Mathematical Models of Seaside Operations in Container Ports and their Solution A thesis submitted for the degree of Doctor of Philosophy Department of Mathematical Sciences University of Essex by Ghazwan Alsoufi July, 2017 Dedicated to My wife for her patience, kindness, help and support. My dear children Humam, Harith and Reham. My affectionate parents and all who continually pray for my fortune. Acknowledgements I would like to express my deepest gratitude to Almighty Allah, for giving me strength, courage and the best blessing to complete this work and guide me all the way in my life. This thesis is the culmination of input, work and encouragement of many people who have helped and accompanied me for the four years that I have spent at University of Essex. First of all, my deepest gratitude goes to my family for their endless love and unconditional support. I could not have achieved this without the continuous support and love of my family. Mom, thank you for everything you did. I would like to express my sincerest thanks to my supervisors, Prof. Abdel Salhi and Dr. Xinan Yang for steering me through and pushing me further than I can imagine. Their eloquence, sharpness and great sense of humor have impressed me deeply and made my every meeting and discussion with them always full of joy and unforgettable memories. They have not only provided me their professional expertise and valuable guidance I needed to complete my Ph.D. study, but also been real friends and true mentors. I feel extremely fortunate to work with them. They led me to expand my knowledge, extend my vision and share with me their academic insights. They have always provided me the freedom to choose my research subjects and encouraged me to be involved in various types of research activities. During our academic discussions, I was very impressed by their enthusiasm and ability in thinking extreme iii iv while keeping the real life applicability of the research high. I learned a lot from them and I am very grateful to have them as my advisor. A huge debt of gratitude is extended to my dear wife Sarah ... There are no words that can help me to express my gratitude to you. You were always with me on rainy days and at sleepless nights. You smiled when I smiled and you provided the shoulder when I cried. You kept me going and you made this real. You are my pulse, my blood, my love...other best Visiting the port of Felixstowe brought us meaningful insights into the fascinating world of shipping in general and more specifically into maritime container transportation. Therefore I would also like to express sincere thanks to Tom Corkhill and Stephen Peck for supplying us with a number of important ideas. For financial support, many many thanks go to the Iraqi Ministry of Higher Education and Scientific Research for sponsoring my scholarship. One of the best parts of attending Essex University has been the wonderful opportunity to be surrounded by the many interesting, intellectually stimulating and impressive fellow students. The list includes: Dr. Omar, Dr. Khattab, Dr. Wesam, Dr. Manhal and Dr. Majeed. Friends in Iraq: Mohammed, Ibraham and Ammar, who make my personal life colorful and shining. Finally, specially thanks to all Department of Mathematical Sciences staff for their help and Essex University for their services. Declaration The work in this thesis is based on research carried out in the Department of Mathematical Sciences, University of Essex, United Kingdom. No part of this thesis has been submitted elsewhere for any other degree or qualification, and it is all my own work, unless referenced, to the contrary, in the text. Copyright c 2017 by Ghazwan Alsoufi. “The copyright of this thesis rests with the author. No quotations from it should be published without the author’s prior written consent, and information derived from it should be acknowledged.”. v Abstract Operational Research and Optimization are fundamental disciplines which, for decades, provided the real-world with tools for solving practical problems. Many such problems arise in container ports. Container terminals are important assets in modern economies. They constitute an important means of distributing goods made overseas to domestic markets in most countries. They are expensive to build and difficult to operate. We describe here some of the main operations which are faced daily by decision makers at those facilities. Decision makers often use Operational Research and Optimization tools to run these operations effectively. In this thesis, we focus on seaside operations which can be divided into three main problems: the Berth Allocation Problem (BAP), • the Quay Crane Assignment Problem (QCAP), • the Quay Crane Scheduling Problem (QCSP). • Each one of the above is a complex