eindhoven university of technology master optimizing

Eindhoven University of Technology

MASTER

Optimizing storage assignment in a 3PL warehouse with stochastic non-stationary demand

Verlinden, T.C.W.

Award date:2018

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https://research.tue.nl/en/studentTheses/c3147ce9-d884-4888-b7d0-8ace4cdcb739

Optimizing storage assignment in a 3PL warehouse with stochastic non-stationary demand

by:

Thomas Verlinden

Student identity number: 0898071

In partial fulfillment of the requirement for the degree

Master of Science

In Operations Management and Logistics

Supervisors:

dr. ir. R.A.C.M Broekmeulen

dr. N.R. Mutlu

Company Mentors:

R. Rutten

R. van der Linden

January 24, 2018

[Master Thesis] Thomas Verlinden

TUE, School of Industrial Engineering. Series Master Theses Operations Management and Logistics

Subject Heading:class-based storage, non-stationarity demand, discrete event sample-path simulation.

I


Abstract

In this paper, a business problem-solving project is discussed. In this project, the goal is minimizing

material handling by improving the class-based storage assignment. The storage assignment is

modeled as a knapsack model with a space forecast model based on Little’s Law for the weight

factor and daily average outflow as profit factors. The knapsack problem is evaluated with a greedy

algorithm on specific points in time. The research is done in a third-party warehouse with stochastic

non-stationarity inflow and outflow. The storage is done in different types of storage systems. 80

different scenarios are tested with changing the following parameters: treatment of input of the

forecast model, period between the evaluation of the storage assignment, storage lane depth in

block-stacking, number of storage classes in the multi-level storage rack, change strategy after

evaluation and different cost of the change strategy after evaluation. With the use of the forecast

model, everyday evaluation and changing the storage assignment with the put-away strategy, the

model could save 10% material handling in time over the sample path of one and a half year in

comparison with the company model.

II


Preface

In this chapter, I would like to thank everyone that helped me with this master thesis project. After

finishing my bachelor at Fontys Hogescholen Eindhoven, I started my education at the TUe. When

I finished the pre-master, I was able to start the master Operations Management and Logistics.

During the master I liked the courses and learned a lot, especially modeling courses I found

interesting. After a great 5 months studying at the TU of Munich, I started my graduation project

at Arvato Benelux in Heijen.

I liked the project because I was able to use my theoretical knowledge in a practical situation. I

learned a lot from implementing mathematical models in the simulation. This was not possible

without the support of my mentor dr. ir. Rob Broekmeulen. I learned a lot from our discussions.

Also, my company mentors Roger Rutten and Ralph van der Linden were great to discuss the

models and helped to make them useful in a practical situation. Next to my company mentors,

I like to thank the other employees of Arvato they were always willing to answer my questions,

especially the employees of the Control tower who got me most of the data.

I also like to thank my friends from de TUe for being helpful in my time at the university. My

special thanks go to my girlfriend Karin to be there when I was working hard to accomplish my

goal of graduation.

Thomas Verlinden Eindhoven, The Netherlands January 2017

III


Management summery

This report is the result of a master thesis project that is done at Arvato Benelux in Heijen. Arvato

Benelux is part of the Bertelsmann company. The research is focused on the class-based storage

assignment strategy for unit-loads with stochastic non-stationary demand. There is a lot of research

done on storage assignment, but most research is done for storage assignment with stationary

demand situations.

Analyze & DiagnoseThe warehouse operates as a distribution warehouse with value-added services. This means re-packthe stock keeping unit (SKU) in a country-specific or marketing campaign specific package. Thewarehouse has the following processes: inbound, put-away, assembly, replenishment to forwardareas, picking, accumulation and shipping. The inbound, assembly, accumulation and shippingprocesses after picking are not taken into account in this research. The following challenges existfor the storage assignment system:

• Stochastic non-stationary inflow and outflow of unit-loads caused by SKU launches and seasonality.

• Two forward areas which add two outflow point and allocation of unit-loads over forward and reserve area.

• Block stacking and multi-level storage rack which leads to a need for allocation over these two areas.

• Assembly process which creates an extra inflow and outflow point.

• Imperfect information about inflow, duration of stay (DOS) and outflow of unit-loads.

• There is also an overflow area in the warehouse, which lead to the need for the assignment between normal

reserve stock and overflow stock.

These challenges lead to the following research question:

In which way should the storage assignment of unit-loads be designed to deal with a high variation

in inventory levels caused by SKU launches and seasonality in demand of the high-tech client to

minimize material handling

Design

To minimize the material handling the storage assignment in the reserved areas is modeled as

a knapsack model. The weight factors of the knapsack model are based on a forecast model.

The profit factors are the average daily outflow. The knapsack model is solved with a greedy

algorithm. The forecast model is based on the most fundamental law in queuing, Littles Law.

IV


Given the average daily inflow of unit-loads and the average DOS of unit-loads that already left

the warehouse, the average storage use could be calculated. This forecast model is used to reserve

space for a SKU in a storage system and storage class for the period of evaluation. The SKUs

with the highest outflow will be assigned firstly. When the calculated storage need is higher then

the depth of the storage lane in the block stacking area, the SKU is assigned to the block stacking

area. When the calculated storage need is lower, the SKU is assigned to the multi-level rack until

this rack is full. When both storage systems are full, the SKUs is assigned to the overflow storage

system. With Dijkstra algorithm, the distances and travel times are calculated. In the multi-level

rack, five new storage classes are created with locations that have almost the same travel time to the

inflow and outflow points: Conveyor area, Wide Aisle area, assembly inbound, assembly outbound

and the inbound and outbound dock. For the forward-areas also a knapsack model is designed. The

model is used to determine which SKUs stay in the forward area. The SKUs that not stay in the

forward area need to be moved back to the reserved area. The model has as profit factor the

probability that demand for a SKU occurs in the forward area in de future. This probability is

calculated with an exponential smoothing forecast based on the days of picking in an evaluation

period of 25 days. The weight factor is the current inventory of the SKU in the forward area. The

knapsack problem is solved with a greedy algorithm, the SKUs with the lowest probability leave

the forward-area until there is space enough free for the new SKUs.

In the reserved area model these parameters could be changed: The treatment of DOS in the

forecast model, the period between evaluation, number of storage classes in the multi-level rack,

number of unit-loads in the storage lane in the block stacking area, the change strategy after

evaluation and the cost of the change strategy. The DOS in the forecast model is evaluated with the

average DOS of unit-loads that already left the warehouse and with the given DOS of incoming

unit-loads based on there historical DOS in the company data. The period of evaluation is tested

with these settings: every day, one month before and after the peak, 13 days before and after the

peak and at the start and end of the peak. To change the storage assignment two strategies could be

used, put-away change strategy and re-warehousing strategy. The re-warehousing strategy is also

evaluated with non valued working hours. The number of unit-loads in the storage lane in the block

stacking area is evaluated with two levels: same depth over the sample-path and the combination of

V


normal depth storage lanes in low season and double deep storage lanes in the peak. The number of

storage classes in the multi-level storage system with the following levels: five storage classes over

the sample-path and the combination of five storage classes in the low season and three classes in

the high season. All these parameters lead to 80 scenarios which are evaluated in a sample-path

simulation and compared with the worst case of not evaluation SKUs and the assignment based on

the company model. The forward areas model is implemented in each scenario.

Results

The best performing scenario has a daily evaluation and the put-away change strategy. In this

scenario, the model is able to decrease the material handling over the sample-path with 10%. The

re-warehousing change strategy is only able to save material handling when the re-warehousing

movements are done with different valued working hours and daily evaluation. The effect of

changing the number of storage classes and depth of storage lane has not a big effect on the

material handling over the sample-path. The forward area model was able to decrease the number

of cleanups with 22 % and replenishments with 14% in comparison with the company model based

on expert knowledge.

Conclusion

This research is done to solve a business problem end extend the existing literature about storage

assignment in warehouses. The model discussed in this research is able to decrease material

handling which is solving the business problem of the company. The literature is extended with a

model that is able to deal with non-stationarity in demand and inflow. The model is built with data

from one company which is a limitation. The forward area demand is assumed to be known a day

before the demand occurs. Also, the availability of material handling equipment is assumed to be

unlimited at any moment. Future research could be done with implementing capacity constraints in

the material handling equipment and testing the model with different company data. The practical

contribution could be the implementation of the forecast model and evaluation system. The trust

in the model of the company can be improved by firstly using it as an expert system.

VI

List of Figures

1.1 Place of the warehouse in supply-chain . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Best application of storage systems . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Unit-loads demand of raw material per month . . . . . . . . . . . . . . . . . . . . 16

3.2 Current process of Arvato . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Unit-loads demand of raw material per month . . . . . . . . . . . . . . . . . . . . 18

3.4 Unit-loads demand of raw material versus inflow of unit-loads from inbound per

month . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Unit-loads demand of raw material versus inflow assembly per month . . . . . . . 20

3.6 Unit-loads demand of finished goods in unit-loads per month versus inflow from

assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.7 Less than a unit-load per month from the forward areas . . . . . . . . . . . . . . . 22

3.8 Replenishments to forward areas per month . . . . . . . . . . . . . . . . . . . . . 23

3.9 Inflow and outflow per month . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.10 Inventory in the warehouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.11 Duration of stay of unit-loads demand per month . . . . . . . . . . . . . . . . . . 26

3.12 Comparison Little versus actual inventory . . . . . . . . . . . . . . . . . . . . . . 27

3.13 Inflow and demand of one SKU . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.14 SKU launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.15 Transition periods for dealing with both seasonality and product launches . . . . . 33

5.1 New SKU process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 Leaving unit-load process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

VII


5.3 Storage assignment evaluation process . . . . . . . . . . . . . . . . . . . . . . . . 43

5.4 Storage Assignment Evaluation forward area process . . . . . . . . . . . . . . . . 44

7.1 Forecast model evaluated in comparison company model and worst case. . . . . . 58

7.2 Period of evaluation evaluated in comparison company model and worst case. . . . 59

7.3 Change strategy evaluated in comparison company model and worst case. . . . . . 60

7.4 Storage lane size evaluated in comparison company model and worst case. . . . . . 61

7.5 Number of storage classes evaluated in comparison company model and worst case. 62

7.6 Cost of re-warehousing evaluated . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.7 Cleanup movement forward areas savings model in comparison with company model 64

7.8 Best performing scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

VIII

List of Tables

3.1 Storage systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

IX

Contents

1 Introduction 1

1.1 Problem introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Company background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Place warehouse in supply chain the high-tech client . . . . . . . . . . . . . . . . 2

1.4 Project motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Project approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Report outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Literature overview 5

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Forward-reserve problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Storage assignment policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Single period models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Multi-period demand models . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Gap in literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Analyses 15

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Assortment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Processes in the warehouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 Receiving and put away processes . . . . . . . . . . . . . . . . . . . . . . 17

3.3.2 Assembly process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.3 Picking, accumulation and packing process . . . . . . . . . . . . . . . . . 20

X


3.3.4 Replenishment process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4 Stability of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4.1 Short term stochastic non-stationary demand and inflow variation . . . . . 27

3.5 Storage locations system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Current storage assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Diagnosis 34

4.1 Challenges of the storage assignment system . . . . . . . . . . . . . . . . . . . . . 34

4.2 Solutions suggested by literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 Research question . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Research design 38

5.1 Conceptual model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 Detailed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.3 Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.1 Example of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.4 Design parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.5 Key performance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6 Simulation model 54

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.2 Experimental setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.3 Validity and reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7 Results 57

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.2 Forecast model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

7.3 Period of evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

7.4 Change strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.5 Storage lane size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7.6 Number of storage classes change . . . . . . . . . . . . . . . . . . . . . . . . . . 61

XI


7.7 Cost of re-warehousing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.8 Assignment of SKUs to the two forward areas . . . . . . . . . . . . . . . . . . . . 63

7.9 Best performing scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

8 Implementation 67

8.1 Implementation plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

8.2 Feasibility of implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

9 Conclusion & recommendations 69

9.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

9.1.1 Analyze & Diagnose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

9.1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

9.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

9.2 Contributions to theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

9.3 Practical contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

9.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

9.5 Opportunities for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Bibliography 73

Appendices 76

A Valid paths 77

B Visual model of the warehouse 78

C Deterministic lower bound model 79

D Summed up travel time based storage classes 82

E Auto correlation 85

F Evaluation of α and days of evaluation in forward area model 86

XII

G Scenarios 88

H Scenario results 91

Chapter 1

Introduction

In the first chapter of the master thesis, the problem and the company will be discussed. Also the

motivation for starting the project and the project approach will be discussed.

1.1 Problem introduction

This project is focused on the class-based storage assignment strategy for unit-loads with stochastic

non-stationary demand. A unit-load is a pallet where pieces or case packs of the same stock

keeping unit (SKU) are stored on together. This unit-load could be placed in a multi-level-storage

rack or on the floor. The storage assignment strategy is the way that inventory of SKUs is assigned

to storage locations. Storage assignment is researched extensively with stationary demand, but not

as much as stochastic non-stationary demand. This research is done to solve a company problem

and extend the existing research on this topic. The research is conducted at Arvato Benelux.

1.2 Company background

Arvato is part of the Bertelsmann company which is home-based in Germany. Besides Arvato,

there are seven different companies part of the Bertelsmann company: The RTL group, Penguin

Random House, Gruner+ Jahr, BMG, Bertelsmann Printing Group, Bertelsmann Education Group

and Bertelsmann Investments. Arvato has 70,000 employees in more than 40 countries and is the

largest company in the Bertelsmann company. Arvato had a turnover of 4.7 billion in 2015. The

1


company has six solutions departments:

• Corporate information management

• Customer Services

• E-commerce Solutions

• Financial Solutions

• Marketing Solutions

• Supply chain management and Logistics solutions.

The graduation project is conducted in the supply chain management and logistics solution department

at the warehouse based in Heijen, on the border of Germany. The warehouse in Heijen started its

operations in April 2016 with a surface of 30,000 m2 but is recently extended with 20,000 m2.

They could expand to 70,000 m2 in the future. The warehouse is a multi-client warehouse. It

is AEO and TAPA-A certified and operates as a bonded warehouse. The company also conducts

value-added services for their clients. These services are:

• Localization of the SKUs. (Repack the pieces of a SKU for each country of destination)

• Configuration of the SKUs. (Repack the pieces of a SKU for each marketing campaign)

The warehouse serves high-tech clients and health-care clients. The project is executed on the part

of the warehouse that serves one high-tech client.

1.3 Place warehouse in supply chain the high-tech client

The warehouse serves as a distribution center between production in Asia and Europe and retailers

in Europe and the Middle-East. Part of the outflow goes direct to the retail and the other part of the

outflow goes to other distribution warehouses that distribute the SKUs to the retail. The position

of the warehouse in the supply chain is illustrated in the figure 1.1.

2


Figure 1.1: Place of the warehouse in supply-chain

The inflow from production in Europe is first processed in the warehouse of Arvato before it is

shipped to retailers or other distribution warehouses.

