OPTIMIZATION OF STORAGE CATEGORIZATIONumu.diva-portal.org/smash/get/diva2:1214830/FULLTEXT01.pdf ·...

Master thesis, 30 ECTS

Master of Science in Industrial Engineering and Management, 300 ECTS

Spring 2018

OPTIMIZATION OF STORAGE CATEGORIZATION

A simulation based study of how categorization

strategies affect the order fulfillment time in a

multi-picker warehouse

Linnea Nilsson & Linnea Tiensuu

Abstract

The most costly and labor-intensive activity for almost every warehouse is the orderpicking process and a key challenge for manufacturing companies is to store parts inan efficient way. Therefore, to minimize the order retrieval time when picking from astorage, the need of a sufficient storage categorization strategy becomes vital.

One of the logistics centers at Scania in Sodertalje stores parts that will be transportedto the chassis assembly and the assembly of gearboxes and axles when needed in theproduction. In one of the storage areas at the logistics center, namely the PS storage,the forklift drivers picking from the storage have experienced congestion in the storageaisles and that it might be possible to reduce the order fulfillment time when pickingthe orders.

This master thesis aims to investigate the possibility of optimizing the picking processin the PS storage, with respect to the order fulfillment time for the forklift drivers,with categorization of the goods. This has been analyzed with a heuristic optimizationapproach and with the use of a discrete event simulation model, where different cat-egorization strategies have been applied on the storage and compared to the currentstate.

By categorizing the goods in the PS storage, a reduction of the order fulfillment time canbe done of around 4% - 5% compared to the current state with all tested categorizationstrategies. The strategy which has been shown to give the largest improvement is bycategorizing the parts in the storage according to their final delivery address at theproduction line, which would reduce the order fulfillment time by 5.03% compared tothe current state. With this categorization method, parts that are picked on the sameroute are located close to each other.

Keywords: Storage categorization, Multi-picker system, Multi-item order system, Stor-age Location Assignment Problem, Discrete event simulation

Sammanfattning

Den mest kostsamma och arbetsintensiva aktiviteten i nastan alla lager ar plockningspro-cessen, darav ar en av de storsta utmaningarna for tillverkande foretag att lagerhallaartiklar pa ett effektivt satt. For att minimera orderhamtningstiden i ett lager ar darforen lamplig kategorisering av artiklarna i lagret nodvandig.

Ett av logistikcentrena pa Scania i Sodertalje lagerhaller artiklar som sedan ska trans-porteras till chassimonteringen och monteringen for vaxellador och axlar nar de behovsi produktionen. I ett av lageromradena pa logistikcentret, namligen PS-lagret, hartruckforarna upplevt trangsel i lagergangarna samt att det kan vara mojligt att minskakortiden nar de plockar i lagret.

Syftet med detta examensarbete ar att undersoka mojligheten att optimera plockn-ingsprocessen i PS-lagret, med avseende pa truckforarnas orderhamtningstid, genom attkategorisera artiklarna i lagret. Detta har analyserats med ett heuristiskt angreppssattoch med anvandningen av en diskret handelsesimulering, dar olika kategoriseringsstrate-gier har implementerats i lagret och jamforts med nulaget.

Genom att kategorisera artiklarna i PS-lagret kan orderhamtningstiden minskas medomkring 4% - 5% jamfort med nulaget, med alla testade kategoriseringsstrategier. Denstrategi som visade sig ge den storsta forbattringen var att kategorisera artiklarna ilagret enligt deras slutliga leveransadress vid produktionen, vilket skulle minska or-derhamtningstiden med 5.03% jamfort med nulaget. Med denna kategoriseringsstrategiplaceras artiklar som plockas pa samma runda nara varandra.

Nyckelord: Lagerkategorisering, Multi-picker system, Multi-item order system, StorageLocation Assignment Problem, Diskret handelsesimulering

Svensk titel: Optimering av forradskategorisering

Acknowledgements

We wish to thank all people that have contributed to this master thesis. Firstly, we wishto sincerely thank Pal Skogtjarn at Scania for the opportunity to perform this masterthesis at the OLSX division and for believing in us and our work. We would also liketo thank our supervisor at Scania, Carl Esping, for all the support and for providing uswith all necessary resources and always answering our questions.

An extra thanks also goes to Par Martensson at Scania, for all the support and helpfultips about the simulation software ExtendSim and for your guidance when building ourown simulation model.

We also wish to thank our supervisor at Umea university, Jonas Westin, for all thevaluable support and feedback throughout this project. Your expertise within the opti-mization area, your enthusiasm and your ability to see our problems in new perspectiveshave been very valuable for us during this project.

Last but not least we wish to thank everyone else at the OLSX division at Scania andall involved operators at the Logistics Center for always taking the time to answer ourquestions, encouraging our work and always making us feel welcome.

SodertaljeMay 24, 2018

Linnea Nilsson & Linnea Tiensuu

Contents

1 Introduction 1

1.1 Scania CV AB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Scania Logistics Center in Sodertalje, OLS . . . . . . . . . . . . . 1

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.5 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.6 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.7 Disposition of project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.8 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Description of Current State 7

2.1 Logistics Engineering, OLSX . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Storage of goods to the chassis assembly . . . . . . . . . . . . . . . . . . 8

2.2.1 Program, Master and Development picking . . . . . . . . . . . . 8

2.2.2 The PS Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Theoretical Background 13

3.1 Storage management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Storage assignment strategies . . . . . . . . . . . . . . . . . . . . 13

3.2 Clustering analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Jaccard’s similarity index . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Optimization theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3.1 Assignment Problem . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3.2 Storage Location Assignment Problem . . . . . . . . . . . . . . . 16

4 Method 19

4.1 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.1 ExtendSim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.2 Microsoft Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

vii

viii CONTENTS

4.3 Mathematical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3.1 Formulation of model . . . . . . . . . . . . . . . . . . . . . . . . 22

4.4 Categorization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.4.1 Description of categorization strategies . . . . . . . . . . . . . . . 23

4.5 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.5.1 Description of model . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.5.2 Verification of model . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.5.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.6 Construction of simulation tool . . . . . . . . . . . . . . . . . . . . . . . 29

5 Result 31

5.1 Simulation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1.1 Queuing time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.3 Number of racks per route . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6 Discussion 37

6.1 Choice of optimization method . . . . . . . . . . . . . . . . . . . . . . . 37

6.2 Analysis of simulation result . . . . . . . . . . . . . . . . . . . . . . . . . 37

6.2.1 Analysis of queuing time . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.3 Further factors affecting the result . . . . . . . . . . . . . . . . . . . . . 40

6.4 Implementation of a categorization in practice . . . . . . . . . . . . . . . 41

6.5 Wider perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7 Conclusions 43

8 Future Research 45

References 47

A Pseudo code I

A.1 ABC-classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

A.2 Classification according to program . . . . . . . . . . . . . . . . . . . . . II

A.3 Classification according to delivery address . . . . . . . . . . . . . . . . II

A.4 Classification according to Jaccard’s similarity index . . . . . . . . . . . III

A.5 Random location strategy . . . . . . . . . . . . . . . . . . . . . . . . . . IV

B Simulation model V

List of Figures

2.1 An overview of the area where buildings 210, 230 and 270 are located. . 8

2.2 Overview of the layout design of the racks for the PS, CHP and LVF

storage areas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.1 Overview of a part of the simulation model from ExtendSim. . . . . . . 26

5.1 Savings in order fulfillment time compared to the current state. . . . . . 32

5.2 Total order fulfillment time in proportion to the current state. . . . . . . 33

5.3 Sensitivity analysis of the use of different disruptions in the model. . . . 34

5.4 Average number of racks visited per route with the different categoriza-

tion strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

B.1 Overview of the whole simulation model from ExtendSim. . . . . . . . . VI

B.2 Example of the input file which is inserted in the simulation model in

ExtendSim. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

B.3 Example of output from the simulation model in ExtendSim. . . . . . . VIII

ix

x LIST OF FIGURES

List of Tables

2.1 Distribution of the activity in the storage area. . . . . . . . . . . . . . . 9

3.1 Table of commonly used divisions of ABC-classification. . . . . . . . . . 14

5.1 Savings in order fulfillment time for each categorization strategy com-

pared to the current state. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Percentage of total order fulfillment time which was spent queuing. . . . 33

5.3 Average and maximum number of visited racks per route. . . . . . . . . 35

xi

xii LIST OF TABLES

Abbreviations and Terminology

Abbreviations

AP Assignment Problem

FIFO First In First Out

LC Logistic Center

RCAP Resource Constraint Assignment Problem

SLAP Storage Location Assignment Problem

Terminology

Development picking Picking process for picking parts to the development line.

Master picking Picking process for picking low volume parts into cages.

MS The chassis assembly.

Multi-picker system Picking system with multiple pickers operating in the stor-age area.

OL Scania Logistics Center Sweden, the department responsi-ble of Scania’s logistics activities in the Swedish factories.

OLS Scania’s logistics center for the chassis assembly and theaxle and gearbox assembly in Sodertalje.

OLSX The department of Logistics Engineering at OLS inSodertalje.

Order fulfillment time The total time of retrieving an order from the storage, in-cluding driving time, picking time and queuing time.

Picker-to-part system A picking system where the picker travels to the storagelocation of the parts.

Program picking Picking process for picking low volume parts into pallets.

Routing policy Policy for determining the driving behavior and routes oftraveling.

xiii

Chapter 1

Introduction

This chapter gives an introduction to the project, including the problem background,purpose and the research questions that have been formulated for the project. Also, thedelimitations which have been made, related studies and the disposition of the projectare presented.

1.1 Scania CV AB

This master thesis has been carried out with help from and in collaboration with ScaniaCV AB in Sodertalje. Scania CV AB (henceforward entitled as Scania) is a globalautomotive manufacturer of commercial vehicles, producing heavy trucks and buses aswell as diesel engines and other general industrial applications. Scania was foundedin 1891 and has since then had the headquarter in Sodertalje. Scania is a part ofVolkswagen Truck & Bus and has more than 49 000 employees in 100 countries all overthe world [1].

1.1.1 Scania Logistics Center in Sodertalje, OLS

Scania Logistics Center Sweden, OL, handles Scania’s logistics activities in the Swedishfactories and is divided into three areas in Sodertalje and Oskarshamn. One of thetwo logistics centers in Sodertalje, OLS, is responsible of the delivery of material tothe chassis assembly and the assembly of gearboxes and axles, and they also handlepackaging decomposition [8]. The OLS is managing the receiving of 2 200 units per day,which are stored in a 17 000 square meter storage area. The storage area consists of28 000 box store locations and 13 000 pallet store locations, from where 3 900 picks aredone per day. Each day, 2 100 pallets and 1 500 boxes are delivered from the storagearea to the chassis assembly and to the assembly of gearboxes and axles. The goodsare delivered and received with logistics trains, each hour 14 trains go out from and 30trains go in to the logistics center.