optimization problem in its own right. However, solving them individually without the consideration of the others may lead to overall suboptimal solutions. For this reason we will investigate the pairwise combinations of these problems vi vii and their total integration In addition, several important factors that affected on the final solution. The main contributions of this study are modelling and solving of the: Robust berth allocation problem (RBAP): a new efficient mathematical model is for- • mulated and a hybrid algorithm based on Branch-and-Cut and the Genetic Algorithm is used to find optimal or near optimal solutions for large scale instances in reasonable time. Quay crane assignment and quay crane scheduling problem (QCASP): a new math- • ematical model is built to simultaneously solve QCASP and a heuristic based on the Genetic Algorithm is developed to find solutions to realistic instances in reasonable time. Berth allocation, quay crane assignment and quay crane scheduling problem (BA- • CASP): an aggregate model for all three seaside operations is proposed and to solve realistic instances of the problem, an adapted variant of the Genetic Algorithm is implemented. Keywords: berth allocation; quay crane assignment; quay crane scheduling; terminal operations; genetic algorithm Contents Acknowledgements iii Declaration v Abstract vi 1 Introduction 2 1.1 Containerization and Trends in Maritime Logistics: Research Background .2 1.2 An Overview of the Container Terminal and Quayside Operations . .6 1.3 Research Objectives, Scope and Organization . .9 2 Literature Review 13 2.1 The Berth Allocation Problem (BAP) . 13 2.2 The Quay Crane Assignment Problem (QCAP) . 17 2.3 The Quay Crane Scheduling Problem (QCSP) . 18 2.4 The Berth Allocation and Quay Crane Assignment Problem (BACAP) . 21 2.5 The Quay Crane Assignment and Scheduling Problem (QCASP) . 23 2.6 The Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problem (BACASP) . 25 viii Contents ix 2.7 Methodology . 28 2.8 Solution approaches . 29 2.8.1 Exact approaches . 29 2.8.2 Meta-heuristics . 36 2.9 Genetic Algorithm . 39 2.9.1 Solution representation: chromosome . 41 2.9.2 Fitness function . 41 2.9.3 Generating next populations . 41 2.9.4 Stopping criteria . 42 2.10 Summary . 43 3 Robust berth allocation problem 44 3.1 Introduction . 44 3.2 Mathematical formulation . 47 3.2.1 Assumptions . 47 3.2.2 Parameters . 48 3.2.3 Binary decision variables . 49 3.2.4 Continuous decision variables . 49 3.2.5 The mathematical model . 50 3.3 Numerical example . 53 3.4 B&C and GA hybrid algorithm for BAP . 54 3.4.1 Solution representation: chromosome . 54 3.4.2 Initial population . 55 Contents x 3.4.3 Fitness function with a penalty term . 55 3.4.4 Generating next populations . 58 3.5 Computational experiments . 60 3.6 Summary . 62 4 Quay crane assignment and quay crane scheduling problem 63 4.1 Introduction . 63 4.2 Mathematical formulation . 66 4.2.1 Assumptions . 67 4.2.2 Indices . 67 4.2.3 Parameters . 68 4.2.4 Binary decision variables . 69 4.2.5 Continuous decision variables . 70 4.2.6 The mathematical model . 70 4.3 Numerical examples . 76 4.4 Application of GA to QCASP . 78 4.4.1 Solution representation: chromosome . 78 4.4.2 Solution validation . 80 4.4.3 Evaluation of fitness . 81 4.4.4 Generating next populations . 82 4.5 Computational experiments . 83 4.5.1 Test results . 84 4.6 Summary . 85 Contents xi 5 Berth allocation, quay crane assignment and quay crane scheduling problem 87 5.1 Introduction . 87 5.2 Mathematical formulation . 89 5.2.1 Assumptions . 90 5.2.2 Indices . 91 5.2.3 Parameters . 91 5.2.4 Binary decision variables . 92 5.2.5 Continuous decision variables . 93 5.2.6 The mathematical model . 94 5.3 Numerical examples . 99 5.4 Application of GA to BACASP . 102 5.4.1 Solution representation: chromosome . 102 5.4.2 Solution validation . 103 5.4.3 Evaluation of fitness . 103 5.4.4 Generating next populations . 104 5.5 Computational experiments . 105 5.6 Summary . 108 6 Conclusions and future work 110 6.1 Main conclusions . 110 6.2 Suggestions for further work . 114 List of Figures 1.1 The OECD Industrial Production Index and indices for world GDP, mer- chandise trade and seaborne shipments (1975 - 2014) (base year 1990 = 100)4 1.2 Global containerized trade, 1996-2015 (million TEUs and percentage annual change) . .5 1.3 Schematic representation of a container terminal (Steenken et al., 2004) . .6 1.4 A container terminal at the Port of Felixstowe . .8 3.1 Illustration of no overlap in time between vessels i and j ........... 51 3.2 Illustration of overlap in time between vessels i and j ............. 51 3.3 Illustration of no overlap in location between vessels i and j ......... 52 3.4 Illustration of overlap in location between vessels i and j ..........