Analysis and improvement of inbound transportation at ...838725/FULLTEXT01.pdf · Inbound...

Royal Institute of Technology

Master Thesis

Analysis and improvement ofinbound transportation at

DeLaval TumbaA vehicle routing problem case study

Authors:

David Mar Sigurdsson

Dora Bjork Thrandardottir

A thesis submitted in fulfilment of the requirements

for the degree of Master’s of Production Engineering and

Management

in the

Department of Production Engineering

June 2015

https://www.kth.se/

http://www.johnsmith.com

http://www.johnsmith.com

https://www.kth.se/en/itm/inst/iip

ROYAL INSTITUTE OF TECHNOLOGY

AbstractProduction Engineering and Management


Master’s of Production Engineering and Management

Analysis and improvement of inbound transportation at DeLaval

Tumba

by Dora Bjork Thrandardottir and David Mar Sigurdsson

Transportation plays a significant role in the supply chain. The total transporta-

tion cost can be up to about 20% of the final value of a product, so it is important

to make good decisions in both inbound and outbound transportation.

Inbound transportation at DeLaval Tumba is an area that has not been investi-

gated for a long time. There is a need to set up a good overall inbound trans-

portation strategy. It was decided to limit the study to cover only suppliers from

Poland, and to apply the best resulting method on the Malmo area. In order to set

up the transportation strategy, the open vehicle routing problem was solved. The

results gave a solution implying routes for a vehicle that minimized the kilometers

driven for a given demand. Some suppliers were put together on routes, forming

so-called milk-runs, but sometimes it was more cost-beneficial to transport via

less than truckload. Four different approaches were chosen to solve the problem

that differ both in difficulty in execution and how good the solution is. A major

3PL carrier was contacted in order to get cost quotations on the resulting desired

routes, and consequently, it was possible to decide when it is feasible to transport

via milk-runs and when LTL is feasible.

By implementing the proposed transportation network, it is believed that DeLaval

Tumba could save up to 10% of inbound transportation in Poland. It was found

that despite the increasement in inventory cost, the new transportation network

in Poland should have a cost-beneficial effect on the supply chain.

Keywords: Supply Chain, Inbound Logistics, Transportation, Heuristics, Meta-

heuristics, Optimization, Vehicle Routing Problem (VRP)

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ROYAL INSTITUTE OF TECHNOLOGY

SamanfattningProduction Engineering and Management


Master’s of Production Engineering and Management

Analysis and improvement of inbound transportation at DeLaval

Tumba

by Dora Bjork Thrandardottir and David Mar Sigurdsson

Transportmedel spelar en viktig roll i leveranskedjan. Den sammanlagda trans-

portkostnaden kan vara upp till ca 20% av det slutliga vardet av en produkt, och

darfor ar det ar viktigt att fatta bra beslut i bade inkommande och utgaende

transport.

Inkommande transport pa DeLaval Tumba ar ett omrade som inte har undersokts

under en langre tid. Det finns ett behov av att inratta en bra overgripande

inkommande transportstrategi eftersom en bra overgripande inkommande trans-

portstrategi saknas. Denna undersokning ar begransad och omfattar endast lever-

antorer fran Polen samt Malmo-omradet. For att skapa en transportstrategi, lostes

oppet fordon routing problemet (the open vehicle routing problem). Resultatet

visar vilka vagar ett fordon bor kora for att minimera korda kilometer enligt en

given efterfragan. Vissa leverantorer sattes ihop till rutter, eller sa kallade mjolk-

korningar (milk runs), men ibland var det mer kostnadseffektivt att transportera

via mindre an fullast. Fyra olika strategier valdes for att losa problemet, bade

svarighet i utforande och hur bra losningen ar varierar mellan de olika strategierna.

En stor 3PL barare blev kontaktad for att fa kostnadsforslag pa de resulterande

onskade rutterna, och darfor var det mojligt att avgora nar det ar mojligt att

transportera via milk-runs och nar LTL ar genomforbart.

Genom att implementera det foreslagna transportnatet, ar det troligt att DeLaval

Tumba skulle kunna spara upp till 10% av inkommande transporter i Polen. Det

konstaterades att trots okning i lagerkostnad, bor det nya transportnatet i Polen

att ha en kostnadseffektiv paverkan pa leveranskedjan.

Nyckelord: Leverantorskedja, Inkommande Logistik, Transport, Heuristik, Meta-

heuristics, Optimering, Vehicle Routing Problem (VRP)

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Faculty Web Site URL Here (include http://)


Acknowledgements

This thesis project was carried out in cooperation with DeLaval International AB,

at their manufacturing site in Tumba, Sweden. The thesis project was the final

part of the Master programme of Production Engineering and Management at the

Royal Institute of Technology (KTH), Stockholm Sweden.

We would like to express our sincere gratitude to Gustav Nordlander, our DeLaval’s

supervisor, for giving us the opportunity to work on this exciting project. He

provided us with the all the support and guidance needed throughout the project

and always kept his the door open for us. We also want to thanks the many

employees at DeLaval Tumba for taking the time to discuss and collaborate on

our ideas.

Moreover, we want to thank Hakan Akillioglu, our academic supervisor at KTH,

for his excellent supervision and guidance during the project. He provided us with

extremely positive and useful feedback and encouragement when we truly needed.

A special thanks to Optilon AB, and especially Emma Tranarp Mann, for taking

the time to help and support us with this project.

Last but not least, we would like to thank our families for the endless support

during our studies at KTH and especially during the Master thesis work.

David Mar Sigurdsson

Dora Bjork Thrandardottir

Stockholm, June 2015

iv

Contents

Abstract ii

Samanfattning iii

Acknowledgements iv

Contents v

List of Figures vii

List of Tables ix

Abbreviations xi

1 Introduction 1

1.1 Logistics and Transportation . . . . . . . . . . . . . . . . . . . . . . 1

1.2 DeLaval International AB . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Problem Statement 7

2.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Literature Review 13

3.1 The Supply Chain and Transportation . . . . . . . . . . . . . . . . 13

3.2 The Traveling Salesman Problem . . . . . . . . . . . . . . . . . . . 18

3.3 The Vehicle Routing Problem . . . . . . . . . . . . . . . . . . . . . 20

3.4 Methods to Solve the VRP/OVRP . . . . . . . . . . . . . . . . . . 25

3.4.1 Heuristic Methods . . . . . . . . . . . . . . . . . . . . . . . 25

3.4.2 Optimal Solution Methods . . . . . . . . . . . . . . . . . . . 31

v

Contents vi

4 Data Analysis and Implementation 35

4.1 Data Analysis for the Poland Region . . . . . . . . . . . . . . . . . 35

4.2 Data Analysis for the Malmo Region . . . . . . . . . . . . . . . . . 39

4.3 Solution Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3.1 Clarke & Wright Savings Method . . . . . . . . . . . . . . . 42

4.3.2 OptaPlanner - Java . . . . . . . . . . . . . . . . . . . . . . . 43

4.3.3 Lingo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3.4 Transportation Guru . . . . . . . . . . . . . . . . . . . . . . 44

4.4 Surcharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5 Results 47

5.1 Poland Region Results . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.1.1 The Savings Algorithm . . . . . . . . . . . . . . . . . . . . . 47

5.1.2 OptaPlanner - Java . . . . . . . . . . . . . . . . . . . . . . . 49

5.1.3 Lingo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.1.4 Transportation Guru . . . . . . . . . . . . . . . . . . . . . . 59

5.1.5 Comparison of the Solution Approaches . . . . . . . . . . . . 64

5.1.6 Cost Comparison . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2 Malmo Region Results . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2.1 Cost Comparison . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3 Surcharge Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6 Conclusion and Discussion 71

6.1 Poland Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1.1 Backhaul Options . . . . . . . . . . . . . . . . . . . . . . . . 72

6.1.2 New Supplier or Change in Demand . . . . . . . . . . . . . . 73

6.1.3 Potential Yearly Savings . . . . . . . . . . . . . . . . . . . . 74

6.1.4 Trade-Offs With Inventory Cost . . . . . . . . . . . . . . . . 75

6.2 Malmo Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.3 Surcharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Bibliography 81

List of Figures

1.1 Tetra Laval group consists of Tetra Pak, DeLaval and Sidel (Nord-lander, 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Manufacturing units of DeLaval International AB (Nordlander, 2014). 3

2.1 Research methodology followed in the thesis . . . . . . . . . . . . . 10

3.1 A simple overview of a SC, showing inbound and outbound logistics(Chopra and Meindl, 2007). . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Direct shipments from suppliers to buyers (Chopra and Meindl, 2007). 16

3.3 Direct shipments from suppliers to buyers using milk-runs (Chopraand Meindl, 2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 All shipments via DC between suppliers and buyers (Chopra andMeindl, 2007). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.5 The traveling salesman problem, unsolved network on the left anda feasible solution showing Hamiltonian cycle on the right . . . . . 20

3.6 The vehicle routing problem, showing three separate routes servingall the customers, symbolized with circular nodes. . . . . . . . . . . 23

3.7 The Open Vehicle Routing Problem, showing three separate routesinbound to the depot . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.8 The difference between going back to P0 after each stop or not . . . 26

4.1 Demand over a whole year for the suppliers in the Poland region. . 36

4.2 Demand over a whole year for the selected suppliers in the Malmoregion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.1 The output from OptaPlanner when running the data for the lowdemand week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.2 The output from OptaPlanner when running the data for the mediumdemand week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3 The output from OptaPlanner when running the data for the highdemand week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Output window in Lingo showing results for the low demand weekin Poland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.5 Output window in Lingo showing results for the medium demandweek in Poland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.6 Output window in Lingo showing results for the high demand weekin Poland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

vii

List of Figures viii

5.7 Results output from Transportation Guru (1/2). . . . . . . . . . . . 59

5.8 Results output from Transportation Guru (2/2). . . . . . . . . . . . 60

5.9 A map showing the routes found for the low demand week in Poland. 61

5.10 A map showing the routes found for the medium demand week inPoland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.11 A map showing the routes found for the high demand week in Poland. 63

5.12 Comparison of the different methods, based on kilometers driven ineach reference week. . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.13 Proposed routes for a low demand week . . . . . . . . . . . . . . . . 66

5.14 Proposed routes for a medium demand week . . . . . . . . . . . . . 67

5.15 Proposed routes for a high demand week . . . . . . . . . . . . . . . 67

6.1 The three reference weeks generalizing the actual demand fluctua-tion for a whole year in the Poland region. . . . . . . . . . . . . . . 74

List of Tables

4.1 Polish suppliers and their demand for each reference week. . . . . . 37

4.2 Distances between the manufacturing site in Tumba and the chosenPolish suppliers in km. . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Accumulated demand for each reference week and LTL prices forthe Poland region. . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Malmo suppliers and the demand for the reference week. . . . . . . 40

4.5 Distances between the manufacturing site in Tumba and the Malmoregion suppliers chosen in km. . . . . . . . . . . . . . . . . . . . . . 41

4.6 Accumulated demand for the reference week and LTL prices for theMalmo region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.7 Savings in km achieved between each supplier in Poland. . . . . . . 43

4.8 Surcharge currently used for each defined geographical region. . . . 46

5.1 Savings in decending order, relevant connected suppliers and result-ing routes for each reference week. . . . . . . . . . . . . . . . . . . . 48

5.2 Results from the Savings method, total distance driven and utiliza-tion of the trucks for each route. . . . . . . . . . . . . . . . . . . . . 49

5.3 Results from OptaPlanner, total distance driven and utilization ofthe trucks for each route. . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Output from Lingo for the low demand week . . . . . . . . . . . . . 53

5.5 Output from Lingo for the medium demand week . . . . . . . . . . 54

5.6 Output from Lingo for the high demand week . . . . . . . . . . . . 55

5.7 Resultsfrom Lingo, total distance driven, utilization of the trucksfor each route, number of iterations and the time it took to solveeach week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.8 Results from Transportation Guru: total distance driven, utilizationof the trucks for each route and the time it took to find each route. 63

5.9 LTL and FTL with Milk-run cost for the optimal routing in eachreference week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.10 Feasible selection of routes and the cost reduction of selecting themcompared to only shipping via LTL . . . . . . . . . . . . . . . . . . 65

5.11 Results from Lingo, total distance driven, utilization of the trucksfor each route, number of iterations and the time it took to solveeach week. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.12 LTL and Milk-run cost compared for both scenarios. . . . . . . . . 69

ix

List of Tables x

5.13 Allocation of consumption data and transportation cost in 2014.Recommended surcharge based on those numbers is shown. . . . . . 69

6.1 Estimated yearly savings . . . . . . . . . . . . . . . . . . . . . . . . 75

6.2 Total demand shipped in each reference week and the part whichwill undergo changes and use milk-run demand . . . . . . . . . . . . 76

Abbreviations

3PL 3rd Party Logistics

DC Distribution Center

FCA Free CArrier (Incoterms)

FTL Full Truck Load

LAHC Late Acceptance Hill Climbing

LDM Loading Meter

LTL Less than Truck Load

OVRP Open Vehicle Routing Problem

SA Simulated Annealing

SC Supply Chain

SCM Supply Chain Management

TS Tabu Search

TSP Traveling Salesman Problem

VRP Vehicle Routing Problem

xi

Chapter 1

Introduction

In this chapter, the role and different aspects of transportation within the supply

chain is briefly discussed. Furthermore, a comprehensive background on the case

study’s company is presented and finally, the structure of the thesis report is

shortly discussed, presenting the forthcoming chapters.

1.1 Logistics and Transportation

The study of a typical production system is not only concerned with a specific

manufacturing process, a stationery manufacturing cell or individual factory unit.

The production discipline deals with the problem of linking the individual sys-

tems and processes together and making them work together as one. When a

production flow is being analyzed in particular, the whole supply chain (SC) has

to be considered. It represents the whole network related to the activities of a firm

that connects together individual suppliers, manufacturing units, warehouses and

last but not least, the customer. This SC network requires extensive management

of goods, money and information among all the relevant stakeholders (Nahmias,

2009).

