder β ooo The target aggregate fill rate The inventory holding costs per time unit are c h i S i and the cost per time unit for emergency shipments are μ i 1 β i (S i ) c ee ii. C i,j s i,j = c h E(II) i,j + β ii μ i,j L i,j + μ i,j 1 β i,j s i,j c ee (8.17) And the total average cost is equal to C(s) = i I j J C i,j s i,j and the objective is to minimize the cost under the aggregate fill rate constraint. Min Subject to C(s) β(s) β ooo This is solved using the greedy algorithm. The first step is to find the reorder level s ii,ll where the costs are minimal when emergency shipment costs are applied. s ii,ll min s ii N ΔC ii s ii > 0 i I, j J (8.18) Then the following algorithm is applied: Step 1 Step 2 Set s ii = s ii,ll for all i I and j J Compute C(s) and β(s) Γ ii = (Δβ ii s ii /ΔC ii s ii for all i I, j J k = aaaaaa Γ ii ; i I, J J s = s + e k Appendix I. System Approach 71

90 Step 3 Compute C(s) and β(s) If β(s) β ooo A case study shows that the use of commonality, even be it small, has an impact on the inventory costs. Appendix I. System Approach 72

91 Appendix J. Manual calculation In this appendix the manual calculations and results from the coded program are compared. First the EOQ and transportation mode calculations are compared, then the calculation of the fill rate is shown, then the system approach is calculated and lastly classification is checked. EOQ AND TRANSPORTATION MODE The parts considered are listed in Table 18 and the respective costs in Table 19. TABLE 18 PRODUCTS IN MANUAL CALCULATION Warehouse Product nr. Price Mean Volume Weight CLMBS 1 $ CLMBS 2 $ Euro ($1.06) Dollar Cost ocean/m $ Cost air/kg 4.50 $ 4.76 Cost emergency $ fixed order cost 5 $ 5.29 Holding cost rate 20% This led through the calculations to the results as given in Table 19. TABLE 19 RESULTS CALCULATED THROUGH PROGRAM Warehouse Productnr Cost transport Emergency Shipment cost Q L Mode CLMBS Air CLMBS Air For the manual calculation the following steps have been followed. Firstly with the parameters given the transportation mode and costs of both parts can be calculated following Appendix D. TABLE 20 CALCULATION OF TRANSPORTATION MODE WITH LEAST COST Transportation mode Air Cost Ocean Cost Inventory Transport Sum Inventory Transport Sum Mode CLMBS 1 $ 0.01 $ 0.01 $ 0.02 $0.02 $0.00 $0.02 Air CLMBS 2 $ 0.78 $ 0.90 $1.68 $2.34 $0.05 $2.39 Air Appendix J. Manual calculation 73

92 The following step is calculation of the emergency shipment cost by subtracting the transportation cost from the emergency shipment cost (Table 21). TABLE 21 EMERGENCY SHIPMENT COST Cost / shipment Transportion Emergency CLMBS 1 $ 0.01 $ CLMBS 2 $ 0.90 $ For calculation of the optimal batch size the EOQ is calculated first, followed by the calculation of the integer optimal batch size. The last step is maximizing the batch size by a half year of demand. This is done following Appendix C. TABLE 22 THE CALCULATION OF EOQ AND OPTIMAL BATCH SIZE EOQ Qoptim EOQmax $2.46 $ $ $ All manual calculations matched the outcomes of the program. FILL RATE AND COST For the fill rate and cost calculation the master data considered are listed in Table 23 and the respective demand for the parts are listed in Table 24 and Table 25. TABLE 23 MASTER DATA SELECTED PARTS Warehouse Productnr Price Mean cte Q L CLMBS 1 $ $ CLMBS 2 $ $ TABLE 24 PDF (CLMBS,1) (CLMBS,1) X P(D(L)=X) P(D(L+R) = X) E-06 TABLE 25 PDF (CLMBS,2) (CLMBS,2) X P(D(L)=X) P(D(L+R) = X) E-06 In this section the formulas used from Axsäter (2015) (Appendix H) are applied in order to find the fill rate and costs of the reorder levels. These numbers (see next two pages) are compared to the outcomes of the program and matched. Appendix J. Manual calculation 74