1.4 Project motivation

The company needs to deal with the high variation in inventory levels of unit-loads. This variation

causes the problem of too much inventory in the warehouse at peak periods. This results in more

material handling and the company needed to store SKUs in overflow storage systems. Putting

unit-loads in the overflow storage systems is increasing the cost for the high-tech client because

this client has to pay for the overflow storage systems. When putting the inventory in the overflow

locations, it makes this inventory also more expensive to reach. Arvato wants to minimize the

overflow transfers and improve the storage process to be the best third-party logistics provider for

the high-tech client. The company wants a model that can allocate inventory over the different

storage and the overflow storage systems based on the actual and forecast demand and inflow that

minimizes material handling. This lead to the following research goal:

In which way could material handling be decreased by changing the storage assignment strategy?

3


1.5 Project approach

The project could be classified as a business problem-solving project. The typical problem-solving

regulative cycle by (Strien, 1986) is recommended for problem-solving projects. The model

defines the project in the following steps:

1. Problem definition

2. Diagnose

3. Design of a solution

4. Implementation of the solution

5. Evaluate the solution

The design of a solution is done as an extension of the literature about storage assignment. The

literature is used to build a model for storage assignment which is able to deal with the demand

and inflow changes. The extended model is implemented in a simulation to show the effect of

this model on the decrease of material handling. This is the implementation step. When the

simulation shows an improvement that is big enough for the company to change the storage

assignment strategy they want to implement the model in their warehouse management system.

The model needs to be robust enough to deal with variation in the inventory of raw materials and

finished goods. The robustness will be tested with one and half year company movement data in

the simulation. The test is the evaluation step.

1.6 Report outline

The report starts with the literature review. This chapter discusses the current literature about

storage assignment. In the second chapter, the analysis of the current processes and the flows

of unit-loads to these processes are discussed. Also, the current storage assignment and location

system is discussed. The fourth chapter discusses the research question, sub-questions and the

scope of this research. The fifth chapter describes the research design and the scenarios that are

tested. In the sixth chapter, the simulation model will be explained. The seventh chapter describes

the results of the simulation experiments. Chapter eight discusses the implementation plan for the

new storage assignment model. The last chapter describes the conclusion and recommendations.

4

Chapter 2

Literature overview

To find an improvement model for storage assignment that is an extension of the existing knowledge,

the current literature about storage assignment will be discussed in this chapter. First, an introduction

to storage assignment will be given. Also, the factors that influence storage assignment will

shortly be discussed. Next, the connection between the storage assignment problem and the

forward-reserve problem is discussed. In the other sections, the storage assignment problem

solutions and the gap in the literature will be explained.

2.1 Introduction

The storage assignment problem is researched extensively. Storage assignment is one of the most

important processes in a warehouse. The literature reviews about warehousing (de Koster et al.,

2007), (Gu et al., 2007) and (Rouwenhorst et al., 2000) all describe storage assignment.

Storage assignment is influenced by a couple of factors. The first factor that influences storage

assignment is the physical storage system. There are different ways that unit-loads could be stored:

1. Mobile multi-level rack

2. Single-deep storage multi-level rack

3. Push-back multi-level rack

4. Double-deep storage multi-level rack

5


5. Drive-in multi-level rack

6. Drive-thru multi-level rack

7. Block stacking

All these types of storage have different storage possibilities and accessibility. The differences

make the multi-level racks more suitable for specific combinations of a number of unit-loads on

stock and demand of the SKU. The suitability of the storage racks is shown in figure 2.1

Figure 2.1: Best application of storage systems

When looking at the investment cost of these systems, block stacking is the least expensive solution.

This way of storage wastes storage capacity when the storage hall is high, and the level of stacking

that is allowed is lower as the height of the storage hall. When multiple stock keeping units (SKUs)

are stored in one storage lane, the operation costs of these lanes are high. Unit-loads need to be

moved before a unit-load with the needed SKU could be received.

Multi-level mobile systems are the most expensive investment solution, but use almost all storage

capacity and stay relative easy reachable. When looking at accessibility of single deep multi-level

racks, they are the most accessible for standard warehouse handling equipment. Push-back and

double deep multi-level racks are useful when more than one unit-load of the same SKU needs

to be stored. Push-back multi-level racks are more expensive than double deep multi-level racks,

but for double deep multi-level racks, specialized equipment is needed. Drive-in and multi-level

drive-thru racks are less accessible as block stacking, but waste less storage space when a storage

hall is high, and the level of stacking is lower. The effect of block stacking is also dependent on

6


a number of unit-loads that could be placed in a storage lane. (Bartholdi et al., 2014) discuss that

more unit-loads per storage lane lead to less waste of storage space. This could be explained by

fewer drive paths. They also show that when there are too much unit-loads in a storage lane, there

is also a waste of storage space. This second source of waste is called honeycombing. They also

discuss a formula for the optimal line depth based on the order quantity, demand, available space

and unit-load size.

The other factors that influence the effectiveness of storage assignment policies are the level of

automation of the storage and retrieval processes, which also has an impact on the effectiveness

of the storage assignment policy. Routing and batching of incoming picking orders also influence

the effectiveness of storage assignment policies. The same holds for the layout of the warehouse

and the command-mode of the storage and retrieval processes. More about these factors could be

found in, (Verlinden, 2017).

2.2 Forward-reserve problem

The storage assignment problem is also connected to the forward-reserve problem. This problem

is first researched by (Hackman & Platzman, 1990). The forward-reserve problem is the problem

of splitting the warehouse into two areas, the forward area, and the reserve area. This splitting

could be done to save travel time because the forward area is meant to be smaller as the reserve

area. When the splitting is done, extra replenishment movements are needed. In this way, it is

only useful to split the warehouse into these two areas when less than one full unit-load orders

are collected by the warehouse. When the warehouse collects these orders, a picker saves material

handling each time an order is picked until the unit-load has no stock. At that point, a new unit-load

need to be replenished. The replenishment is only carried out once for each unit-load. The total

savings are dependent on the replenishment material handling and the picking material handling.

The replenishment material handling is the travel time from the assigned position of the SKU in

the reserve area and the position of the SKU in the forward area. The picking material handling

is the travel time from the assigned position of the SKU in the forward area and the inflow and

outflow point of the SKUs. The dependency of the assigned locations in the forward area and the

7


reserve area link the forward-reserve problem to the storage assignment problem.

(Frazelle et al., 1994) extend the model by making the size of the forward area a decision variable.

(van den Berg et al., 1998) take into account busy and idle times. The replenishments between

the forward and reserve area are conducted in idle times. They came up with a knapsack-based

heuristic to minimize labor time for picking and replenishment. (van den Berg et al., 1998)

allows also picking from the reserve area and unit-load replenishments to the forward area. All

these papers assume a deterministic and stationary demand situation. When this is not the case,

assignment of SKUs to the forward area need to be changed when demand changed. When SKUs

are only replenished from the reserve area to the forward area for one batch of orders, the storage

assignment is called dynamic storage (de Koster et al., 2007). The paper of (Yu & de Koster, 2010)

describe a system of dynamic storage. The authors describe a system where orders are batched and

picked in the forward area. This model is interesting but is assumes that orders could be batched.

This model also leads to less than full unit-load replenishments which take longer than unit-load

replenishments. This system adapts to demand changes and could be used in a warehouse with

stochastic non-stationary demand.

With the factors that influence the effectiveness of a storage assignment policy and the connection

to the forward-reserve problem, the storage assignment policies are described in the next section.

2.3 Storage assignment policies

The literature describes five different storage storing policies: dedicated storage, random storage,

picking frequency based, affinity-based and duration of stay based (DOS). These policies could be

generalized to a class-based storage policy. Random storage and dedicated storage are the most

extreme types of class-based storage. With dedicated storage, the number of classes is the same as

the stock keeping units (SKUs). With random storage, there is only one class. Frequency-based

and affinity-based policies could be used to allocate SKUs to classes. In literature also closest to

open location storage assignment is discussed. Incoming unit-loads are assigned to the first open

location from the inflow and outflow point. (Hausman et al., 1976) point out that this policy is the

8


same as the random policy when only unit-loads are moved. Little’s Law could be used to calculate

the DOS of a unit-load. Also, the average storage space that is needed could be calculated with the

Law of Little.

In the literature, shared storage is discussed. All the storage policies that are not dedicated are

shared storage policies. The SKUs share their storage location with other SKUs. Shared storage

is used because storage space could be saved when using the same location for different SKUs.

With dedicated storage and stationary deterministic demand, on average 50% of the total storage

capacity of the warehouse is used when the inflow is based on economic order quantity inventory

model (Bartholdi et al., 2014). With shared storage in a class-based situation, it is assumed that

the required storage space is the average inventory (Hausman et al., 1976). However, (Guo et al.,

2016) showed that the average required storage space depends on the popularity of the SKU in

comparison with the other SKUs.

In the early years before computers were used, dedicated storage was the only workable policy.

Employees were obligated to memorize the storage location to obtain the SKU. When the first

computers were introduced, the dedicated storage policy is partly replaced by other policies, but it

is still in use. The dedicated policy could be combined with other policies, so it is not described

separately.

Random storage is a policy that can not be optimized. It is used as a worst-case benchmark for the

other policies because it leads to more material handling in most cases. The positive side of random

storage is that it is possible to use all locations for each SKU which leads to the highest possible

storage utilization (Frazelle & Sharp, 1989). (Guo et al., 2016) shows that when the skewness of

the demand curve is increasing, the one-way travel distance in this policy is decreasing. Between

20/20% ratio and the 29%/90% the one-way travel distance decrease with 40%. This implies that

when the skewness of the demand is high, the number of storage classes should be low. Because

random storage assignment could not be optimized this policy is not described separately.

The focus of the next subsection is on the single period models based on picking frequency, DOS

9


assignment policies. The subsection after the next subsection is discussing the multi-period models

that are researched. The single period models assume stationary deterministic demand or stationary

stochastic demand. The single period affinity-based policies can be found in (Verlinden, 2017).

They are not described here because they are not relevant to this research. The multi-period models

could deal with non-stationary demand because they evaluate the inflow and outflow of each period.

After evaluation changes to the storage assignment could be done with the change of the put-away

strategy or with relocating all unit-loads in the warehouse to the right storage location or class.

This is called re-warehousing.

2.3.1 Single period models

One of the first models that were developed where picking frequency-based models. Picking

frequency based storage assignment means assigning SKUs with high demand to storage locations

close to the inflow and outflow point of the warehouse. The first paper about this topic was written

by (Heskett, 1963). He came up with the cube-per-order index (COI), which is the ratio of the

maximum allocated storage space to the number of storage/retrieval operations per unit of time.

SKUs with the lowest COI were allocated to the storage locations with the lowest retrieval time.

The model of (Heskett, 1963) is designed for a deterministic dedicated storage system. The first

paper that introduces a class-based system was (Hausman et al., 1976). (Hausman et al., 1976)

used the picking frequency model in a class-based situation. This model is called the turnover

class-based policy. First, an ABC Pareto analysis is done to divide the SKUs into three turnover

classes. SKUs in the A group are assigned to the class that is located closest to the inflow and

outflow point of the warehouse. The assignment of unit-loads in the class is done randomly. The

model also assumes the same travel distance to each storage location in its class. (Hausman et

al., 1976) assumes a deterministic stationary demand model and a single command situation. This

makes the model of (Hausman et al., 1976) more useful for the reserve area with deterministic

stationary demand. (Chan & Chan, 2011) test class-based storage in comparison with random

storage and dedicated storage with different routing policies and layouts of the warehouse. They

show with simulation that a vertical class-based policy is decreasing travel times in a warehouse

with manual picking and multi-level racks.

10


(Thonemann & Brandeau, 1998) extend the model of (Hausman et al., 1976) with a stationary

stochastic demand model. The paper is also assuming a single command situation. They also

assume a different demand model. The unit-loads are stored in the system until a re-order level

occurs. Unit-loads are retrieved in the sequence of indexes. Unit-loads with the lowest index are

retrieved first. The storage is done to a re-order level at the end of the day. This is only working

when the supply of the warehouse is done at the end of the day. Alternatively, unit-loads have to

wait at the inbound area to be stored at the end of the day. (Thonemann & Brandeau, 1998) test

the model with uniform and exponential demand. They show that most of the gain, that could be

achieved with the class-based model in deterministic demand is also gained with stochastic demand

if stock-out probabilities are low. Their paper is not considering non-stationary demand.

All these models only evaluate the demand and inflow at one point in time. They optimize the

storage assignment based on the historical demand in a deterministic or stochastic way. The

stochastic model could deal with variation in inflow and demand, but with non-stationarity, the

variation is increasing. This could lead to a less correct assignment model. The other solution

is to evaluate the storage assignment policy every time the demand changes to adapt to these

changes with changing the put-away strategy or doing a re-warehousing operation. The papers that

discusses one of these systems are described in the next subsection.

2.3.2 Multi-period demand models

(Manzini et al., 2015) came with an extension of the turnover class-based model of (Hausman et

al., 1976) which evaluates demand and inflow data for each period. The model suggests changing

unit-loads from class to class in each period when the demand or inflow changes. The model of

(Hausman et al., 1976) assumes that demand and inflow information is known in advance. This

data could be captured from demand forecasts. In this way, the model is a deterministic model.

The authors came up with a model that takes the SKU life-cycle into account. The first research on

SKU life-cycle management was mainly focused on marketing. The authors describe that it could

be useful in logistics too. The authors came up with two multi integer problem (MIP) models

11


to solve turnover class-based storage assignment over the life-cycle of a SKU. The first MIP is a

continuance model which allocates a SKU to a storage class and determines the storage capacity

of that class. The second MIP is a discrete model which only allocate a SKU to a class with a finite

capacity. SKUs could be moved from one SKU class to the other SKU class from period to period.

The costs of these movements are taken into account. They assume a SKU is only assigned to one

storage class in each period. The model of (Manzini et al., 2015) improves the model of (Hausman

et al., 1976) and (Thonemann & Brandeau, 1998) because it can adapt to non-stationary demand

changes but only when the demand is deterministic. The model is not discussing if the warehouse

operates in single or multi-command mode. They use different storage and retrieval cost for each

SKU class based on the level of automation of the class. The authors are also not discussing the

layout they used in each class. The effect of this parameter is captured in the cost of storage and

retrieval in that class. Next to the model of (Manzini et al., 2015) the paper of (Ang et al., 2012)

describes a model for storage assignment under non-stationarity demand situations. The model

of (Ang et al., 2012) uses robust optimization to assign unit-loads to storage locations in storage

classes. The model of (Ang et al., 2012) assumes stochastic inflow and stochastic demand. The

way they deal with the stochastic demand and inflow is a factor based demand model. The model

evaluates these factors every period. With this model non-stationarity is captured by a stochastic

model.

Next to picking frequency based storage assignment also the expected DOS of a unit-load could be

used to allocate a unit-load to a storage location. DOS based storage assignment means to assign

a unit-load to a location based on the expected time of stay in the warehouse. A unit-load with a

short expected stay is stored near the inflow and outflow points of the warehouse, and a unit-load

with a longer expected stay is stored further away from that point. The first paper about DOS

is written by (Goetschalckx & Ratliff, 1990). This paper tries to minimize material handling by

using shared storage locations. This article discusses two models; the first model assumes that the

DOS of unit-loads is known at the start of each period. The model tries to maximize the use of

the locations that are as close to the I/O point in the warehouse by assigning unit-loads with the

shortest DOS to these locations with the use of a greedy heuristic. This is a deterministic model.