Inbound logistics is the part of the SC that deals with the flow of material from

outside stakeholders, such as individual suppliers, into a manufacturing unit, the

customer in that case. The manufacturing of the finished good desperately de-

pends on the availability of these materials as it can lead to production stops and

1

Chapter 1. Introduction 2

therefore can have a negative impact on the profitability and service level to the

end customer (Stock and Lambert, 2001).

One of the most significant areas that logistic departments deal with is transporta-

tion. The main function of transportation is to move goods from one place within

the SC to another. The choice of transportation type in a company can have a big

influence on both position of facilities and the inventory level of a company, and

thus it impacts the company’s cost structure significantly (Chopra and Meindl,

2007).

Transportation has a big effect on the SC’s responsiveness and effectiveness. The

reason is that transportation can be very costly. SC that thrives for responsiveness

usually has a very high transportation cost, since the customers expect their goods

to arrive quickly. Consequently, the aim has to be to transport often with small

shipments. On the other hand, when a SC thrives for effectiveness, economies

of scale can be achieved because then it is possible for the SC to aggregate the

deliveries and transport fewer times with larger shipments (Hugos, 2011).

The total transportation costs can account for much as 20 percent of the finished

product price and sometimes even more (Stock and Lambert, 2001). For that

reason, effective controlling and management of transportation can result in sub-

stantial improvements in efficiency and total profitability of a company (Chopra

and Meindl, 2007).

1.2 DeLaval International AB

This thesis was carried out in co-operation with the dairy product manufacturer

Delaval International AB, more precisely their manufacturing site in Tumba, Swe-

den.

DeLaval is a leading manufacturer in the area of food producing equipments for

dairy farms. The company helps farmers keeping a good environmental status in

addition to providing equipment with state of the art technology. As visualized

in Figure 1.1, DeLaval is part of the Tetra Laval Group along with the companies

Sidel and Tetra Pak (Nordlander, 2014).


Figure 1.1: Tetra Laval group consists of Tetra Pak, DeLaval and Sidel (Nord-lander, 2014).

The company was founded by Gustaf de Laval after inventing the cream separator

in 1883. Since then, the company has grown tremendously and now counts over

4.500 employees all over the world (DeLaval, 2011). The company thrives on pro-

viding dairy farmers with a complete service and solutions for the whole milking

process, from animal care to the dairy production itself. As a result, DeLaval is

able to serve customers having from 1 to 50.000 dairy cows. DeLaval has manu-

facturing units and other departments distributed all over the world, as visualized

in Figure 1.2 (Nordlander, 2014).

Figure 1.2: Manufacturing units of DeLaval International AB (Nordlander,2014).


The figure shows the manufacturing units of DeLaval International AB and what is

being manufactured in each site. MQ&AH stands for Milking Quality and Animal

Health.

The main focus of this thesis will be within the area of inbound transportation,

moving material from suppliers, to DeLaval’s manufacturing site in Tumba, which

is highlighted with red marking in Figure 1.2. The main merchandize DeLaval

Tumba manufactures, is the so-called Voluntary Milking System (VMS), an auto-

matic milking robot system that does not require human labour, but the manufac-

turing unit also produces the more traditional manual milking systems (DeLaval,

2013).

The manufacturing site in Tumba has suppliers all over the world. The geograph-

ical regions that cover the suppliers with most value and demand are Poland,

the Malmo region and the Stockholm region. In addition, DeLaval Tumba has

suppliers scattered all over the rest of Europe and in China.

Currently, the inbound truck transportation is handled by four different 3rd party

logistics (3PL) carriers where one of them is by far used the most. However,

there is no strategy for the inbound transportation within the company in Tumba.

These 3PL providers consolidate shipments from various non related customers

through distribution centers and hubs, making the transportation as economically

beneficial for themselves as possible. In some cases, suppliers even take care of

the shipments themselves, and later invoice DeLaval Tumba. In addition, DeLaval

Tumba receives a full truck load (FTL) from one supplier in Poland three times a

week since it is one of their biggest and most important supplier. These concepts

will be further explained in Chapter 3.

In the near future, DeLaval Tumba will adapt some changes regarding their sup-

pliers, and especially in the Poland region. This change will have a great impact

on the inbound transportation, which will be further explained in the following

chapters.


1.3 Structure

The structure of this thesis is as follows:

Chapter 2 describes the problem at hand in DeLaval Tumba and ends by stating

the research questions that will be the main focus of this thesis. Following that,

a literature review will be performed in order to explain the main concepts and

methods used to answer the research questions. Chapter 4 covers the methods

used to solve the problems at hand which leads to Chapter 5, which reveals the

final results from the alternative methods. Finally, these results are discussed in

Chapter 6, along with suggestions on future research on the matter.

Chapter 2

Problem Statement

In this chapter a description of the problems at hand will be described thoroughl,

leading to the thesis research questions along with its delimitations. Finally, the

research methodology for this thesis will be presented.

2.1 Problem Description

Over the years, DeLaval Tumba has devoted much more attention to the outbound

transportation of finished goods to customers rather than the inbound transporta-

tion of supplies to their manufacturing site in Tumba, Sweden.

As for the inbound logistics, DeLaval Tumba is responsible for all transportation

activities of components from their suppliers according to Free Carrier (FCA) In-

coterms, meaning that the buyer, DeLaval Tumba, arranges and pays for the ship-

ment (International Chamber of Commerce, 2010). As DeLaval Tumba does not

own their own trucks, they sub-contract all transportation activities to a handful

of 3PL carriers.

DeLaval Tumba only keeps track of the total transportation cost invoiced by each

3PL carrier. Therefore the company does not have a complete overview of the

transportation cost for the individual supplier or each shipment that comes in-

bound to their manufacturing site.

To make sure that this incurred transportation cost is definitely covered in the final

pricing of finished goods, a certain surcharge percentage is added to the monetary

7

Chapter 2. Problem Statement 8

value of the supplies used to manufacture the product. The surcharge percentage

value currently differs by four geographical regions, but it is unknown when and

how these percentage ratios were determined as they are today. Further detail on

the matter may be found in Chapter 4.4.

When comparing the actual total transportation cost and the total surcharged

value for the year 2014, it appears that DeLaval Tumba have been overcharging

inbound transportation cost, generating notable surplus for that year. The man-

agement in DeLaval Tumba is therefore particularly interested in knowing how this

surplus was generated and what surcharge percentages should in fact be used for

each of the geographical regions to cover the corresponding transportation costs.

Currently there are significant changes in the pipeline, particularly in the Poland

region, where suppliers are increasing in numbers along with the demand for the

existing ones. For this reason and because the area of inbound transportation has

not been studied for some time at the company, detailed investigation is necessary

to determine if any improvements can be made.

There is a need for a new inbound transportation strategy that is based on moving

components from the suppliers to the manufacturing site in the most cost efficient

way as possible. This problem at hand is often called the Vehicle Routing Problem

(VRP) or Open Vehicle Routing Problem (OVRP) which is an extremely complex

combinatorial optimization problem that then needs to be solved. These concepts

will be further described in Chapter 3.

2.2 Research Questions

From the problems described in section 2.1, the following research questions have

been outlined:

1: What methods exist to solve the VRP/OVRP efficiently and how can they

be used for DeLaval Tumba in the Poland region?

2: What transportation strategy should DeLaval Tumba use which accompa-

nies the routing solution?


3: What surcharge percentage should be added to the value of goods in order

to cover the actual inbound transportation cost?

2.3 Delimitations

The project scope is extremely wide and it is therefore necessary to establish some

reasonable boundaries to make sure the thesis work will finish within the given

time frame. The following delimitations are recognized for this thesis project.

The thesis will only cover inbound truck transportation, moving components from

the company’s European suppliers to DeLaval’s manufacturing site in Tumba,

Sweden. As there are numerous suppliers scattered around the continent, it is

necessary to sort them into workable sub-sets, based on their geographical location.

Two of the proposed regions will be analyzed more specifically in this thesis;

primarily the Poland region and then the Malmo region.

The focus of this thesis is on improving logistics activities related to transportation.

Other connected subjects such as inventory management and lead time are not

part of the project but will be discussed where it is applicable.

All demand data needs to be of the same unit size and therefore the unit of

loading meter (ldm) will be used throughout the analysis, as historic information

exists in that format. Moreover, the trucks used for transportation are assumed

to be identical in terms of loading capacity. The analysis is based on historical

data from the year 2014 along with estimated increase in demand according to

DeLaval’s sources.

2.4 Research Methodology

Figure 2.1 shows an overview of the research methodology followed during the

thesis project.


Figure 2.1: Research methodology followed in the thesis

The first step was to form a clear project scope definition. This involved going

through four sub-steps, represented with the wheel in figure 2.1. These sub-steps

consisted of interviewing key personnel at DeLaval Tumba and to make all neces-

sary observations at the manufacturing site. These steps were important in order

to increase the general understanding on the problem at hand. A preliminary


study of literature was then carried out, both to get the basic academic perspec-

tive on the matter but also to understand the literature background within the

research field. Finally, after acquiring thorough understanding on the problem,

appropriate research questions were formed.

The project scope along with the research questions were then evaluated, making

sure the thesis topic met all academic requirements and that it was closely enough

related to the Master programme’s subject area. If these requirement were met,

the project work continued with the steps of literature research and data gathering.

Otherwise, the first step of project scope definition had to be repeated.

The data gathering consisted mostly of contacting and interviewing multiple de-

partments within the company but also exporting relevant historic data from the

company’s databases. The step of literature research involved searching for journal

articles, books and other theoretical material on the thesis topic through academic

databases. Furthermore, the course Information Retrieval, Source Criticism and

Literature Studies (LI1102) was undertaken, with the sole intention of increasing

the quality of the literature research process. This step of literature research led

to the closely related step of the study of suitable solution approaches for the de-

fined problem. This mainly involved finding appropriate software tools, contacting

software vendors and obtaining necessary license keys.

Completing these step led directly to the step of analyzing, organizing and con-

verting the datasets into usable inputs for the solution approaches implementation

step that followed. The last two steps of the research methodology procedure in-

volved generating and analyzing the results and lastly to interpret them in the

final step of conclusions and discussions.

Chapter 3

Literature Review

In order to gain more knowledge and general understanding of the problems de-

scribed in Chapter 2, a thorough literature review was performed. The literature

review covers how transportation of goods fits within the supply chain before an

extensive research on the subject of vehicle routing is conducted. Last but not

least, appropriate heuristics, metaheuristics and exact methods for solving the

vehicle routing problem are studied.

3.1 The Supply Chain and Transportation

The handling of raw material and goods to and from a manufacturing company can

generally be divided into inbound and outbound logistics. The inbound logistics

are mainly concerned with the material flow into the manufacturing site while the

outbound logistics involves the flow of finished goods to the customer. Figure 3.1

shows a structure of a typical SC and how it is divided into inbound and outbound

logistics. Within the SC, the transportation function plays a significant role when

it comes to movement of goods and raw material (Stock and Lambert, 2001).

13

Chapter 3. Literature Review 14

Figure 3.1: A simple overview of a SC, showing inbound and outbound logis-tics (Chopra and Meindl, 2007).

Transportation can add up to a high cost in the SC. In the perfect circumstances,

a manufacturer should only use FTL to a point near the customers, and then use

milk-runs from the consolidation point to the suppliers. For inbound transporta-

tion, this could be transformed, so the suppliers use milk-runs to a consolidation

point that is fairly close to them, from where trucks transport the raw material to

the manufacturer with direct shipment and FTL (Chopra and Meindl, 2007).

The cost of transporting goods can differ from being around 1%-50% of the value

of the product, and sometimes even more. In general, the percentage becomes

higher when transporting basic goods like coal or sand. When a product becomes

more valuable, the percentage of the value tends to be lower (Stock and Lambert,

2001). In order to cover this incurred transportation cost, companies sometimes

add a surcharge on the final product value, like mentioned earlier.

The decision on what transportation mode and network should be used falls into

the supply chain strategy or design. The decisions made in this phase are long-term

and should be decided with the overall SC’s surplus in mind. These decisions can

have a great impact on how the SC operates.

Transportation is one of three logistical drivers in the SC. All in all there are six

different drivers of the SC that are most important when it comes to the perfor-

mance of the SC. They are: Facilities, inventory and transportation as logistical

drivers, and information, sourcing and pricing as cross-functional drivers. It is


important that those drivers fit together in order to get the most out of the SC

(Chopra and Meindl, 2007). The management of each SC must have a good knowl-

edge and understanding of all the different drivers because they affect each other

greatly. It is important to know what the SC’s purpose and goals are in order to

know how it is supposed to react to changes in different drivers. The changes can

have great impact on the SC’s effectiveness and it’s capability (Hugos, 2011).

A transportation network is a collection of nodes and links between them. The

traveling happens on the links and the nodes are the start and end point, and

the stops along the way. A transportation mode is the type of vehicle used to

transport the goods. The main different modes used in transportation are: Air,

package carriers, truck, rail, water, pipeline and intermodal (Chopra and Meindl,

2007). In addition to this, electronic transport is used when transporting certain

types of material. This material can for example be data and electric energy

(Hugos, 2011).

Only truck transportation will be covered in this thesis since it is the most used

transportation mode at DeLaval Tumba. The two main parts that need to be con-

sidered when working with truck transportation are FTL and less than truck load

(LTL). FTL shipments usually have relatively low fixed cost and offer economies

of scale. LTL are shipments that are transported in small lots. The shipments are

usually not more than half a truck because if the shipments become more than

that, it tends to become feasible to transport it via FTL. Shipments via LTL usu-

ally take more time than FTL because of more frequent stops along the route to

pick up shipments. In order to keep the LTL cost as low as possible, it is good to

set up consolidation points (or centers) where many small shipments come together

and are then shipped together to the destination point. This is done in order to

utilize the trucks as well as possible, even though it can increase the delivery time.