1

2 Chapter 1. Introduction

1.2 Background

Every truck produced at Scania is unique and therefore different components need to beused for different trucks. Because of this, a lot in the production processes have to becoordinated, and it is important that the right parts are at the right place at the righttime. If this is not done successfully, it will affect the production flow in several mannersand furthermore it might lead to disruptions in the processes. The production systemat Scania is based on a PULL-system, i.e. what is produced is based on the customers’orders. This also means that the consumption of material and parts differs dependingon what the customer has ordered. Scania offers a variety of products for the customersand several extra options are available, which increase the number of unique parts andthe demand of storage. This also entails that all the material and parts used in theassemblies can not be placed in direct connection to the production line. To handle allthe material it is necessary to have logistics centers, LC’s, where low volume and bulkyparts can be stored before they are transported to the assemblies in the right time forthe production.

To have a productive and efficient storage management, it is crucial to categorize thegoods in an optimal way. A good way of categorizing the goods can minimize the drivingtime and distance for the forklift drivers working in the storage, which in turn reducesthe non-value-adding time [15]. In one part of the storage area at the LC, namely the PSstorage, it has been experienced that the forklift drivers some times have to wait in lineto be able to pick their orders due to congestion in the storage aisles, and that it mightbe possible to reduce the driving distance while picking the orders. This specific storagedoes not have a specified categorization of the goods in it and it has been suggested thatthis might be the reason for the experienced inefficiency.

1.3 Purpose

The purpose of this master thesis is to analyze and examine if it is possible to optimizethe picking process, with respect to the order fulfillment time for the forklift drivers,in a certain storage with categorization of the goods. The project should also result ina general method of how to categorize a storage, that can be applied on other storageareas with similar conditions.

1.4 Research questions

Based on the problem background and the purpose of the project, two research questionshave been specified to define the most important areas to investigate.

– Is it possible to optimize the picking process, with respect to minimizing the orderfulfillment time for the forklift drivers, by categorizing the goods?

– What characteristics of the goods need to be considered for obtaining an optimalcategorization?

1.5. Delimitations 3

1.5 Delimitations

To make the project possible to go through with within the given time frame, thefollowing delimitations regarding the scope of the project has been made.

– The optimization of storage categorization will be executed on a certain storage,the PS storage.

– Order history is only possible to receive from four months, and will be collectedfrom the period May 29th 2017 to January 30th 2018.

– To achieve a trustworthy result of the study, the choice has been made to disregardpotential changes that can be made in the specific storage area during the project’stime frame. Hence, new categorization methods will be executed on the currentconditions of the storage area and will not consider planned reconstructions.

– The study has been made without consideration of the possibility that the capac-ities (sizes) of the storage locations can be changed, hence the current sizes of thestorage locations have been used for all analyzes. This further entails that otherstorage units within the concerned racks will remain at the same locations as inthe current state.

– The categorization will only concern parts picked in one of the three picking pro-cesses in the PS storage, namely the picking process called Program picking.

– Parts entitled as heavy parts will not be considered in the categorization, and theseparts will remain located at the specific area designated for this kind of parts.

1.6 Related work

A lot of papers have been published within the area of storage management, containingstudies of how to locate the goods in a storage in order to obtain an optimal storageassignment. Most studies have focused on reducing travel distance when picking in thestorage. However, a study performed by Pan, Shih and Wu [13] has shown that witha multi-picker system, congestion may occur and it might therefore be more useful toinstead aim to reduce the total order fulfillment time including both travel distance andwaiting time.

Another study worth mentioning was performed by Mindi, Manzini, Pareshi and Re-gattieri at the University of Bologna [3], who investigated different storage assignmentsof a warehousing system of an Italian food service company. Their results showed thatby categorizing the warehouse according to different similarity indexes, a reduction ofdriving distance could be made of 5% - 6% compared to a random location strategy.Their study suggests that parts which often are on the same order in a multi-item ordersystem are preferable to store close to each other.


1.7 Disposition of project

The first phase of this project has been to understand and examine the current processof handling the material flow in the specific storage area. Relevant theories within theareas of storage management, categorization of warehouses and optimization modelsthat can be applied to the problem were then evaluated. The next phase in the projecthas been to gather and analyze data about the different parts in the storage, collectorder history and timekeeping of the forklifts working in the area.

The theory, together with the data analysis and the analysis of the current state, hasbeen used as a basis and motivation for the chosen categorization methods to test. Withthe use of a constructed simulation model of the storage area, the process of picking thegoods has been simulated both with the current storage locations of the goods and withthe chosen categorization methods. The total order fulfillment times with the use ofthe different categorization strategies have then been compared to find the best way ofstoring the goods. Finally, the procedure of categorizing the goods was compiled intoa tool to be used at Scania, which also can be applied on other storages with similarconditions.

1.8 Outline

This project report is divided into the following eight chapters:

– Chapter 1 contains a presentation of the project, including the problem back-ground which has been used as a motivation for why this subject is interesting toinvestigate further, the purpose of the project and a description of the delimita-tions which have been made.

– Chapter 2 specifies the current methods of handling material in the specific area,including a description of the current method of locating the goods in the ware-house, as well as an accurate explanation of the process of picking goods in thestorage.

– Chapter 3 evaluates different theories which are of relevance for the project, suchas different categorization methods and a general mathematical model which canbe applied to the problem.

– Chapter 4 describes in detail the method which has been used to solve the problem.This includes the collection of data, collection of measurements important forthe construction of the simulation model, which software that have been used, aformulation of a mathematical model of the problem and an in-depth explanationof the simulation model constructed in ExtendSim.

– Chapter 5 presents the results generated from the simulation model and explainsthe main findings from the study.

– Chapter 6 contains an analysis and discussion of the results presented in chapter5, as well as an evaluation of the choice of method and the implementation of theresult in practice.

1.8. Outline 5

– Chapter 7 presents a few conclusions which can be drawn from this study anddescribes under what circumstances the conclusions are valid.

– Chapter 8 presents suggestions of future work and development of this research.

Chapter 2

Description of Current State

The following chapter contains a description of the operations at the concerned storagearea at the logistic center, including an explanation of the current location of the goodsand the picking process in the storage. The information in this chapter is gatheredby communication with employees working with the concerned storage area and frominternal documents at Scania.

2.1 Logistics Engineering, OLSX

To manage all material that is needed in the production, it is necessary to have logisticscenters, LC’s, where goods that could not be stored at the material facades at theassembly lines due to lack of storage capacity can be stored. When the goods arrive tothe LC, it is sorted and transported to different areas of the storage depending on whatbuilding the goods will be transported to from the LC. The goods are transported totheir final destinations from the LC with logistics trains continuously.

The department of Logistics Engineering, OLSX, is a part of one of the logistics centersin Sodertalje, and focuses on logistical challenges regarding material flows and storageareas for parts that will be transported to the chassis assembly and the assembly ofgearboxes and axles. In Figure 2.1, an overview of the area where these assemblies arelocated can be seen, where the chassis assembly is in building 230 and the axle andgearbox assembly is in building 210. All operations for the OLSX division take placeforemost in building 270. The logistics developers at the OLSX division are responsiblefor planning and executing logistics projects in close collaboration with the productionline organization. They participate in on-going improvement projects and work withhandling of deviations and risks in the storage operations [2].

7

8 Chapter 2. Description of Current State

Figure 2.1: An overview of the area where buildings 210, 230 and 270 are located.

2.2 Storage of goods to the chassis assembly

The storage area for parts going to the chassis assembly, MS, is divided into the followingsix different storage units, depending on what format the goods are stored in and in whatsize and frequency they are transported to the assembly.

PS Storage for low volume parts that are often specific for a specific truck orbus and are picked out of pallets. This is explained in detail later in thereport, see Section 2.2.2.

LVF Storage for parts picked out of boxes, which are used in the developmentline for new trucks.

CHP Storage for parts picked out of pallets, which are used in the developmentline for new trucks.

CB Storage for smaller low volume parts that are picked out of boxes.

NCP Storage for parts that are transported in full pallets to the assembly.

LV Storage for low value parts, as for example screws, that are transported tothe assembly in different packages.

2.2.1 Program, Master and Development picking

Goods stored in the PS, LVF and CHP storages are all located within the same storagearea, consisting of 16 racks of different sizes, see Figure 2.2 of the layout design of the

2.2. Storage of goods to the chassis assembly 9

area. However, most of the storage locations within these racks are designated to thePS storage. The vertical lines in Figure 2.2 represent the storage racks and the squaremarked as input/output gates represents where the picking processes start and end.The picking in these specific racks is mostly done in accordance with three differentmaterial flows, which are collected in three different picking processes called Programpicking, Master picking and Development picking respectively. Program picking refersto the picking of low volume parts into pallets, mostly picked from the PS storage anda fractional part in the CB storage area. Master picking is the picking of low volumeparts into cages which are needed at the assembly line just-in-time for a specific truck,mostly picked from the CB and PS storage areas. Development picking refers to thepicking of parts to the development line for new trucks, mostly picked out of the CHPand LVF storages. However, each of these three picking processes might also includepicks from other storage areas than these primary ones.

Different people are working with different material flows, and currently three forkliftsfor Program picking, two for Master picking and one to two for Development pickingare circulating within these 16 racks at the same time. Within these specific racks, thedistribution between the activity from Program, Master and Development picking ispresented in Table 2.1. The category called Other represents a number of other minorpicking activities in the area.

Table 2.1: Distribution of the activity in the storage area.

Picking process Distribution of total activity in the areaProgram picking 51,33%Development picking 23,20%Master picking 12,15%Other 13,32%

Since Program picking is the picking process representing the largest part of the activityin the area, this project has focused on optimizing only that picking process. Theoptimization was done with respect to the order fulfillment time for the forklift drivers,by categorization of the goods in this storage. As Program picking is mostly done fromthe PS storage area, the categorization only concerns parts picked from this storagewithin the process Program picking.


Figure 2.2: Overview of the layout design of the racks for the PS, CHP and LVF storageareas.