93 CALCULATION FILL RATE AND RESPECTIVE COST FOR (CLMBS,1) TABLE 26 PROBABILITY MATRIX FOR IL IN LEADTIME TABLE 27 INVENTORY LEVEL MATRIX IN LEADTIME To IL (b) In lead time From IL (k) P(X=k-b) TABLE 28 PROBABILITY MATRIX FOR IL IN LEADTIME AND REVIEW PERIOD s P(IL = b) * b EIL+ EIL EIL TABLE 29 INVENTORY LEVEL MATRIX IN LEADTIME AND REVIEW PERIOD To IL (b) In lead time From IL (k) P(X=k-b) TABLE 30 FILL RATE AND CORRESPONDING COST s P(IL = b) * b EIL+ EIL EIL s P2 IL Inventory Cost Emergency Shipment cost Cost Delta Cost Delta P2 Gamma cte 25 Delta Inventory cost Gamma cte % 0.37 $ 9.32 $ $ % 1.21 $ $ $ % 2.17 $ $ 7.34 $ % 3.16 $ $ 1.00 $ % 4.16 $ $0.09 $

94 CALCULATION FILL RATE AND RESPECTIVE COST FOR (CLMBS, 2) TABLE 31 PROBABILITY MATRIX FOR IL IN LEADTIME TABLE 32 INVENTORY LEVEL MATRIX IN LEADTIME In lead time From IL (k) P(X=k-b) TABLE 33 PROBABILITY MATRIX FOR IL IN LEADTIME AND REVIEW PERIOD To IL (b) s P(IL = b) * b EIL+ EIL EIL TABLE 34 INVENTORY LEVEL MATRIX IN LEADTIME AND REVIEW PERIOD To IL (b) In lead time From IL (k) P(X=k-b) s P(IL = b) * b EIL+ EIL EIL Table 35 Fill rate and corresponding cost s P2 IL Inventory Cost Emergency Shipment cost Cost Delta Cost Delta P2 Gamma cte 25 Delta Inventory cost Gamma cte 0-1 0% 0.00 $- $ $ % 0.95 $ 0.20 $ 1.01 $ % 1.95 $ 0.40 $ 0.01 $ % 2.95 $ 0.60 $ - $ % 3.95 $ 0.80 $ - $ Appendix J. Manual calculation 76

95 SYSTEM APPROACH In order to check the application of the system approach Appendix G is applied. In the last two pages the difference in cost and fill rate can be found and the resulting Γ ij (s ij ) can be found. The objective aggregate fill rate is set to 95%. The system approach is calculated two times, once with 25 emergency shipment cost (Table 36) and once with 0 emergency shipment cost (Table 37), because in the first scenario the objective aggregate fill rate is already met when the combination with the lowest cost is taken. In both scenarios outcomes of the manual calculation and the program match. TABLE 36 SYSTEM APPROACH 25 EMERGENCY SHIPMENT COST s Gammamax Item Agg P2 Cost (1,1) $ TABLE 37 SYSTEM APPROACH 0 EMERGENCY SHIPMENT COST s Gammamax Item Agg P2 Cost (-1,-1) (CLMBS,2) $ 9.32 (-1,0) (CLMBS,2) $ 9.51 (-1,1) (CLMBS,1) $ 9.71 (0,1) CLMBS,1) $ (1,1) $ CLASSIFICATION For the classification two things are checked. First of all it is checked that the right class-sizes are created. This is done by setting the steps in threshold values to 0.2 on a 3x3 classification. The number of different scenarios can be calculated as follows. For a 3x3 classification there are 2 threshold values for each dimension. The first threshold has to be smaller than the second threshold (otherwise overlapping or empty classes are created). Thus for one threshold value the values can be [ 0.2 ; 0.4 ; 0.6 ; 0.8 ]. When the first class is 0.2 there are three possibilities for the second class [0.4 ; 0.6 ; 0.8]. When the first class is 0.4 there are two possibilities left, and when the first class is 0.6 only one. This gives us 6 different possibilities for one dimension. Because every combination between the dimensions can be made the total number of scenarios can be 6x6. This is also the result of the program as can be seen in Table 38. TABLE 38 ENUMERATION OVER CLASS-SIZES index Dimension 1 Dimension 2 index Dimension 1 Dimension 2 index Dimension 1 Dimension

