LOCATION-ALLOCATION-ROUTING APPROACH TO SOLID WASTE COLLECTION AND ...

239 Pages·2017·1.62 MB·English

LOCATION-ALLOCATION-ROUTING APPROACH
TO SOLID WASTE COLLECTION AND DISPOSAL
By
ADELEKE, OLAWALE JOSHUA
Matric Number: CUGP120438
MARCH, 2017
LOCATION-ALLOCATION-ROUTING APPROACH TO SOLID WASTE
COLLECTION AND DISPOSAL
By
ADELEKE, OLAWALE JOSHUA
B.Tech Mathematics (Ogbomoso)
M.Sc Mathematics (Ilorin)
Matric Number: CUGP120438
A THESIS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS, COLLEGE OF
SCIENCE AND TECHNOLOGY, COVENANT UNIVERSITY, OTA, IN PARTIAL
FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF Ph.D DEGREE IN
INDUSTRIAL MATHEMATICS
MARCH, 2017
ACCEPTANCE
This is to attest that this thesis is accepted in partial fulfilment of the requirements for the
award of the degree of Doctor of Philosophy in Industrial Mathematics, College of Science
and Technology, Covenant University, Ota.
Philip John Ainwokhai ...............................
Secretary, School of Postgraduate Studies Signature & Date
Prof. Samuel T. Wara ................................
Dean, School of Postgraduate Studies Signature& Date
i
DECLARATION
I, ADELEKE, Olawale Joshua, (CUGP120438), declare that this research was carried
out by me under the supervision of Prof. Aderemi Oluyinka Adewumi of the Department of
Computer Science, School of Mathematics, Statistics and Computer Science, University of
KwaZulu Natal, Westville Campus, Durban, South Africa and Prof. Samuel Azubuike Iyase
of the Department of Mathematics, Covenant University, Ota, Nigeria. I attest that the
thesis has not been presented either wholly or partly for the award of any degree elsewhere.
All sources of data and Scholarly information used in this thesis are duly acknowledged.
ADELEKE Olawale Joshua ...................0.9./0.3./.2.0.1.7..
Signature & Date
ii
CERTIFICATION
We certify that this thesis titled “Location-Allocation-Routing Approach to Solid Waste
Collection and Disposal” is an original work carried out by ADELEKE, Olawale Joshua,
(CUGP120438), in the Department of Mathematics, College of Science and Technology,
Covenant University, Ota, Ogun State, Nigeria, under the supervision of Prof. A. O.
Adewumi and Prof. S. A. Iyase. We have examined and found the work acceptable for
the degree of Doctor of Philosophy in Industrial Mathematics.
Prof. Aderemi O. Adewumi . . . . ........................
Supervisor Signature & Date
Prof. Samuel A. Iyase ................................
Co-Supervisor Signature & Date
Dr. Timothy A. Anake ...............................
Acting Head of Department Signature & Date
Prof. Olabode M. Bamigbola ............................
External Examiner Signature & Date
Prof. Samuel T. Wara ................................
Dean, School of Postgraduate Studies Signature & Date
iii
DEDICATION
To God Almighty, the Giver and Sustainer of my life, for His abiding grace and presence all
through the course of this study.
To my wife, Victoria Ajibola Adeleke, for her unwavering support towards the comple-
tion of this thesis.
To our daughter, ModupeOluwa Peace Adeleke, whose arrival during the course of my study
brought additional joy.
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ACKNOWLEDGMENT
I would like to acknowledge the following people for their contributions towards the success
of this work.
Foremost, my profound gratitude goes the Visioner and Chancellor of Covenant University,
Dr. David O. Oyedepo, for establishing the platform on which this research was conducted.
His wealth of wisdom is indeed a source of inspiration to me and many others. May the Lord
bless him with length of years and more fruitful labour in His Vineyard. The management
of Covenant University and the leadership of the School of Postgraduate Studies are deeply
appreciated. I thank my examiners and assessors for their great contributions and and
constructive criticisms. God bless all of them.
My heartfelt appreciation goes to my supervisor, Prof. A. O. Adewumi, who used his
wealth of experience to provide necessary guidance and valuable suggestions. Thank you
Sir for affording me the rare opportunity to visit the School of Mathematics, Statistics and
ComputerScience(SMSCS)oftheUniversityofKwazulu-Natal(UKZN),WestvilleCampus,
Durban, South Africa. This is an experience I will cherish and appreciate forever. Sir, God
blessyouandrewardyouabundantly. AlsotomyCo-supervisor, Prof. S.A.Iyase, fortaking
time to read through the work and for providing valuable suggestions on how to improve
the contents of the work.
TheimmediatepastActingHeadofDepartmentofMathematics,Dr. E.A.Owoloko,current
Acting Head of Department of Mathematics, Dr. T. A. Anake and other faculty and Staff
of the Department of Mathematics are deeply appreciated for their constructive criticisms
and suggestions in the various seminars.