2.2.2 The PS Storage

The PS storage is a storage area of low volume parts that often are specific for a par-ticular truck or bus. The parts are stored in full sized or half sized pallets, from whichthe parts are picked when they are needed at the assembly.

Current location strategyToday, there is no efficient way of categorizing the goods in the PS storage. It has beensaid that all parts should be assigned a number in the range of one to four, dependingon how frequently it is used in the production. Category one is for parts with highconsumption and category four is for parts with zero consumption. The idea has beenthat category four should be located furthest away from the input/output gates, andcategory one should be located closest to the input/output gates. What has happenedlately, though, is that almost every part has been assigned to category one and the rackfurthest away has been used as a back-up for when the other racks are filled. As a resultof this, there is hardly any categorization in practice and almost every rack containsitems of only category one. Furthermore, this has led to the case that zero consumptionparts have been assigned to store locations close to the input/output gates, which mightbe of better use for parts ordered with higher frequency.

Additionally, when an incoming pallet is assigned a certain store location, there are twofurther things that need to be taken into consideration. First, the weight of the goodssets limits of how high up in the racks it can be placed. Secondly, the store locationneeds to be at least of the required size for that specific pallet and it is desirable thatthe pallet occupies the minimum possible space. When a new pallet is going to be

2.2. Storage of goods to the chassis assembly 11

located in the storage, the system searches for a store location constructed for the sizeof that specific pallet. If all those store locations are used already, the system searchesfor the next available location ordered by size from the smallest possible until a freestore location is found. New pallets are inserted in the racks continuously during theday, i.e. replenishment in and picking from the storage is done simultaneously.

Picking ProcessProgram picking represents the largest activity in the PS storage. During this pickingprocess, individual parts are sequentially retrieved according to a predetermined listand put into a pallet. Hence, the Program picking process represents a multi-item ordersystem, where several parts are picked during one route into the same pallet.

The Program picking from the PS storage is done according to a predetermined dailyschedule, which is divided into five different picking blocks, so called programs (thereofthe name of the picking process). These programs represent five different platformsat MS, to where the goods will be transported: three platforms for the production oftrucks and two for the production of buses. One program represents what should bepicked from the PS storage in order to cover the demand at the specific part of MS thatprogram refers to. One program covers the demand during half a day in that specificpart of MS, i.e. the parts picked during the first part of the day are intended to coverthe demand during the second part of the day. Each program is picked one at the timein the PS storage by three forklift drivers simultaneously. Thus, the program picking inthe PS storage represents a multi-picker system.

The first step in the process is taking place at the printing station, where orders of whatis needed at MS from the PS storage are received. At the printing station, documentsof what should be picked in a specific program are printed. One document shows whatone of the forklift drivers are to pick and put into one pallet during one route. Whatparts that should be collected during the same route in the storage is decided dependingon what delivery address at MS the parts have, which represent where the parts areneeded at the production line. All the parts in one pallet should have the same deliveryaddress. For each of the printed documents, tags for all the parts that will be pickedduring that route are attached and sorted by what rack the parts are located in.

When the documents and their respective tags are printed and sorted, the forklift driversgo to the printing station and pick a document. Thereafter, an empty pallet is put ontothe forklift and then all the parts on that specific document are collected from thestorage. The driver is free to pick the parts from the storage in the order he/she desires,thus they are not obligated to follow the order of the tags predetermined at the printingstation. When all parts are picked, the pallet is driven to a so called filter station andthen the forklift driver goes to the printing station again to get a new document with anew picking route on. This process is repeated until a whole program has been picked,hence all forklift drivers work on one program at the same time, after which the nextprogram in the schedule is printed.

At the filter station, a person verifies that all parts in the pallet have been collectedcorrectly. The pallet is then moved to a pickup position, before it is transported toan area where material is gathered to be driven by trains to the assembly. The trainsdepart at scheduled times and go to one of the platforms.

Chapter 3

Theoretical Background

This chapter discusses theoretical background relevant for the project. This includes adescription of different categorization strategies for warehouses and a general optimiza-tion model which can be applied to the problem.

3.1 Storage management

55% of all operating costs in a typical warehouse has been estimated to arise due tofactors related to the order picking process, which has been identified as the most costlyand labor-intensive activity for almost every warehouse [12]. There are especially fourparameters that have to be taken into consideration in order to establish an efficientstorage management: layout design of the storage area, picking policies, where itemsare to be stored in the warehouse, i.e. storage assignment, and routing policies [5].

The two most commonly used routing policies are called the S-shaped policy and thelargest-gap policy. The S-shaped policy entails that any aisle containing at least one itemto pick is traversed through its entire length, while with the largest-gap policy a pickerenters an aisle from the side that is nearest the item that should be picked and leavesthe aisle from the same side as it was entered [16]. However, the factor affecting thepicking performance the most is the storage assignment, and by optimizing the locationof the goods in the storage a lot of savings can be done in terms of costs and labor [5].

3.1.1 Storage assignment strategies

In general, the storage assignment strategies for assigning parts to storage locationscan be divided into three broad categories: randomized storage, dedicated storage andclass-based storage [10].

Randomized storageThe random storage strategy allows to store parts on an arbitrary empty location inthe storage with the same probability. This strategy is easy to use and ensures that thespace is highly utilized, but might on the other hand increase the travel distance whenpicking the goods in the storage [5].

13

14 Chapter 3. Theoretical Background

Dedicated storageThe dedicated storage only allows a certain pallet to be stored at a specified locationbased on factors such as average demand, unit traveling cost and order frequency. Incontrast to the randomized strategy, the dedicated storage often results in shorter trav-eling distance but lower space utilization [6].

Class-based storageThe class-based strategy is a mix of a random and dedicated storage, where parts aredivided into different classes based on the order frequency or based on some charac-teristics. Each class is assigned to a certain area of the storage, but within each classthe storage locations are random. There are mainly two types of class-based storagestrategies; ABC-classification and family-based classification [10].

ABC-classificationWith ABC-classification, the items are assigned to three different classes dependingon their order frequency, where category A contains the parts with the highest orderfrequency. This policy assigns the nearest locations from input/output gates to the mostfrequently used items [5]. A widely used division of items into A, B and C classes isshown in Table 3.1. Note that the fractions can differ from case to case [12].

Table 3.1: Table of commonly used divisions of ABC-classification.

ABC class Percentage of parts Percentage of consumptionA 10-20% 70-80%B 15-25% 10-20%C 65-75% 5-10%

The ABC-classification can either be horizontal or vertical. Horizontal ABC class-basedstorage refers to assigning A-items closer to the input/output gates to reduce traveldistance. Vertical ABC class-based storage refers to assigning A-items to lower levels ofthe racks, which reduces the order retrieval time [5].

Family-based classificationWith family-based classification, items are clustered together according to relations orsimilarities between products or orders. However, grouping according to characteristicsoften results in a long order fulfillment time since components within the same ordercan have many different characteristics and are thereby spread over a large area. Amore suitable way of clustering items into different families is to store goods that arelikely to appear on the same order together. In industrial storages, items which will betransported to the same platform or assembly are often likely to appear in the sameorder. By storing items with demand dependence together, there is a great opportunityof reducing the routing length for a given list of orders [4].

3.2 Clustering analysis

When performing a classification for a class-based storage assignment, a useful tool isclustering analysis. Clustering analysis is a set of algorithms and methods for groupingitems of similar kind into categories or classes. The aim is to group individuals in sucha way that the degree of correlation between two items is maximal if they belong to thesame cluster and minimal otherwise [17].

3.3. Optimization theory 15

Two widely used clustering analysis methods are Hierarchical cluster analysis and K-means cluster analysis. Hierarchical clustering identifies groups of related objects bysuccessively linking objects with related characteristics based on a distance matrix toform a tree structure. With the K-means method, the number of groups is determinedin advance and then objects are allocated to appropriate cluster depending on the clus-ter’s mean value and the distance matrix. The distance matrix can be in the formof a similarity matrix containing the correlation between every pair of objects in theclassification [11].

3.2.1 Jaccard’s similarity index

Jaccard’s similarity index, si,j , is a widely used measurement of correlation between twoproducts i and j, and is calculated by the following [3]:

si,j =a

a + b + c(3.1)

where a is the number of times both product i and j belonged to the same order, b isthe number of times only product i belonged to an order and c is the number of timesonly product j belonged to an order.

3.3 Optimization theory

Storage assignment is a matching problem of assigning a set of parts to a set of locations,and it is thereby similar to the family of Assignment Problems. This section presentsrelevant optimization models for the concerned problem.

3.3.1 Assignment Problem

The Assignment Problem, AP, is a well-known optimization problem which consistsof finding a one-to-one matching between n tasks and n agents, with the objective tominimize the total cost of assigning tasks to agents [14].

The AP can be formulated as [19]:

min

n∑i=1

n∑j=1

cijxij (3.2)

s.t.n∑

i=1

xij = 1, j = 1, ..., n (3.3)

n∑j=1

xij = 1, i = 1, ..., n (3.4)


xij =

{1, if agent i is assigned to task j0, otherwise

(3.5)

where cij is the cost of assigning agent i to task j.

The objective function (3.2) aims to minimize the total cost of assignments, constraint(3.3) ensures that each task is assigned to exactly one agent and constraint (3.4) ensuresthat each agent is assigned exactly one task.

Resource Constraint Assignment ProblemResource Constraint Assignment Problem, RCAP is a formulation of the AP with anadditional side constraint to limit the use of resources. The constraint for limitation ofresources can be formulated as:

n∑i

n∑j

rijkxijk ≤ bk (3.6)

where rijk is the amount of resource k which is used if agent i is assigned to task j, andbk is the amount of resource k available [14].

3.3.2 Storage Location Assignment Problem

The Storage Location Assignment Problem, SLAP, belongs to the family of AssignmentProblems and refers to the problem of determining a way of assigning items to storageracks in order to maximize the picking efficiency, which also means to minimize thewarehouse operational cost [20]. SLAP is classed as an NP-hard problem [13], whichmeans that it is not proven to be solved in polynomial time [7], and therefore manyheuristic methods for the problem have been proposed [13].

There is no universally agreed measurement for the SLAP, but one of the most commonlyused measures is the total picking distance [21]. In a picker-to-part system with severalpickers operating in a certain storage area it might however be more relevant to measurethe total picking time, since the congestion in the aisles can have a significant effect onthe order picking process [13].

