ALFRED ASASE THESIS

104 Pages·2012·1.51 MB·English

THE TRANSPORTATION PROBLEM
CASE STUDY :( GUINESS GHANA LIMITED)
BY
ALFRED ASASE

A THESIS SUBMITED TO THE DEPARTMENT OF
MATHEMATICS
FACULTY OF PHYSICAL SCIENCE AND TECHNOLOGY
KUMASI

IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE

(INDUSTRIAL MATHEMATICS)

OCTOBER 2011
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Declaration

I hereby declare that this submission is my own work towards the MSc and
that, to the best of my knowledge, it contains no material previously published
by another person, nor material, which has been accepted for the award of any
other degree of university, except where due acknowledgement has been made
in the text

Alfred Asase : .. ....………............ ...................

(PG2007408) Signature Date

(Student‟s Name and ID)

Mr. Kwaku Darkwah: …… …………. …. .……….

(Supervisor) Signature Date

Mr. Kwaku Darkwah: ………………. ………….

(Head of Department) Signature Date

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Dedication
This study is dedicated to Almighty God, Asase family, my wife Olivia
and my two lovely daughters Ohemaa and Awuraakua.

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Acknowledgements

First and foremost, I thank God the Almighty for given me this opportunity and
carrying me through this thesis successfully.
This thesis could not have been completed without the support and encouragement
from several people. I am deeply indebted to my supervisor, Mr. Kwaku Dakwah, for
his excellent direction, invaluable feedback, his constructive suggestions, detailed
corrections, support and encouragement played enormous role resulted in this
successful project.
I would like to extend my gratitude to all the academic and administrative staff of the
department of mathematics of KNUST.
I also own thanks and appreciate to the entire Asase family for their encouragement
and support.
I thank the Managers of Guinness Ghana Limited-Kumasi, for providing the data for the
study.
Finally, this effort would not be possible without my wife; her efforts and sacrifices

have been of great helped towards the completion of this thesis.

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Abstract
The proposed transportation model of manufacturing goods to customer
(Key Distributors) is considered in this research. The data gathered were modelled as a
Linear Programming model of transportation type and represent the transportation
problem as tableau and solve it with the computer software solver to generate an
optimal solution.
This transportation model will be useful for making strategic decisions by the logistics
managers Guinness Ghana LTD in making optimum allocation of the production
from the two plants (KAASI and ACHIMOTA) to the various customers(key
distributors) at a minimum transportation cost.

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Table of Contents

Content Page
Declaration................................................................................................................................................ i.
Dedication…………………………….................................................................................................. ii.
Acknowledgements………………………........................................................................................... iii.
Abstract............................................................................................................................. iv

CHAPTER 1: INTRODUCTION
1.1 A Brief Review of the Transportation Problem........................................................................ 1
1.2.0 Background to the Study. …..................................................................................................... 3
1.2.1 Background of company....................................................................................................... 6
1.2.1.1 COMPANY PROFILE.............................................................................................................. 6
1.2.1.3 Company Brands... ............................................................................................................. 7
1.2.1.4 Manufacturing................................................................................................................... 7
1.2.1.5 Warehouse......................................................................................................................................... 7
1, 2.16 Distribution............................................................................................................................... 8
1.3 Problem Statement. ......................…………………………........................................................... 8
1.4 Objective............................................................................................................................ 8
1.5 Methodology.................................................................................................................... 8
1.6 Justification........................…………………………………....................................... 9
1.7 Organization of Thesis.............................…………………………................................. 9

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CHAPTER 2: LITERATURE REVIEW

2.1 Definition................................................................................................................... 11
2.2 Literature Review....................................................................................................... 11

CHAPTER 3: METHODOLOGY
3.1 Introduction............................................................................................................... 19
3.2 Transportation problem.............................................................................................. 19
3.3 Mathematical Formulation............................................................................................. 20
3.3.1 The Decision variables........................................................................................ 21
3.3.2 The Objective Function........................................................................................ 21
3.3.4 The Constraints..................................................................................................... 22
3.4 Transportation Tableau............................................................................................ 25
3.5 Network Representation of Transportation Problem.................................................. 26
3.6. Solution for a Transportation Problem....................................................................... 29
3.6.1 Flow Chart Solution For the transportation Problem..................................................... 29
3.6.2 Solution Algorithm For the transportation Problem...................................................... 30
3.6. 3 Finding Initial Basic Feasible Solution of Balanced Transportation Problems.......... 31
3.6.3.1 Northwest Corner Method.................................................................................. 31
3.6.3.2 The Minimum Cell Cost Method....................................................................... 36
3.6.3.3 Vogel‟s Approximation Method......................................................................... 39
3.6.4 Methods for Solving Transportation Problems to Optimality............................... 43
3.6.4.1 An Optimal Solution.......................................................................................... 43
3.6.4.2 Stepping Stone Method...................................................................................... 45
3.6.4.3 The Modified Distribution Method.................................................................... 53
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3.7 Solving Transportation Problem with Mixed Constraints........................................ 57
3.7.21 Mathematical Model for the Transportation Problem with Mixed Constraints.... 58
3.7.2 Zero Point Method......................................................................................... 61
3.7.4 Optimal More-For-Less Procedure.......................................................................... 63
3.8 Sensitivity Analysis for the Transportation Problem................................................. 68

CHAPTER 4: DATA COLLECTIONS AND ANALYSIS

4.0 Introduction......................................................................................................... 69
4.1 Data Collection............................................................................................... 70
4.2 Data Source...................................................................................................... 70
4.3 JULY07-JUNE08 TRANSPORTATION MATRIX FOR GGL PROBLEM.... 71
4.3.1 Formulation Problem...................................................................................... 72
4.3.2 Optimal Solution-July2007-June2008......................................................... 73
4.3.3 Computational Procedure................................................................................ 75

4.3.4 Results and Discussions............................................................................ 76
4.3.5 The sensitivity Analysis..................................................................................... 78

4.4 JULY08-JUNE09 TRANSPORTATION MATRIX FOR GGL PROBLEM.... 79
4.4.1 Formulation Problem....................................................................................... 80
4.4.2 The Management Scientist Solution (July2008-June2009).......................... 81
4.3.4 Results and Discussions........................................................................... 84

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CHAPTER 5: CONCLUSION AND RECOMMEMDATION

5.1 Conclusion...................................................................................................... 86
5.2 Recommendations........................................................................................... 87

REFERENCES...................................................................................................... 88
APPENDIX............................................................................................................. 91

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LIST OF FIGURES
Figure
page
Figure 1: Network Representation of the transportation problem............................... 26
Figure 2: The flow chart showing the transportation problem approach…………….. 29

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