96 In order to control if the program classifies items well the 100 items that are also taken for Section 3 are checked. These 100 items have been classified in four classes with threshold values 0.89, 0.96 and on the criterion D/BP. The D/BP column has been calculated to see if the sequence of the items is correct. Then the Cumulative Mean was calculated, followed by a translation to percentages. These match with the percentages that were the outcome of the program. Lastly the items have been checked on the classes they belong to, which corresponds with the cut-off values. TABLE ITEMS CLASSIFIED ON D/BP CRITERION Warehouse Productnr Price Mean Q D/BP Cumulative Mean Appendix J. Manual calculation Cumulative Mean% Calculated Cumulative Mean% Program CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS Class 78

97 CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS CLMBS Appendix J. Manual calculation 79

98 Appendix K. Classification with 50 emergency shipment costs TABLE 40 RESULTS OF CLASSIFICATION OF 100 PARTS WITH 50 EMERGENCY SHIPMENT COSTS Criteria Demand / (Batch * Price) Nr of classes 90% 95% 98% 2 $22, $24, $28, $22, $24, $28, $22, $24, $28, $22, $24, $28, $22, $24, $28, Demand/Price 2 $22, $24, $28, $22, $24, $28, $22, $24, $28, $22, $24, $28, $22, $24, $28, Annual Dollar Volume 2 $22, $24, $29, $22, $24, $29, $22, $24, $29, $22, $24, $29, $22, $24, $28, Demand & Price 2 x 2 $22, $23, $28, x 3 $22, $23, $28, Demand & Frequency 2 x 2 $22, $23, $29, x 3 $22, $23, $29, Item approach $30, $34, $37, System $22, $23, $28, % 108% 106% 104% 102% 100% FIGURE K.1 COMPARISON OF CLASSIFICATION WITH THE SYSTEM APPROACH (50E EMERGENCY SHIPMENT COSTS) Appendix K. Classification with 50 emergency shipment costs 80

99 Appendix L. Comparison R,s,S and R,s,Q The R,s,S policy order in batches as well as the R,s,Q policy. However, in the latter the batch size is fixed to a multiple of Q, while in the R,s,S policy the batch size is dependent on the current inventory position and S, the order-up-to-level. Axsäter (2015) explains that the (R,s,S) policy is from a theoretical point the most advantageous. However, he notes that the differences are, in general, very small. FIGURE L.1 GRAPHIC REPRESENTATION OF THE R,S,Q POLICY (AXSÄTER 2015) FIGURE L.2 GRAPHIC REPRESENTATION OF THE R,S,S POLICY (AXSÄTER 2015) In the R,s,S policy the batch sizes are bigger or equal to the R,s,Q policy if S s = Q. This is because of the undershoot, the amount of demand that is under the reorder point on review. Axsäter(2015) describes that a (R,s,S) policy is similar to an (R,s,Q) policy but that for an (R,s,S) policy the inventory position after review is not a uniform distribution between [s + 1, S + Q] as in an (R,s,Q) policy. Following chapter 5.11 and in Axsäter (2015) the distribution between [s + 1, S] has been determined for the selected items. With this distribution the (R,s,Q) policy has been adapted to a (R,s,S) policy and programmed in python. To quantify the difference between the two policies a comparison has been made where S s = Q. To do this 100 items have been randomly selected from the OIP group and the system approach has been applied to bring the aggregate fill rate to 95%. This aggregate fill rate has been chosen because this is the real objective aggregate fill rate of the RSHQ CUSA and the system approach has been taken in order to get a realistic setting of the reorder levels. The detailed results can be found in Table 43 and a summary of the results in Table 41. TABLE 41 SUMMARY COMPARISON OF R,S,S - R,S,Q (S - S = Q) R,s,S R,s,Q Difference Difference Q>1 P2 95.5% 95.0% 0.4% 0.8% IL % 5.6% As can be seen there is a slight difference in the aggregate fill rate and a quite significant difference in expected inventory level, which is directly related with the inventory cost. To show the effect an extra column has been added to show the difference when the batch size is bigger than one, since for a batch size equal to one the (R,s,S) and the (R,s,Q) policy are the same (the probabilities on inventory position (S + 1) after review is in both cases equal to one). Appendix L. Comparison R,s,S and R,s,Q 81