Furthermore, I deeply appreciate Dr. Michael Olusanya, Dr. Martins Arasomwan, Akinyelu
Ayobami, Alochukwu Alex Somto and other members of Optimization Group of the Depart-
ment of Computer Science, UKZN, Westville campus, for providing necessary assistance and
materials for the numerical computations in this thesis and for their various constructive
and valuable contributions. Also in this class are all the members of Deeper Life Campus
Fellowship, UKZN, Westville Campus, for their love and care all through my stay in UKZN.
I cannot forget the warm affections of Dr. Moses and Raphel Angulu, my residence and
office mates respectively, both of who are citizens of Kenya. I thank them for being my
friends.
My appreciation also goes to Robert Fourer of AMPL Optimization Inc., for providing
necessary assistance and materials needed for coding and running the models on AMPL.
Thanks especially for answering many of my questions directly. I owe much to him for the
results in this thesis.
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I am totally short of words in expressing my gratitude to my parents, Dcn. & Mrs. G.
O. Adeleke, and to my siblings (Jacob, Matthew, Joseph, Samson and Thomas). I cannot
forget the words of encouragement and prayers of my in-laws, the Ogundele’s family. I
deeply appreciate them all for their unalloyed supports and understanding.
Finally, I must say a big thank you to my wife, Victoria, and daughter, Peace, for being
such an ever-refreshing spring of happiness to me. I thank God for blessing me with them.
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TABLE OF CONTENTS
Acceptance i
Declaration ii
Certification iii
Dedication iv
Acknowledgment vi
Table of Content vi
List of Tables x
List of Figures xii
List of Abbreviations xv
List of Symbols xvi
List of Appendices xvii
Abstract xviii
CHAPTER ONE: INTRODUCTION 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 The Concept of Optimization . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2 Classification of Optimization Problems . . . . . . . . . . . . . . . . 12
1.1.3 Deterministic Optimization Problems . . . . . . . . . . . . . . . . . . 14
1.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Significance of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Research Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.1 Integer Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.2 Lagrangian Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.6.3 Sub-gradient Optimization . . . . . . . . . . . . . . . . . . . . . . . . 34
1.7 Limitation and Scope of the Study . . . . . . . . . . . . . . . . . . . . . . . 34
1.8 Definition of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.9 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
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CHAPTER TWO: LITERATURE REVIEW 37
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Vehicle Routing Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.1 Capacitated Vehicle Routing Problem . . . . . . . . . . . . . . . . . . 38
2.2.2 Vehicle Routing Problem with Time Windows . . . . . . . . . . . . . 44
2.2.3 Periodic Vehicle Routing Problem . . . . . . . . . . . . . . . . . . . . 48
2.2.4 Vehicle Routing Problem with Split Delivery . . . . . . . . . . . . . . 51
2.2.5 Dynamic Vehicle Routing Problem . . . . . . . . . . . . . . . . . . . 51
2.3 Common Solution Techniques for FLP and VRP . . . . . . . . . . . . . . . . 57
2.4 Applications of Lagrangian Relaxation and Sub-gradient Optimization Meth-
ods to FLP and VRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.5 Identification of Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
CHAPTER THREE: METHODOLOGY 67
3.1 Lagrangian Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1.1 Some Properties of Lagrangian Dual Function . . . . . . . . . . . . . 70
3.1.2 Construction of Lagrangian Relaxation . . . . . . . . . . . . . . . . . 74
3.2 Sub-gradient Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.1 Formulation of Solid Waste Collection Model . . . . . . . . . . . . . . 82
3.3.2 Formulation of Solid Waste Disposal Model . . . . . . . . . . . . . . 85
3.4 Analysis of Solid Waste Collection Model . . . . . . . . . . . . . . . . . . . . 87
3.5 Relaxation, Reformulation and Analysis of SWD Model . . . . . . . . . . . . 93
3.6 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.7 Data Description and Characteristics . . . . . . . . . . . . . . . . . . . . . . 98
3.7.1 Description and Characteristics of Data Sets for Implementing Solid
Waste Collection Model . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.7.2 Description and Characteristics of Data Sets for Implementing Solid
Waste Disposal Model . . . . . . . . . . . . . . . . . . . . . . . . . . 103
CHAPTER FOUR: RESULTS 104
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 Results from the Implementation of the SWC Model . . . . . . . . . . . . . 104
4.3 Results from the Implementation of SWD Model . . . . . . . . . . . . . . . . 121
CHAPTER FIVE: DISCUSSION 140
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.2 Discussion of Results on the Implementation of SWC Model . . . . . . . . . 140
5.3 Discussion of Results on the Implementation of SWD Model . . . . . . . . . 141
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