Mathematical modelBased on the formulation of an AP, the model for an SLAP can mathematically beformulated as follows:

min

n∑i=1

n∑j=1

cijxij (3.7)

s.t.n∑

i=1

xij = 1, j = 1, ..., n (3.8)

n∑j=1

xij = 1, i = 1, ..., n (3.9)

3.3. Optimization theory 17

xij =

{1, if item i is assigned to location j0, otherwise

(3.10)

where the cost function c represents the time it takes to pick item i from location j andn is the total number of items/locations.

The objective function (3.7) aims to minimize the total time it takes to pick all items,constraint (3.8) ensures that each location is assigned to exactly one item and constraint(3.9) ensures that each item is assigned exactly one location.

However, depending on the circumstances in the concerned warehouse, the model needsto be developed with further constraints for those particular conditions. This can dependon the layout design of the storage area, picking policy and routing policy. In most ofthe cases, constraints need to be added regarding limitations of where the pallets canbe located in the storage due to size and weight of the pallets.

Chapter 4

Method

In this chapter, the method used to solve the problem is presented and has been dividedinto separate parts. First, the data and software which have been used for the simulationand categorization is described. Thereafter, the constructed mathematical model of theproblem is presented and how it differs from a traditional SLAP is discussed. The chosencategorization methods and the constructed simulation model are then further describedin the later part of the chapter.

As described in Section 3.3.2, SLAP is an NP-hard problem, hence it is not possible tofind an optimal solution in polynomial time and therefore heuristic methods are usedin order to solve these kinds of problems. Furthermore, in practice an optimal locationof the goods in the storage might not be optimal after all. This since it can be hard todistinguish what characteristics the parts located close to each other have in common,and thereby it would be hard to maintain the storage assignment over time. Also, theoptimal solution would only be valid for the specific storage and the specific parts, andtherefore hard to apply on other storage areas. Additionally, since what is stored inthe storage depends on the customers’ orders in this case, the parts in the storage canvary over time and every time a new part is introduced a new optimal solution will beneeded. Therefore, the choice has been made to solve the problem in this project witha heuristic approach by testing different categorization strategies with simulation andcomparing the total order fulfillment time for the strategies with the current state.

The number of racks that need to be visited on a picking route depends on the locationof parts, and may therefore vary for the different categorization strategies. Since thiscan cause longer picking time, the number of racks visited per route was calculated andcompared for the tested categorization strategies.

4.1 Data collection

In order to build a simulation model representing the picking process in the storage area,relevant data have been collected. First, information about the parts stored in the PSstorage is essential to be able to categorize the parts in different groups based on theircharacteristics. This have been provided in the form of different Microsoft Excel-files,

19

20 Chapter 4. Method

containing information such as:

• Part number

• Storage location

• Weight

• Pallet size

• Picking program

• Delivery address at MS

Secondly, order history from the PS storage, travel pattern of the forklifts in the area,timekeeping of the forklifts and information about the capacity of the storage locationswere needed in order to build the model and have been collected from provided dataand observations.

Order historyOrder history in the PS storage from the period May 29th 2017 to January 30th 2018has been used to represent a sample of the picking process in the storage. This samplewas used in the simulation model to test different location strategies of the parts whichhad been picked during this time. The order history contained executed date and timeof when the different parts have been ordered during this period and from what locationin the storage it was picked.

Travel pattern of forkliftsIn order to recognize a travel pattern of the forklifts in the storage area and to geta perception of the congestion in the storage aisles at the current state, a spaghettidiagram of the movement in the area was constructed. By accompanying forklift driversduring the picking process, tours for different routes were noted. This, together withthe order history, was used as a basis for constructing a network of nodes and paths inthe simulation model representing the travel pattern in the storage.

Timekeeping of forkliftsTo collect data of what time it takes for the forklifts to drive the different paths in thenetwork of the picking process, timekeeping of the forklifts has been done. Timekeepingof the additional activities in the picking process was also done, which includes bothretrieving an order, picking an empty pallet, picking one item from the storage anddelivery at the filter station. These collected times have been used in the simulationmodel to get a perception of the total time of the picking process.

Capacity of the storage locationsData of the capacity of the current storage locations have been used to compile thenumber of storage locations in each rack for each pallet size. This information is neededto ensure that the parts in the storage are stored in a storage location of the desiredsize.

4.2. Software 21

4.2 Software

The software which has been used in this project are Microsoft Excel and ExtendSim.The areas of use for each software are presented in Sections 4.2.1 and 4.2.2.

4.2.1 ExtendSim

ExtendSim is a simulation software for modeling discrete event, continuous, agent-based,and discrete rate processes [18]. In this project, ExtendSim has been used to model adiscrete event simulation over the picking process in order to compare which storagecategorization that results in the shortest order fulfillment time. The simulation modelis described further in Section 4.5.

Discrete event simulationDiscrete event simulation models are used for analyzing and predicting the behavior ofcomplex systems and to get an understanding of the output of a new system before it isimplemented in reality. Discrete event models pass entities (called items) between blocksas different events occur in a time sequence. The items are usually generated randomlyor from a scheduled list and contains properties, such as attributes and priorities, withinformation to make them correspond more closely to the real life. Items are processedby activities, in which the processing time often depend on the availability of requiredresources [9].

4.2.2 Microsoft Excel

Microsoft Excel has been a widely used tool in this project, where it has been used fordata analysis as well as for programming in Visual Basic for Applications, VBA. Codingin VBA has been done in order to group parts according to the different categorizationsstrategies, search for new storage locations and to construct the input files for thesimulation.

4.3 Mathematical modelling

In order to understand the problem, an optimization model has been constructed, withthe objective to find a location strategy that minimizes the cost of the picking process.The problem needs to be represented by an integer optimization model since each part isassigned to an exact number of locations. The problem has been formulated as a variantof an SLAP as described in Section 3.3.2, since it is a matching problem of assigning aset of parts to a set of locations. However, the objective function and the constraintshave been reconstructed for this specific case. Also, since the locations have limitedstorage capacity, the model is further developed with a resource constraint similar towhat is described in Equation (3.6).

In a general SLAP, the objective function is designed according to a picking processwhere the parts are picked one at the time. However, in this case the parts are pickedin routes, where several parts are picked on the same route, which makes the problem


more complex. Because of this, the constructed objective function in Equation (4.1)differs from the traditional SLAP in Equation (3.7), and will be solved with simulation.

4.3.1 Formulation of model

The mathematical formulation of the model is described as follows:

Definition of objective functionThe objective is to minimize the total cost C, which is a function of the location strategyX. The total cost C is the sum of the cost of picking all orders ok, where ok is a list ofparts to collect, k = 1, ..., N and N is the total number of orders in a chosen sample.c(X, ok) is a cost function specifying the cost of picking the parts in list ok conditionalon the storage location X. The cost function c is given by the result of a simulation foreach X. The objective function is formulated as:

minX

C(X) = minX

N∑k=1

c(X, ok) (4.1)

where X is a set of variables xi,j representing the location of parts, given a set of partsI and a set of locations J, where i ∈ I, j ∈ J and

xij =

{1, if part i is assigned to location j0, otherwise

(4.2)

where each location j represents two location spots in the storage, but is referred to asone location spot in the model since the locations are in the same rack.

Definition of constraintsSince there are more available locations than parts, each location j is set to have atmost one part assigned to it: ∑

i∈Ixi,j ≤ 1, ∀ j ∈ J (4.3)

Each part i is assigned to exactly one location:

∑j∈J

xi,j = 1, ∀ i ∈ I (4.4)

The size of part i can not exceed the capacity of location j :

aixi,j ≤ bj ∀ i ∈ I, j ∈ J (4.5)

where ai is the required storage capacity for part i and bj is the storage capacity oflocation j.

4.4. Categorization methods 23

4.4 Categorization methods

The location of the goods with five different categorization strategies have been testedin the simulation model, and the total order fulfillment time for each strategy have beencompared to the order fulfillment time with the goods located as in the current state.

For each categorization method, a new input file to the simulation model has beenconstructed, representing the picking routes with that specific categorization strategy.These input files have been constructed in Microsoft Excel after relocating the parts inthe storage according to the different methods, as described in Section 4.4.1. The meth-ods which have been tested are horizontal ABC-classification, three different types offamily-based classification strategies and a random location strategy. The three family-based classification strategies which have been investigated are classification accordingto program, classification according to the parts’ delivery addresses at MS and classifi-cation according to Jaccard’s similarity index. It is not possible to maintain a dedicatedstorage assignment in this specific storage area, since what is stored in the area dependson what the customers have ordered and varies a lot. As a dedicated storage would notbe possible to maintain, it has not been considered as an option in this case. For allmethods, the relocation of parts have been done according to the current capacity ofthe storage locations and with respect to the fact that the pallets should occupy theminimum possible space.

In the current state, the programs are picked one at the time by three forklift driverssimultaneously. By storing the parts according to a family-based classification there isa risk that the congestion will increase since the forklift drivers are picking the sameprogram. Because of this, the choice has been made to also test to pick three programsat the same time, so that the three forklift drivers pick one program each. This wasdone in order to try to restrict the forklifts to work in different areas of the storage.

In practice, different parts could require different number of storage locations dependingon the order frequency and quantity in the pallets. Because of this, an agreement inthe storage has been made, which implies that the storage should contain at least 1.7location spots per part. According to this agreement, when relocating the parts in thestorage it was considered that each part occupies two locations within the same rackin order to ensure that the capacity of the storage is as close to the reality as possible.Hence, in the formulation of the model in Section 4.3.1 each location represents twolocation spots in the storage. This means that each part gets one new storage location,but the remaining storage capacity decreases with two locations of the concerned sizefor each relocated part.

4.4.1 Description of categorization strategies

In this section, the chosen categorization strategies which have been tested in the sim-ulation are described. For more details about the procedure of categorizing the goods,see pseudo code in Appendix A.

ABC-classificationIn order to perform an ABC-classification of the storage, the order history was used asa basis for grouping parts according to their order frequency during this period. Theparts were sorted in order from the most frequently ordered part to the least frequently


ordered part and the cumulative percentages of all orders were calculated. With Table3.1 as a basis, the parts which together represented up to 70% of all the orders gotassigned to category A, parts representing the next 20% got assigned to category B andthe parts representing the last 10% of all the orders got assigned to category C. Parts incategory A were then located in the racks closest to the input/output gates, category Bwas located in the middle of the storage area and category C furthest away. In this way,the fastest moving items were stored in the most advantageous locations. See AppendixA.1 for pseudo code and more details of the procedure.

Classification according to programWith this categorization method, the parts were classified according to which programthey belonged to. For this, the order history was used to examine from which programeach part has been picked. The classes were then located in the storage area with respectto the number of routes each program contained according to the order history, withthe program containing the most number of routes located closest to the input/outputgates, and so on. See Appendix A.2 for pseudo code and more details of the procedure.