The main goal of LTL carriers is to set up consolidation centers (or distribution

centers) in a way that it neither increases delivery time nor decreases reliability

(Chopra and Meindl, 2007).

The decision on which transportation network to use can have a big impact on how

well the SC operates. Various networks exist and can be implemented between all

different stages in the SC. In the following section, some of the main networks will

be described.


A Direct Shipment Network is a network where shipments go straight from

the supplier to the buyer. There are no intermediate warehouses and in each

truck, there are only goods from a particular supplier to the buyer of those goods.

One of the biggest advantages of this type of network is that there is no need for

consolidation centers of any kind, and therefore the shipping time is minimized

between suppliers and buyers. In addition, there is no need to change the whole

network if there is a change in one route within it. The decisions are completely

local, so they do not affect other routes. When deciding if a direct shipment

network should be used or not, it is vital to bare in mind how much demand there

is at each buyer from each supplier. If the demand is too low, the high fixed cost

of FTL shipments can become too high. Figure 3.2 shows an example of direct

shipment network. A direct shipment network decision can be made if the shipped

goods are so large that the high fixed cost of FTL is justified.

Figure 3.2: Direct shipments from suppliers to buyers (Chopra and Meindl,2007).

Direct Shipping With Milk-Runs is similar to the direct shipment network,

but in this case, a truck either picks up goods from several suppliers and takes

them to a single buyer or it takes goods from one supplier and delivers them

to multiple buyers. This setup is shown in Figure 3.3. Similarly to the direct

shipment network, the need for any kind of intermediate warehouses is eliminated

which can save a big amount of time and increase the security and reliability. The

consolidation of shipments happens at the different suppliers locations, where the

trucks pick up the goods. In this case, it is not important that the lot size of

goods from one supplier is so big that a FTL should be justified because goods

from several suppliers are put together on one route. A big advantage of this


network is that there is the possibility to utilize the truck capacity up to a very

high percentage with a relatively low cost.

Figure 3.3: Direct shipments from suppliers to buyers using milk-runs (Chopraand Meindl, 2007).

All Shipments Via Central DC uses a network where all suppliers send their

goods to one distribution center (DC) using separate trucks. Consequently, the

buyers have separate trucks that pick up the goods destined to them in the DC.

Figure 3.4 shows the setup of this network.

Figure 3.4: All shipments via DC between suppliers and buyers (Chopra andMeindl, 2007).

The DC is both able to serve the SC as an inventory and as a transfer location,

even cross-docking the goods in some cases. It is located somewhere in between

the suppliers and the buyers. There is also the possibility to have several DC’s,


and then the suppliers and buyers are splitted up into different geographical areas

where each area has one DC. When buyers are located far from their suppliers, a

DC is able to reduce the cost in the whole SC. By using a DC, it is also possible to

acquire economies of scale because the suppliers are able to send goods destined

to many buyers to the DC. When the shipments acquire economies of scale, it is

sometimes possible to use the DC as a cross-docking station. In that case, a FTL

truck arrives to the DC with goods to different buyers. It is very important that

the incoming and outgoing orders are very synchronized so that the process can run

smoothly. If cross-docking is successful, it minimizes the inventory needed and in

addition, the product flow becomes better. Furthermore, to lower inventory cost,

handling cost can decrease using cross-docking because the only handling needed

for the goods is moving it from one truck to another instead of moving it first to

an inventory storage.

Shipping Via DC Using Milk-Runs is a good network to use if shipments from

the suppliers to the DC are small and/or if the demand of the buyers from the DC

is low. In that case, a truck is able to pick up shipments from several suppliers

and ship to the DC. Then, a truck picks up the orders from the DC and ships to

several buyers. Having this kind of network can decrease the total transportation

cost because of shorter distances traveled.

A company is not forced to pick only one of these above mentioned networks.

Instead, it is quite common that companies mix the networks together in a tailored

network that fits precisely to their transportation strategy (Chopra and Meindl,

2007). A lot of research has been made in the area of transportation routing. Some

of this research and main problems will be described in the following subsections.

3.2 The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a classic combinatorial optimization

problem within the field of operations research. The problem has been known

among mathematicians under various names over the years but it was possibly

first recognized as the concerned traveling salesman problem in a technical report

by Robinson (1949). It wasn’t until with the work of Dantzig et al. (1954) that a

systematic study of the TSP began (cited in Gutin and Punnen (2002), p.2).


The problem consists of a home base (depot), a salesman and a prescribed set of

n nodes (cities) which the salesman must visit. The route of the salesman begins

and ends at the depot and the salesman has to go to each city exactly once. The

problem is then to determine the optimal sequence in how the salesman visits the

cities so that the total distance is minimized (Nahmias, 2009).

Even though the TSP does not seem to be very complex in terms of routing, it

is considered to be very hard to solve as the number of possible routing sequence

grows exponentially with the number of cities the salesman has to visit (Gutin

and Punnen, 2002). In a TSP where the distance between two different cities does

not depend on the direction of travel, known as symmetric TSP, there are a total

of 12·n! possible routings (Dantzig and Ramser, 1959). This means that with only

n= 20 cities, 1.216.451 trillion possible combinatorial routings exists, making the

exact solution not so obvious to find. TSP is consequently known in mathematics

as a NP-hard (Non-deterministic Polynomial-time) problem, which means that the

time it takes to solve the TSP is not a polynomial function but an exponential

function of n (Nahmias, 2009).

A formal mathematical definition of the TSP can be stated as follows: Consider

a network G = [n,A,D] where A denotes the number of links between the nodes

and D = [di,j] is a distance matrix. Within the matrix, the distance di,j is then

measured from node i to node j. The main concern of the TSP is to find a

Hamiltonian cycle within the network G of minimum total distance, where the

Hamiltonian cycle is a cycle passing through each node exactly once (Bodin et al.,

1983). Figure 3.5 below shows a typical TSP network with numerous routing

possibilities. A feasible solution is indicated with red arrows on the same figure

to the right.


Figure 3.5: The traveling salesman problem, unsolved network on the left anda feasible solution showing Hamiltonian cycle on the right

3.3 The Vehicle Routing Problem

The Vehicle routing problem (VRP) is closely related to the TSP. The problem

is also a NP-hard problem as for the TSP but it is a much more complex combi-

natorial optimization problem to solve in practice. The VRP was first introduced

in a journal article by Dantzig and Ramser in 1959 under the title “The Truck

Dispatching Problem” (Laporte, 2009). The article’s main topic is to find the

optimum routing of a fleet of petrol delivery trucks between a central depot and

service stations. They describe their work as a generalization of the TSP and

provide a near optimal solution procedure based on linear programming formu-

lation (Dantzig and Ramser, 1959). In 1964, Clarke and Wright then introduced

the famous Savings method, an improved and effective greedy heuristic algorithm

that will be discussed in more detail later in this chapter. Since then, the topic of

VRP has been studied extensively with hundreds of optimal and near-optimal al-

gorithms and methods published for the many different versions of the VRP. It has

been shown in practice that the use of these methods in solving the VRP, yields in

better vehicle utilization and significant savings in terms of overall transportation

costs.

There are many variations of the VRP that exist but the most studied version

of the problem is the Capacitated Vehicle Routing Problem (CVRP) and will be

referred as the VRP in this thesis. As with the TSP, the VRP has a central


depot, N = {1, 2, ..., n} stops, each having predetermined demand and one or

more available delivery vehicles K = {1, 2, ..., |K|}. Each vehicle is assumed to

have identical capacity in terms of weight, maximum volume, number of pallets

or other common unit size and are all based at the central depot (Toth and Vigo,

2014). A common unit is Loading Meter (ldm), which can be defined as one meter

of goods placed in a truck or a trailer. A standard European truck is 13,6 meter

long, so it is possible to fit 13,6 ldm’s within a FTL (CargoTrans, 2014).

The problem’s main objective is to assign the vehicles to the customer’s locations

and at the same time to meet the customer’s demand at the minimum cost in terms

of travel time or distance (Nahmias, 2009). A formal mathematical definition of

the VRP can be stated as follows. Consider a network graph G = (V,A) where

V signifies the vertex set V = {0, ..., n} and A signifies the arc set A = {(i, j) :

i, j ∈ V, i 6= j}, connecting the vertices together. Vertex 0 then represents the

central depot but the remaining vertices relate to the N number of customers

(Laporte, 2009). A fleet of K = {1, 2, ..., |K|} homogeneous vehicles, all with the

capacity Q are initially located at the central depot 0. A cost matrix exists for

the arc set A in that way if a vehicle travels from customer i to j, it incurs the

travel cost cij (Toth and Vigo, 2014). The VRP is then to assign the K number of

vehicles to routes so each and every customer is visited exactly once, their demand

fulfilled and the vehicle capacity does not exceed its limit Q, at the lowest possible

cost. For simplicity reason, it is assumed that the cost cij is a function of distance

between customer i and j and that the problem is symmetric, that is cij = cji for

all (i, j) ∈ A (Laporte, 2009).

A traditional notation for a directed VRP was introduced by Laporte et al. (1986).

For that notation, let S be a random subset of vertices V. The in-arcs of S are then

defined as δ−(S) = {(i, j) ∈ A : i /∈ S, j ∈ S} and the out-arcs of S are similarly

defined as δ+(S) = {(i, j) ∈ A : i ∈ S, j /∈ S}. Then A(S) = {(i, j) ∈ A : i, j ∈ S}for all arcs in the subset of S. Moreover, let r(S) be the minimum number of

vehicles to serve all customers in the subset of S. In the model, integer decision

variables xij for {i, j} ∈ A are used.

According to Toth and Vigo (2014) the notation model can then be stated as

follows:

minimize∑

(i,j)∈A

cijxij (3.1)


Subject to:

∑j∈δ+(i)

xij = 1 ∀i ∈ N (3.2)

∑i∈δ−(j)

xij = 1 ∀j ∈ N (3.3)

∑j∈δ+(0)

x0j = |K| (3.4)

∑(i,j) ∈δ+(S)

xij ≥ r(S) ∀S ⊆ N,S 6= 0 (3.5)

xij ∈ {0, 1} ∀(i, j) ∈ A (3.6)

A similar model notation on a two-index formulation for the undirected VRP was

introduced by Laporte et al. (1985), but is beyond the scope of this thesis.

In the model notation above, formula 3.1 states the main objective of the VRP, of

minimizing the total routing costs. Constraint 3.2 makes sure that precisely one

arc enters each node vertex and similarly 3.3 makes sure that exactly one arc leaves

each node vertex. Constraint 3.4 makes sure that |K| routes are created, equal

to the number of vehicles used. Constraint 3.5 ensures that the vehicle capacity

constraint are fulfilled but also makes sure that connectivity requirements of the

solution is enforced. The last constraint 3.6 assures that the decision variables xij

are binary. If a decision variable xij is equal to 1, a vehicle will travel the arc from

i to j, but is otherwise set to zero (Toth and Vigo, 2014) and Laporte (1992).

Figure 3.6 illustrates a feasible solution of a VRP with K = 3 vehicles, serving all

the customers exactly once, in as many routes. All the vehicles start and return

to the central depot 0.


Figure 3.6: The vehicle routing problem, showing three separate routes servingall the customers, symbolized with circular nodes.

In most cases of the VRP, it is assumed that goods are being transported outbound,

from a central depot to a number of different customers at various locations. In

the case discussed in this thesis, the flow is reversed in a way that the goods are

being transported inbound, from numerous suppliers to a single manufacturing

site or a depot. This kind of collection is called pickups and the VRP task is then

to transport supplies to the depot, so the cost in terms of distance or travel time is

minimized and the trucks are being utilized in the best possible way by combining

shipments when beneficial. The comparability of this kind of inbound pickups

VRP versus the ordinary outbound delivery VRP, turns out to be of equivalence

by simply reversing the routes (Toth and Vigo, 2014).

As DeLaval Tumba does not own their own vehicles, all transportation activities

for the Tumba factory are outsourced to a 3PL carrier. Consequently, the vehi-

cles do not need to return to their starting location and the routes become open

loops. This exemplifies one variant of the VRP, called the Open Vehicle Routing

Problem (OVRP). The OVRP has been studied for more than 20 years, but it is

just recently that the variant has attracted serious attention, mainly due to the

practical solutions it provides for real-world cases.

In the more traditional outbound version of the OVRP, a vehicle does not return

to the depot after servicing the last customer on its route. Real-world cases in-

clude companies that use 3PL carriers and are not paying after servicing the last


customer in a delivery route and want to have as efficient path as possible, not

taking the return trip into account (Golden et al., 2007). The simplest mathemat-

ical alteration possible of the VRP formulation, is to set the routing cost for the

return trip to zero (Toth and Vigo, 2014).

In the case of DeLaval Tumba, the transportation routes are reversed and the

supplies move inbound from various suppliers to their manufacturing site. Figure

3.7 shows this particular case of inbound OVRP.

Figure 3.7: The Open Vehicle Routing Problem, showing three separate routesinbound to the depot

Comparing Figure 3.6 showing the traditional VRP and the case in Figure 3.7,

one can see that the vehicles won’t necessarily follow the same routing sequence,

when solving the problems. This may happen even though the network graphs

are identical, because the OVRP is optimized without taking the return trip into

account, while the VRP solution does the opposite.

There are many more variants and extensions that exists for the VRP, but they

are beyond the scope of this thesis. A survey of the most significant results in the

literature on that matter may be found in a book by Toth and Vigo (2014).

As mentioned earlier, the VRP has been a known problem for over 50 years. A

lot of research has been made on the matter and a few studies will be described

in the following subchapter.


3.4 Methods to Solve the VRP/OVRP

Many different methods and algorithms are available to solve the VRP. The meth-

ods vary both in difficulty of implementation and in the quality of the results. The

time given for the research of this thesis is brief, and so four different methods

were analyzed and applied to the case study. The methods compared are both

heuristic and optimal. The different types chosen are:

• Constructive Heuristics (the Savings Algorithm)

• Metaheuristics (Tabu Search, Simulated Annealing and Late Acceptance)

• Optimal solution (Branch-and-Bound)

Those methods will be explained in more detail in the following subsections.