The other model assumes that groups of SKUs could be made which have the same expected DOS

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at the start of each period. The expected inflow and outflow of the arriving unit-loads define the

size of the storage class. (Goetschalckx & Ratliff, 1990) assume that the size of a class is defined

by the maximum inventory in each period. This leads to empty storage locations in idle periods,

which is not preferred. Otherwise, the size of each class needs to be changed each period, which

leads to re-warehousing every period when the inflow and outflow is not balanced.

Another way to adapt to demand and inflow changes is by healing. This concept means changing

the storage assignment every day to adapt to demand changes. The first paper about healing was

written by (Kofler et al., 2011). (Kofler et al., 2014) extend the model of (Kofler et al., 2011)

with a multi-period model. Both papers could not prove that healing is effective with normal

valued working hours and actual moving unit-loads from locations to locations. It could still be

useful when only the assignment of incoming unit-loads is assigned to more favorable locations,

put-away change strategy, or when the healing is done with non-valued working hours.

13


2.4 Gap in literature

The gap in the literature could be found in applying storage assignment in a stochastic non-stationary

demand situation without an accurate forecast. The model of (Manzini et al., 2015) assumes that

the demand and inflow data is deterministic. This is not the case in some warehouses. The model

of (Manzini et al., 2015) could only be used to calculate the yearly cost with all the inflow and

outflow data given. This could be used as a lower-bound. The model of (Ang et al., 2012) could

deal with uncertain forecasts. (Ang et al., 2012) assume that the demand is based on three uncertain

factors. Introducing these factors lead to a stochastic linear program. When historical demand says

nothing about the distribution of demand and inflow in the future the situation is called an online

problem. This will be the case when the demand and inflow are totally unpredictable. This is

most of the time, not the case because even new arriving SKUs in the warehouse could derive

some demand and inflow information from SKUs with the same characteristics which lead to a

stochastic situation. The models of (Manzini et al., 2015) and (Ang et al., 2012) are working with

picking frequency; another solution could be the DOS of a unit-load. (Goetschalckx & Ratliff,

1990) discusses a system with a fixed re-order point and stochastic demand, but the DOS model

could also be used with stochastic inflow and demand. The DOS could be calculated based on

historical data of the DOS of unit-loads from SKUs with the same characteristics.

The model of (Manzini et al., 2015) also assumes that the inflow is in unit-loads, but the outflow is

in pieces. When the outflow changes from pieces to unit-loads, the model needs to be changed. The

models of (Ang et al., 2012) and (Goetschalckx & Ratliff, 1990) only worked with unit-loads. The

models of (Manzini et al., 2015), (Ang et al., 2012) and (Goetschalckx & Ratliff, 1990) could also

be combined with the forward-reserve problem when part of the demand is in unit-loads and the

other part in less than unit-loads. When demand changes the assignment of SKUs to the forward

area could also change.

14

Chapter 3

Analyses

In this chapter, the current warehouse processes will be discussed. Also, the location system and

the current storage assignment will be discussed. All the information is based on data from the

company from the period March-2016 to October-2017.

3.1 Introduction

There are different types of warehouses as discussed by (Bartholdi et al., 2014). The warehouse

of Arvato could be classified as a 3PL distribution warehouse. The inflow of these warehouses

originates from factories, and the outflow goes to customers. The warehouse works as a buffer

between production and demand. With the localization and configuration activities, the warehouse

of Arvato does the last step of production for the high-tech client. This step will be called the

assembly process. The assembly activities make it for the high-tech client possible to adapt to

demand changes between customers without creating more variability in their production process.

The production only makes one type of SKU for all customers, and the warehouse makes the SKUs

customer and country-specific. The production of the high-tech client works with an aggregated

demand planning. This makes centralizing the production in a low-cost country possible.

15


3.2 Assortment

As discussed in the introduction section the warehouse deals with a relatively low number of SKUs

of raw materials and a bigger number of SKUs of finished goods with the exception of the SKU

type P5. There are four SKU types, namely P1, P2, P3, P5. P5 is packaging. This raw material has

more SKUs, namely 2388. Figure 3.1 shows the number of SKUs per SKU type of raw materials

and finished goods. The raw material is received from outside the warehouse and finished goods

are created in the warehouse with the assembly process. Each SKU type could have both finished

goods SKUs and raw materials with the exception of P5 because packing is always raw material.

Figure 3.1: Unit-loads demand of raw material per month

The number of SKUs expands because the SKUs are made country and marketing campaign

specific.

3.3 Processes in the warehouse

A warehouse has a couple of standard processes as described by (de Koster et al., 2007):

1. Receiving

16


2. Put away

3. Pallet picking

4. Replenishment

5. Case picking

6. Broken case picking

7. Accumulation, sorting and packing

8. Shipping

Because this warehouse has assembly operations a couple of processes are done twice. The

processes are displayed in the figure 3.2 in a process schema.

Figure 3.2: Current process of Arvato

3.3.1 Receiving and put away processes

The inflow is based on the production planning of the high-tech client and the variability in

travel times from the factory in Asia and Europe to the warehouse in the Netherlands. Part of

17


the SKUs is arriving in containers from the factories in Asia. The other SKUs are arriving in

trucks. Arvato could leave containers in the port if there is not sufficient storage space, but this

is not recommended. When containers and trucks arrive, they are unloaded onto one of the 25

unloading lanes. This is done with electronic pallet trucks (EPT). When the SKUs are booked in

the warehouse management system (WMS), they are moved to the reserve area. This is done with

reachtrucks. The reserve area is partly block stacking and partly multi-level rack. Part of the SKUs

is de-stacked before the stock is moved to the reserve area. The reason for de-stacking is that

unit-loads are too high for employees in the assembly process to take case packs of the unit-load.

The SKUs that are coming in by containers are mostly stored in block stacking locations. The block

stacking area contains storage lanes of 12 or 14 unit-load positions. Only one material is stocked in

one storage lane. Next to the normal block stacking, the warehouse also has two different storage

halls with block stacking. These areas are used in the peak period to adapt to the inflow changes.

The inflow of unit-loads is non-stationary as is shown in figure 3.3. The inflow is also stogastic

because the inflow is not known in advance.

Figure 3.3: Unit-loads demand of raw material per month

3.3.2 Assembly process

The assembly activities are controlled by orders arriving from the high-tech client. The demand for

raw material is generated from these orders. When orders arrive, raw materials are picked from the

18


reserve area. The packaging material is first replenished to less than full unit-load picking storage

locations. The exact demand for one assembly order is picked before the assembly processes start

and put into the inbound assembly buffer. The assembly process is done on assembly lines. There

are 24 assembly lines that produce finished goods. The lines are utilized based on the arriving

assembly orders. When SKUs are assembled, they are placed on unit-loads and moved to the

assembly outbound buffer. From the assembly buffer, unit-loads are moved to the reserve area.

The demand for raw materials into the assembly process in comparison with the inbound of

unit-loads is shown in figure 3.4. The outflow from the reserved area to assembly inbounds is

non-stationary as could be seen in the figure 3.4. This process is also stochastic because the inflow

and outflow into assembly the inflow and outflow are not known in advance.

Figure 3.4: Unit-loads demand of raw material versus inflow of unit-loads from inbound per month

The output of assembly to the warehouse is also non-stationary as is shown in figure 3.5. The

figure shows the inflow to assembly and the outflow of assembly in unit-loads. This process is

also stochastic because the inflow into and outflow out of the assembly process are not known in

advance.

19


Figure 3.5: Unit-loads demand of raw material versus inflow assembly per month

The volume of unit-loads coming from assembly is bigger than the inflow because less pieces could

be stored on a unit-load. On average only 60% of pieces of a raw material unit-load are placed on

the finished goods unit-load. This effect is seen in figure 3.5.

3.3.3 Picking, accumulation and packing process

Incoming orders are classified as full truckloads or less than full truckloads. With full truckloads,

the order is picked by reachtrucks and put on an outbound lane. These orders could also be picked

in the overflow areas. The picking is done on First In First Out (FIFO) principle. When an order

is less than a full truckload, the order is linked to a truck. The full unit-loads that are in this order

are picked from the reserve area by reachtrucks in single-command, to the outbound lane. The

SKUs that are needed in less than a unit-load are picked from two forward areas. SKUs that are

needed in a less than one full unit-load quantity are classified based on their required volume. The

order could contain case packs or actual pieces. When this volume is less than 0,4 m2, the SKU is

picked from storage locations near a conveyor. This is called the Conveyor forward area by Arvato.

Units are picked and need to be packed in a carton box next to the conveyor. The pickers in the

20


Conveyor area are assigned to a specific picking zone. This is called picker-to-part-system with

zoning by (de Koster et al., 2007). When an order has less volume than one unit-load, the order

always goes over the conveyor and is allocated to a unit-load at the end of the conveyor. Part of

the storage locations next to the conveyor are flow-racks locations. Only SKUs from SKU type P2

could be placed here. The purpose of installing a conveyor is to decrease travel time of a picker

when visiting more than one location. The actual situation is that 76% of the customer orders that

go over the conveyor contain one SKU. So the conveyor is in that case not saving much travel time.

The orders with volume less than one unit-load that are combined on one unit-load at the end of

the conveyor make the conveyor still useful.

When SKUs are needed in quantities of more than 0,4 m2, they are picked from floor locations of

the multi-level rack. This is called a picker-to-part system by (de Koster et al., 2007). This area is

called the Wide Aisle forward area by Arvato. In the Wide Aisle area, only case packs are picked.

Pickers follow an s-routing heuristic to pick the SKUs when more than one SKU for one order

needs to be picked. This is only happening for 15% of the orders from the sample period. The

flows from one order from the Conveyor and the Wide Aisle area are combined in the sealing area.

The SKUs are packed on a unit-load, this unit-load is sealed and placed in the outbound lane.

The demand in full unit-loads of finished goods is non-stationary as is shown in figure 3.6. The

outflow of full unit-loads is also stochastic because the outflow is not know in advance.

21


Figure 3.6: Unit-loads demand of finished goods in unit-loads per month versus inflow from

assembly

The demand is compared with the inflow of finished goods unit-loads. In figure 3.7 the outflow

of the forward areas is shown. As is shown in the figure these outflows are also subject to

non-stationary. This process is also stochastic because the outflow is not known in advance.

Figure 3.7: Less than a unit-load per month from the forward areas

3.3.4 Replenishment process

The forward area locations are filled by replenishment orders. This is a manual process. Employees

calculate the demand for a SKU on a specific day and round this up to unit-loads. The unit-loads

22


are then replenished to the storage locations in the forward areas. When there are no free storage

locations available, a cleanup movement is done. Unit-loads from the forward area are moved to

the reserve area. 4% of the replenishment movements are cleanup movements from one of the two

forward area to the reserve area. This goes against the most important rule of logistics, decrease

the number of pickups of a unit-load. When there is less than a unit-load of a specific SKU, it

could be the case that part of the orders needs to be picked from the Conveyor area and the other

part of the orders from the Wide Aisle area. The unit-load is then first replenished from the reserve

area to one of the two forward areas. At the first forward area, part of the unit-load is taken. Next,

there is a movement from one forward area to the other forward area, and the rest of the unit-load

is taken. 6% of the replenishment movements is moved from the Conveyor area to Wide Aisle area

and from the Wide Aisle area to the Conveyor area. These movements are also against the most

important rule in logistics of minimizing the number of pickups of a unit-load. The replenishments

also follow a non-stationary flow as is shown in figure 3.8. Because the outflow in the forward-area

is stochastic also the replenishments are stochastic.

Figure 3.8: Replenishments to forward areas per month

In the next section the stability of the warehouse is discussed.

3.4 Stability of the system

Because the warehouse deals with stochastic non-stationary inflow and outflow, it is important to

find out if the inflow and outflow are balanced. When the warehouse is not balanced, the inventory

in the warehouse increases until the warehouse is fully loaded. To find out if the warehouse is

23


stable the Law of Little could be used to check the inflow in comparison with the outflow. When

the average inflow is higher as the average outflow for a longer period the warehouse is not stable

and will be overloaded.

The inflow is the number of unit-loads that arrive on the inbound dock and the assembly outbound.

The outflow is the sum of shipments to assembly inbound, replenishment to the Conveyor and Wide

Aisle and the full unit-load shipments to the outbound dock. In figure 3.9 the inflow of unit-loads

per day averaged per month are shown:

Figure 3.9: Inflow and outflow per month

The average inflow and outflow are almost balanced each month. When the average inflow and

outflow of unit-loads is averaged over the last year the average inflow/outflow of unit-loads is 1.04.

So the system is not balanced, the inventory is growing is shown in figure 3.10.

24


Figure 3.10: Inventory in the warehouse

At the end of the peak in December 2017, the inventory levels stay higher as what is expected from

the inflow and outflow. To protect the warehouse of overflowing the high-tech company needs to

decide which SKUs could be moved out of the warehouse, to create free space in the warehouse.

The difference in inflow and outflow over each month and the inventory level could be illustrated

with the duration of stay (DOS) of a unit-loads of a SKU. Based on expert knowledge from

employees from the company finished goods are staying in the warehouse for seven days. For

raw material, there is no set DOS. Raw material needs to be in the warehouse at least two days

before assembly. The average DOS of all the unit-loads was 13 days in the sample period. The

average DOS of a unit-load of raw materials was 17 days. There are some differences in DOS per

SKU type. Unit-loads of raw material SKU type P1 stayed on average 13 days in the warehouse.

Unit-loads from SKU type P2 23 days, P3 18 days and P5 35 days. For finished goods, the

unit-loads stayed nine days in the warehouse. There is some difference in DOS of a unit-load

per SKU type. Unit-loads of P1 stayed on average seven days in the warehouse, unit-loads of SKU

type P2 stayed on average 32 days in the warehouse. Unit-loads of SKU type P3 stayed 13 days in

the warehouse.

25


There are also differences in DOS each month, this is shown in figure 3.11.

Figure 3.11: Duration of stay of unit-loads demand per month

In figure 3.11 is shown that in the low season the raw material and finished goods stay longer in the

warehouse than in the high season. When the DOS in the peak period was the same as in the low

period, the warehouse overflowed during the peak period. The extremely high DOS of March 2016

is caused by the fact that the warehouse started his operations in that period and the unit-loads were

taken from the old 3PL of the high-tech client and were moved in. One year later in Match 2017,

a part of these unit-loads is moved out of the warehouse because they were not used anymore. The

peak in July-2016 is caused by the fact that unit-loads were moved to the overflow warehouse.

These unit-loads had a long DOS.

Based on the average inflow λ and average DOS W 13 days, the expected inventory L could be

calculated with the Law of Little. The expected inventory is calculated by the following formula:

L = λ ∗W (3.1)

The expected inventory L and the actual average inventory per month are shown in figure 3.12

26


Figure 3.12: Comparison Little versus actual inventory

As is shown in the figure the reality is different from what the Law of Little expects. The reason is

that the DOS of unit-loads in the peak period is lower than the DOS in the low season. This lead

to a higher L in the peak as the actual inventory and a lower L in the low season period.