Classification according to delivery addressThis categorization method can be seen as an extension of the above described classifi-cation according to program, and entails that the parts are divided into further classeswithin each program depending on delivery address at the chassis assembly. Parts shar-ing the same delivery address are picked during the same route into the same pallet, andare with this categorization method located close to each other in the storage. In orderto perform this method, the order history was used to group parts with the same deliveryaddress within the same program. If parts had more than one delivery addresses at theassembly, these addresses were merged into the same group. The same location strategyhave been used as for classification according to program, i.e. the program with themost number of routes are located in the most favorable positions, but with the furtherdivision into smaller categories within each program. Within each program class, theaddress class with the most number of routes are located closest to the input/outputgates. See Appendix A.3 for pseudo code and more details of the procedure.

Classification according to Jaccard’s similarity indexBased on the theory described in section 3.2.1, Jaccard’s similarity index was calculatedfor every pair of parts in the PS storage for each program respectively. This index showsthe correlation between parts, i.e. the probability that the parts will be on the sameroute, and was calculated based on the order history. These calculations resulted insimilarity matrices, one for each program, containing Jaccard’s similarity index for allpair of parts belonging to each program respectively.

These similarity matrices were then used as distance matrices when performing Hierar-chical cluster analysis and K-means cluster analysis with the use of built in functionsin R Studio and MATLAB. It was noted that this gave an unusable result and becauseof that, an alternative method of clustering according to Jaccard’s similarity index wasconstructed.

From the similarity matrices for each program, the parts with the highest value ofJaccard’s similarity index were grouped together, and each part with a correlation tothese two firstly grouped parts were also assigned to the group. After that, the tworemaining parts with the highest correlation were assigned to a new group together withthe other parts with a correlation to these two, and the process was repeated until allparts were assigned to a group. This was done for each program separately. Similar to

4.5. Simulation model 25

classification according to program, the program with the most routes was located closestto the depot. See Appendix A.4 for pseudo code and more details of the procedure.

Random location strategyA random location strategy has been performed to be used as a comparison to the othercategorization strategies. When a part randomly had been selected it was assigned anumber between 1-16 representing what rack it should be located in. This was doneuntil all parts were assigned a new location. In order to obtain an expected value ofthe total time of the picking process, the simulation model was run 30 times with 30different random locations of the parts in the storage. See Appendix A.5 for pseudocode and more details of the procedure.

4.5 Simulation model

The simulation model has been constructed based on the current layout of the PS storageand the picking process described in Section 2.2.2. The simulation covers the pickingprocess from the printing station to the filter station. In the simulation, orders aregenerated according to a scheduled time and retrieved when a forklift is available. Ac-cording to the picking process, the forklift first picks up an empty pallet before travelingto the storage racks to collect all parts on the picking order, to then deliver the palletto the filter station. An S-shape routing policy has been applied in the model, wherethe identified driving pattern has been the basis of this decision. Due to simplification,the routing is further limited to always start by traveling to the rack furthest awayamong the racks in the order list, to then systematically travel back to the filter stationaccording to the S-shape routing policy. In practice, this is also a matter of safety sinceit is safer to drive the longest way with an empty pallet.

4.5.1 Description of model

An overview of one part of the simulation model from ExtendSim can be seen in Figure4.1. The four vertical pathways with a square at the middle correspond to the fourstorage racks closest to the input/output, and the model contains 12 more of these tothe left of what is shown in Figure 4.1. The big circles at the end of each rack containa decision of whether a forklift should enter that rack or not. The different parts of thesimulation model are described in detail below and an overview of the full model can beseen in figure B.1 in Appendix B.


Figure 4.1: Overview of a part of the simulation model from ExtendSim.

Order generatorThe input file constructed in Microsoft Excel is inserted in the order generator, markedas 1 in Figure 4.1. Each order contains the following attributes:

• Create time

• Item quantity

• Item priority

• Picking time in each rack

• First pick

• Congestion time

• ID

• PR value

The orders are generated according to the attribute Create time and placed in an orderqueue. One order corresponds to one picking route, hence it contains all necessary infor-mation for the forklift to visit the required racks for collection of parts. The attributesItem quantity and Item priority are required by the software, and are always set to thevalue one. First pick determines which rack the forklift will visit first, to further con-tinue to visit all racks with picking time greater than zero. When the simulation starts,Congestion time is set to zero to then be updated every time the forklift spends time ina queue. In the end, it contains the total time the forklift spent queuing on the specific

4.5. Simulation model 27

route. The attribute ID is an index for the order and PR value contains informationabout which program the order belongs to. An example of an input file can be seen infigure B.2 in Appendix B.

Resource poolIn the resource pool, marked as number 2 in Figure 4.1, the number of resources, in thiscase forklifts, is determined. The simulation has been performed with a resource poolwith three forklifts, in accordance with the number of forklift drivers working in the areain reality, where each order requires one forklift. The orders will be placed in the orderqueue, marked as number 3 in Figure 4.1, until one forklift is available. In the casewith classification according to program, delivery address and Jaccard’s coefficient, ithas also been tested to pick three programs at the same time, where the forklift driverspick different programs, as described in Section 4.4. In the simulation model, this isrepresented by the use of three resource pools, one for each of the three forklifts workingin the storage. In this case, the forklift drivers collect one category each at the sametime in the storage, and the orders are placed in three different order queues dependingon which category it belongs to according to the PR value attribute. This entails thatthe forklifts are restricted to work in different parts of the storage area.

Activities and queuing systemEach storage rack has an activity block, marked as number 4 in Figure 4.1, whichrepresents the picking from that storage rack. The time in the activity is determinedby the picking time in that specific rack. Since the forklifts should not drive by anotherforklift, the activities are limited to one forklift at the time. If a forklift arrives to therack when the activity is occupied, the forklift will be placed in a queue with FIFOpolicy, marked as number 5 in Figure 4.1. Since it is possible to enter an aisle fromboth ends of the rack, one queue has been placed at each end. In the case where it existforklifts in both queues, FIFO according to both queues has been applied.

In the simulation model, there are also activity blocks representing retrieving an order,picking an empty pallet and delivery to filter station, marked as number 6, 7 and 8 inFigure 4.1 respectively. Picking an empty pallet and delivery to the filter station havecapacity of two forklifts, while retrieving an order has capacity of one.

Measurement of total order fulfillment timeFrom the data with the collected times of driving and the activities in the pickingprocess, described in Section 4.1, an average time has been calculated for each path andactivity, and implemented in the simulation model. To get an as accurate total orderfulfillment time as possible, a work shift was also implemented in the model representingthe actual working time in the storage. This entails that when it is a scheduled breakfor the workers, it is not possible to retrieve a new picking order and the model standsstill for as long as the break is scheduled.

DisruptionsIn reality, there are more forklifts operating in the area apart from the three forkliftsperforming the Program picking. These are forklifts working with Master picking, De-velopment picking and replenishment. This might lead to more congestion in the storageaisles and because of this, disruptions for Master picking, Development picking and re-plenishment have been implemented in the model to make it closer to the reality. Inorder to implement disruptions for replenishment in the model, data of how often eachrack has been replenished per day during one month has been analyzed. Disruptions forMaster and Development picking have been implemented based on the order history of


number of picks per day. This was used to make sure that the disruptions occur with atrustworthy frequency. In the model, the activity block for each rack was set to be shutdown at a calculated frequency for each disruption, to represent when replenishment,Master picking or Development picking occur.

Simulation outputIn the simulation, the time it takes for each picking route, from retrieving the orderuntil the forklift delivers the pallet to the filter station, has been measured and storedin a table which can be retrieved from the block marked as number 9 in Figure 4.1.In order to compare the total time it takes to collect all orders and how the queuingvaries for the different categorization methods, the total queuing time during each routehas also been measured and stored in the table. The simulation has been run for eachcategorization strategy separately. In the case with the random location strategy, thesimulation was run several times and an expected value of the total picking time wascalculated. In figure B.3 in Appendix B, an example of the simulation output can beseen.

Limitations of the simulation modelSince the problem is a complex process with many contributing factors, there are somelimitations in the model. First of all, the simulation model is a static model whichmeans that all parameters are set in advance and will not change during the simulation.Hence, the output from the simulation depends entirely on the input, which in this caseis the input file. This means that how the parts during time will move in the storage,due to replenishment, is not a factor the simulation model takes into account.

In reality, the human mind constantly makes decisions, for example which path to choosedepending on external conditions. This is not possible to implement in a discrete eventsimulation model, therefore in reality, the forklift drivers may not strictly follow anS-shape routing policy as implemented in the model.

Another limitation in the model is that it does not consider the time it takes to travelvertically. When identifying the driving behavior, it was noticed that when havingto travel vertically, the forklift travels forward and upwards simultaneously. The factthat it might take longer time to travel both forward and upward than just forward issomething that is not considered.

The simulation is based on data collected by manual timekeeping, which probably con-tains a margin of error. This can affect the resulting times in the simulation. However,since all categorization strategies are based on the same data, it will not have an effecton the final result.

4.5.2 Verification of model

The verification of the quality and correctness of the simulation model was firstly doneby testing and debugging smaller parts of the model, to make sure there were no errorsor defects in the model which could cause an incorrect result.

Secondly, the model was also verified by discussing the structure of the model and theconstructed network of paths with the people responsible for the picking process in thePS storage, to make sure the model represented the reality as good as possible. Whatwas mainly said during the discussion was that in reality there are often more than one

4.6. Construction of simulation tool 29

forklift picking in an aisle at the same time, while in the model the activities representingthe picking in the racks are limited to one picker at the time. This is something whichhas been considered when interpreting the results. However, it is still possible for morethan one picker to be in the aisles at the same time in the model if someone is locatedin the transport section of the aisles. According to an agreement in the storage, forkliftscan not drive by each other in the aisles in the model.

4.5.3 Sensitivity analysis

To make sure the result from the simulation model is accurate, a sensitivity analysiswas performed. This was done to the extent that the model was run both with all threedisruptions mentioned in Section 4.5.1, as well as without the disruption representingreplenishment and without any disruptions at all. This was done to examine whetherthe result would change with the different number of disruptions.