3.4.1 Heuristic Methods

When solving the VRP, finding the optimal solution with a mathematical program

can be very time consuming when it comes to more than 100 suppliers (or cus-

tomers). Optimal solution methods can become too time consuming in real life

cases when companies want to solve large scale problems as quickly as possible.

In those cases, it can be effective to solve the problem using heuristic methods.

Heuristic methods do not provide the exact optimal solution in all cases, but they

can give a relatively good solution (Toth and Vigo, 2014). The methods are capa-

ble of dealing with large scale problems and should, in most cases, give a solution

that is very close to being optimal. They should also be able to tell if there is

no feasible solution available for a certain problem. Finding a solution with a

heuristic method includes using iterative algorithms in an effort to find a better

solution than the one before. In most cases, heuristic methods are relatively easy

to use and simple, but it is important to choose a method that fits the problem.

Thus, heuristic methods are often designed to fit certain types of problems, rather

than fitting a number of different problems (Hillier and Lieberman, 2010).

Heuristic methods include constructive heuristics, improvement heuristics and

metaheuristics, which is the most sophisticated of them. Constructive heuris-

tics are often aimed to give a good starting point or a starting solution for an

improvement heuristic or a metaheuristic solution. However, developments in

metaheuristics for the last years have made them more sophisticated, so they can


be applied first hand, without the groundwork of constructive heuristics. The rea-

son for this is that when it comes to research connected to heuristic in VRP, the

main focus of the last 10 years has been on metaheuristics (Toth and Vigo, 2014).

When it comes to metaheuristics, they are able to generate both a good structure

of the solution and a good heuristic guideline for a method on how to solve certain

types of problems (Hillier and Lieberman, 2010).

Even though the use of constructive heuristics has decreased in recent years be-

cause of a broad selection of metaheuristic available, it is considered interesting

to try one classic method to see how it performs compared to other methods.

The constructive heuristic method chosen is called Clarke and Wright’s Savings

Algorithm, hereafter referred to as the savings algorithm.

The Savings Algorithm is one of the oldest and most popular heuristic way to

solve the VRP, developed in 1964. The method is used to find the optimum (or

near-optimum) solution to a routing of trucks, with different capacity Q, delivering

to multiple stops, P , with a given distance (di,j), between them. In this case,

di,j = dj,i is assumed. The stops have different loads or demand (q). In order to

use the method, there must be a single depot (P0), where all the trucks start and

end their route. The trucks are assigned to multiple stops, so the demand at each

stop is usually lower than the truck’s capacity. If the truck’s capacity is more than

the demand for all the stops, the problem will become the TSP. By connecting

two stops in one route, a certain distance is saved because the truck does not need

to go back to the depot between the stops. These savings can be calculated as:

si,j = d0,i + d0,j − di,j (3.7)

where si,j denotes the savings achieved from node i to node j, and d represents the

distance between different routes. The savings can also be described graphically,

like in Figure 3.8.

Figure 3.8: The difference between going back to P0 after each stop or not


It is clear from the figure that if the amount that is demanded in P1 and P2 is

lower than the capacity of the truck, it is feasible to connect the stops into one

route.

The savings are calculated for every possible connection of the stops. The savings

are then sorted in a descending order, where the top connection is considered to be

the most beneficial milk-run and so forth. In order to find all the feasible routes,

and in some cases, the best solution, the savings are evaluated from top to bottom

and feasible stops connected. A stop is feasible if the demand does not exceed

Q for all P. If two connections have the same savings, the order of them should

be picked randomly. Each saving is evaluated until all stops have a connection to

another stop or to the depot (Clarke and Wright, 1964). When the savings have

been calculated, it is possible to assemble them by using two different methods,

namely the Parallel version and Sequential version. In the parallel version, savings

are assembled from top to bottom from the highest savings to the lowest until no

arcs remain. Therefore, one can be working on two or more routes at once. In the

sequential version, one must continue with the first route until no other assembly is

possible for that particular route and then go back and pick the highest remaining

saving in order to begin a new route. In most cases, the parallel version has given

better results, and is therefore used for this thesis (Toth and Vigo, 2002).

Note that the method is able to take in different sizes of trucks, but in this case

study there is only one size of trucks available (13,6 ldm’s). In that case, the

method tends to lay more weight on utilizing the trucks capacities instead of mini-

mizing the total distance of the routes. If the case study would take in more variety

of trucks, the outcome of the method would be different (Clarke and Wright, 1964).

A positive factor in this method is that it is easy to perform and relatively fast

(Toth and Vigo, 2014). On the other hand, the method is aimed at finding and

assembling the best routes first, leading to unattractive routes that are lower in

the queue (Toth and Vigo, 2002).

As discussed earlier in this chapter, metaheuristic methods have developed greatly

for the past 10 years. It would be nearly impossible to discuss every one of them,

but instead a few common methods will be explained which are later used in

the case study. Those methods are: Tabu Search, Simulated Annealing and Late

Acceptance.


Tabu Search (TS) is a metaheuristic method that begins by only accepting

solutions from the iteration step that give better solutions than the step before. By

doing so, the local optimum is found. This procedure is called local improvement

procedure. After this step, a subroutine called local search procedure is applied,

which is able to accept solutions that do not give a better solution than the step

before. However, this solution must be in the neighbourhood of the local optimum

found earlier. The method is continued and iterated until a better solution is

found in the area of the trial solution currently used, and a new local optimum is

found by using the local improvement procedure again. This procedure can also

be explained as a trip up a hill. The method always chooses the steepest way up,

and if it sees no possible way up in the next step, it chooses a way downhill that

drops down the shortest amount of distance in an attempt to find another way

up. This is sometimes called the steepest ascent/mildest descent approach (Hillier

and Lieberman, 2010). In order to prevent the method going back to the same

local optimum as before, stops that have too many similar attributes in common

with the current move are temporarily forbidden (Toth and Vigo, 2014). A tabu

list collects the moves that are forbidden (tabu), and those moves are called tabu

moves. An exception is made if the tabu move will result in a better solution than

the best known trial solution.

All tabu search methods are designed to try to find a way from the local optimum

in a search for a better solution. Using this described base, a tabu search needs

to be tailored to the specific problem being addressed using different procedures

for different elements and details of the problem. When those details have been

worked out, the tabu search can be used to find the structure and a good strategy

guideline in order to generate a successful heuristic solution (Hillier and Lieberman,

2010). Over the last 20 years, many new tabu search methods have been proposed

which give more diversity and options to solve different kind of problems (Toth

and Vigo, 2014). For the reader’s interest, the articles from Brandao (2004) and

Fu et al. (2005) are recommended for further reading on tabu search methods.

Simulated Annealing (SA) is a similar method to TS. The method is aimed

at finding the local optimum in different areas and in the end finding the global

optimum. However, the main focus is always on finding the global optimum instead

of wasting time on iterations in different local optimums. Again, it is possible to

describe the method with hill climbing. The first steps are to select random

directions in order to find the highest top (global optimum) and rejecting most


of the ways that go downwards. These random directions are taken in order to

be able to explore as big area as possible in the beginning of the method. Most

of the directions that are accepted are upwards, so the method always gets closer

and closer to the global optimum. When the method has been iterated for some

time, it has rejected most directions that go downwards, and is able to reach the

near-optimum quite fast.

The main difference on the iteration steps in the tabu search and the simulated

annealing is how the next trial solution in the neighbourhood is selected. The

parameters used are:

• Zc = objective function value for the current trial solution.

• Zn = objective function value for the current candidate to be the next trial

solution.

• T = a parameter that measures the tendency to accept the current candidate

to be the next trial solution if this candidate is not an improvement on the

current trial solution.

When those parameters have been found, the move selection rule is used in order

to see if Zn is a good immediate neighbour enough to be the next trial solution.

If a maximized final solution is the objective of the move selection rule, it goes by

the following criteria:

• If Zc ≤ Zn, then Zn should be the next trial solution.

• If Zn < Zc, then Zn should be accepted as the next trial solution with a

probability of Prob{acceptance} = ex, where x = Zn−Zc

T

If the method should find the minimized solution, the first two formulas should

be reversed. These steps are iterated with random immediate neighbour until no

more neighbours remain. These formulas represent that if the next trial solution

is better than the current one, it should always be accepted, and if it gives a

worse solution, the probability of it getting accepted is depending on how much

worse it is and therefore on the value of T. Consequently, it is more likely that

the method accepts the new candidate if it is only slightly worse (only goes a few

steps down the hill), than if the difference is large (and has to go further down the

hill). As T becomes smaller, the probability of acceptance becomes smaller, and

the method should have a less chance of accepting worse solutions. The random

factor mentioned earlier thus gets smaller, since the method accepts fewer and


fewer downhill ways as T decreases through the method (Hillier and Lieberman,

2010). The decreasement of T is sometimes called a cooling schedule (Burke and

Bykov, 2012). When the Prob{acceptance} has been found, it is compared to a

random number between 0 and 1, and if random number < Prob{acceptance}, the

downwards step should be accepted. Otherwise the step is rejected.

Important steps for the effectiveness of this method are to specify the starting

point, and deciding how many iterations should be done for each value of T. This

is chosen differently for each type of problem (Hillier and Lieberman, 2010).

Late Acceptance or Late Acceptance Hill Climbing (LAHC) is a similar

method to the ones described before. The main difference between LAHC and SA

is that it doesn’t use a cooling schedule. It uses an Adaptive Memory Programming

(AMP) where it takes the current trial solution, and compares it with a solution

that was ”current” several iterations before. The moves accepted are the ones that

involve a better or equal cost function than it was a few steps back.

The method, just like the other metaheuristics methods described before, starts

with a random initial solution. In each step (or each iteration) it evaluates if

the next trial solution should be the new current trial solution or not. In order

to do so, the method remembers a fixed amount of previous steps of the prior

current trial solutions and is able to compare the current cost to the cost in the

oldest step in the memory. If the cost function of the next trial solution is not

worse than the cost function of the last step, it is accepted. Consequently, the last

step is taken out of the memory, and the current trial solution is placed in the

front. This memory list is different from the one used in TS in the sense that in

TS, the memory list remembers different moves, but in LAHC the list remembers

the values of cost functions. In addition, instead of comparing all the solutions

accepted, LAHC compares the current trial solution to the oldest trial solution on

the list.

Burke & Bykov (2012) suggested two improvements on LAHC. Firstly, it was

thought to be good to make the processing time of the method relatively as long

as the length of the list. This is done by stopping the whole list to shift with each

iteration.

In some cases, LAHC is able to accept candidates that contains worse cost function

than the current candidate. This characteristic is in most cases good since it

can make the search procedures stronger. However, with the original LAHC, the


method was sometimes able to reject non-worsening candidates over the current

candidate. This is not considered a desirable behaviour. Therefore, the second

improvement factor was to employ the late acceptance for moves that are worsening

and, in addition, in order to accept moves that are not worse. The authors of the

method found that when the method is in acceptance state in the ith iteration, it

can be stated as

C∗i ≤ Ci−Lfa

or

C∗i ≤ Ci−1

Here, C∗i denotes the candidate cost, Ci−Lfa denotes the cost of the current solution

that is in the back of the memory list, and Ci−1 denotes the current cost (Burke

and Bykov, 2012).

3.4.2 Optimal Solution Methods

The TSP has been studied for decades with numerous optimal algorithms devel-

oped for solving the problem successfully. Because the VRP is an extension of the

TSP, many of the exact algorithms used for the VRP are based on the successful

development devoted to the optimal solution for the TSP (Toth and Vigo, 2014).

Laporte and Nobert (1987) provided one of the first complete work on exact algo-

rithms for the VRP. Since then, numerous papers have been published focusing on

exact algorithm analysis for the problem. This includes work by Laporte (1992),

Toth and Vigo (2002, 2014), Naddef and Rinaldi (2001) and Baldacci et al. (2010,

2011).

One of the most studied algorithms for solving the VRP, is based on a technique

called Branch-and-Bound. This section will be devoted to this particular tech-

nique.

To find the exact solution of a VRP, by trying all possible routing sequences can be

enormously time consuming and even impossible in real-world cases. The Branch-

and-Bound technique is a cleverly designed procedure that can be used for solving

integer programming problems, such as the VRP. The procedure is structured in

a way that only a fraction of all the feasible solutions needs to be examined in the

search for the optimal solution.


The branch-and-bound technique uses the so-called divide and conquer strategy.

The dividing (branching) involves splitting the original and difficult problem into

smaller and smaller subsets of feasible solutions in the way they can be conquered

(fathomed). The fathoming involves bounding the best feasible solution found

in a branched subset. The subset is discarded if the bound does not contain the

optimal solution for the original problem. This is done for all the branched subsets

until the optimal solution is found. The three basic steps of branching, bounding

and fathoming will now be explained further.

Branching is the first step of the algorithm and divides the original problem in

half. The most straightforward way to do that is by assigning fixed values to an

unknown variable of the problem, called branching variable, and in the progress

create two new subproblems. This branching procedure is then carried out on

each remaining subproblem, dividing them into even smaller subproblems until a

desired solution is found.

Bounding is the step involving finding out the best feasible solution of each

branched subproblem from the step before. The most typical way of finding this

best solution is to solve relaxation of the subproblem. A relaxation of a subproblem

is found by simply deleting one set of constraints that makes the problem difficult

to solve to begin with. The integer value of the solution is then the bound for the

subproblem.

Fathoming is the last step of the Branch-and-Bound procedure. It conquers the

subproblems bound by dismissing (fathom) it from further consideration in the

search for the optimal solution. The subproblem relaxation is fathomed if:

1. Its bound is not better than the best solution already found, or

2. The subproblem has no feasible solutions, or

3. The optimal solution of the subproblem is integer and it becomes the prob-

lem’s incumbent solution Z*.