3.4.1 Short term stochastic non-stationary demand and inflow variation

Next to the increase of inflow and demand in the peak season and decrease of inflow and outflow

after the peak season, there is also variation in inflow and demand of each specific SKU. Especially

in finished goods. In figure 3.13 is the demand and inflow of one SKU in unit-loads shown.

27


Figure 3.13: Inflow and demand of one SKU

The SKU is assembled in a big batch the first day. The first demand is mainly in full unit-loads,

and after a few days, the demand is taken in case packs or less than case packs in the forward areas.

First raw material arrives in the warehouse, that will be assembled into finished goods. Figure 3.14

show the inflow and outflow in unit-loads until the launch.

Figure 3.14: SKU launch

In the next section the storage location system is discussed.

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3.5 Storage locations system

In this section, the current storage system will be discussed. There are different storage locations;

the differences are based on the unit-load hight, the capacity of unit-loads and if less than a

unit-load or a case pack picking is allowed. If picking of less than a unit-load is allowed, there

is a split in locations that allow placing unit-loads with serialized SKUs and unit-loads without

serialized SKUs. Serialized SKUs are SKUs that are identified by a unique number of the customer.

SKUs that are serialized could only be picked in a storage system that is designed to deal with

serialized SKUs. The less than one unit-load locations are also split into fixed locations and flex

locations. Based on this different storage systems are made. This is done because the WMS works

with this storage system. The WMS describe these systems as storage types. Storage locations are

assigned to a section in a storage system. A storage section is a storage class. The WMS works

with the following storage systems:

Storage system Type of storage Number of location

113 Multi-level storage rack one of different type of unit-loads deep 8529

118 Block stacking for 14 block unit-loads of the same raw material 112

Overflow-118 Block stacking for 26 block unit-loads of the same raw material 390

119 Block stacking for 12 Euro unit-loads of the same finished goods 50

Overflow-119 Block stacking for 16 Euro unit-loads or 19 Euro unit-loads of the same finished goods 83

120 Fixed locations in the Conveyor area for non-serialized SKUs for 2 to 12 unit-loads of all types of unit-loads 220

121 Fixed locations in the Conveyor area for serialized SKUs for one unit-load of all types of unit-loads 17

128 Flex locations in the Conveyor area for non-serialized SKUs for one unit-load of all types of unit-loads 256

129 Flex locations in the Conveyor area for serialized SKUs for one unit-load all types of unit-loads 53

130 Fixed locations in the Wide Aisle area for non-serialized SKUs for 2 to 20 unit-loads of all types of unit-loads 220

131 Fixed locations in the Wide Aisle area for serialized SKUs for 2 to 20 unit-loads all types of unit-loads 17

138 Flex locations in the Wide Aisle area for non-serialized SKUs for one unit-load of all types of unit-loads 256

139 Flex locations in the Wide Aisle area for serialized SKUs for one unit-load of all types of unit-loads 53

170 Assembly less than unit-pick locations 154

Table 3.1: Storage systems

3.6 Current storage assignment

In this section, the current storage assignment system will be discussed. Incoming unit-loads from

both the actual inbound area and assembly outbound are first assigned to a storage system. Part of

the raw material SKUs is assigned to the block stacking storage system for raw materials; the other

incoming SKUs are assigned to the multi-level rack storage system. SKUs from raw material SKU

type P1 are first placed in the block stacking storage system for raw materials. When this storage

29


system is full, the SKUs of raw material SKU type P1 will be placed in the overflow block stacking

storage system. The assignment between the block stacking storage systems and overflow storage

system is done on the expected DOS of the SKU for assembly. When the overflow is also full, the

unit-loads of SKUs are stored in containers in the port.

For the finished goods SKUs, part of these SKUs are assigned to the block stacking storage system

for finished goods or the overflow block stacking storage system, the other part of the SKUs are

assigned to the multi-level rack storage system. The assignment of unit-loads to the finished goods

block stacking storage system, overflow storage system and the multi-level rack storage system

is based on the inventory level of the SKU and the shipment mode. The assignment between

the multi-level rack storage systems and block stacking storage system for finished goods is done

based on the inventory level of a specific SKU. When this SKU has a high inventory level, the

SKU is placed in the block stacking storage system for finished goods. When the inventory level is

low, the SKU is placed in the multi-level rack storage system. The assignment of unit-loads to the

block stacking overflow is done when the block stacking storage systems for finished goods and

the multi-level rack are almost full, and the SKU is always shipped in full truckloads.

The block stacking storage systems have only one storage class. The unit-load will be assigned

to a specific location where the unit-load with the same SKU is already assigned too. When there

is no existing storage location assigned to this SKU, or that storage location is already full, a new

location is assigned to that SKU. The search for this location is random. The storage assignment

in the block stacking storage systems could be classified as random storage. The picking policy in

this area is last in first out (LIFO). Rotation is not necessary.

In the multi-level rack storage system, the WMS looks for a free location where the unit-load could

be placed. The storage assignment in this storage system could be classified as class-based storage,

as discussed by (Hausman et al., 1976). The WMS looks for a location based on the height and

SKU type of the unit-load. Unit-loads are assigned to the storage classes in the multi-level rack

storage system with a preference model. The unit-load is first allocated to the most preferred

storage class based on the SKU type. If that class is full, the second storage class for this SKU

30


type is selected. If that class is also full, the other class is selected. In each class, the assignment

of a unit-load to storage location is done randomly.

At the moment storage systems 120, 121, 130 and 131 in the forward areas have dedicated storage

assignment. The SKU will be coupled to a storage location for a period. Because the WMS has

some limitations, it is not possible to have flex storage locations with more than one unit-load,

so part of the fixed locations is used as flex locations with more than one unit-load. The picking

locations for more than one unit-load are used to make the replenishment process easier. When

SKUs are needed in high quantities, and there are no more than one unit-load picking locations

available, the employees that control the replenishment processes have to manually create the

number of replenishment orders to move unit-loads from the reserve stock to a couple of the

picking locations in the Conveyor and Wide Aisle area. When the replenishments are automated,

the picking locations could be changed to single unit-load locations. This change gives more

flexibility in the picking area because more locations are available. This could lead to fewer

clean-up movements. For the flex locations in the Wide Aisle WMS system also uses a preference

model. These storage systems could also be classified as class-based storage. The employees

assign a SKU to storage systems 138 or 139 in the forward area, and the system looks for the best

location based on the SKU type. In the Conveyor area, the system looks for a random storage

location in the flexible storage systems 128 and 129.

3.7 Conclusion

The main conclusion that could be drawn from the analyses is that the company deals with stochastic

non-stationary demand and inflow. This stochastic non-stationary variation is seen in the total

demand and inflow. In the total demand, there is seasonality. To prove seasonality two years of data

are necessary. Because the company is not operational for two years this data is not available. Still,

it could be said that the demand is subject to seasonality because the SKUs of the high-tech client

following a seasonal pattern as is discussed in (Johnson, 2001). The season starts in September

and ends in December. Next to the stochastic non-stationary variation in the total demand and

inflow also the demand of a single SKU or a group of SKUs is subject to stochastic non-stationary

31


variation. This variation is caused by a SKU launch. These two variations are also connected

because there are SKU launches in the peak and low season. The start of the season and the end of

the season are not fixed and could fluctuate. This variation is depended on the point retailers decide

to start ordering for their peak period. For the stochastic non-stationary variation that is caused by

SKU launches, this is different. The date of the launch is set beforehand. The time SKUs are

shipped, depends on the country of destination but this time is also fixed. The variability is mostly

caused by the inflow of both raw materials and finished goods. The inflow of raw materials is

mostly affected by the seasonality stochastic non-stationary variation. The inflow of assembled

SKUs is affected by both stochastic non-stationary variation sources.

Because the warehouse has forward areas to deal with less than unit-load orders the assignment of

unit-loads to these forward areas is also subject stochastic non-stationary variation sources. A SKU

launch leads to high inflow of finished goods and demand in the week before the launch. When

the launch is done, the demand is decreasing. Also, the balance of demand in full unit-loads and

less than full unit-loads change after the launch. This effects the assignment of unit-loads of the

SKU that is launched. In the week before the launch, the SKU is mostly picked in full unit-loads

and case packs picks. After this week less than full unit-loads are picked, and more case packs and

pieces are picked. Next to the SKU launch variation also the seasonality affects the assignment of

unit-loads to the forward areas. In the peak season, the retailer’s order in higher quantities which

lead to more full unit-loads and case packs. In the low season less full unit-loads are shipped, and

more case packs and pieces are picked.

The utilization of the warehouse is in the peak season at its highest level. In this season optimizing

material handling is limited by the available storage space. The utilization of the normal warehouse

is going to 100%, and the overflow storage locations need to be used. Because the overflow

locations are creating more material handling, the use of these locations needs to be minimized.

When even the overflow locations are full, containers need to be stored in the port. Containers

in the port are even less accessible. The point in time to decide when unit-loads are stored in the

overflow and the port is the start of the transition period. The transition could start well ahead

before the season start or just before the season start. When the start of the transition period is

32


set too early, unit-loads will be moved to the overflow when this is not needed, because there is

enough space in the normal warehouse. This leads to more material handling as needed.

The company already has a model to assign unit-loads to storage locations, but this model is not

able to deal with the stochastic non-stationary variations in the level of inventory over time and

only works for a part of the storage system and not for all the storage systems. This could lead to

more material handling than needed. The assignment is mostly done based on expert knowledge of

the employees. Also, the time that an evaluation of the storage assignment is done is not fixed, and

the change is mostly done when the warehouse is already full, and something has to be changed.

Only the assignment of unit-loads to the multi-level storage system is done with an assignment

model, but this model is only taking the SKU types of the SKUs into account. This model is also

not evaluated every period that the demand or inflow changes. This is a reactive strategy.

The problem is to decide when to change the storage assignment of a single SKU or group of

SKUs. The change of storage assignment of a single SKU could be useful when a SKU subject

to a SKU launch. The point of change of the storage assignment of all SKUs could be useful too

when the warehouse is moving into the peak season. Both changes lead to a transition period. The

length of the transition period is dependent on the starting point of the transition and the way the

transition is done. The transition period for seasonality in all SKUs is shown in figure 3.15a. The

blue blocks are symbolizing the transition period.

(a) Transition period for all SKUs (b) Transition period one SKU

Figure 3.15: Transition periods for dealing with both seasonality and product launches

33

Chapter 4

Diagnosis

In this chapter, the challenges of the storage assignment system and suggestions for solutions by

the literature are discussed. Also the research question will be set and the subquestions will be

defined.

4.1 Challenges of the storage assignment system

The following challenges exists in the storage assignment system:

• Non-stationary inflow and outflow of unit-loads caused by SKU launches and seasonality.

• Two forward areas which add two outflow point and allocation of unit-loads over forward

and reserve area

• Block stacking and multi-level storage rack which leads to a need for allocation over these

two areas

• Assembly process which creates an extra inflow and outflow point

• Imperfect information about inflow, duration of stay (DOS) and outflow of unit-loads

• There is an overflow area in the warehouse, which lead to the need for the assignment

between normal reserve stock and overflow stock.

34


4.2 Solutions suggested by literature

The storage assignment of unit-loads between multiple block stacking areas, a multi-level rack

and multiple forward areas with stochastic non-stationary demand and inflow has not often been

researched before. Especially when the stochastic non-stationary is caused by two factors and the

demand and inflow are not precisely known in advance.

A model is suggested by (Manzini et al., 2015). They use a multi-period multi-storage system

model to evaluate when re-warehousing makes sense. The problem with this model is that they

assume inflow and outflow data are known beforehand. This is not the case in this project. In this

way, the model of (Manzini et al., 2015) could only be used as a lower-bound. Because the DOS

of a unit-load of a specific SKU could be determined based on the date of the SKU launch. Also

the model of (Goetschalckx & Ratliff, 1990) could be used to allocated unit-loads of a SKU to

the right storage system. The model suggests creating storage classes for unit-loads with the same

DOS.

The assignment between multi-level storage racks and block stacking is discussed by (Bartholdi et

al., 2014). (Bartholdi et al., 2014) discusses that the use of block stacking is more useful when a

small number of SKUs with high inventory levels and high demand are in the warehouse. To make

the block stacking useful, stacking of unit-loads must be possible. Because the company uses block

stacking, it is useful to evaluate the depth of the storage lanes in the block stacking. (Bartholdi et

al., 2014) discusses a formula for the optimal line depth based on the order quantity, demand

available space and unit-load size. The use of multi-level storage racks is useful with more SKUs

with a lower inventory level. The assignment of unit-loads over the forward and reserve area is

discussed by (Hackman & Platzman, 1990), in a static way. To deal with stochastic non-stationary

demand (de Koster et al., 2007) came up with a pick to zero system. In this system, only the

amount of pieces are replenished to the forward area that is needed for a pick wave.

Next to the storage assignment, the way to change the storage assignment is important. The way

that the storage assignment is changed is affecting the duration of the transition period. The change

35


of storage assignment could be done with re-warehousing or by changing the put-away strategy.

When re-warehousing is done, all unit-loads are relocated based on the new storage assignment

model. The transition period with re-warehousing is one day or a weekend. The cost of these

re-warehousing movements are almost the same as the cost they save according to (Kofler et al.,

2014). This holds when the re-warehousing movements are done with the same valued working

hours. When the put-away strategy is used, new arriving unit-loads are assigned to a storage

location based on the new storage assignment model. The put-away strategy takes longer to take

effect. The duration of the transition is then based on the DOS of a unit-loads in the warehouse.

When only the expected most beneficial SKUs are re-located this strategy is called healing. The

concept of healing is firstly discussed by (Kofler et al., 2011) and later extended to a multi-period

model by (Kofler et al., 2014). (Kofler et al., 2014) could not prove that they could save material

handling with healing, but they use the same valued working hours for the healing operations as

for the regular operations.

4.3 Research question

As described in the introduction and analyses chapter the company wants a better model for

the assignment of unit-load inventory to storage systems. In chapter analyses, the stochastic

non-stationary in the inflow and demand is shown.

Based on the introduction and analyses chapters the following research question could be set: In

which way should the storage assignment of unit-loads be designed to deal with a high variation



There could be assumed that the order size of a SKU, when it is launched or when the warehouse

is in high season, will be bigger than in low season or after the launch. When the order size is

higher, it is less effective to assign a SKU to the forward area (Bartholdi et al., 2014). The fixed

assignment of the SKU to the forward area could be more interesting in the low season and the

36


period after the launch. This lead to the first subquestion.

• 1. Needs the assignment of SKUs to the forward area storage systems be constant over time?

Also, the rate of adapting to changing inventory levels is interesting. Are relocation movements

only executed at the start of the high season period and before a SKU launch or is the storage

assignment adapting to inventory level changes more often? This lead to the second subquestion.

• 2. What is the effective period between adjustments of the storage assignment to inventory

level changes?

When there could be assumed that the company has different valued working hours. When re-warehousing

operations are done in the non-valued working hours, are they saving material handling cost in the

long term? This question leads to the third subquestion.

• 3. Is re-warehousing unit-loads saving material handling cost in the long-term when it is

carried out with non-valued working hours in compression with valued working hours?