4.6 Construction of simulation tool

Since one part of the purpose of this master thesis has been to construct a generalmethod of how to categorize a storage, a categorization tool has been created for theuse at Scania where different categorization methods can be tested and analyzed beforeimplemented in reality. This tool consists of the constructed simulation model of thePS storage in ExtendSim and different Microsoft Excel workbooks where the input filesfor the simulation model are created. The simulation model can easily be modified toalso apply on other storage areas. To ensure that the tool is easy to use, macro buttonsin Microsoft Excel have been implemented and all necessary steps in the process areexecuted automatically as far as possible.

Additionally, a manual of how to use the categorization tool and how to interpret theresult has been created in order to ensure that all necessary information is transferredto the concerned employees at Scania.

Chapter 5

Result

In this chapter, the results from the simulations are presented and the result from thesensitivity analysis is explained.

5.1 Simulation result

The results from the simulation experiments are presented in Tables 5.1 and 5.2 andFigures 5.1 and 5.2. The result is generated from the constructed simulation model, forone and three order queues separately, based on the different input files for each catego-rization strategy and with disruptions implemented for replenishment, Master pickingand Development picking. To avoid that the result is interpreted as a measurement ofworkload, the actual order fulfillment times in seconds will not be presented. Instead, theresult will be presented in percentages representing the differences each categorizationstrategy would make compared to the current state.

Table 5.1 presents the savings in order fulfillment time in percentage which can be doneby using each categorization strategy, in relation to the current state. The results incolumn Saving % of order fulfillment time (ref. current state) show what improvementsa categorization can make compared to the current location of parts in the storage,which can also be seen in Figure 5.1.

31

32 Chapter 5. Result

Table 5.1: Savings in order fulfillment time for each categorization strategy comparedto the current state.

Categorizationstrategy

Model Saving % of order fulfillmenttime (ref. current state)

ABC 1 order queue 4.00Program 1 order queue -1.7

3 order queues 4.14Delivery address 1 order queue 0.48

3 order queues 5.03Jaccard’s coefficient 1 order queue 0.77

3 order queues 4.70Random 1 order queue -4.41

Figure 5.1: Savings in order fulfillment time compared to the current state.

As one can see in Table 5.1, the categorization strategy which gives the largest savingsin order fulfillment time is by classifying the parts according to their delivery addressand when using three order queues. Thereafter, classification according to Jaccard’ssimilarity index gives the second largest savings, also with three order queues. This canalso be seen in Figure 5.1, showing the savings that can be done compared to the currentstate.

The results also show that larger savings can be done with the use of three order queuesinstead of one for all categorization strategies where this was investigated. Furthermore,classification according to program with one order queue and the random location strat-egy give negative savings compared to the current state, which will be further discussedin Section 6.2.

5.1. Simulation result 33

5.1.1 Queuing time

Table 5.2 and Figure 5.2 present, for each categorization strategy and model, how muchof the total order fulfillment time that consists of time spent queuing. Figure 5.2 alsopresents the total order fulfillment time for each categorization in relation to the currentstate.

Table 5.2: Percentage of total order fulfillment time which was spent queuing.

Categorizationstrategy

Model Queuing time in % of totalorder fulfillment time

Current state 1 order queue 2.97ABC 1 order queue 4.34Program 1 order queue 6.79

3 order queues 1.14Delivery address 1 order queue 5.44

3 order queues 0.95Jaccard’s coefficient 1 order queue 4.47

3 order queues 0.91Random 1 order queue 1.25

Figure 5.2: Total order fulfillment time in proportion to the current state.

The percentage of the time spent queuing for each categorization strategy is presentedin Table 5.2. This percentage should be interpreted as the amount of time when it hasbeen congestion in the storage aisles, and hence two or more pickers have been in anaisle at the same time. As one can see in Table 5.2, classification according to programwith one order queue generates the largest amount of time spent in congestion, followedby classification according to delivery address with one order queue. When using threeorder queues, the queuing time becomes substantially lower compared to the use of oneorder queue for all methods where this have been tested.


This result is also presented in Figure 5.2, which shows the total order fulfillment timefor each categorization in relation to the current state. The marked upper part of thebars in the plot represent the time spent queuing. Also in Figure 5.2, it can be seenthat classification according to program with one order queue is the strategy with thelargest proportion of queuing time. When the time spent queuing is excluded, one cansee that ABC-classification generates the shortest order fulfillment time (see lower partof the bars in Figure 5.2).

5.2 Sensitivity analysis

In order to analyze how consistent the results obtained from the simulation model are, asensitivity analysis of the implemented disruptions was performed. Figure 5.3 presentsa comparison of the savings in percentage which can be done in relation to the currentstate, with different numbers of disruptions implemented in the simulation model. 3disruptions implies that disruptions for both replenishment, Master picking and Devel-opment picking are implemented in the model, while 2 disruptions implies that onlydisruptions for Master picking and Development picking are implemented and in thecase of No disruptions there are no disruptions in the model. The order fulfillment timefor the different methods are in relation to the current state with the same number ofdisruptions implemented.

Figure 5.3: Sensitivity analysis of the use of different disruptions in the model.

As one can see in Figure 5.3, classification according to delivery address gives the largestsavings regardless of what disruptions that are implemented in the simulation model,which confirms the results presented in Section 5.1. When using two disruptions orno disruptions instead of three, the only difference which can be noticed is between

5.3. Number of racks per route 35

ABC-classification and classification according to program. With three disruptions,classification according to program with three order queues is slightly better than ABC-classification, while with two or no disruptions, ABC-classification gives larger savings.However, it should also be noted that the difference between ABC and program classi-fication is considerably small.

5.3 Number of racks per route

In Figure 5.4, the average number of racks that have been visited in one picking routefor each categorization strategy is presented. Table 5.3 presents the average and themaximum number of racks per route.

Table 5.3: Average and maximum number of visited racks per route.

Categorization strategy Average racksper route

Max racks perroute

Current state 1.82 10ABC 1.52 9Program 1.33 6Delivery address 1.26 5Jaccard’s coefficient 1.27 5Random 2.05 12

Figure 5.4: Average number of racks visited per route with the different categorizationstrategies.

As one can see in Figure 5.4, the random categorization results in the highest numberof racks per route, followed by the location of parts in the current state. Classificationaccording to delivery address has the lowest number of racks per route, closely followedby classification according to Jaccard’s similarity index.

Chapter 6

Discussion

This chapter contains an analysis and discussion of the results presented in the previouschapter. The choice of method is discussed, as well as contributing factors which mayhave affected the results.

6.1 Choice of optimization method

The objective with this project has been achieved with the use of a discrete eventsimulation model and with a heuristic optimization approach. This choice of method wasdone because of the fact that an SLAP is seen as an NP-hard problem, i.e. impracticalor impossible to solve optimally. However, this entails that the best found categorizationmethod is not assured to be the optimal solution and the gain of categorizing a storagecould possibly be even higher.

With the use of a discrete event simulation model, it follows a few limitations which areimportant to keep in mind. First, the constructed model is static and the result of thesimulation depends entirely on the input, which increases the importance of creatinga correct input file. Furthermore, a discrete event simulation model does not considerdecisions the human mind can make during the simulation, which might not always bein line with the predetermined sequence of events in the model.

Additionally, with the problem formulated as a variant of an Assignment Problem,it follows that each part will be assigned exactly one storage location. In practice,this might not always be the case since different parts could require different numberof locations depending on the order frequency and quantity in the pallets. This is alimitation in the choice of optimization method, which can be handled with furtherconstraints or with the use of another mathematical model.

6.2 Analysis of simulation result

When interpreting the results presented in Chapter 5, it is important to keep in mindthat these results are derived from a simulation model representing a specific storage

37

38 Chapter 6. Discussion

and picking method. Hence, the results are not assured to be valid for every type ofstorage layout design, routing and picking policy, but can be assumed to apply on otherstorage areas with similar conditions. It is also important to remember that the resultsare based on a sample of order history from a limited period of time which may haveaffected the results, but an analysis has been performed to ensure that the sample oforder history was stable during the chosen period.

In Table 5.1 and Figure 5.1, it can be seen that the difference in savings that thetested categorization methods would generate is considerably small when three orderqueues were used for the family-based classifications. Compared to the current state,all categorization methods except for the random location strategy generate savings inorder fulfillment time of around 4% - 5%. Because of this substantially small difference,the constructed categorization tool for the use at Scania will be able to be used to tryout all the tested categorization methods.

What can also be seen from Table 5.1 and Figure 5.1 is that all tested categorizationmethods gave a positive result compared to the random location strategy, since thatstrategy resulted in the largest negative savings of order fulfillment time. This showsthe positive effect which can be attained by implementing a categorization strategy ina storage. From Table 5.1 it can be calculated that compared to the random locationstrategy, all categorization strategies give an improvement of order fulfillment time of8% - 9%.

These results can be compared to the case study performed by Bindi, Manzini, Parechiand Regattieri [3] mentioned in Section 1.6, in which categorization according to differentsimilarity indexes, such as for example Jaccard’s similarity index, were investigated.Their study showed a reduction of driving distance with 5% - 6% compared to a randomlocation strategy, which can confirm that the results presented in this report could be ofreasonable size. However, it might be difficult to compare different studies, since layoutof the storage, picking policy and routing policy can differ and thereby affect the result.

From the results, it can be seen that categorization according to delivery address withthree order queues generates the largest savings. However, it should also be noted thatcategorization according to Jaccard’s similarity index almost generates as good savingsas categorization according to delivery address. This finding is not very surprising, sinceboth methods locate the parts in accordance to which parts that are likely to appearon the same order and therefore likely to be picked on the same route. Categorizationaccording to delivery address with three order queues would give 5.03% shorter orderfulfillment time compared to the current state, which corresponds to 23 saved minutesper day or 1.9 saved hours per week, under the assumption that one working day is 460minutes excluding breaks.

Furthermore, in Table 5.3 and Figure 5.4 it can be seen that categorization according todelivery address and Jaccard’s similarity index result in the lowest number of racks thatneed to be visited on one route. This is one reason of why these methods generate theshortest order fulfillment times. In Figure 5.4, it can also be seen that categorizationaccording to program gives a slightly higher number of average racks per route, whichshows that the further breakdown into delivery address or Jaccard’s similarity indexgenerates shorter picking routes.

In Figure 5.1, it is shown that categorization according to program with one order queueand the random location strategy generate negative savings, which indicate that these

6.2. Analysis of simulation result 39

location strategies result in longer order fulfillment times than today’s location of partsin the storage. As one can see in Table 5.2, program categorization with one order queuegenerates a large amount of time spent queuing, which is one reason of why this strategyresults in a long order fulfillment time. One reason of why the random strategy resultsin a long order fulfillment time might be because the number of racks that are visitedon one route is high compared to the other strategies, which can be seen in Table 5.3and Figure 5.4. However, this is something one can expect since with a random locationthe parts are spread evenly in the storage area.