This procedure involving the steps of branch, bound and fathoming is then contin-

ued until there are no remaining subproblems to iterate and the best incumbent

solution becomes the optimal solution. The problem has however no feasible so-

lution if no incumbent solution is found during the iteration process (Hillier and

Lieberman, 2010).


There are many more exact algorithms that have been developed for solving the

VRP over the years but it is beyond the purpose of this thesis to discuss. Further

insight along with information about recent development in this field of study can

be found in an extensive survey made by Toth and Vigo (2014).

Chapter 4

Data Analysis and

Implementation

In the following subchapters, the data analysing process and the alternative meth-

ods used to solve the OVRP will be described. In order to compare the different

methods, a case study was performed on two predefined geographical regions of

Poland and Malmo. All cost figures have been altered due to confidential reasons.

4.1 Data Analysis for the Poland Region

The Poland region was chosen as the primary region for this case study mainly

due to the ever increasing demand at the region’s existing suppliers but also due

to the newly recruited suppliers. Moreover, the transportation cost for Poland is

very high in comparison to the rest of the regions. Poland was therefore considered

interesting for the case study.

DeLaval Tumba produces high-tech milking machinery that is assembled from

numerous different components. As the articles are different from each other in

terms of bulkiness and value, it was necessary to generalize demand figures from

each supplier to a common unit size of ldm’s. The main reason for choosing ldm’s

as a common unit size was that most historical data provided was given in ldm’s.

Furthermore, as vehicle capacity is also measured in ldm, it made it easier to

utilize the trucks and to handle the difference in size and bulkiness of the articles.

Since the data analysis was based on historical data of ldm’s, it was not possible

35

Chapter 4. Data Analysis and Implementation 36

to say anything about stacking of goods inside the trucks since, as described in

Chapter 3.3, ldm is only a measure of meters of goods in the truck.

DeLaval Tumba experiences substantial seasonal fluctuation in demand within

the Poland region. Therefore three different reference weeks were chosen with

the aim of covering all possible scenarios, one week with low demand, one with

medium demand and the last one with high demand. The demand for each week

is presented later in this chapter in Figure 4.1 and in Table 4.1.

The information about supplier’s demand had to be gathered from three differ-

ent sources within DeLaval Tumba; Transportation solution management (TSM)

department, the economical control department and the logistics management.

One of the suppliers was contacted separately in order to determine their demand

shipped to Tumba (Labaz, 2015). These mentioned sources were able to give both

historical data and, in addition, advice on how to assume the increasing demand

in the region, both in terms of additional demand for individual suppliers and

increased number of suppliers. Consequently it was possible to gather all demand

data for further analysis. The graph shown in Figure 4.1 shows the fluctuation

in demand for a whole year in the Poland region alone. The data is based on

actual historical data from 2014 along with future assumed regional increase in

suppliers demand. The selected reference weeks are specifically indicated with red

markings.

Figure 4.1: Demand over a whole year for the suppliers in the Poland region.


The suppliers chosen for the Poland region were 9 in total. They were chosen

because of their geographical location. All suppliers along with their demand for

each reference week can be seen in Table 4.1.

Reference Weeks [ldm]

Supplier # Low Demand Medium Demand High Demand

1 33,6 33,6 49,2

2 - 10,8 10,8

3 1,2 1,2 0,8

4 1,0 1,0 1,0

5 - 1,9 1,9

6 0,5 0,5 0,5

7 0,5 0,5 0,5

8 3,6 3,6 6,8

9 2,4 0,4 2,8

Table 4.1: Polish suppliers and their demand for each reference week.

Road distances between the suppliers and the manufacturing site in Tumba were

found using Google Maps. All distances, in km, can be found in Table 4.2. The row

that shows the distance from Tumba (Mfg) to all the suppliers is kept 0 because

the case deals with the OVRP as described in Chapter 3.3, and therefore the trucks

do not need to begin in Tumba.

Mfg Sup1 Sup2 Sup3 Sup4 Sup5 Sup6 Sup7 Sup8 Sup9

Mfg - 0 0 0 0 0 0 0 0 0

Supplier1 1.410 - 80 17 303 32 1 256 373 536

Supplier2 1.464 80 - 70 320 71 84 273 448 611

Supplier3 1.395 17 70 - 293 47 20 246 384 546

Supplier4 1.687 303 320 293 - 264 306 147 400 588

Supplier5 1.441 32 71 47 264 - 32 217 372 533

Supplier6 1.414 1 84 20 306 32 - 259 373 535

Supplier7 1.640 256 273 246 147 217 259 - 364 551

Supplier8 1.651 373 448 384 400 372 373 364 - 193

Supplier9 1.813 536 611 546 588 533 535 511 193 -

Table 4.2: Distances between the manufacturing site in Tumba and the chosenPolish suppliers in km.


Along with the distances and the demand from each supplier, the size of the

trucks had to be determined. One type of standard trucks used to move goods

within Europe has a capacity of 13,6 ldm’s (DB SCHENKERroad, 2009), so it was

decided to use those dimensions for the final input in the methods. In addition,

the carrier DeLaval Tumba mainly uses for inbound transportation, already uses

this type of trucks.

When demand from one of the suppliers exceeds the maximum truck capacity

of 13,6 ldm, it is assumed that FTL is used as it is in fact the most efficient in

terms of cost. The remaining demand from that particular supplier can then be

used as an input for the OVRP. For example, since Supplier 1 had a demand of

33,6 ldm’s for the low and medium week, it was assumed that the supplier would

have two FTL trucks and the remaining 6,4 ldm’s would then be the input for the

algorithms.

In order to calculate how much the current (LTL) transportation cost is, a quota-

tion file was received from the major 3PL provider with negotiated transportation

rates for DeLaval Tumba for the time period 2014-2016. This file includes all

nodes in the transportation network in Poland for DeLaval Tumba and the cost

for transporting goods between them and the manufacturing site. Furthermore,

the cost between nodes depends on the load that is being transported. To be able

to sort out the information needed for the purpose of the thesis, only relevant

information was extracted from the file. Table 4.3 shows the accumulated demand

and LTL prices for each reference week in SEK. The currency used in this thesis

is the Swedish Krona (SEK). In the cases where the data received was in EUR,

the conversion rate of 1 EUR = 9,0961 SEK was used throughout the thesis.

Reference Week Demand [ldm] LTL Price [SEK]

Low 15,6 47.272

Medium 26,3 66.283

High 33,5 75.552

Table 4.3: Accumulated demand for each reference week and LTL prices forthe Poland region.

As stated earlier, it is assumed that Supplier1 sends as many FTLs as possible.

Therefore, those ldm’s already shipped via FTL are not considered in Table 4.3.


4.2 Data Analysis for the Malmo Region

All the data needed for the Malmo region was handled the same way as for the

Poland region. 15 different suppliers were chosen in total. Only one reference week

was selected, unlike for the Poland region, which represents a typical medium week

for the suppliers. The data for the Malmo region included more assumption based

demand because, for some reasons, the 3PL carriers mainly used for the region

did not have as accurate data as the main carrier in the Poland region. The

graph shown in Figure 4.2, represents the demand for a whole year for the selected

suppliers in the Malmo region.

Figure 4.2: Demand over a whole year for the selected suppliers in the Malmoregion.

As can be seen from the figure, week 17 was chosen to be the reference week as it

contained demand from all the suppliers in the region for that week. It can also

be noted that the demand for that particular week is fairly average, compared to

all the weeks. A list of the suppliers and their demand for the selected week can

be seen in Table 4.4.


Supplier # Demand [ldm]

1 1,3

2 0,3

3 0,2

4 0,4

5 1,5

6 3,1

7 2,0

8 0,9

9 0,5

10 0,2

11 0,1

12 0,2

13 0,2

14 0,5

15 0,5

Table 4.4: Malmo suppliers and the demand for the reference week.

As can be seen from the table, the demand for each of the suppliers is fairly low,

ranging from 0, 1− 3, 1 ldm’s.

When the demand had been identified, the distance between each supplier and the

manufacturing site in Tumba was found in the same way as for the Poland region.

The resulting values are presented in Table 4.5.


Mfg S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15

Mfg - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

S1 393 - 3 19 19 21 22 22 30 59 59 62 52 58 95 57

S2 393 3 - 21 21 23 24 24 32 61 61 64 55 61 96 58

S3 374 19 21 - 6 6 6 6 15 44 43 45 36 42 85 47

S4 378 19 21 6 - 10 10 10 18 47 47 49 40 47 82 43

S5 371 21 23 6 10 - 4 4 11 40 39 42 33 39 88 49

S6 370 22 24 6 10 4 - 1 9 39 38 40 31 38 88 50

S7 370 22 24 6 10 4 1 - 9 39 38 41 31 38 88 50

S8 370 30 32 15 18 11 9 9 - 38 39 41 23 30 96 58

S9 335 59 61 44 47 40 39 39 38 - 1 2 57 53 125 87

S10 334 59 61 43 47 39 38 38 39 1 - 2 57 53 125 87

S11 334 62 64 45 49 42 40 41 41 2 2 - 59 55 128 90

S12 341 52 55 36 40 33 31 31 23 57 57 59 - 13 119 81

S13 328 58 61 42 47 39 38 38 30 53 53 55 13 - 125 87

S14 457 95 96 85 82 88 88 88 96 125 125 128 119 125 - 52

S15 419 57 58 47 43 49 50 50 58 87 87 90 81 87 52 -

Table 4.5: Distances between the manufacturing site in Tumba and the Malmoregion suppliers chosen in km.

Similarly to Table 4.2, the distance from the manufacturing site in Tumba to the

suppliers is set to zero since the OVRP is being addressed.

Lastly, the same assumptions apply for the size of the trucks as for the Poland

region, were trucks with the maximum capacity of 13,6 ldm are used.

It was decided to apply the method firstly on all the 15 selected suppliers in the

region, and again only covering suppliers 1-11. This decision was made because

suppliers 12-15 are quite remote, compared to suppliers 1-11. The main purpose

was to see if the results for the region would vary in any way by narrowing down

the region’s perimeter.

In order to calculate how much it costs to transport the demand via LTL, a similar

file was received with quotations for the Malmo region as for the Poland region.

The accumulated demand for the reference week and associated LTL cost can be

seen in Table 4.6.


Suppliers’ grouping Demand [ldm] LTL Price [SEK]

Suppliers 1-11 10,5 18.274

Suppliers 1-15 11,9 19.357

Table 4.6: Accumulated demand for the reference week and LTL prices forthe Malmo region.

None of the suppliers in the Malmo region have a demand that exceeds a FTL, so

the demand shown in Table 4.6 is the actual assumed demand for those suppliers.

In the following subchapter, each solution approach used to solve the OVRP will

be described.

4.3 Solution Approaches

Four different solution approaches or tools were found to be interesting to use

for solving the OVRP of the case study. All approaches were first implemented

on the Poland region in order to find which of them gave the best results, and

consequently, one approach (Lingo) was chosen to solve the Malmo region case.

The alternative solution approaches are:

• Clarke & Wright Savings method

• OptaPlanner - Java

• Lingo

• Transportation Guru (LLamasoft)

4.3.1 Clarke & Wright Savings Method

For this method, the same procedure as described in Chapter 3.4.1 was performed.

The distance table shown in Table 4.2 was used in order to generate a savings table,

shown in Table 4.7.


Sup2 Sup3 Sup4 Sup5 Sup6 Sup7 Sup8 Sup9

Supplier1 2.794 2.788 2.794 2.819 2.823 2.794 2.688 2.687

Supplier2 - 2.789 2.831 2.834 2.794 2.831 2.667 2.666

Supplier3 - - 2.789 2.790 2.789 2.789 2.662 2.662

Supplier4 - - - 2.864 2.795 3.180 2.938 2.912

Supplier5 - - - - 2.823 2.864 2.720 2.721

Supplier6 - - - - - 2.795 2.692 2.692

Supplier7 - - - - - - 2.927 2.902

Supplier8 - - - - - - - 3.271

Table 4.7: Savings in km achieved between each supplier in Poland.

For example, by combining demand from Supplier 1 and Supplier 2 in a route, the

distance saved will be: 1.410 + 1.464 − 80 = 2.794 km, according to Formula 3.7

and Figure 3.8.

When connecting the feasible routes together, the parallel version was used in

order to find the feasible routes. This is further explained in Table 5.1. Finally,

the connection from the depot to the first supplier was eliminated since the case

study deals with the OVRP.

4.3.2 OptaPlanner - Java

One of the method to solve the OVRP case was to use an open source constraint

satisfactory solver, called OptaPlanner. This particular solver is written in the

common programming language JAVA and the source code is released under an

Apache Software License 2.0, which means that users are allowed to reuse the

code for commercial purposes. The solver combines various types of optimization

heuristics and metaheuristics such as Tabu Search (TS), Simulated Annealing (SA)

and Late Acceptance Hill Climbing (LAHC), discussed in Chapter 3.4.1. These

methods should deliver a near-optimum or optimum solution in a timely manner

(OptaPlanner team, 2015).

An integrated development environment (IDE) software called IntelliJ IDEA was

used to run the OptaPlanner source code and an XML editor was used to generate

a code containing all the case study’s predefined parameters of vehicle capacity,

supplier demand and the distances between all parties involved.


The solver initially presumes that a vehicle returns to the depot after it has served

the last customer, as in the traditional VRP formulation. This means that the

solver takes the return trip into account when finding a feasible solution. As

mentioned earlier, this case is an OVRP. This simply means that the vehicles do

not need to return to their starting location after they have served the last stop.

Therefore the source code needed to be configured so that the solver would not

take the final return trip into account. As the OptaPlanner solver provides visual

effects for the user, showing the suppliers locations and routing network, the code

for the Graphical User Interface (GUI) had to be reconfigured as well.

For some reason, the solver would not take in non-integer numbers, so instead of

using the capacity of 13,6 ldm’s, the input for capacity was set to 136 ldm’s. The

demand figures were also converted in this way in order to get correct results.