37

Chapter 5

Research design

The purpose of this research is to find a model for storage assignment of unit-loads to the different

storage classes in the storage systems to decrease material handling. The analyses chapter showed

that all the processes in the warehouse are subject to stochastic non-stationary unit-load flows over

the sample-path. The improvement model needs to take this into account. Also, the fact that the

inflow and outflow are not known beforehand needs to be taken into account.

5.1 Conceptual model

In this chapter, the conceptual model is discussed. The main purpose of this research is to find a

new storage assignment model that is decreasing material handling while taking the capacities of

the different storage system into account. The problem with the current models is that they are

only focused on part of the problem. Starting with the most basic concept, the storage assignment

could be modeled as two knapsack problems. One knapsack problem for the reserved area storage

system and one for the forward-area storage systems. Firstly the knapsack problem is discussed

for the reserved area. Afterwards, the knapsack problem of the forward area is discussed.

Reserved areas

The model for the reserved area is modeled as a knapsack problem. The weight factor is the storage

space that a SKU needs. The profit factor is the daily average outflow of each SKU. In the situation

38


of this company, the weight factor and profit factor are stochastic and non-stationary. There is

not only one knapsack but different knapsacks which are the storage systems: the multi-level

storage system and the block stacking areas. In the multi-level storage system, there are storage

classes which are knapsacks in the knapsack. In the block stacking storage systems, there are

multiple storage lanes which could store one SKU. Storage classes are not relevant in the block

stacking area. Together this leads to a stochastic multiple knapsack problem which is NP-hard.

When assuming that the demand is deterministic and the non-stationarity is adopted by periodical

evaluation of the knapsack problem and only storage systems are taken into account the situation

is modeled by (Manzini et al., 2015). The extension of the model of (Manzini et al., 2015) with

storage classes for the multi-level storage system is discussed in Appendix C. Because the inflow

and outflow are stochastic this model could only be used as a lower-bound. The actual model is

still a stochastic multiple knapsack problem that is evaluated every time the demand changes. This

model is inspired by (Goetschalckx & Ratliff, 1990) and uses the Law of Little to calculated the

amount of storage space a SKU needs in each period. This is the weight factor of the knapsack

model. The weight-factor is calculated with the average inflow of a SKU and average duration

of stay of the unit-loads of the SKU that already left the warehouse. When these two factors are

multiplied the average storage space for each SKU is found. To decide with SKU is assigned to the

block-stacking area the SKU that has a higher average storage space than the depth of the storage

lane, the SKU will be assigned to the block-stacking area. The evaluation of the heuristic is done

every period with a greedy algorithm. The heuristic is implemented in a sample-path simulation,

which will be discussed more extensively in the section detailed model.

Forward-area

The forward area knapsack problem is actually an invert knapsack problem because the decision

is not to decide which SKUs are allocated to the forward areas but deciding which SKUs need

to leave the forward area. The reason for this behavior is that when there is less than a unit-load

demand on a SKU the SKU needs to be assigned to the forward area. The situation could be

modeled as a pick to zero system discussed by (Yu & de Koster, 2010). In this case no cleanups

are needed because only the amount of pieces that are demanded are moved to the forward area.

There are several problems to use this model in the company that is researched. The model of (Yu

39


& de Koster, 2010) is assuming that replenishments are done in pieces and orders are batched. The

company is not batching orders yet. The replenishments are also done in unit-loads. For these

reasons, it is not useful to implement the model directly. The concept of everyday evaluation of the

assignment could still be useful. The daily evaluation is used in the to design a new model. The

model is designed as a stochastic knapsack problem. With exponential smoothing, the probability

that a SKU is picked in the future is calculated. This probability is calculated as the weighted

average of the number of days in the period of evaluation that picks occur on a SKU. This means

that when picks occurred yesterday, they are increasing the probability that demand occurs in the

future more as when picking occurred two weeks ago. This probability is multiplied by the cost of

replenishment as cost factor of the knapsack problem. The weight factor is the number of unit-loads

that a SKU has currently in the forward area. The knapsack problem is every day evaluated with

a greedy algorithm which is implemented in a sample-path simulation, which is discussed in more

detail in the section detailed model.

5.2 Detailed model

In this section, the detailed model is discussed. Firstly the worst case the assignment without

evaluation is discussed, in the next subsection the model for the reserved areas is discussed.

Afterwards, the model for the forward areas is discussed. Because the multi-level rack has different

heights per storage locations, the height of the unit-loads needs to be calculated after pieces are

picked from this unit-load. This is discussed in the last subsection.

Assignment without evaluation

When a unit-load of a SKU arrives, it needs to be assigned to a storage location in one of the storage

systems. When a unit-load of a SKUs is moved in the warehouse for the first time, the unit-load

will be assigned to the multi-level storage rack. In this storage rack, the SKU is assigned to the

storage class which has space left. When there is no space left in the multi-level rack, the unit-load

is moved to the overflow storage. The reason that the SKU is first assigned to the multi-level rack

is that there is no information about the average inflow (λ), daily average outflow (µ) of a SKU.

When an evaluation has taken place, it could still be the case that there is not enough space in the

40


assigned storage system. In that case, the unit-load is moved to the overflow storage system.

Reserved areas model

In this section, the heuristic that is used to each period evaluated the stochastic multiple knapsack

problem is discussed. Firstly the forecast model is described to calculate the weight factors.

Afterwards, the use of the weight factors and profit in the heuristic are discussed.

To get the weight factors firstly, the duration of stay and average inflow of a SKU need to be

calculated. When the SKU is in SKU launch in the future, the DOS (W) is known until the launch.

When the SKU is not in a SKU launch the DOS (W) could be derived from other SKUs with the

same SKU type and country code. This is modeled with an artificial SKU (ASKU). This ASKU

has the (λ) and (µ) and DOS(W) of all SKUs with the same SKU type and country code. Next

to the DOS (W) also the average inflow (λ) and outflow (µ) from the new SKU are derived from

the ASKU. When there is also no information about the DOS from the ASKU or SKU launch the

DOS is set to the average DOS over the sample period, 9 days for finished goods and 17 days for

raw materials. This is done to make (L) more accurate. This model is shown in figure 5.1.

Figure 5.1: New SKU process

41


When a unit-load of a SKU leaves the DOS, inflow and outflow need to be calculated. This is

shown in figure 5.2.

Figure 5.2: Leaving unit-load process

Every day the (µ) over the last 13 days is calculated. Next to the (µ) also the (λ) over the last 13

days is calculated. The (µ) is the profit factor. The average over the last 13 days is chosen because

it is the average duration of stay of all SKUs over the sample-path. Also the average (W) of a SKU

is calculated over all the SKUs that already left the warehouse. When a SKU is in product launch

in the future (W) is known. Based on the (λ) and (W) the weight factor expected average inventory

(L) is calculated with the following formula:

L = λ ∗W (5.1)

The same is done for the ASKU.

Each evaluation the following knapsack problem need to be solved:

max

N,K,C∑i,k,c

xi,k,cµi (5.2)

n∑i

xi,k,cLi =< capk,c∀K,C (5.3)

(5.4)

k= Storage systems

C= storage classes

42


When the weight factor and profit factor are discussed and the knapsack problem is described, the

greedy algorithm could be described. The SKUs are each evaluation period sorted based on there

(µ). The SKU with the highest (µ) is first evaluated. When the SKUs (L) is higher as the size of the

block stacking lane, the SKU is assigned to one of the block stacking systems. Finished goods are

assigned to the finished goods block stacking storage system, and raw materials to raw materials

block stacking storage system. When the raw materials block stacking storage system and for the

block stacking storage system for finished goods are full (85%) based on the sum of the (L) of the

already assigned SKUs, the SKUs with a (L) higher than the storage lane depth will be assigned to

the multi-level rack. When also the multi-level rack is full (85%) SKUs with a (L) higher than the

storage lane depth will be assigned to the storage systems in the overflow. SKUs with a (L) lower

as the storage lane depth will be assigned to the multi-level storage system until this is full (85%).

When the multi-level rack is full (85%) the SKUs will be assigned to the multi-level rack storage

system in the overflow. There is one exception to this assignment. When a number of pieces on a

unit-load are less than a full unit-load, the unit-load is always assigned to the multi-level storage

system because there is assumed that less than full unit-loads could only be stored and picked in

the multi-level rack. When the SKU is assigned to the multi-level rack the SKU with the highest

average daily outflow is assigned to the storage class with the lowest distance to the in and outflow

points in the warehouse. This process is shown in figure 5.3

Figure 5.3: Storage assignment evaluation process

43


Forward areas assignment model

The replenishment to the forward areas is done every night. It is assumed that the demand is known

the night before the demand occurs. Every night the stock in the two forward areas are evaluated

based on the demand of the next day. When there is not enough space for the replenishment of

SKUs that are not in the forward area yet, but are needed tomorrow, the unit-loads of the SKUs

with the lowest probability of being picked the day after the next day will be moved back to the

multi-level storage system. This decision process is shown in figure 5.4

Figure 5.4: Storage Assignment Evaluation forward area process

To come up with the probability, a forecast model is used. As the parameter is the number of days

that in evaluation period T of 25 days a SKU is picked. 25 days is based on the autocorrelation

between picking days as shown in Appendix E and testing different days shown in Appendix F.

The reason for choosing days of picking and not picks is the fact that SKU launches could create

one or two days of high levels of picking and afterward, there are no picks anymore. The SKU

that was in launch stays in this way longer in the forward area than a SKU that is picked almost

every day in the period of evaluation. When this SKU is moved out, there is a high probability

that the SKU is needed in the forward area in the future and need to be replenished back. Because

when the SKU is picked today the probability that it will be picked tomorrow is higher when it was

picked 10 days ago. So a weighted average is used to calculate the probability that demand occurs

in the future days pri. Based on the autocorrelation in appendix E the correlation is decreasing

in an exponential matter which is the reason to use normalized exponential smoothing with the

44


following formula:

pri =

∑Tt xt∑T

t (1− α)t(5.5)

pt > 0→ xt = (1− α)t (5.6)

pt > 0→ xt = 0 (5.7)

pt picks in the forward area at day t days ago.

Testing different values of alpha get the α of 0.15. The results of the number of cleanups could be

found appendix F. The cost per SKU is the probability that a new replenishment movement needs

to be done to serve future demand the replenishment cost cr. This cost function is constraint by the

sum of the stock Ii of the SKUs that stay in the forward area. This need to be lower as the capacity

of the forward area. Together the cost function and the constraints are modeled as a minimizing

knapsack problem:

minn∑i

xipricr (5.8)

n∑i

xiIi =< cap (5.9)

The minimizing function needs to be evaluated every day for each forward area. The knapsack

problem could be solved by optimizing software, but this is NP-hard. Another solution is the

greedy algorithm which means in this problem sorting the SKUs based on the cost and taking the

SKUs with the lowest cost out of the forward area until the capacity constrains are met. The SKUs

that are needed the next day are not moved out because there is assumed that the orders for the

next day are available the day before. So it makes no sense to move these SKUs out of the forward

area.

Unit-load height calculation model

In the multi-level rack, there are different locations. The difference is based on the fact that there

are different heights of locations and not all unit-load could be placed in each location. The

unit-load need to fit in the location. For that reason, the model checks the unit-load height. When

there are pieces picked the height of the unit-load changes. The model uses a bin-packing model

45


to calculate the new height. The following model is used (Tsai et al., 2015).

With the model explained the experimental design could set in the next section.

5.3 Experimental design

The two heuristics are tested in a sample-path simulation with different parameters that influence

the effectiveness of storage assignment strategy. Different levels of these parameters are tested. In

the multi-period storage assignment model for the reserved area the following parameters could be

changed:

• Treatment of duration of stay in forecast model

• The length of the evaluation period t

• Number of storage classes in the multi-level storage system at each period t

• Number of unit-loads in a storage lane in the block-stacking area in each period t

• Storage assignment change strategy.

• Valuation of the cost of the change strategy.

For the forward areas there are no parameters changed. The forward areas model is implemented

in combination with all the levels of the parameters of the reserved area. In the best performing

scenario, the results of the forward-area model are evaluated in the results chapter. In the following

subsections, the parameters with there levels are discussed.

Treatment of duration of stay in forecast model

To test the predictive effect of the average duration of stay (W) based on already left unit-loads

also the given duration of stay is tested. This is the historical DOS of a unit-load. At the point, a

unit-load is received in the warehouse the historical duration of stay is recorded and taken in the

average duration of stay that is used to calculate the expected inventory. This lead to two levels of

this parameter: average DOS based on already left unit-loads and average DOS based on historical

DOS of a unit-load in the company data.

46


Evaluation period

As mentioned in the sub research question the period between adjustments to the storage assignment

is part of this research. The first level is adapting at the start and the end of the high season. Based

on the analyses chapter the peak starts in September and ends in December. The second evaluation

is 13 days before 15 December or and 13 days before 15 December. Also the change in the month

before the end and start of the peak is tested. The reason for this level is the fact that the model

has more time to adapt to the stochastic non-stationary change in inflow and outflow. Next to the

evaluation of before and after the peak also the evaluation of a SKUs is done every day. This is

chosen to adopt the changes caused by SKU launches. This lead to four levels of this parameter:

everyday evaluation, one month before the start and end of the peak evaluation, 13 days before the

start and end of the peak period and at the start and end of the peak period.

Number of storage classes in the multi-level storage system

The current storage classes of the multi-level storage system are not dividing the storage locations

into groups with even distances to the inflow and outflow points of the warehouse. The number

of storage classes needs also be lower as five suggested by (Guo et al., 2016). The warehouse has

different I/O points because there are two forward areas and the assembly process also creates an

inflow and outflow point. To solve this problem the travel time from each location to the inflow

and outflow points is calculated and summed up. The locations are then divided into five storage

classes with more equal distances to the inflow and outflow points. The new storage classes could

be found in appendix D. Fewer storage classes in the peak period could lead to lower material

handling because the skewness in demand could increase in the peak period. This is caused by the

fact that SKUs are ordered in higher quantities. To test if this is decreasing material handling the

number of storage classes will be decreased to three storage classes. This lead to two levels of this

parameter: five storage classes over the sample-path and the combination of five and three storage

classes. Five storage classes in low season and three storage classes in the peak period.

Storage lane depth in block stacking area

The depth of the storage lanes in the block stacking area is evaluated. (Bartholdi et al., 2014) shows

that deeper storage lanes lead to more storage locations but less accessibility. In the peak season,

47


more unit-loads of the same SKU will be on stock which makes storage lanes with more unit-loads

more useful. (Bartholdi et al., 2014) using the following formula to calculated the optimal line

depth:

√√√√(α

2)(1

n)(

n∑i=1

qizi) (5.10)

(5.11)

zi= stacking hight of SKU i

qi = stock of each SKU i

α =storage space in unit-loads

When the average inventory of a the SKUs increase also the storage lane depth increases is shown

by this formula. That is the reason that the depth of the storage lanes is increased in the peak

period. This lead to two levels of this parameter: normal depth during the total sample-path and

the combination of normal depth and double depth with half the number of storage lanes.

Assignment change strategy

The change of assignment could be done with two strategies. Re-warehousing and change of

put-away strategy. When the change of put-away strategy is used the SKU is only assigned to

another storage system if there are no unit-loads left in the storage system of the second last change.