6.2.1 Analysis of queuing time

As described in Section 5.1.1, the amount of time spent queuing shown in Table 5.2 andFigure 5.2 should be interpreted as the time when two or more forklifts have been in thesame storage aisle at the same time. Hence, it should not be interpreted as actual waitingtime but rather as an indication of the congestion. When making a recommendationof which categorization method that is preferable, this measure of queuing time is aninteresting factor to keep in mind. It is desirable to adapt a categorization strategy witha low value of queuing time, since this entails less congestion in the storage aisles.

It had been noticed that the forklift drivers some times experience that they have towait in line to be able to pick their orders due to congestion in the storage aisles, andbecause of this the simulation has been run both with one and three order queues. Inthe case with three order queues, one for each forklift, the forklifts are restricted towork in different parts of the storage in order to reduce the experienced congestion. InTable 5.2 and Figure 5.2, it can be seen that for all categorization methods where ithave been tested, three order queues generates less queuing time compared to one orderqueue. This shows that it is advantageous to let the forklift drivers pick one programeach in different parts of the storage area, instead of all picking the same programsimultaneously. With three order queues, it is also shown in Figure 5.1 that the totalsavings which can be done compared to the current state are larger with three orderqueues than with one order queue. One reason for this is the lower amount of queuingtime these methods result in.

These findings are in line with the study performed by Pan, Shih and Wu mentionedin Section 1.6, which as Figure 5.3 showed that in a multi-picker system, congestionmay represent a considerably large part of the total order fulfillment time and shouldtherefore also be included in the analysis.

In Table 5.2, it can also be seen that when comparing ABC-classification with the family-based classifications with three order queues, ABC-classification generates a higheramount of time spent queuing. This implies that ABC-classification is more sensitive tocongestion and if the number of forklifts would increase in the storage, this may affectthe ABC-classification negatively. Since the amount of time spent queuing is consider-able small for the methods using three order queues, these methods would be able tomanage an increase in the number of forklifts since the operations in the storage arespread out.


6.2.2 Sensitivity analysis

A sensitivity analysis was performed in order to analyze how sensitive the results fromthe simulation model are with regards to the implemented disruptions. The modelwas run with both three disruptions, two disruptions and no disruptions, as describedin Section 5.2, representing the other activities in the concerned storage area. Thedisruption representing replenishment in the model might however be a bit higher than inreality, since people working with replenishment have to show precedence for the forkliftspicking in the storage. Furthermore, breaks are scheduled at different times during theday for people working with replenishment and picking to reduce the congestion, but thishas not been taken into consideration in the model. This means that in reality, the resultfrom the simulation might be even better considering the potential excessive disruptionfor replenishment. Because of this, the model was also run without the disruption forreplenishment.

What could be seen in the sensitivity analysis in Figure 5.3 is that the use of differentnumber of disruptions does not affect the result remarkably. Categorization accordingto delivery address and Jaccard’s similarity index still give the best result, regardlessof what disruptions that are implemented, which confirms that the result in Section5.1 is stable. However, as mentioned in Section 5.2, ABC-classification gives a slightlybetter result than categorization according to program with the use of fewer than threedisruptions. This difference is barely noticeable.

6.3 Further factors affecting the result

The results presented in this report are naturally affected by the prevailing conditionsin the investigated storage area, as well as by the delimitations which have been maderegarding the scope of the project.

The layout design of the storage area, with input/output gates located on one side ofthe storage racks, see Figure 2.2, has an impact on what categorization strategy thatgives the best result. If queuing time is excluded, one can see in Figure 5.2 that ABC-classification gives the largest improvement compared to the current state. The reasonfor that might be that the most frequently used parts are located closer to the depotand hence the driving distance becomes smaller. Classification according to program, onthe other hand, results in longer driving distance since there are classes located furtheraway from the depot and the forklifts have to travel the distance to the racks assignedto those classes on every route. If the input/output gates were located in the middleof the storage area the result might have been different and classification according toprogram with three order queues could become more advantageous.

Also, the picking policy influences the obtained result. In this concerned storage area,several parts are picked on the same picking route, which has to be taken into consider-ation when locating the parts in the storage. If the parts were picked one at the time,one can assume that the most favorable strategy would be to locate the parts with thehighest order frequency closest to the input/output gates.

Lastly, some data exclusions have been made regarding the scope of this master thesis.The categorization in the storage has been limited to only cover the parts picked fromone of three picking processes in the concerned storage area, namely the picking process

6.4. Implementation of a categorization in practice 41

called Program. Furthermore, parts with missing information of, for example, size ororder date have been excluded in the analysis. This data exclusion which has beenmade could have affected the result regarding the availability of storage locations andthe actual storage capacity may potentially be smaller than what is assumed in thisproject. This can be modified by also categorizing parts belonging to the other pickingprocesses and by extending the simulation model to also cover these movements in thestorage.

6.4 Implementation of a categorization in practice

When interpreting and making conclusions of the results, there are a few further aspectsand analyzes which need to be taken into consideration apart from the ones presentedin this report, before implementing any categorization strategy in practice.

First, the categorization model which is chosen to be implemented in the storage hasto be able to be maintained over time in the storage, i.e. the function of replenishmentneeds to be considered. Since the simulation model is static, this is not something thatis implemented in the model. What is stored in the storage depend on the customer’sorder, therefore the content in the storage varies over time. Because of this, one canargue that categorization according to delivery address and Jaccard’s similarity index areharder to maintain than ABC or program classification. Since the classes within thesemethods are restricted to fewer storage locations, the risk is higher that these exactlocations will be filled and parts have to be located outside of the storage locationsassigned to a specific class.

However, classification according to delivery address can be easier to maintain thanclassification according to Jaccard’s similarity index considering the introduction of newparts in the storage. This since it is easy to see what delivery address the new parthas and assign it to the corresponding class, but a new article does not have correlationwith any other part in the storage and hence is hard to assign to any class according toJaccard’s similarity index.

Second, when implementing a storage categorization, the cost of moving the parts totheir new storage locations needs to be taken into consideration and an analysis ofwhat time it will take to reach break-even between these costs and the earnings of thecategorization has to be made.

Apart from the results presented in this report concerning what savings different catego-rization strategies can make, this master thesis has also resulted in a categorization toolwhich can be used at Scania for testing the outcome of different categorization methods.This tool consists of the created simulation model of the PS storage in ExtendSim, aswell as Microsoft Excel workbooks where the input files for the simulation are created.To ensure all necessary information is transferred to the concerned employees at Scania,a manual of how to use the tool and how to interpret the results has been created.

The categorization tool can be used for ABC-categorization, categorization according toprogram and delivery address and for a random location strategy. The choice has beenmade to not implement categorization according to Jaccard’s similarity index in thetool, due to the difficulties to maintain the strategy over time and due to the similaritieswith categorization according to delivery address.


6.5 Wider perspective

When performing a project like this master thesis, many different people are involved inthe process and have interest in the result. Therefore, it is of great importance that theresult is presented in a way that does not affect anyone’s work situation negatively. Thishas been taken into account by not presenting any results in seconds, only in percentages,since presenting the exact order fulfillment times could open up for discussions aboutworkload which might be a sensitive topic.

Furthermore, in today’s society, the environment has become a very important aspectto take into account for many companies when introducing new projects. In this masterthesis the environmental aspect has been considered in terms of the electricity whichcan be saved when the forklifts drive shorter distances and when the time spent queuingbecomes smaller.

Chapter 7

Conclusions

The purpose of this master thesis has been to analyze and examine if it is possible tooptimize the picking process, in terms of order fulfillment time for the forklift drivers,in a certain storage with categorization of the goods. Important to keep in mind whenmaking conclusions of the results presented in this report is that the result only holdsfor the conditions in this specific storage area and under the chosen delimitations madefor this project.

One of the main findings in this master thesis has been that regardless of what cate-gorization strategy that is used, it is shown to be beneficial to categorize the storagein terms of order fulfillment time compared to a random strategy. Most of the testedcategorization methods in this study generate considerably similar result, and hencewhich strategy to be used depends on what factors one considers as the most importantto take into account.

If only the driving time and distance is of interest to measure, ABC-classification shouldbe the preferred categorization strategy since this method generates the shortest drivingtime. However, when the total order fulfillment time including both driving, picking andqueuing time is considered, classification according to program, delivery address or Jac-card’s similarity index should be chosen with three order queues. These methods spreadthe traffic across the area and reduce the congestion, which could also be preferable ifthe number of forklifts in the area will be increased.

Furthermore, a great difference has been showed between the use of one and threeorder queues in the case of family based classification. This shows that it might beadvantageous to restrict the forklifts working in the storage to different parts of the areaand pick different programs in order to reduce the congestion.

Based on the result in this study, categorization according to delivery address with threeorder queues is the preferable categorization strategy for this specific storage area andwould result in a reduction of the order fulfillment time of 5.03%. This strategy willlocate parts which are picked on the same route close to each other and hence minimizethe total order fulfillment time for the forklifts. However, if it is desirable to maintainthe picking process of picking one program at a time, ABC-classification is the preferablestrategy. This since the family-based classifications then would result in high congestion.

43

44 Chapter 7. Conclusions

The findings in this project of the positive savings which can be done by categorizing astorage will hopefully be helpful for the logistics engineers at OLSX at Scania when itcomes to how a storage should be categorized in order to minimize the order fulfillmenttime for the forklift drivers. There are often great opportunities to make improvements ofthe storage assignment in warehouses, and the results in this report and the constructedcategorization tool may be used as guidelines for this type of decisions.

Chapter 8

Future Research

This project has shown that applying a categorization strategy in the investigated stor-age would generate positive savings in terms of order fulfillment time, but a lot of workcan still be done to develop the findings of this study.

First, in order to verify the result, further verification and evaluation of the simulationmodel should be performed apart from what is covered by the scope of this masterthesis. This should include empirical testing by comparing simulation results of thepicking process with the reality. Also, in order to implement the chosen categorizationmethod in practice, the model should be extended to be in line with the changes inthe storage which has been made during the time frame of this project, but have beenexcluded due to a chosen delimitation.

Second, the other picking processes which are circulating in the concerned storage areashould be taken into further consideration and how these processes are affected of apotential categorization should be analyzed.