4.3.3 Lingo

To be able to solve the OVRP case optimally, a software called Lingo from Lindo

Systems Inc. was used. Lingo is a sophisticated but still relatively easy to use

modeling language and an optimizer that can be used to model all kinds of prob-

lems. The software is equipped with a powerful optimization solver that uses

algorithms based on the Branch-and-Bound technique, discussed in Chapter 3.4.2,

that yields the best possible solution for a given problem. To be able to fully

access this function of the software along with unrestricted use of integers and

constraints variables that was needed in this case, an educational research license

was obtained directly from Lindo Systems.

Lindo Systems provides a comprehensive and thorough online user manual on their

website that was indeed used to help with the modeling of the OVRP for this

thesis (Lindo systems inc., 2013). As for the other approaches, the code included

the vehicle capacity, the demand from suppliers and distance matrices.

4.3.4 Transportation Guru

One of the alternative solution methods involved finding an appropriate software

that was actually being used in the industry to solve similar problems as in the

case study. An American based company called LlamaSoft was contacted with


the intention of trying out their software called Supply Chain Guru. LlamaSoft’s

affiliate partners in Stockholm, a company called Optilon AB, provided all neces-

sary licensing and training so the software could be successfully used to solve the

OVRP.

Transporation Guru is a module within the software that is specifically useful for

transportation network design, routing analysis and optimization. The software

module allows the user to include detailed constraints to the network model, mak-

ing it possible to simulate extremely realistic conditions. Moreover, the software

provides a user-friendly environment, making it easy for the user to input the

data and to finally visualize the vehicle routing results on a map (LLamasoft inc.,

2015).

As the data used in this case is limited to the supplier demand, truck capacity and

the inter-distances between stakeholders, only a portion of the software’s capability

was tested.

Similarly to OptaPlanner, Transportation Guru would not take in non-integer

numbers, so the same procedures were made with the capacity of the trucks and

the suppliers demand in order to get the correct results. All data was imported

from predefined MS Excel sheets which included the capacity, the demand and all

distances.

4.4 Surcharge

DeLaval Tumba is responsible for the arrangement and execution of all inbound

transportation to their manufacturing site according to FCA incoterms, but all

transportation activities are sub-contracted to several 3PL carriers.

To cover the transportation cost that is incurred by the 3PL carriers, DeLaval

Tumba uses a certain surcharge that is later added to the end product price. The

surcharge is a fixed percentage that differs between geographical regions according

to Table 4.8.


Region Current Surcharge

Poland 3, 2%

China 8, 0%

Flextronics 2, 5%

External and others 2, 4%

Table 4.8: Surcharge currently used for each defined geographical region.

The Poland and China regions are pretty much self-explanatory, only including

suppliers from those countries. The Flextronics region contains a single high de-

mand supplier located within Sweden. The last category contains all other sup-

pliers within Europe, most of them residing in Sweden.

DeLaval Tumba is interested to see if the correct surcharge percentage is being

used or not for the given regions. The surcharge percentage ratio can be calculated

using historical data with the following equation:

Surcharge ratio =Actual transportation cost

Actual consumption value(4.1)

The actual transportation cost was found by going through incurred invoices and

data from the year 2014, provided by one of the major 3PL carriers. The data ac-

quired could be filtered down to individual suppliers, making it possible to bench-

mark each supplier in a given region.

The actual consumption value refers to the monetary value of supplies used by the

manufacturing site during a given time period. A controller at DeLaval Tumba

provided this information for the year 2014. The level of detail is down to each

component used, but was summarized to each supplier to match the level of detail

in the data of actual transportation cost. The result from this analysis can be

found in Chapter 5.3.

Chapter 5

Results

In this chapter, the results of the case study will be presented. The first section

addresses the results of all the alternative methods follows for both the Poland

and Malmo region. The input used for all methods was the distance matrices, the

demand weeks, and the capacity of trucks, described in Chapters 4.1 and 4.2. The

last section discusses the calculated surcharge ratio for the defined regions.

5.1 Poland Region Results

After applying the different methods on the OVRP case as described in Chapter

4.3, the results were analyzed. The results and a brief description will be presented

in the following sections.

5.1.1 The Savings Algorithm

The descending savings found by following the procedure described in Chapter

4.3.1, can be seen in Table 5.1. As can be seen, two routes were found for each

week using the Savings algorithm. In the case of Supplier 2 and Supplier 5, there

is no demand appearing in the low demand week, and therefore, it is not possible

to use the connections connected to them in that case. In the medium and high

demand weeks, Supplier 1 has a demand exceeding the truck capacity limits of

13,6 ldm’s. Therefore, a separate truck is needed to deliver FTL from Supplier 1

to Tumba in those cases, generating the third route.

47

Chapter 5. Results 48

Savings [km] Connected

suppliers

Low Demand Medium Demand High Demand

3.271 8-9 Route 1 Route 1 Route 1



2.927 7-8 n/a n/a n/a

2.912 4-9 n/a n/a n/a

2.902 7-9 n/a n/a n/a

2.864 4-5 No Demand n/a n/a

2.864 5-7 No Demand Route 1 Route 1

2.834 2-5 No Demand Exceeds Capacity Exceeds Capacity




2.823 1-6 Route 2 Exceeds Capacity Exceeds Capacity


2.795 4-6 n/a n/a n/a

2.795 6-7 Exceeds Capacity n/a n/a

2.794 1-7 Exceeds Capacity n/a n/a



2.794 1-4 n/a n/a n/a


2.789 3-7 Route 1 n/a n/a


Table 5.1: Savings in decending order, relevant connected suppliers and re-sulting routes for each reference week.

From Table 5.1 it is possible to assembly the following possible routes for the low

demand week :

Route 1: Supplier 9 =⇒ Supplier 8 =⇒ Supplier 4 =⇒ Supplier 7 =⇒ Supplier 3 =⇒Tumba

Route 2: Supplier 1 =⇒ Supplier 6 =⇒ Tumba


The routes assembled for medium demand week are:

Route 1: Supplier 9 =⇒ Supplier 8 =⇒ Supplier 4 =⇒ Supplier 7 =⇒ Supplier 5 =⇒Supplier 6 =⇒ Tumba


Route 3: Supplier 1 =⇒ Tumba

Finally, the routes for the high demand week are:




The total kilometers driven and the utilization of the trucks used are then calcu-

lated in order to be able to compare this solution approach to others that follow.

Table 5.2 shows the final results of the Savings method.

Reference Week Total Distance [km] Utilization of trucks

Low demand 3.796 R1: 64%, R2: 51%

Medium demand 5.278 R1: 58%, R2: 88%, R3: 47%

High demand 5.278 R1: 99%, R2: 85%, R3: 62%

Table 5.2: Results from the Savings method, total distance driven and uti-lization of the trucks for each route.

As mentioned earlier, up to three FTLs are sent directly from one of the suppliers.

These routes are not taken into account in these calculations.

5.1.2 OptaPlanner - Java

The output from OptaPlanner was in the form of maps, with the nodes (suppliers)

and arrows between them, so no work had to be put in to interpret the output in

order to get the results. The resulting routes for the low demand week are:




Figure 5.1 shows the output generated from OptaPlanner for the low demand week.

As can be seen, the output is in the form of nodes (suppliers and the manufacturing

site), the desirable links between them and information on how much was fitted

in each truck.

Figure 5.1: The output from OptaPlanner when running the data for the lowdemand week.

The resulting routes for the medium demand week are:


Route 2: Supplier 4 =⇒ Supplier 7 =⇒ Supplier 2 =⇒ Supplier 3 =⇒ Tumba

Figure 5.2 shows the output generated from OptaPlanner for the medium demand

week.


Figure 5.2: The output from OptaPlanner when running the data for themedium demand week.

The resulting routes for the high demand week are:




Figure 5.3 shows the output generated from OptaPlanner for the medium demand

week.


Figure 5.3: The output from OptaPlanner when running the data for the highdemand week.

Table 5.3 shows the accumulated kilometers driven if OptaPlanner is used to find

the results and the associated utilization of the trucks.

Reference Week Total Distance [km] Utilization of trucks

Low demand 3.663 R1: 44%, R2: 71%

Medium demand 3.893 R1: 94%, R2: 99%

High demand 5.116 R1: 71%, R2: 90%, R3: 85%

Table 5.3: Results from OptaPlanner, total distance driven and utilization ofthe trucks for each route.

5.1.3 Lingo

The result file generated by Lingo was a list of all connections possible between

all suppliers. Each possibility was marked with a binary notation, whereas if 1

appeared next to the connection, those suppliers should be connected in a route.

The results files for each reference week can be seen in Tables 5.4, 5.5 and 5.6. It

should be noted that in the tables, DeLaval Tumba is marked as node 1, so each

supplier is marked one number higher than usually in the thesis. In addition, the


counting only goes up to 8 in the low demand week, since two of the suppliers do

not have any demand.