This is done to protect having unit-loads in all storage systems when the evaluation period is short.

Unit-loads are first picked from the old storage system until the old storage system has no stock left

of the SKU. When the re-warehousing strategy is used, all the unit-loads of the SKU will be moved

to the new assigned storage system. The SKU is picked from the new assigned storage system and

storage class after the re-warehousing process. This lead to two levels of this parameter: put-away

change strategy and re-warehousing change strategy.

Cost of re-warehousing

There could be a difference in material handling cost from busy to idle periods. The company

uses partly fixed workforce and partly flexible workforce. The flexible workforce need to ramp-up

48


before the peak moment because they have to be trained. The time they are trained, and the peak

season is not started, the time of this workforce is different valued in comparison with busy times.

In the idle period, the flexible workforce is decreasing, but the company has still fixed workforce

that needs to do useful activities. These times could be valued differently as the time in busy

periods. In this way, it makes sense to test re-warehousing. The transition period from low season

to high-season could use to optimize the warehouse for the peak period. This lead to two levels

of this parameter: normal valued working hours for re-warehousing and no cost of re-warehousing.

Together the levels of these parameters lead to 128 scenarios. The scenarios are discussed in

Appendix G.

5.3.1 Example of the system

To illustrate the model the way one SKU goes to the warehouse is explained as an example. A

SKU with the country of destination 1005 and SKU type P1 arrives for the first time at inbound

dock inflow point. The average DOS of SKUs with SKU type P1 with the country of destination

1005 is five days. The average inflow per day is two unit-loads per day. With the Little’s Law, the

average inventory is calculated (L). The (L) is 5*2= 10; Until the evaluation period the unit-loads

of the SKU will be assigned to the multi-level rack.

At period t an evaluation is done, the average inventory (L) is the same as in the last is still below

the storage lane dept, but the average daily outflow is four per day. The SKU is now switched with

the other SKU that was in the most favorite storage class but has an average daily outflow of three

per day.

When there is demand for this SKU in one of the forward areas number of unit-loads that is needed

to fulfill the demand is moved to the forward area. When there is not enough space, the unit-loads

of the other SKU are moved to the multi-level rack. This is the SKU with the lowest probability of

having future picking days.

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With the experimental setting set, the design parameters of the sample path simulation model could

be set.

5.4 Design parameters

In this section the design parameters of the simulation model are discussed. A SKU i as described

in section detailed model could be assigned to a storage system k and storage class c for period

t. This could be modeled with the following decision variable: Xi,k,c,t. Storage classes are only

relevant for the multi-level storage system. For the other storage systems c=0;

When a SKU is moved from a specific storage class c in storage system k to a new storage class d

in storage system p, this is modeled with the following decision variable: zi,k,p,c,d,t. This variable is

multiplied by the cost of replacement from storage class c in system k to storage class d in system p.

This is only true when is decided to move the unit-loads from storage system k to storage system

p, the re-warehousing strategy. The cost of replacement are defined as relCk,p. The parameter

relCk,p is the travel time from the source location in storage system k to the destination storage

location in storage system p for all unit-loads of the SKU that is moved. The way travel time is

calculated will be explained in the section key performance indicator. The inventory of SKU i in

unit-loads at the end of period t in storage system k and storage class c. This parameter is defined

as Inventoryi,k,t.

Next to the inventory also the average DOS of a SKU i in days need to be measured. When

the SKU is in a SKU launch this value is given. This parameter is modeled with the following

parameter DOSi. This parameter is the average of all the unit-loads of SKU i that are moved out

of the warehouse. To assign a new arriving SKU also the average DOS of an artificial SKU ai need

to be modeled with the parameter DOSai. This is the average DOSi of all SKUs i with the same

country of destination and SKU type that is moved out of the warehouse.

Next to the DOS also the average daily inflow of the SKU i need to be measured. This is modeled

with the parameter λi. For the assignment of new arriving SKUs also the average daily inflow of

50


the artificial SKU ia need to be measured with parameter λai. This parameter is the average of all

the unit-loads of SKU i that are moved into the warehouse. For the assignment of SKUs to the

right storage class and storage system is also the average daily outflow is measured with parameter

µi. For the new arriving SKUs the average daily outflow of all SKUs with the same SKU type and

country of destination are measured with parameter µai.

With the DOS,average inflow and outflow, the average inventory could be calculated with the Law

of Little. This will be done in parameter Li. This parameter is used to decide if the SKU is placed

in a block stacking storage system or the multi-level rack storage system. The parameter is also

used to block the number of locations in the multi-level storage rack for SKU i when the SKU is

assigned to this multi-level storage rack. Next to the average inventory of a SKU i the average

inventory of the artificial SKU ai, the combination of the country of destination and SKU type

need to be calculated to assign new arriving SKUs to the right storage system. The parameter is

modeled with Lai .

For the greedy heuristic that is used to solve the knapsack problem in the forward areas replenishment

cost constants crC and crW are calculated. Also the picks per day t are calculated per SKU i for

the Wide Aisle and the Conveyor with parameter pwi,t and pci,t. This is used to check if a SKU

had a pick on a specific day.

Next to outflow points, there is also replenishment from on storage system to the forward area

storage system in period t. The number of unit-loads that move from the reserve storage system to

a forward-storage system because of replenishment are modeled as integer decision variable repRt

for the Wide Aisle area and repCt for the Conveyor area . Also the number of cleanups per period

t is calculated with the parameter cleanWt for the Wide Aisle area and cleanCt for the Conveyor

area.

To decide when to use the overflow block staking storage system, the utilization of the storage

system needs to be measured. This will be done with Utilizationk.

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With the design parameter set, the key performance indicator could be set in the next section.

5.5 Key performance indicator

Material handling is the number of seconds a reachtruck needs to spend for the movement of a

unit-load from one point to another point in the warehouse.

This time is calculated based on the distance that has to be traveled and the number of levels a

reachtruck has to reach. The distance is calculated with a model based on the X and Y coordinates

of the aisle corners. With the Dijkstra algorithm, the distance between these locations is calculated.

To get valid distance, paths between x and y points are evaluated. Only the valid paths are taken

into account in the calculation of the distance from x to y. See Appendix A. With the shortest

distance between the aisle known, the distance between each location could be calculated based on

the shortest distance between the different aisle corner points. Each rack has a couple of sections;

each section is 3.6 meters long. The model evaluates which corner point of the source rack is the

shortest connection to the destination rack. The distance to the source corner point plus the distance

between the corner points and the distance from the destination corner point to the destination

storage location are added together to the total travel distance.

With the distance given, the travel time could be calculated. The reachtruck in this warehouse

could drive 2.77 m/s the reachtruck. The reachtrucks do not drive this speed on average. After

evaluation of 15 movements with a self-made Android application, the actual speed is calculated.

Also, historical movements in the warehouse are used to evaluate the actual movements. With both

these values, the actual speed is calculated as 1.05 m/s.

Next to the travel time, the time to reach to higher locations is calculated. This is done by

calculating the height and divided this number by the speed of reaching with a unit-load. Also,

the time to reach the location without a unit-load is calculated. The theoretical speed of reaching

with a unit-load is 0.51 m/s, without a unit-load the reaching speed is 0.7 m/s. This is not accurate

because some balancing and preparing time need to be taken into account. 15 time measurements

52


with the same Android application are used to calculate speed upwards and downwards. The actual

speed upwards is 0.05 m/s, and the actual speed downward is 0.05 m/s.

The sum of the travel time and reach time is the key performance indicator. The mathematical

formulation of this calculation is shown below:

tr = di,j ∗ v + vue ∗ hi + vdf ∗ hi + vuf ∗ hj + vdf ∗ hj (5.12)

v is horizontal speed

vue is speed up empty

vdf is speed down full

vuf is speed up full

vdf is speed down empty

di,j distance from start i to destination j

hi height of start.

hj height of destination

The material handling is calculated to monthly average employees needed.

empolyees =

∑d0 (mh/8)

d(5.13)

mh = tr/3600; (5.14)

mh Material handling in hours.

d Days in that month

tr Travel time calculated with function 5.12

Only the cost of the movements from inflow points to storage locations, storage locations to outflow

points and replenishment movements are calculated. The travel time from conveyor locations to

the Conveyor and Wide Aisle locations to the packing department are not taken into account.

This was the last subsection of the design chapter. In the next chapter, the simulation model will

be discussed.

53

Chapter 6

Simulation model

In this chapter, the simulation model will be discussed. After the introduction, the experimental

setting is discussed. In the last subsection, the validity of the simulation model is explained.

6.1 Introduction

The simulation is used to evaluate the improved storage assignment strategy. The heuristics that

allocate a SKU to a storage system in a specific time period are implemented in the simulation.

Also the different levels of the parameters that influence the storage assignment are implemented

in the simulation. The current storage assignment strategy is also implemented in the simulation

to compare the current situation with the improved storage assignment with the inflow and outflow

of unit-loads of the last one and a half year.

6.2 Experimental setting

The warehouse is modeled as a virtual warehouse in Java. The simulation is based on the DesmoJ

framework. The simulation is a discrete event sample-path simulation. The arrivals of unit-loads

and orders are pushed in the simulation on the historical date and time that they were moved into

the warehouse historically. The simulation is modeled as a combination of arrival processes and

queues. There are a couple of arrival processes:

• Inflow of unit-loads from inbound to the warehouse

54


• Outflow of unit-loads from assembly to the warehouse

• Arrival of unit-load orders to outbound

• Arrival replenishment orders to Conveyor locations

• Arrival replenishment orders to Wide Aisle locations

• Arrival Assembly orders from assembly

• Arrival of customer orders on the Conveyor

• Arrival of customer order on Wide Aisle

• Arrival of Cleanup order on Wide Aisle

• Arrival of Cleanup order on Conveyor

• Arrival of Cleanup order on Multi-level rack

• Arrival of Cleanup order on Block stacking

There are the following queues:

• Inbound unit-loads queue

• Assembly outbound unit-load queue

• Production order queue

• Outbound order queue

• Conveyor replenishment order queue

• Wide Aisle replenishment order queue

• Conveyor order queue

• Wide Aisle order queue

• Cleanup order queues

There is also a visual interface of the warehouse where stocked unit-loads are showed in different

colors. See Appendix B. The unit-loads are objects that are stored in a storage object. In this

object, the unit-load objects are stored with their location as id. In the block stacking storage

systems, part of the picking locations and the overflow storage take place in storage lanes. In these

lanes, more than one unit-load is stored. The storage of unit-load objects is done in a storage lane

object. The storage lanes objects are stored in the storage object based on their id. In each storage

lanes, there could be only one SKU. The customer orders on the Conveyor and Wide Aisle are less

than a unit-load and take pieces or case packs from the unit-loads.

55


The movements of unit-loads are done by reachtruck objects. The number of reachtrucks is

assumed to be unlimited because the research is only looking at the total travel time and not on the

allocation of jobs to reachtrucks. The arriving unit-loads that are placed in the queues are taken

out by the reachtruck and put into the storage object. The orders that are put in the order queues

are also taken out by the reachtruck.

The movements on the Wide Aisle are done by EPTs, and the movements on the Conveyor are

done by people. The number of people on the Conveyor is assumed to be unlimited and the same

holds for the number of EPTs.

The matching of customer orders to unit-loads is done on their stock keeping unit (SKU) number.

The put-away algorithm looks for a free location in the assigned storage system. The location

needs to have the approved storage class and height when the unit-load is placed in the multi-level

rack.

6.3 Validity and reliability

The model is validated with the two company supervisors. There were a couple of meeting where

the model was shown. The model is adapted to the comments given in these meetings.

56

Chapter 7

Results

7.1 Introduction

In this chapter, the results will be presented. From the 80 scenarios, 9 scenarios decrease material

handling over the total sample-path in comparison with the company model. The decrease in

% in material handling in comparison with the company model and worst case per scenario are

shown in Appendix H. In this chapter, the effects of each level of the parameters are discussed per

parameter. After discussing the results per parameter the best performing combination of levels of

each parameter is discussed in the last subsection.

7.2 Forecast model

In this section the results of the forecast model are discussed. There are 40 scenarios with the

forecast model and 40 scenarios with the given DOS model. The figure 7.1. shows the average of

these scenarios.

57


Figure 7.1: Forecast model evaluated in comparison company model and worst case.

The forecast model is performing almost just as well as the given DOS model. In some scenarios,

the forecast model is performing even better as the given DOS model. The reason is the fact

that the unit-loads in the tested scenarios could have a different DOS as what the unit-load had

historically. A unit-load could be taken earlier or later which influences the DOS. Also the way the

unit-loads are moved in the two forward-areas and out of the forward area could change the DOS

of a unit-load. The company model is performing better in figure 7.1, but this is caused by the fact

that this figure shows the average of all scenarios including the less effective scenarios. At the end

of this chapter, the best performing scenario is discussed.

7.3 Period of evaluation

In this section, the results of the different evaluation periods are discussed. There are 20 scenarios

with daily evaluation. The same holds for a month before the peak evaluation, average DOS before

and at the peak evaluation. The results are shown in figure 7.2 are the averages of these scenarios.

58


Figure 7.2: Period of evaluation evaluated in comparison company model and worst case.

As shown in the figure 7.2 the everyday evaluation is outperforming all other evaluations in most of

the months. From the scenarios that are saving material handling eight are using daily evaluation.

The one month before the peak evaluation scenario is also performing well. This level of the

parameter period of evaluation is decreasing the material handling by 1% in comparison with the

company model over the sample-path. The average DOS before the peak and after the peak is

performing the worst.

7.4 Change strategy

In this section, the results of the different change strategy are discussed. There are 16 scenarios

with the change strategy and 64 re-warehousing scenarios. In figure 7.3 only the average over

16 re-warehousing scenarios are taken into account. The other re-warehousing scenarios are the

storage lane depth change and different valued working hours scenarios. These are not relevant to

the put-away strategy, so they are not taken into account in this comparison.

59


Figure 7.3: Change strategy evaluated in comparison company model and worst case.

The put-away strategy is outperforming the re-warehousing strategy in each month.

7.5 Storage lane size

In this section the results of the different storage lane depth are discussed. In figure 7.4 the results

are shown. There are 16 scenarios with normal storage lane depth and 16 with different storage

lane depth in the peak period.

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Figure 7.4: Storage lane size evaluated in comparison company model and worst case.

The effect of changing the storage lane depth is small. The change of storage lane depth is

decreasing the material handling a bit in the peak period in comparison with keeping the normal

depth. When looking at the total material handling over the sample-path this effect is small as is

shown in appendix F.

7.6 Number of storage classes change

In this sections, the results of the change of storage classes are discussed. The results are shown in

figure 7.5. These results are based on 40 scenarios for five storage classes and 40 scenarios where

the storage classes are changed to three storage classes in the peak period.

61


Figure 7.5: Number of storage classes evaluated in comparison company model and worst case.

The change to three storage classes in the peak period is not decreasing material handling. The

reason for this behavior could be found in the fact that re-warehousing cost is increasing the

material handling too much. When comparing the number of classes changed in the peak period

with different levels of change strategy, the put-away change strategy is giving the best results,

9% decrease in comparison with the company model when the evaluation is done daily. This is

less than when the number of classes stays five. When the number of classes stays five the saving

is 10% in comparison with the company model when also daily evaluation is done. When the

class change is combined with re-warehousing, this leads to 3% less material handling when the

re-warehousing cost is not taken into account and daily evaluation is done. The saving is the same

as not changing the storage class.