An interesting development opportunity of this master thesis would be to examine howa change in the layout design of the storage area would affect the result. An examplecould be to analyze what impact an aisle located in the middle of the storage acrossthe racks would have on the result. This could be done by comparing the savings of acentral aisle with the cost of loosing part of the storage locations.

Another interesting extension of this project would be to investigate the opportunityof implementing a vertical ABC-classification, i.e. locating the most frequently orderedparts to lower levels of the racks. This could be done by also including the vertical traveltime for the forklifts and implement this in the simulation model.

45

46 Chapter 8. Future Research

References

[1] Scania CV AB. About Scania. Scania CV AB.https://www.scania.com/global/en/home/experience-scania/about-us.html, 2017.Retrieved 2018-05-21.

[2] Scania CV AB. Production and Logistics. Scania CV AB.https://www.scania.com/group/en/production-and-logistics/, 2018.Retrieved 2018-02-22.

[3] F. Bindi, R. Manzini, A. Pareschi, and A. Regattieri. Similarity coefficient andclustering techniques for the correlated assignment problem in warehousing systems.International Conference on Production Research, 19.

[4] H. Brynzer and M. I. Johansson. Storage location assignment: Using the prod-uct structure to reduce order picking times. International Journal of ProductionEconomics, 46:595–603, 1996.

[5] F. T. S. Chan and H. K. Chan. Improving the productivity of order picking ofa manual-pick and multi-level rack distribution warehouse through the implemen-tation of class-based storage. Expert systems with applications, 38(3):2686–2700,2011.

[6] U. S. S. Dharmapriya and A. K. Kulatunga. New strategy for warehouse opti-mization – lean warehousing. Proceedings of the 2011 International Conference onIndustrial Engineering and Operations Management, pages 513–518, 2011.

[7] J. Du and J. Y.-T. Leung. Minimizing total tardiness on one machine is NP-hard.Mathematics of Operations Research, 15(3):484, 1990.

[8] Scania Group. Logistikutvecklare till logistikcenter (OL). Linked In.https://se.linkedin.com/jobs/view/logistikutvecklare-till-logistikcenter-%28ol%29-at-scania-group-538849572, 2018.Retrieved 2018-01-23.

[9] Imagine That Inc. ExtendSim 9 User guide. Imagine That Inc, 2017. pages 101-104.

[10] J. Karasek. An overview of warehouse optimization. pages 1–5, 2013.

[11] N. Lathia. What is the difference between k-means and hierarchical clustering?Quora. https://www.quora.com/What-is-the-difference-between-k-means-and-hierarchical-clustering.Retrieved 2018-04-09.

47

48 REFERENCES

[12] T. Le-Duc and R. (M.) B. M. De Koster. Travel distance estimation and storagezone optimization in a 2-block class-based storage strategy warehouse. InternationalJournal of Production Research, 43(17):3561–3568, 2005.

[13] J. C.-H. Pan, P.-H. Shih, and M.-H. Wu. Storage assignment problem with traveldistance and blocking considerations for a picker-to-part order picking system. Com-puters Industrial Engineering, 62(2):529, 2012.

[14] D. W. Pentico. Assignment problems: A golden anniversary survey. EuropeanJournal of Operational Research, 176(2):775–782, 2007.

[15] H. A. Rahmna, C. Wang, and I. Y. W. Lim. Waste processing framework for non-value-adding activities using lean construction. Journal of Frontiers in ConstructionEngineering, 1(1):8–13.

[16] K. J. Roodbergn and I. F. A. Vis. A model for warehouse layout. Expert systemswith applications, 38(10):799–803, 2006.

[17] Statsoft. How To Group Objects Into Similar Categories, Cluster Analysis. Statsoft.http://www.statsoft.com/Textbook/Cluster-Analysis.Retrieved 2018-03-21.

[18] Wikipedia. ExtendSim.Wikipedia. https://en.wikipedia.org/wiki/ExtendSim, 2018.Retrieved 2018-04-10.

[19] L. A. Wolsey. Integer programming. Wiley-Interscience publication, 1998. page 57.

[20] J. Xiao and L. Zheng. A correlated storage location assignment problem in a single-block-multi-aisles warehouse considering BOM information. International Journalof Production Research, 48(5):1321–1338, 2009.

[21] J. Xie, Y. Mei, A. T. Ernst, X. Li, and A. Song. A bi-level optimization model forgrouping constrained storage location assignment problems. IEEE Transactions onCybernetics, 48(1):385, 2018.

Appendix A

Pseudo code

A.1 ABC-classification

Step 1. Given a number of parts i = 1, ..., N , let fi define the order frequency for part i.Let X be an N × 3 matrix.

Step 2. Calculate the total order quantity F =∑N

i=1 fi.

Step 3. For i = 1, ...N :

• Calculate the ratio ri = fi/F .

• Set X[i, 1] = i and X[i, 2] = ri

Step 4. Sort X with respect to ri in a descending order.

Step 5. For k = 1, ..., N :

• Calculate cumulative sum ck, of the ratios ri

∗ If k =1:

ck = X(k, 2)

∗ Otherwise:

ck = ck−1 + X(k, 2)

• Assign classification

∗ If ck < 0.7:

Set X[k, 3] = A

∗ Else if 0.7 ≤ ck < 0.9:

Set X[k, 3] = B

∗ Else:

Set X[k, 3] = C

Step 6. Collect matrix X.

I

II Chapter A. Pseudo code

A.2 Classification according to program

Step 1. Let P = {p1, ..., pm} be a set of programs, where m is the number of programs.Given a number of parts i = 1, ..., N , let fP,i define the order frequency of part iwithin program P .

Step 2. For i = 1, ..., N :

• Set maxf = 0

• For k = p1, ..., pm:

∗ If fk,i ≥ maxf

maxf = fk,i

prgi = k

• Collect classification prgi

A.3 Classification according to delivery address

Step 1. Let P = {p1, ..., pm} be a set of programs, where m is the number of programs,and A = {A1, ..., AM} be a set of addresses, where M is the number of addresses.Given a number of parts NP within program P , let i = 1, ..., N define the parts.

Step 2. Collect a sample of order history containing part number partk, delivery addressaddressk ∈ A and program prgk ∈ P , where k = 1, ...,K represents the order.

Step 3. Set Class number = 1

Step 4. Let ck, where k = 1, ...,K, be a variable representing the class order k belongs to.

Step 5. For k = 1, ...,K

• Set Row address = 0 and Row part = 0

• If k = 1

∗ Set ck = Class number.

∗ Update Class number.

• Else:

∗ For j = 1, ...., k − 1:

· If addressk = addressj and prgk = prgjSet Row address = j

· If partk = partj and prgk = prgjSet Row part = j

∗ If Row address = 0 and Row part = 0

· Set ck = Class number.

· Update Class number.

∗ If Row address > 0

· Set ck = cRow address.

∗ If Row address > 0 and Row part > 0

A.4. Classification according to Jaccard’s similarity index III

· If cRow address 6= cRow part

Replace all ck = cRow part with cRow address.

∗ If Row address = 0 and Row part > 0

· Set ck = cRow part.

Step 6. Collect unique part numbers and corresponding class.

A.4 Classification according to Jaccard’s similarityindex

Step 1. Let P = {p1, ..., pm} be a set of programs, where m is the number of programs.Given a number of parts NP within program P , let i = 1, ..., NP and j = 1, ..., NP

define the parts.

Step 2. Calculate a Jaccard’s similarity matrix SPNP×NP

, containing Jaccard’s similarityindex si,j for every pair of parts, for each program P .

Step 3. For P = p1, ..., pm:

• Set Class number = 1.

• Find smax = max{SPi,j} and save corresponding i and j to imax and jmax

respectively.

• While smax > 0:

∗ Assign parts i and j corresponding to smax to class Class number.

∗ Add all parts with simax,j > 0 or si,jmax > 0 to class Class number indecreasing order.

∗ Update Class number.

∗ Find next smax = max{SPi,j} among the remaining parts and save corre-

sponding i and j to imax and jmax respectively.

Step 4. Step through all remaining parts i not yet assigned to any class:

• If si,j = 0 ∀ si 6=j

∗ Assign to separate class.

• Else:

∗ Find simax = max{Si,j} ∀ j.

· If part j corresponding to simax is assigned to a class:Assign i to the same class.

· If part j corresponding to simax is not assigned to a class:Create separate class for i and j.

Step 5. Collect classes.

IV Chapter A. Pseudo code

A.5 Random location strategy

Step 1. Given a number of parts i = 1, ..., N and a number of racks r = 1, ..., R, let si bethe required storage size for part i.

Step 2. Let X be an N × 2 matrix where the first column contains i = 1, ..., N and thesecond column is initially empty.

Step 3. Let usedi be a variable indicating if part i has been assigned a location, defined as:

usedi =

{1, if part i has been assigned to a location0, otherwise

Step 4. For k = 1, ..., N

• Generate u1 ∼ U(1, N)

• Set part nr = X(u1, 1)

• While usedpart nr = 0

∗ Generate u1 ∼ U(1, N)

∗ Set part nr = X(u1, 1)

∗ If part nr > 0:

Set usedpart nr = 1

• While Check = False

∗ Generate u2 ∼ U(1, R)

∗ Set rack nr = u2

∗ Search for available location in rack rack nr, from smallest to largestcapacity of storage location, but with capacity larger than or equal to si.

∗ If available location exist:

Set X[k, 1] = part nr

Set X[k, 2] = rack nr

Check = True

• Set Check = False

Step 5. Collect matrix X.

Appendix B

Simulation model

In Figure B.1, an overview of the whole simulation model in ExtendSim can be seen.Figure B.2 presents an example of an input file which will be inserted in the simulationmodel in ExtendSim. Figure B.3 shows an example of an output from the simulationmodel in ExtendSim.

V

VI Chapter B. Simulation model

Fig

ure

B.1:

Overv

iewof

the

wh

ole

simu

latio

nm

od

elfro

mE

xten

dS

im.

VII

Fig

ure

B.2

:E

xam

ple

of

the

inp

ut

file

wh

ich

isin

sert

edin

the

sim

ula

tion

mod

elin

Exte

nd

Sim

.

VIII Chapter B. Simulation model

Figure B.3: Example of output from the simulation model in ExtendSim.

OPTIMIZATION OF STORAGE CATEGORIZATIONumu.diva-portal.org/smash/get/diva2:1214830/FULLTEXT01.pdf ·...

Documents

Transcript of OPTIMIZATION OF STORAGE CATEGORIZATIONumu.diva-portal.org/smash/get/diva2:1214830/FULLTEXT01.pdf ·...