Variable Value Variable Value Variable Value

X( 1, 1) 1.000000 X( 3, 7) 0.000000 X( 6, 5) 0.000000

X( 1, 2) 0.000000 X( 3, 8) 0.000000 X( 6, 6) 0.000000

X( 1, 3) 0.000000 X( 4, 1) 0.000000 X( 6, 7) 0.000000

X( 1, 4) 1.000000 X( 4, 2) 0.000000 X( 6, 8) 0.000000

X( 1, 5) 0.000000 X( 4, 3) 0.000000 X( 7, 1) 1.000000

X( 1, 6) 0.000000 X( 4, 4) 0.000000 X( 7, 2) 0.000000

X( 1, 7) 0.000000 X( 4, 5) 0.000000 X( 7, 3) 0.000000

X( 1, 8) 1.000000 X( 4, 6) 1.000000 X( 7, 4) 0.000000

X( 2, 1) 0.000000 X( 4, 7) 0.000000 X( 7, 5) 0.000000

X( 2, 2) 0.000000 X( 4, 8) 0.000000 X( 7, 6) 0.000000

X( 2, 3) 0.000000 X( 5, 1) 0.000000 X(7, 7) 0.000000

X( 2, 4) 0.000000 X( 5, 2) 0.000000 X( 7, 8) 0.000000

X( 2, 5) 1.000000 X( 5, 3) 1.000000 X( 8, 1) 0.000000

X( 2, 6) 0.000000 X( 5, 4) 0.000000 X( 8, 2) 0.000000

X( 2, 7) 0.000000 X( 5, 5) 0.000000 X( 8, 3) 0.000000

X( 2, 8) 0.000000 X( 5, 6) 0.000000 X( 8, 4) 0.000000

X( 3, 1) 1.000000 X( 5, 7) 0.000000 X( 8, 5) 0.000000

X( 3, 2) 0.000000 X( 5, 8) 0.000000 X( 8, 6) 0.000000

X( 3, 3) 0.000000 X( 6, 1) 0.000000 X( 8, 7) 1.000000

X( 3, 4) 0.000000 X( 6, 2) 1.000000 X( 8, 8) 0.000000

X( 3, 5) 0.000000 X( 6, 3) 0.000000

X( 3, 6) 0.000000 X( 6, 4) 0.000000

Table 5.4: Output from Lingo for the low demand week



X( 1, 1) 1.000000 X( 4, 5) 0.000000 X( 7, 9) 0.000000

X( 1, 2) 0.000000 X( 4, 6) 0.000000 X( 7, 10) 0.000000

X( 1, 3) 0.000000 X( 4, 7) 0.000000 X( 8, 1) 0.000000

X( 1, 4) 0.000000 X( 4, 8) 0.000000 X( 8, 2) 0.000000

X( 1, 5) 1.000000 X( 4, 9) 0.000000 X( 8, 3) 1.000000

X( 1, 6) 0.000000 X( 4, 10) 0.000000 X( 8, 4) 0.000000

X( 1, 7) 0.000000 X( 5, 1) 0.000000 X( 8, 5) 0.000000

X( 1, 8) 0.000000 X( 5, 2) 0.000000 X( 8, 6) 0.000000

X( 1, 9) 0.000000 X( 5, 3) 0.000000 X( 8, 7) 0.000000

X( 1, 10) 1.000000 X( 5, 4) 0.000000 X( 8, 8) 0.000000

X( 2, 1) 1.000000 X( 5, 5) 0.000000 X( 8, 9) 0.000000

X( 2, 2) 0.000000 X( 5, 6) 0.000000 X( 8, 10) 0.000000

X( 2, 3) 0.000000 X( 5, 7) 0.000000 X( 9, 1) 0.000000

X( 2, 4) 0.000000 X( 5, 8) 1.000000 X( 9, 2) 0.000000

X( 2, 5) 0.000000 X( 5, 9) 0.000000 X( 9, 3) 0.000000

X( 2, 6) 0.000000 X( 5, 10) 0.000000 X( 9, 4) 0.000000

X( 2, 7) 0.000000 X( 6, 1) 0.000000 X( 9, 5) 0.000000

X( 2, 8) 0.000000 X( 6, 2) 0.000000 X( 9, 6) 1.000000

X( 2, 9) 0.000000 X( 6, 3) 0.000000 X( 9, 7) 0.000000

X( 2, 10) 0.000000 X( 6, 4) 0.000000 X( 9, 8) 0.000000

X( 3, 1) 0.000000 X( 6, 5) 0.000000 X( 9, 9) 0.000000

X( 3, 2) 0.000000 X( 6, 6) 0.000000 X( 9, 10) 0.000000

X( 3, 3) 0.000000 X( 6, 7) 1.000000 X( 10, 1) 0.000000

X( 3, 4) 1.000000 X( 6, 8) 0.000000 X( 10, 2) 0.000000

X( 3, 5) 0.000000 X( 6, 9) 0.000000 X( 10, 3) 0.000000

X( 3, 6) 0.000000 X( 6, 10) 0.000000 X( 10, 4) 0.000000

X( 3, 7) 0.000000 X( 7, 1) 0.000000 X( 10, 5) 0.000000

X( 3, 8) 0.000000 X( 7, 2) 1.000000 X( 10, 6) 0.000000

X( 3, 9) 0.000000 X( 7, 3) 0.000000 X( 10, 7) 0.000000

X( 3, 10) 0.000000 X( 7, 4) 0.000000 X( 10, 8) 0.000000

X( 4, 1) 1.000000 X( 7, 5) 0.000000 X( 10, 9) 1.000000

X( 4, 2) 0.000000 X( 7, 6) 0.000000 X( 10, 10) 0.000000

X( 4, 3) 0.000000 X( 7, 7) 0.000000

X(4, 4) 0.000000 X(7, 8) 0.000000

Table 5.5: Output from Lingo for the medium demand week



X( 1, 1) 1.000000 X( 4, 5) 0.000000 X( 7, 9) 0.000000

X( 1, 2) 0.000000 X( 4, 6) 0.000000 X( 7, 10) 0.000000

X( 1, 3) 1.000000 X( 4, 7) 0.000000 X( 8, 1) 0.000000

X( 1, 4) 0.000000 X( 4, 8) 0.000000 X( 8, 2) 0.000000

X( 1, 5) 1.000000 X( 4, 9) 0.000000 X( 8, 3) 0.000000

X( 1, 6) 0.000000 X( 4, 10) 0.000000 X( 8, 4) 0.000000

X( 1, 7) 0.000000 X( 5, 1) 0.000000 X( 8, 5) 0.000000

X( 1, 8) 0.000000 X( 5, 2) 0.000000 X( 8, 6) 1.000000

X( 1, 9) 0.000000 X( 5, 3) 0.000000 X( 8, 7) 0.000000

X( 1, 10) 1.000000 X( 5, 4) 0.000000 X( 8, 8) 0.000000

X( 2, 1) 1.000000 X( 5, 5) 0.000000 X( 8, 9) 0.000000

X( 2, 2) 0.000000 X( 5, 6) 0.000000 X( 8, 10) 0.000000

X( 2, 3) 0.000000 X( 5, 7) 0.000000 X( 9, 1) 1.000000

X( 2, 4) 0.000000 X( 5, 8) 1.000000 X( 9, 2) 0.000000

X( 2, 5) 0.000000 X( 5, 9) 0.000000 X( 9, 3) 0.000000

X( 2, 6) 0.000000 X( 5, 10) 0.000000 X( 9, 4) 0.000000

X( 2, 7) 0.000000 X( 6, 1) 0.000000 X( 9, 5) 0.000000

X( 2, 8) 0.000000 X( 6, 2) 0.000000 X( 9, 6) 0.000000

X( 2, 9) 0.000000 X( 6, 3) 0.000000 X( 9, 7) 0.000000

X( 2, 10) 0.000000 X( 6, 4) 0.000000 X( 9, 8) 0.000000

X( 3, 1) 0.000000 X( 6, 5) 0.000000 X( 9, 9) 0.000000

X( 3, 2) 0.000000 X( 6, 6) 0.000000 X( 9, 10) 0.000000

X( 3, 3) 0.000000 X( 6, 7) 1.000000 X( 10, 1) 0.000000

X( 3, 4) 1.000000 X( 6, 8) 0.000000 X( 10, 2) 0.000000

X( 3, 5) 0.000000 X( 6, 9) 0.000000 X( 10, 3) 0.000000

X( 3, 6) 0.000000 X( 6, 10) 0.000000 X( 10, 4) 0.000000

X( 3, 7) 0.000000 X( 7, 1) 0.000000 X( 10, 5) 0.000000

X( 3, 8) 0.000000 X( 7, 2) 1.000000 X( 10, 6) 0.000000

X( 3, 9) 0.000000 X( 7, 3) 0.000000 X( 10, 7) 0.000000

X( 3, 10) 0.000000 X( 7, 4) 0.000000 X( 10, 8) 0.000000

X( 4, 1) 1.000000 X( 7, 5) 0.000000 X( 10, 9) 1.000000

X( 4, 2) 0.000000 X( 7, 6) 0.000000 X( 10, 10) 0.000000

X( 4, 3) 0.000000 X( 7, 7) 0.000000

X(4, 4) 0.000000 X(7, 8) 0.000000

Table 5.6: Output from Lingo for the high demand week


With this information, it was possible to connect the suppliers together and gen-

erate the following routes for each reference week:

For the low demand week, the resulting routes are:



In addition, a result output appeared where the best objective, number of itera-

tions, elapsed runtime and more information could be obtained. This output is

shown in Figure 5.4.

Figure 5.4: Output window in Lingo showing results for the low demand weekin Poland.

For the medium demand week, the following routes were found to be the best:



Route 2: Supplier 4 =⇒ Supplier 7 =⇒ Supplier 2 =⇒ Supplier 3 =⇒ Tumba

The resulting output can be seen in Figure 5.5.

Figure 5.5: Output window in Lingo showing results for the medium demandweek in Poland.

Finally, for the high demand week, the best routes were found to be:




The following result output can be seen in Figure 5.6.


Figure 5.6: Output window in Lingo showing results for the high demandweek in Poland.

Table 5.7 shows the kilometers driven for each reference week, the number of

iterations calculated in the software and the time it took to solve each reference

week scenario.

Reference Week Total Distance

[Km]

Utilization of trucks Iterations Solver

Time [sec]

Low demand 3.663 R1: 44%, R2: 71% 72 0

Medium demand 3.893 R1: 94%, R2: 99% 1.797 1

High demand 5.116 R1: 71%, R2: 90%, R3: 85% 37 1

Table 5.7: Resultsfrom Lingo, total distance driven, utilization of the trucksfor each route, number of iterations and the time it took to solve each week.


5.1.4 Transportation Guru

The output from Transportation Guru was in the form of tables and maps with the

different routing, combining all the suppliers to the manufacturing site in Tumba.

Figure 5.7 shows the first table generated from the software, showing how many

trucks are needed for each reference week, how much distance each truck drives,

how many stops each truck takes, and the utilization of it’s capacity.

Figure 5.7: Results output from Transportation Guru (1/2).

In addition, another table was generated, showing more detailed information re-

garding each route. Figure 5.8 shows the second output table.


Figure 5.8: Results output from Transportation Guru (2/2).

The resulting routes are listed in the following paragraphs.

The routes for the low demand week are:



Figure 5.9 demonstrates the low demand week graphically, automatically generated

by the software.


Figure 5.9: A map showing the routes found for the low demand week inPoland.

The routes for the medium demand week are:




Figure 5.10 demonstrates the medium demand week graphically.


Figure 5.10: A map showing the routes found for the medium demand weekin Poland.

The routes for the high demand week are:


Route 2: Supplier 9 =⇒ Suppler 8 =⇒ Tumba

Route 3: Suppler 2 =⇒ Tumba

Figure 5.11 demonstrates the high demand week graphically.


Figure 5.11: A map showing the routes found for the high demand week inPoland.

Table 5.8 shows the analyzed results and further information regarding them, using

Transportation Guru.

Reference Week Total Distance [km] Utilization of trucks Solver

Time [sec]

Low demand 3.668 R1: 71%, R2: 44% 19,6

Medium demand 5.116 R1: 79%, R2: 85, R3: 29% 18,7

High demand 5.116 R1: 96%, R2: 71%, R3: 79% 44,6

Table 5.8: Results from Transportation Guru: total distance driven, utiliza-tion of the trucks for each route and the time it took to find each route.


5.1.5 Comparison of the Solution Approaches

The graph shown in Figure 5.12 represents all methods used in terms of kilometers

driven for each week. The y-axis represents the kilometers driven and the different

methods appear on the x-axis, grouped by each selected reference week.

Figure 5.12: Comparison of the different methods, based on kilometers drivenin each reference week.

The different columns represent each method and as can be noted, Lingo and

OptaPlanner generate the best routings in terms of km driven.

5.1.6 Cost Comparison

Since companies often base their decisions on cost, the main 3PL carrier was asked

to give quotations for the routes of the methods that showed the best results, which

were both OptaPlanner and Lingo. The comparison can be seen in Table 5.9.


Demand Milk-run

cost[SEK]

LTL cost [SEK]

Low

R1 23.213 16.928

R2 28.325 30.345

Medium

R1 28.134 33.583

R2 28.343 32.691

High

R1 23.213 21.403

R2 28.234 31.718

R3 23.404 22.431

Table 5.9: LTL and FTL with Milk-run cost for the optimal routing in eachreference week.

From Table 5.9, it is notable that it is not always cost efficient to use the proposed

milk-runs since the milk-run quotation sometimes exceeds the LTL cost. Therefore,

the most cost-efficient way is to have a mix of milk-runs and LTL transportation.

Table 5.10 shows what solutions should be selected for each reference week and

the cost decrease in percentages compared to shipping everything via LTL as is

currently is being done.

Demand week Feasible composition Cost reduction

Low R2 + LTL 4%

Medium R1 + R2 14%

High R2 + LTL 5%

Table 5.10: Feasible selection of routes and the cost reduction of selectingthem compared to only shipping via LTL

The resulting routes shown in Table 5.10 can be visualized in the following figures.

Figure 5.13 shows the selected routes for a low demand week. For this scenario,

only one FTL route with a milk-run is recommended as it seems to be more cost


beneficial to ship the goods from the more remote suppliers via LTL routing, using

the 3PL carrier network. For this case, two of the suppliers are idle and have no

planned shipments.

Figure 5.13: Proposed routes for a low demand week

Figure 5.14 shows the selected routes for a medium demand week. For this sce-

nario, all the region’s suppliers have a planned shipment within two recommended

FTL routes in a milk-run.


Figure 5.14: Proposed routes for a medium demand week

Figure 5.15 shows the selected routes for a high demand week. Although the

demand is high, it is only recommended to have one FTL route in a milk run and

the other shipments via LTL within the 3PL carrier’s network.

Figure 5.15: Proposed routes for a high demand week

The results will be further discussed in Chapter 6.


5.2 Malmo Region Results

The data analyzed for the Malmo region was used as an input for Lingo. The

output was in terms of one route, both in the case of using 15 suppliers and 11

suppliers.

For all 15 suppliers, the route became:

Route 1: Supplier 14 =⇒ Supplier 15 =⇒ Supplier 4 =⇒ Supplier 1 =⇒ Supplier 2 =⇒Supplier 3 =⇒ Supplier 5 =⇒ Supplier 7 =⇒ Supplier 6 =⇒ Supplier 8 =⇒Supplier 12 =⇒ Supplier 13 =⇒ Supplier 10 =⇒ Supplier 9 =⇒ Supplier 11 =⇒Tumba

When the last four suppliers are taken out of the equation, the remaining 11 end

up in the following route:

Route 1: Supplier 2 =⇒ Supplier 1 =⇒ Supplier 4 =⇒ Supplier 3 =⇒ Supplier 5 =⇒Supplier 7 =⇒ Supplier 6 =⇒ Supplier 8 =⇒ Supplier 9 =⇒ Supplier 10 =⇒Supplier 11 =⇒ Tumba

Table 5.11 shows the kilometers driven for each reference week, the number of

iterations calculated in the software and the time it took to solve each week.

Scenario Total

Distance [km]

Utilization of trucks Iterations Solver Time

[sec]

15 suppliers 584 R1: 88% 3.638 1

11 suppliers 423 R1: 78% 66.552 9

Table 5.11: Results from Lingo, total distance driven, utilization of the trucksfor each route, number of iterations and the time it took to solve each week.

5.2.1 Cost Comparison

Similarly to the Poland region, a major 3PL carrier was asked to give cost quota-

tions on these specific routes. The cost can be seen in Table 5.12, compared to the

LTL cost found with data from the same 3PL carrier described in Chapter 4.2.


Scenario LTL cost

[SEK]

Milk-run cost

[SEK]

Change in cost

15 suppliers 19.357 26.460 26,8%

11 suppliers 18.274 18.101 ≈ 0%

Table 5.12: LTL and Milk-run cost compared for both scenarios.

Since the cost change for the scenario of 11 suppliers is so small, the cost change is

approximated to 0. In the case of 15 suppliers, the cost would increase by 26,8%

if FTL with milk-runs would be implemented.

5.3 Surcharge Results

The total factory consumption of supplies for the whole factory in 2014 was ap-

proximately 534 MSEK. At the same time, the corresponding inbound transporta-

tion cost was around 11 MSEK. Table 5.13 shows these figures and how they are

allocated between the different geographical regions. The surcharge percentages

presented are based on actual cost information gathered from the controller de-

partment in DeLaval Tumba. They are considered to be as correct as possible for

the case of 2014.

Surcharge calculations (2014 data, SEK)

China Flextronics Poland Other TOTAL:

Actual consumption 13.580.199 73.488.694 74.247.896 392.497.188 553.813.976

Actual transport cost 901.732 358.651 3.806.258 5.947.716 11.014.357

Current surcharge 8,00% 2,50% 3,20% 2,40% 2,66%

Recommended surcharge 6,64% 0,49% 5,13% 1,52% 1,99%

Table 5.13: Allocation of consumption data and transportation cost in 2014.Recommended surcharge based on those numbers is shown.

Furthermore, the table shows the currently used surcharge percentages and the

calculated recommended surcharge percentage, using Equation 4.1, based on the

actual data provided.

In the following chapter, the results obtained will be discussed.

Chapter 6

Conclusion and Discussion

In this chapter, the results of the preceding chapters will be analyzed and discussed

in detail. Firstly, a discussion on the case study’s results is represented. After that

the findings on the actual transportation cost and surcharge ratio used within the

company will be addressed. The chapter is concluded with thoughts about possible

future work.

6.1 Poland Region

As the results in Chapter 5 show, significant savings can be obtained by improving

the inbound transportation for the Poland region.

Currently, no certain inbound transportation strategy is in place, other than sub-

contracting all transportation activities to 3PL carriers, as mentioned in Chapter

1. This thesis work has shown that if DeLaval Tumba plans the consolidation of

shipments on their own terms, substantial savings can be realized.