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7.7 Cost of re-warehousing

In this section the results of the different cost of re-warehousing are shown in figure 7.6. The results

in figure 7.6 are the average of 32 scenarios of normal cost of re-warehousing and 32 scenarios of

no cost for re-warehousing.

Figure 7.6: Cost of re-warehousing evaluated

The figure shows that the cost of re-warehousing are a small part of the average number of

employees per month that are needed. Re-warehousing with different valued working hours is

saving 3 % when the evaluation is carried out every day.

7.8 Assignment of SKUs to the two forward areas

The assignment of unit-loads to the forward areas is done with the knapsack model discussed in

the chapter design. The greedy algorithm discussed in the design chapter is implemented in the

simulation. The evaluation of the results of this model is only done for the best performing scenario

with daily evaluation, the put-away change strategy, five storage classes and no change of storage

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lane depth.

First the cost of replenishment crc and crw need to be determined. To solve this problem a location

in the middle of the Conveyor area and Wide Aisle are used to calculate the material handling to

replenish to these locations. crc and crw are set to 264 sec. This is the average travel time from all

locations in the warehouse to the Conveyor and Wide Aisle.

The company did cleanups to keep space in the forward areas. The model was able to decrease the

number of cleanups with 22%. The model was not able to save cleanups in each month as is shown

in figure7.7.

Figure 7.7: Cleanup movement forward areas savings model in comparison with company model

Next to the saving in cleanups, the model was also able to save 14 % of the replenishment

movements. Together these reduce in movements lead to a decrease in material handling over the

sample-path of 26% when only looking at the cleanup movements and replenishment movements.

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7.9 Best performing scenario

In this section the best performing scenario is discussed. In figure 7.8 the average needed employees

per month are shown.

Figure 7.8: Best performing scenario

This scenario implements the forecast, everyday evaluation, and the put-away change strategy. This

scenario is outperforming the worst case in each month and also the company model in the first 11

months. When looking at the total material handling tr over the sample-path the combination of

the levels of each parameter in this scenario are decreasing material handling with 10%.

7.10 Conclusion

The scenarios show the difficulty to outperform the company model every month, but over the total

sample-path, the models are able to save material handling. With the results given the answers of

the sub-questions could be given:

• 1. Need the assignment of SKUs to the forward area storage systems be constant over time?

65


No, the assignment is not constant over each period. The greedy algorithm is able to save material

handling over the sample-path. The number of cleanups could be decreased with 22 % and the

replenishments could be decreased by 14%.

• 2. What is the effective period between adjustments of the storage assignment to inventory

level changes?

The scenarios are showing that daily evaluation is performing the best in combination with the

put-away change strategy. Also the one month before the peak evaluation could save material

handling, but these savings are lower.

• 3. Is re-warehousing unit-loads saving material handling cost in the long-term when it is

carried out with non-valued working hours in comparison with valued working hours?

Actually, re-warehousing unit-loads could save material handling when the re-warehousing is

carried out with non-valued working hours. The problem is that the evaluation needs to be done

every day. This means also doing re-warehousing every day, assuming that there are other valued

working hours every day. The effects of changing the number of storage classes and depth of the

storage lane are only saving a 3% amount of material handling in comparison with the company

model when they are combined with the different valued working hours and everyday evaluation.

66

Chapter 8

Implementation

In this chapter, the implementation of the models is discussed briefly. In the first subsection, the

implementation plan is explained. In the second section, the feasibility of the implementation is

discussed.

8.1 Implementation plan

The model could be implemented in the current warehouse management system of the company.

To implement this system, the following steps need to be done:

1. Create new storage classes in the warehouse management system.

2. Allocated storage locations multi-level rack storage system to the new storage class

3. Creating of the ASKUs in the warehouse management system.

4. Implementation of greedy heuristic for the forward-areas.

5. Implementation of the forecast model in the warehouse management system.

6. Implementation of a dynamic SKU allocation table for allocation of unit-loads in the multi-level

rack storage system.

7. Implementation of a dynamic SKU allocation table for the allocation of the different storage

systems.

8. Implementation of daily KPI calculation.

9. Implementation of daily evaluation based on the forecast model.

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8.2 Feasibility of implementation

The implementation of the models discussed in chapter design lead to implementation cost. There

is no need for physical changes only system changes. The creation of the new storage classes is not

that much work. A script needs to be written to assign the storage locations to the newly created

storage classes. Also the creation of the artificial SKU (ASKUs) could be done with a script.

To get inflow, outflow and inventory data for these ASKUs, the other SKUs need to be coupled

to the ASKUs. The implementation of the forecast, daily KPI calculation, and daily evaluation

could be done with the scripts of the simulation. They need to be translated into the language of

the warehouse management system. The creation of the SKU allocation tables and the connection

between the evaluation algorithm and the tables are the most challenging. To implement the greedy

heuristic for the forward areas the assumption that demand is known the day before it occurs need

to be met. When this is not possible, the model needs to be evaluated more often.

Next to the system implementation, there is also the adopting of the system by the employees of

the company. The employees also need to trust the forecast and not overrule the system. To get the

trust of the employees, the system could also be used as an expert system in the first place. In that

way the employee is advised to allocate a unit-load to a specific storage system and if relevant the

right storage class. If the employees trust the system when it is advising right, the next step could

be set to let the system also make the decision.

Next to the actual implementation of the system the simulation made for this research could be

used to evaluate the change in inflow and outflow. When the company wants to evaluate physical

changes they could be implemented in the simulation model to evaluated the physical changes.

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Chapter 9

Conclusion & recommendations

In this chapter the conclusion of the research is discussed, starting with the analyses and diagnose

chapter. Afterwards the designed models are discussed and the results of the models are concluded.

The last sections are about the theoretical and practical contribution of the project, the limitations

of the research and the opportunities of further research.

9.1 Conclusion

9.1.1 Analyze & Diagnose

The company has a couple of storage systems that are provided with unit-loads from the inbound

and assembly department and drained by the demand for full unit-load and the replenishment need

for the two forward areas. The inflow and outflow are subject to stochastic non-stationary. The

main three problems are:

1. Non-stationarity inflow and outflow over all SKUs caused by seasonality

2. Non-stationarity inflow and outflow per SKU caused by SKU launches.

3. Different types of a storage system with different operation cost to allocated stock too.

These three problems lead to the dynamic situation that needs a model that is able to allocate stock

to the right storage system while taking the stochastic non-stationary into account. Because the

warehouse is a manual warehouse, employees are the largest cost driver. The company tries to use

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the capacity of these employees in an optimal way. This means minimizing the material handling.

This lead to the research question:

In which way should the storage assignment of unit-loads be designed to deal with a high variation



9.1.2 Model

To solve this problem the research came up with a couple of models for the allocation of unit-loads

to the right storage system. The primary model is the forecast model based on the Law of Little.

This model could be used to calculate the need for storage space for a stock keeping unit (SKU).

This forecast could be used to assign the SKUs with the highest demand and shortest duration

of stay (DOS) to the most favored storage system. Also in the case of multiple storage classes,

the forecast model could also be used to allocated the SKUs with the most demand to the most

favorite storage class. The forecast model makes it possible to reserve a part of the storage system

or storage class for that specific SKU based inflow and DOS of the SKU. In this way, material

handling could be decreased.

Next to the forecast model the greedy heuristic, that is used to decide which SKU is removed from

the forward areas is a more systematic way of deciding with SKU has to leave the forward area.

9.1.3 Results

The results from the 80 scenarios done with a sample-path simulation show that the models are

able to save material handling in comparison with the worst case. Also with the right evaluation

period, the model is able to save material handling in comparison with the company model and over

the total sample-path. The results show that evaluation only at the start and the end of the peak is

partly enough to incorporate the stochastic non-stationary of the SKUs. The results also show that

re-warehousing on every evaluation period is not making sense with regular working hours. When

70


the cost of the re-warehousing operation is set to zero the savings are there but only when everyday

evaluation and re-warehousing is done. This is not a practical setting. This confirms the idea of

minimizing the number of touchings that is standard practice in a warehouse.

The effect of changing the storage lane size and decreasing the number of storage classes is not

much. The reason that the change of storage classes has no significant effect is caused by the fact

that when a unit-load arrives and gets a specific storage class assigned it will be placed to that

storage class only when there is space. When this is not the case, the unit-load is placed in the next

storage class.

The greedy algorithm for forward areas is outperforming the current system based on expert

knowledge. It is able to decrease the number of cleanups and also the number of replenishment.

9.2 Contributions to theory

This research came up with a model that is able to allocate unit-loads to different types of storage

systems based on there inflow, outflow and DOS. There are no other models for the allocation of

unit-loads over different storage systems that are capable of doing this with stochastic non-stationary

inflow and outflow. Most models are assuming at least stationarity in the demand and inflow. Other

models are taking stochastic non-stationary into account but do assume only one type of storage

system, mostly multi-level rack system.

9.3 Practical contributions

The models discussed in this research could be used by the company where the research has taken

place. Next to the implementation of the models for actually controlling the storage assignment

the models could also be used as an expert system. In this way, employees are advised to assign

a SKU to a specific storage system. The simulation model could also be used to evaluate physical

changes in the warehouse or even for new implementations of customers. With the model, the

company could decide which storage systems are most useful with given inflow and demand data.

71


9.4 Limitations

In this section, the limitations of the research are discussed.

1. The model is only tested with the movement data of one company.

2. The availability of equipment is not taken into account when running the simulations

3. The demand for the forward area is assumed to be known the day before it occurs which is

not the case for all SKUs.

4. The setting re-warehousing and put-away are tested separated and not in combination.

5. It is assumed that all SKU could be placed in each location of the forward area which is not

the case for the flow-racks.

9.5 Opportunities for future research

In this section the opportunities for future research are discussed.

1. Implementing known demand and inflow distributions in the model

2. Test the model with different company data

3. Take congestion of inflow and outflow operations into account

4. Implement restricted material handling capacity

5. Evaluation of the multi integer problem discussed in Appendix C

72

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75

Appendices

76

Appendix A

Valid paths

77

Appendix B

Visual model of the warehouse

78

Appendix C

Deterministic lower bound model

The model (Manzini et al., 2015) takes the cost of moving the unit-loads from on storage class to

the other storage class into account. The difference from the situation that (Manzini et al., 2015)

discusses and the situation at Arvato is that Arvato has different storage systems with a couple of

storage classes in each storage system as discussed in the chapter analyses. (Manzini et al., 2015)

also assumes that pieces are picked and in the situation of Arvato also unit-loads are picked. The

model also takes storage cost, and the cost of empty locations into account which is not relevant

to the situation at Arvato because the high-tech client pays a fixed fee each year for all available

space. So there is no difference in storage cost for each storage system.

Next to the decision of change the assignment of a SKU the way of change is important. The model

of (Manzini et al., 2015) discusses moving all unit-loads from one storage system to the another

system which is called re-warehousing. The other solution is only changing the assignment of

new arriving unit-loads of a SKU to the new storage system. The option of re-warehousing is

increasing the material handling by the number of unit-loads that are still in the old storage system

times the cost of moving these unit-loads. When re-warehousing could be done with lower cost

as the normal material handling the cost, it makes sense to do. Otherwise moving unit-loads from

one storage system to the another storage system will have difficulty to save material handling.

The forward areas are not seen as storage system in the model. The are seen as outflow points.

There need for unit-loads is seen as outflow. The model of (Manzini et al., 2015) also assumes one

79


inflow and outflow point, in the case of this warehouse there are more inflow and outflow points.

The following inflow points could be defined:

• Actual inbound

• Outbound assembly

Next to the inflow points there are four of outflow points:

• Assembly inbound buffer

• Outbound dock

• The Conveyor

• Wide Aisle

These parameters are also added to the model of (Manzini et al., 2015).

With the parameters set, the conceptual model could be designed. The inflow is modeled as a set

of An inflow points. The storage systems are modeled as a set of K storage systems. Because

there are different inflow and outflow points, a model is needed to create classes concerning the

in and outflow points. In the block stacking area, there is only one class per storage system. The

distance between all inflow and outflow points and the block staking areas is almost the same. For

the multi-level storage system storage classes are useful. The classes could be made based on the

average travel time between the in and outflow points. The locations could be grouped based on

the different duration of stay groups of unit-loads as suggested by (Goetschalckx & Ratliff, 1990).

The storage classes are modeled as a set of C classes.

When the assignment of a SKU to a storage system is defined as decision variable X. If unit-loads

of a SKU move from one of the storage systems out of the set K to the another storage system of

the set k, the new storage system is modeled as a set of P storage systems. The change from one

storage class c to a new storage class the other classes are modeled as s set of D storage classes.

The changed assignment from on a storage system is modeled with the decision variable z. The

outflow points are modeled as a set of B outflow points. Each storage system and storage class has

a capacity. Material handing effort is created when unit-loads move from an inflow point into in a

storage system, move out of a storage system to an outflow point. The sets are transformed into a

80


multi integer problem which could be used to calculate the lower bound for the stochastic model.

The total cost could be determine with the following function:

n,U,T,K,C∑i,u,t,k,c

K∑p!=k

C∑c!=d

zi,k,p,c,d,tInventoryi,u,trepCkpcd +

n,A,K,C,T∑i,u,a,k,c,t

Xi,k,c,tInflowi,u,a,tcmh,inkca +

n,B,T,K,C∑i,u,b,t,k,c

Outflowi,u,b,tXi,k,c,tcmh,outkcb

(C.1)

This function is constraint to:K,C∑p,d

Xi,k,c,t = 1 ∀i, t (C.2)

Xi,k,c,t +Xi,p,d,t+1 − 1 ≤ zi,k,p,c,d,t ∀i, k, p, c, d, t < T − 1

zi,k,p,c,d,t ≤ Xi,k,c,t ∀i, k, p, c, d, t

zi,k,p,c,d,t ≤ Xi,k,d,t+1 ∀i, k, c, t < T − 1

(C.3)

n∑i

Inventoryi,u,tXi,k,c,t ≤ Capk,c,u ∀k, c, u, t (C.4)

Inventoryi,u,t = Inventoryi,u,t−1 +A∑a

Inflowi,u,a,t −B∑b

Outflowi,u,b,t∀i, u, b, t > 1 (C.5)

Xi,k,c,t =

1 if SKU i is assigned to class c in storage system k in period t

0 otherwise(C.6)

zi,k,p,c,d,t =

1 if SKU i moves from storage system k to p from class c to class d from period t to period t+1

0 otherwise

(C.7)

Yi,k,p,c,d,t >= 0 (C.8)

Constrain C.3 ensures that when an SKU i is moved from storage class c in storage system k to

a new storage class d or storage system p that decision variable zi,k,p,c,d,t is set 1. Constrain C.4

ensures that not more unit-loads are assigned to a class c in a storage system k than the capacity

class c in that specific storage system k in period t. Constrain C.5 calculates the inventory at the

end of period t in the unit-load type of SKU i in storage class c in storage system k. Constraints

C.6, C.7 and C.8 constrain the variable space of these three decision variables.