100 In order to make a better comparison one can also adjust the batch size Q ii with the average undershoot. This is approximated by Baganha & Pyke (1996) but still requires a lot of computation. Therefore another approximation has been used. In the hypothetical situation that the order-up-tolevel S is relatively high one can say that the inventory position crosses the reorder level at a random point. Thus, on average there is a half review period level left until the next review. If the demand is symmetrical, then on average the undershoot is the demand in a half review period. This is used in an approximation of the (R,s,S) with the (R,s,Q) policy. In this approximation Q ii + μ iir 2 = S ii s ii. The detailed results of this comparison can be found in Table 44 and a summary of the results in Table 42. TABLE 42 SUMMARY COMPARISON APPROXIMATION OF R,S,S - R,S,Q R,s,S R,s,Q Difference Difference Q>1 P2 95.1% 95.0% 0.03% 0.26% IL % 2.03% The results show that this is a very close approximation to the (R,s,S) policy with a deviation of the aggregate fill rate of 0.03% and a deviation in inventory level of 1.33%. This approximation is used throughout the thesis when comparing the model with the actual situation. Appendix L. Comparison R,s,S and R,s,Q 82

101 TABLE 43 COMPARISON R,SQ - R,S,S WHERE S-S = Q Warehouse Productnr IL_R,s,Q P2_R,s,Q IL_R,s,S P2_R,s,S Mean Q S S-s CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % Appendix L. Comparison R,s,S and R,s,Q 83

102 CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % Appendix L. Comparison R,s,S and R,s,Q 84

103 TABLE 44 COMPARISON R,SQ - R,S,S WHERE S-S = Q + 0.5MUR Warehouse Productnr IL_R,s,Q P2_R,s,Q IL_R,s,S P2_R,s,S Mean Q S S-s CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % Appendix L. Comparison R,s,S and R,s,Q 85

104 CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % CLMBS % % Appendix L. Comparison R,s,S and R,s,Q 86

105 Appendix M. TABLE 45 NORMALIZED RESULTS OF SYSTEM APPROACH System Approach Comparison Index Grou p P2agg Total Cost Emergency Inventory Order Transporati on 1 (EOQ,TR) FB 98.3% (Cur,Cur) FB 95.0% (EOQ, FB 95.4% Cur) (Cur, TR) FB 98.2% Current FB 95.1% (EOQ,TR) OA 95.3% (Cur,Cur) OA 95.0% (EOQ, OA 95.1% Cur) (Cur, TR) OA 95.5% Current OA 91.5% Appendix M. System Approach Comparison 87

106 TABLE 46 CLASS - SIZE AND COST D/P 2 CLASSES Appendix N. Class size and cost Cut off val Size class C 90% 95% 98% % $25, $30, $35, % $25, $30, $35, % $24, $29, $35, % $24, $29, $35, % $23, $29, $33, % $23, $27, $33, % $22, $27, $33, % $22, $27, $33, % $22, $26, $32, % $20, $26, $32, % $20, $24, $31, % $19, $24, $30, % $18, $23, $30, % $16, $22, $29, % $15, $21, $29, % $15, $21, $28, % $13, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $12, $20, $27, % $21, $26, $33, % $21, $26, $33, % $21, $26, $33, % $22, $27, $34, % $22, $27, $34, % $24, $30, $36, Appendix N. Class size and cost 88

107 Appendix O. Settings for GAIA For Océ it is recommended to set the Demand axis at 65% and 75% of the demand. The frequency axis is recommended to be set at 40% and 75% of the demand. This yields the following main classification table: FIGURE 8.1 SETTINGS FOR THE WFPS GROUP FIGURE 8.2 SETTINGS FOR THE OIP GROUP Appendix O. Settings for GAIA 89