Considering and comparing the results obtained from all the alternative methods,

shown in Figure 5.12, the methods solved with Lingo and OptaPlanner returned

the optimal solution in terms of km driven for all the reference weeks. As distance

is highly correlated with transportation cost when it comes to truck transportation,

those solutions were further analyzed and cost quotations on the proposed milk-run

routes were obtained. Comparison of the milk-run routing cost with the regular

LTL cost for the same shipments can be seen in Table 5.9. It can be seen that the

proposed milk-runs are not always more economically beneficial than sending the

71

Chapter 6. Conclusion and discussion 72

same shipments via LTL. It turns out that a vehicle, with the capacity of 13,6 ldm,

has to be utilized up to 86% in order for a direct shipment, FTL or a FTL with

milk-run, to pay of. This was calculated with data from the main 3PL carrier.

The proposed solution and the transportation strategy, DeLaval Tumba should

follow in Poland, is therefore to combine these methods accordingly. If a vehicle

can be utilized more than 86%, it should always be economically beneficial to

form a milk-run, consolidating shipments from various suppliers. Otherwise, the

company should use the LTL network of the current 3PL carrier. The combination

of LTL and FTL with milk-runs for each reference week can be seen in Table 5.10

and visualized in Figures 5.13, 5.14 and 5.15. The potential savings were 4% for

the low demand week, 14% for the medium demand week and 5% for the high

demand week.

The actual transportation cost for the Poland region in 2014 was substantially

higher than expected as shown in Table 5.13 and further discussed in section 6.3.

With the proposed changes implemented, it can be reasoned that the surcharge in

the region will be lowered.

6.1.1 Backhaul Options

DeLaval Tumba uses specialized steel carriers to transport certain types of com-

ponents from one of their supplier in the Poland region. To be able to reuse these

carriers, they are sent back to the supplier with the FTL vehicles coming from

that particular supplier, making the FTL routing a round trip. It is worth noting

that, according to the TSM department in DeLaval Tumba, these vehicles would

otherwise be going empty to Poland, so they can be hired for a reasonably low

price.

There has been some discussions within DeLaval Tumba to change the design of

the steel carriers, making them foldable, so they can be stacked more efficiently

in the vehicles. The idea is to make sure all the carriers fit into the FTL vehicle

and therefore an additional and more expensive vehicle hire is not necessary.

With an implementation of the suggested mix of milk-run routing and LTL, there

would be one more FTL coming to Tumba during low and high demand weeks and

two more FTL vehicles during a medium demand week. This will give the Tumba


factory more options regarding sending back packaging material to the suppliers

in Poland if needed.

6.1.2 New Supplier or Change in Demand

The results achieved from this thesis are good to use when a new supplier is

recruited to the Poland region. Using the same data from the 3PL carrier as for

calculating the LTL and FTL cost, it is notable that it is possible to find a cut-off

point for each zip-code within Poland and see when it is feasible for a supplier to

send FTL instead of LTL. This cut-off point proved to be 11,7 ldm’s for all the

different zip-codes in Poland, or 86%. Therefore it is easy to take a quick decision

when a new supplier has high demand. If the demand does not exceed 11,7 ldm’s,

there are several questions DeLaval Tumba can ask themselves in order to find the

best strategy for the new supplier. They are:

1. Where is the supplier located?

2. How much demand in ldm’s does the supplier have? (per week, every two

weeks or monthly?)

3. If there is a truck in a route in the same area, is there available space in it?

4. Is the demand takted?

5. How is the seasonality in the demand?

If a new supplier is in the vicinity of a current route, it is presumably a good

idea to add the supplier’s demand to the route given that it can be fitted in the

truck in a given seasonality. However, if there is no space in the truck, the new

information should be added to the existing data, and Lingo or Optaplanner should

be run again in order to find a new optimum routing with the new supplier. This

procedure is also valid if the demand changes for an existing supplier located in

Poland.

Moreover, if the demand is supposed to go to a takted production, it is important

to think about when the goods are supposed to arrive at the factory in order to

have no backlogs. The seasonality has to be taken into account as well, similarly

as was done for the demand in Poland.


6.1.3 Potential Yearly Savings

In the Poland region’s case study, three reference weeks were chosen; a low demand

week, a medium demand week and a high demand week, as previously shown in

Figure 4.1. Vehicle routing cost and potential savings for those weeks were then

presented in Table 5.9 and Table 5.10 respectively.

If all the weeks of the year, shown on the graph in Figure 4.1, were to be generalized

into either low, medium or high demand weeks so their demand requirements

would be approximately fulfilled, one could estimate the potential savings on a

yearly basis. Figure 6.1 shows how the three reference weeks have been arranged

onto all the fluctuating demand weeks of the year.

Figure 6.1: The three reference weeks generalizing the actual demand fluctu-ation for a whole year in the Poland region.

According to Figure 6.1, the whole year consists of 10 low demand weeks, 28

medium demand weeks and 12 high demand weeks. Table 6.1 summarizes the

potential savings according to the figures in Table 5.9.


Potential yearly savings [SEK]

Demand week # of weeks Cost for proposed routes LTL cost Yearly Savings

Low 10 452.531 472.697 20.166 4,3%

Medium 28 1.594.110 1.855.868 261.758 14,1%

High 12 864.830 906.681 41.851 4,6%

Year total 50 2.911.471 3.235.237 323.767 10,0%

Table 6.1: Estimated yearly savings

According to these results, the potential yearly savings are estimated to be around

323.800 SEK that account to about 10% cost reduction compared to the currently

used transportation strategy. It should be noted again that direct FTL shipments

from the main supplier are not taken into account in this table.

6.1.4 Trade-Offs With Inventory Cost

By implementing this new transportation strategy for the Polish suppliers at

DeLaval Tumba, it should be noted that the inventory status of the transported

goods might change. DeLaval Tumba has an inventory cost percentage of 6%.

This means that the yearly inventory cost for a given component is 6% of the

article’s value.

According to the average daily usage of articles supplied from Poland and their

standard price, the cost of adding one day of inventory is 30.000 SEK. This is

calculated by using the standard holding cost of 6% of the value at hand that

DeLaval charges for inventory.

With this information, it is possible to calculate how the inventory cost will change

by implementing the new strategy to the Poland region. Table 6.2 shows how

much the total demand is per week and how much of that demand will undergo

changes in transportation by using milk-runs. Note that these calculations have

the assumption that the manufacturing only takes place 50 weeks per year, since

the data received showed little-to no manufacturing in week 1 and 52.


Type of demand week

Low Medium High

Total demand per week [ldm’s] 42,8 53,5 74,3

Milk-run demand per week [ldm’s] 9,6 26,3 12,3

Table 6.2: Total demand shipped in each reference week and the part whichwill undergo changes and use milk-run demand

With this information it is possible to assume that the total demand for a whole

year adds up to around 2817,6 ldm’s per year. Note that the demand and the fluc-

tuation has been generalized to the reference weeks, as mentioned in the preceding

chapter.

Now, by calculating the weighted average percentage of the demand transported

with FTL milk-runs, it can be calculated that the total changing demand is 34,8%

of the total yearly demand given pre-discussed assumptions.

According to the major 3PL carrier, the time it takes to transport LTL with their

transportation network is 4 days, and the time it takes for them to transport FTL

is 3 days. Now it is assumed that the time for transporting one route of FTL milk-

runs is the same as transporting FTL from only one supplier. Therefore, 34,8% of

all the demand will arrive to DeLaval Tumba one day sooner than usually. This

means that it is possible to decrease the safety inventory stock level by one day.

Since one added day of inventory for all the demand in Poland is estimated to

cost 30.000 SEK, it is possible to assume that by decreasing the inventory stock

by one day for all the demand in Poland, it will lead to savings of 30.000 SEK.

Therefore, by implementing the suggested transportation strategy, it is possible

to save 30.000 SEK ·0, 348 = 10.434 SEK in inventory holding cost.

6.2 Malmo Region

As can be seen in Chapter 5.2.1, no savings are achieved by introducing the FTL

milk-run instead of the usual LTL transportation within the Malmo region. The

main reason for this is the low amount of demand from each suppliers compared

to Poland’s suppliers.


On a regular week, the combined demand from each of the region’s suppliers

wouldn’t even fill a standard 13,6 ldm truck, meaning that a single truck would be

used for the milk-run. The problem at hand will therefore become a TSP instead

of a VRP.

Furthermore, the Malmo region’s suppliers are currently shipping frequently dur-

ing a regular week using the LTL strategy. By using a FTL milk-run vehicle, all

shipments for the week would need to be combined, making it a less attractive

option in terms of the factory takt time, inventory cost and already mentioned

transportation cost.

When looking at the transportation cost for the region on a yearly basis, it was

observed, that the transportation ratio of the monetary value of goods is estimated

to be around 1,9%. The Malmo region is within the geographical surcharge region

of External and Other, where the currently used surcharge percentage to cover the

transportation cost is 2,4%.

It is worth noting that during the data analysis, it was discovered that only around

20% of the transportation cost in 2014 was charged by the regular 3PL carrier.

This suggests that large parts of the shipments are arranged and charged by the

suppliers themselves even though there is a contract in place with negotiated

transportation rates. This implies that the transportation cost for the region can

be reduced with proper coordination.

6.3 Surcharge

From the resulting proposed surcharges shown in Chapter 5.3, it can be seen that

the surcharge percentage actually used is far from what it should be in order to

only cover the corresponding transportation cost.

In the year 2014, DeLaval Tumba overcharged the inbound transportation con-

siderably, generating significant surplus for the factory unit. From Table 5.13, it

can be seen that the geographical regions of China, Flextronics, and External and

Other are the main cause for this.

The surcharge percentage for the China region is 1,36% higher than it should be,

contributing around 185.000 SEK to the 2014 surplus. The Flextronics region,


that consists of only one supplier, is generating around 1,5 MSEK in surplus as

the percentage is around 5 times higher than it should be. The External and Other

region is the largest region in terms of number of suppliers and overall value, has

a surplus of around 3,5 MSEK and a surcharge percentage around 0,9% too high.

The Poland region is the only region that is not contributing to the 2014 surplus.

During that year, the surcharge percentage was around 1,9% too low, generating

a deficit within the region of around 1,4 MSEK.

When taking a closer look at the allocation of transportation cost within the

Poland region, a more detailed picture was depicted. It seems that some of the

suppliers have a very high transportation cost ratio. In the most extreme case

for one of the suppliers, the transportation cost was 29% of the total value they

supplied in the year 2014.

The Poland region is very interesting in terms of transportation. The transporta-

tion cost for Poland was 34,6% of the total inbound transportation cost for the

whole manufacturing unit in 2014. At the same time, supplies from the region rep-

resented only 13,9% of the total factory consumption in terms of monetary value.

It is clear that with ever increasing activity in the region, including three new

suppliers in the case study, the transportation cost for Tumba will only increase

compared to the 2014 data. With all this in mind, it is apparent that there is

room for improvement within the region, as previously shown.

6.4 Future Work

There are numerous tasks that DeLaval Tumba can perform in the near future

after the discoveries of this thesis. The first thing should be to adapt the surcharge

calculations in all four regions. In addition, DeLaval Tumba should increase the

number of regions when it comes to deciding the surcharge to find the appropriate

add-on percentage on the transportation cost for each supplier. Furthermore, the

surcharge percentage should be re-calculated on a regular basis, and especially

when a change occurs within the inbound transportation strategy.

It should be noted that suppliers located in Stockholm next to the manufacturing

site fall into the same surcharge category as suppliers in Spain for example. It


might be interesting for DeLaval Tumba to take a better look at the surcharge

division and further divide the regions.

After applying the different alternative methods to the Poland region, it can be

noted that, by following the method descriptions, it should be an easy task for

the company to apply the methods on the rest of the areas where DeLaval Tumba

has its suppliers. In order to do so, the data needed from those areas has to be

handled and generalized to the right parameters. This brings the matter to the

next point, information flow between suppliers and DeLaval Tumba.

It is considered an important task to undertake and analyze the written contract

between DeLaval Tumba and all its suppliers. It should be a priority that all

suppliers need to give a minimum amount of information about the products they

are supplying and how they supply them. As mentioned earlier, some suppliers in

Poland and Malmo tend to arrange their shipments themselves. It is considered

the best option for DeLaval Tumba to combine and generalize all written contracts

with their 3PL carriers in order to make the routing decision smoother. Therefore,

DeLaval Tumba should renegotiate all the supplier contracts so that every supplier

plays by the same rules when it comes to transportation to Tumba.

Furthermore, there seems to be room for improvement in connecting the different

departments at DeLaval Tumba better. This was noted when gathering data.

Some kind of information improvement project could be set up in order to make

this communication problem smaller. Improving the information flow between the

departments can mean a great time-saver in the future when other projects like

this thesis will be performed.

When the methods are applied to the rest of the regions, the results can be im-

proved by making the codes for Lingo and OptaPlanner more advanced. The first

thing that could be implemented in the codes is making it possible to use a wider

range of trucks with different capacity limits. This change could make the routing

very different from the solutions obtained in Chapter 5, and information about cost

quotation should be gathered again. In addition, time windows could be added

to the codes in order to gain more precise results, with more specific information

about when a truck can pick up supplies at a certain supplier and how the working

schedule for each driver is. Furthermore, it could be calculated how much it would

take to add a consolidation point, for example in Warsaw and how much handling

and inventory cost would be added to the results. This additional consolidation


point could then be added to the programming codes, and a cost quotation gotten

for the resulting routes.

When combining different suppliers to one transportation route, the lead time can

in some cases change. With this change it could be good to perform a study of

the inventory levels at DeLaval Tumba, and if necessary and possible, to level out

the demand for each week so it fits to the transportation routing.

The methods used for this case study have the possibility to be extended in a way

that it can become possible to find the best location available for a consolidation

hub. In addition, the methods can be implemented on the outbound transportation

as well.

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