81

Appendix D

Summed up travel time based storage

classes

Ranking travel time to Assembly

82




83



84

Appendix E

Auto correlation

Mean of all SKUs auto correlation conveyor per day

Mean of all SKUs auto correlation Wide Aisle per day

85

Appendix F

Evaluation of α and days of evaluation in

forward area model

To get the right value of α and the right days of evaluation different values are tested. When

looking at the autocorrelation in Appendix E. There is a positive autocorrelation in both forward

areas 28 back. The starting point was to use 28 days as period of evaluation and with α of: 0.1,

0.15, 0.2, 0,25, 0.3, 0.35 and 0.4. In this evaluation a α 0.15 was leading to the lowest cleanups as

could be seen in figure below.

Different values of α tested

With this α of 0.15 different days of evaluation are tested from 15 to 28 days. The results of this

evaluation are shown in the figure below.

86


Different days of evaluation tested

In this evaluation 25 days is leading to the lowest number of cleanups.

87

Appendix G

Scenarios

In this appendix the scenarios are discussed. The combination of the parameters and there levels

lead to 128 scenarios. Actually, part of the scenarios are not relevant. The different cost of

re-warehousing is only relevant in combination with the re-warehousing change strategy. This

decreases the scenarios to 96. The change of storage lane size could only be combined with

re-warehousing. When the change is combined with the put-away strategy, there are still unit-loads

in a block stacking storage lane that is combined with another lane. This lead to more unit-loads

in the lane as possible. This decreases the scenarios to 80. The scenarios are compared with not

evaluate (Worst case) and the company model.

88


Index Combined settingsStorage

space

per SKU

calculation

(A)

Period of

evaluation

(B)

Change strategy

(C )Storage

lane size

(D)

Number of

classes (E)

Cost of re-

warehousing

(F)

Forward

area

model

DOS

based

on

leaving

unit/loads

Based

on the

DOS

in

sample

path

Every

day

A

month

before

the

peak

Average

DOS

before

start

and

end of

peak

At

start

peak

and

end

Put-away Re-

warehousing

Not

changing

size

Change

size

Not

changing

storage

classes

Changing

the

number

storage

classes

Normal Free Cleanup

model

1 A1-B1-C1-D1-E1-F1-G1 x x x x x x x

2 A1-B2-C1-D1-E1-F1-G1 x x x x x x x

3 A1-B3-C1-D1-E1-F1-G1 x x x x x x x

4 A1-B4-C1-D1-E1-F1-G1 x x x x x x x

5 A1-B1-C2-D1-E1-F1-G1 x x x x x x x

6 A1-B2-C2-D1-E1-F1-G1 x x x x x x x

7 A1-B3-C2-D1-E1-F1-G1 x x x x x x x

8 A1-B4-C2-D1-E1-F1-G1 x x x x x x x

9 A1-B1-C2-D2-E1-F1-G1 x x x x x x x

10 A1-B2-C2-D2-E1-F1-G1 x x x x x x x

11 A1-B3-C2-D2-E1-F1-G1 x x x x x x x

12 A1-B4-C2-D2-E1-F1-G1 x x x x x x x

13 A1-B1-C1-D1-E2-F1-G1 x x x x x x x

14 A1-B2-C1-D1-E2-F1-G1 x x x x x x x

15 A1-B3-C1-D1-E2-F1-G1 x x x x x x x

16 A1-B4-C1-D1-E2-F1-G1 x x x x x x x

17 A1-B1-C2-D1-E2-F1-G1 x x x x x x x

18 A1-B2-C2-D1-E2-F1-G1 x x x x x x x

19 A1-B3-C2-D1-E2-F1-G1 x x x x x x x

20 A1-B4-C2-D1-E2-F1-G1 x x x x x x x

21 A1-B1-C2-D2-E2-F1-G1 x x x x x x x

22 A1-B2-C2-D2-E2-F1-G1 x x x x x x x

23 A1-B3-C2-D2-E2-F1-G1 x x x x x x x

24 A1-B4-C2-D2-E2-F1-G1 x x x x x x x

25 A2-B1-C1-D1-E1-F1-G1 x x x x x x x

26 A2-B2-C1-D1-E1-F1-G1 x x x x x x x

27 A2-B3-C1-D1-E1-F1-G1 x x x x x x x

28 A2-B4-C1-D1-E1-F1-G1 x x x x x x x

29 A2-B1-C2-D1-E1-F1-G1 x x x x x x x

30 A2-B2-C2-D1-E1-F1-G1 x x x x x x x

31 A2-B3-C2-D1-E1-F1-G1 x x x x x x x

32 A2-B4-C2-D1-E1-F1-G1 x x x x x x x

33 A2-B1-C2-D2-E1-F1-G1 x x x x x x x

34 A2-B2-C2-D2-E1-F1-G1 x x x x x x x

35 A2-B3-C2-D2-E1-F1-G1 x x x x x x x

36 A2-B4-C2-D2-E1-F1-G1 x x x x x x x

37 A2-B1-C1-D1-E2-F1-G1 x x x x x x x

38 A2-B2-C1-D1-E2-F1-G1 x x x x x x x

39 A2-B3-C1-D1-E2-F1-G1 x x x x x x x

40 A2-B4-C1-D1-E2-F1-G1 x x x x x x x

89


Index Combined settingsStorage

space

per SKU

calculation

(A)

Period of

evaluation

(B)

Change strategy

(C )Storage

lane size

(D)

Number of

classes (E)

Cost of re-

warehousing

(F)

Forward

area

model

DOS

based

on

leaving

unit/loads

Based

on the

DOS

in

sample

path

Every

day

A

month

before

the

peak

Average

DOS

before

start

and

end of

peak

At

start

peak

and

end

Put-away Re-

warehousing

Not

changing

size

Change

size

Not

changing

storage

classes

Changing

the

number

storage

classes

Normal Free Cleanup

model

41 A2-B1-C2-D1-E2-F1-G1 x x x x x x x

42 A2-B2-C2-D1-E2-F1-G1 x x x x x x x

43 A2-B3-C2-D1-E2-F1-G1 x x x x x x x

44 A2-B4-C2-D1-E2-F1-G1 x x x x x x x

45 A2-B1-C2-D2-E2-F1-G1 x x x x x x x

46 A2-B2-C2-D2-E2-F1-G1 x x x x x x x

47 A2-B3-C2-D2-E2-F1-G1 x x x x x x x

48 A2-B4-C2-D2-E2-F1-G1 x x x x x x x

49 A1-B1-C2-D1-E1-F1-G1 x x x x x x

50 A1-B2-C2-D1-E1-F1-G1 x x x x x x

51 A1-B3-C2-D1-E1-F1-G1 x x x x x x

52 A1-B4-C2-D1-E1-F1-G1 x x x x x x

53 A1-B1-C2-D2-E1-F1-G1 x x x x x x

54 A1-B2-C2-D2-E1-F1-G1 x x x x x x

55 A1-B3-C2-D2-E1-F1-G1 x x x x x x

56 A1-B4-C2-D2-E1-F1-G1 x x x x x x

57 A1-B1-C2-D1-E2-F1-G1 x x x x x x

58 A1-B2-C2-D1-E2-F1-G1 x x x x x x

59 A1-B3-C2-D1-E2-F1-G1 x x x x x x

60 A1-B4-C2-D1-E2-F1-G1 x x x x x x

61 A1-B1-C2-D2-E2-F1-G1 x x x x x x

62 A1-B2-C2-D2-E2-F1-G1 x x x x x x

63 A1-B3-C2-D2-E2-F1-G1 x x x x x x

64 A1-B4-C2-D2-E2-F1-G1 x x x x x x

65 A2-B1-C2-D1-E1-F1-G1 x x x x x x x

66 A2-B2-C2-D1-E1-F1-G1 x x x x x x x

67 A2-B3-C2-D1-E1-F1-G1 x x x x x x x

68 A2-B4-C2-D1-E1-F1-G1 x x x x x x x

69 A2-B1-C2-D2-E1-F1-G1 x x x x x x x

70 A2-B2-C2-D2-E1-F1-G1 x x x x x x x

71 A2-B3-C2-D2-E1-F1-G1 x x x x x x x

72 A2-B4-C2-D2-E1-F1-G1 x x x x x x x

73 A2-B1-C2-D1-E2-F1-G1 x x x x x x x

74 A2-B2-C2-D1-E2-F1-G1 x x x x x x x

75 A2-B3-C2-D1-E2-F1-G1 x x x x x x x

76 A2-B4-C2-D1-E2-F1-G1 x x x x x x x

77 A2-B1-C2-D2-E2-F1-G1 x x x x x x x

78 A2-B2-C2-D2-E2-F1-G1 x x x x x x x

79 A2-B3-C2-D2-E2-F1-G1 x x x x x x x

80 A2-B4-C2-D2-E2-F1-G1 x x x x x x x

90

Appendix H

Scenario results

Scenario % savings compared with company model % savings compared with worst case

A1-B1-C1-D1-E1-F1-G1 -10% -31%

A1-B1-C1-D1-E2-F1-G1 -9% -30%

A2-B1-C1-D1-E1-F1-G1 -4% -26%

A2-B1-C2-D2-E1-F2-G1 -3% -25%

A2-B1-C2-D1-E2-F2-G1 -3% -25%

A2-B1-C2-D1-E1-F2-G1 -3% -25%

A2-B1-C2-D2-E2-F2-G1 -3% -25%

A1-B2-C1-D1-E1-F1-G1 -1% -24%

A1-B2-C1-D1-E2-F1-G1 -1% -23%

A2-B1-C2-D2-E1-F1-G1 0% -23%

A1-B1-C2-D1-E2-F2-G1 0% -23%

A2-B1-C1-D1-E2-F1-G1 0% -23%

A1-B1-C2-D1-E1-F2-G1 0% -23%

A2-B1-C2-D1-E2-F1-G1 0% -23%

A2-B1-C2-D1-E1-F1-G1 0% -23%

A2-B1-C2-D2-E2-F1-G1 0% -23%

A1-B1-C2-D2-E1-F2-G1 1% -23%

A1-B1-C2-D2-E2-F2-G1 1% -22%

A1-B4-C2-D1-E2-F2-G1 2% -21%

A1-B4-C2-D2-E2-F2-G1 2% -21%

A1-B2-C2-D2-E1-F2-G1 3% -21%

A2-B2-C2-D2-E1-F2-G1 3% -21%

A1-B2-C2-D1-E1-F2-G1 3% -21%

A1-B4-C2-D1-E1-F2-G1 3% -21%

A1-B4-C2-D2-E1-F2-G1 3% -21%

A2-B4-C2-D2-E1-F2-G1 3% -21%

A2-B4-C2-D1-E1-F2-G1 3% -21%

A2-B4-C1-D1-E1-F1-G1 3% -21%

A2-B4-C2-D1-E2-F2-G1 3% -21%

A2-B4-C2-D2-E2-F2-G1 3% -21%

A1-B2-C2-D1-E2-F2-G1 3% -21%

A1-B2-C2-D2-E2-F2-G1 3% -21%

A1-B4-C1-D1-E2-F1-G1 3% -21%

A1-B4-C1-D1-E1-F1-G1 3% -20%

91


Scenario % savings compared with company model % savings compared with worst case

A1-B1-C2-D1-E2-F1-G1 3% -20%

A1-B1-C2-D1-E1-F1-G1 3% -20%

A1-B4-C2-D1-E2-F1-G1 4% -20%

A1-B4-C2-D2-E2-F1-G1 4% -20%

A1-B2-C2-D2-E1-F1-G1 4% -20%

A2-B2-C2-D2-E1-F1-G1 4% -20%

A1-B1-C2-D1-E2-F1-G1 3% -20%

A1-B1-C2-D1-E1-F1-G1 3% -20%

A1-B4-C2-D1-E2-F1-G1 4% -20%

A1-B4-C2-D2-E2-F1-G1 4% -20%

A1-B2-C2-D2-E1-F1-G1 4% -20%

A2-B2-C2-D2-E1-F1-G1 4% -20%

A1-B4-C1-D1-E1-F1-G1 3% -20%

A1-B1-C2-D1-E2-F1-G1 3% -20%

A1-B1-C2-D1-E1-F1-G1 3% -20%

A1-B4-C2-D1-E2-F1-G1 4% -20%

A1-B4-C2-D2-E2-F1-G1 4% -20%

A1-B2-C2-D2-E1-F1-G1 4% -20%

A2-B2-C2-D2-E1-F1-G1 4% -20%

A2-B4-C1-D1-E2-F1-G1 4% -20%

A1-B2-C2-D1-E1-F1-G1 4% -20%

A1-B4-C2-D1-E1-F1-G1 4% -20%

A2-B4-C2-D2-E1-F1-G1 4% -20%

A1-B4-C2-D2-E1-F1-G1 4% -20%

A2-B4-C2-D1-E1-F1-G1 4% -20%

A1-B1-C2-D2-E2-F1-G1 4% -20%

A2-B4-C2-D1-E2-F1-G1 4% -20%

A2-B4-C2-D2-E2-F1-G1 4% -20%

A1-B1-C2-D2-E1-F1-G1 4% -20%

A1-B2-C2-D1-E2-F1-G1 4% -20%

A1-B2-C2-D2-E2-F1-G1 4% -20%

A2-B2-C1-D1-E1-F1-G1 5% -19%

A2-B2-C1-D1-E2-F1-G1 6% -18%

A1-B3-C1-D1-E2-F1-G1 8% -17%

A1-B3-C1-D1-E1-F1-G1 8% -17%

A2-B2-C2-D2-E2-F2-G1 9% -16%

A2-B2-C2-D1-E1-F2-G1 9% -16%

A2-B3-C1-D1-E1-F1-G1 9% -16%

A2-B2-C2-D1-E2-F2-G1 9% -16%

A2-B3-C1-D1-E2-F1-G1 9% -16%

A1-B3-C2-D1-E1-F2-G1 10% -15%

A1-B3-C2-D2-E1-F2-G1 10% -15%

A2-B2-C2-D2-E2-F1-G1 10% -15%

A1-B3-C2-D2-E2-F2-G1 10% -15%

A1-B3-C2-D1-E2-F2-G1 10% -15%

A2-B2-C2-D1-E1-F1-G1 10% -15%

A2-B2-C2-D1-E2-F1-G1 11% -15%

A1-B3-C2-D1-E1-F1-G1 11% -14%

A1-B3-C2-D2-E1-F1-G1 11% -14%

A1-B3-C2-D2-E2-F1-G1 11% -14%

A2-B3-C2-D2-E1-F2-G1 11% -14%

A1-B3-C2-D1-E2-F1-G1 11% -14%

A2-B3-C2-D1-E1-F2-G1 11% -14%

A2-B3-C2-D2-E2-F2-G1 11% -14%

A2-B3-C2-D1-E2-F2-G1 12% -14%

A2-B3-C2-D2-E1-F1-G1 12% -13%

A2-B3-C2-D1-E1-F1-G1 12% -13%

A2-B3-C2-D2-E2-F1-G1 13% -13%

A2-B3-C2-D1-E2-F1-G1 13% -13%

92

eindhoven university of technology master optimizing

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