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Optimising Throughput in the Hunter Valley Coal Chain Using Integer Programming Techniques Optimising Throughput in the Hunter Valley Coal Chain Using Integer Programming Techniques Mohsen Reisi Ardali M.Sc. (Mathematics) School of Mathematical and Physical Sciences The University of Newcastle Thesis submitted for the degree of Doctor of Philosophy in Mathematics March 2014 Statement of Originality The thesis contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to the final version of my thesis being made available worldwide when deposited in the University's Digital Repository, subject to the provisions of the Copyright Act 1968. Mohsen Reisi Ardali iii Acknowledgements I wish to express my sincere appreciation to those who have contributed to this thesis and supported me in one way or the other during this amazing journey. First and foremost, I am deeply indebted to my supervisors Prof. Natashia Boland and Prof. Martin Savelsbergh whose positive attitude and insightful thinking have guided me throughout this research. Without the stimulating discussions, guidance, and support, this work would not have been possible. Very special thanks to my previous co-supervisor Dr. Faramroze Engineer for his support in the first year of my PhD. My sincere gratitude is reserved for Dr. Hamish Waterer and the Operations Research group at the University of Newcastle by providing frequent feedbacks and opportunities to discuss my research. I would like to thank the support of the Australian Research Council and the Hunter Valley Coal Chain Coordinator, under the ARC Linkage Project grant LP0990739. I appreciate the help of the CSIRO in supplying data, models and documentation that enabled my project to get off the ground. I would also like to take this opportunity to thank Dr Andreas Ernst from the CSIRO for his useful suggestions. I really appreciate personnels at the HVCCC for their feedback and provision of essential data and information. I am thankful for the help I received from all the people in the Department of Mathematics. Dr. Masoud Talebian, Hadi Charkhgard, Rachel Bunder, Simranjit Kaur, Reena Kapoor, thanks for being there for me through the years. Last but not least, I would like to appreciate my lovely wife, Afsaneh, who supported me in every possible way to see the completion of this work. I owe a lot to my parents, who encouraged and helped me at every stage of my personal and academic life, and longed to see this achievement come true. v Contents Chapter 1. Introduction 1 1.1. The Hunter Valley Coal Chain: An Overview4 1.2. Planning and Scheduling in the Hunter Valley Coal Chain7 1.2.1. Simulation8 1.2.2. Throughput Assessment Tool9 1.3. Integer Programming Background 10 1.3.1. Integer programming 10 1.3.2. Symmetry in Integer Programming 14 1.3.3. Implicit Modelling 15 1.3.4. Polyhedral Analysis 17 1.3.5. Lifting 18 1.4. Contributions 19 1.5. Thesis Outline 20 Chapter 2. Demand Driven Throughput Assessment for the HVCC 23 2.1. Introduction 23 2.2. Literature review 23 2.3. Demand Driven Throughput Assessment Models 27 2.3.1. A Train-job Based Model 27 2.3.2. A Component-job Based Model 34 2.3.3. Strategies to Increase Efficiency 36 2.4. A Computational Study 39 2.4.1. Data sets and their key features 39 2.4.2. Efficiency 43 2.4.3. Throughput and System Analysis 45 2.5. Final Remarks 51 Comparison with Singh, Sier, Ernst, Gavriliouk, Oyston, Giles, and Welgama (2012) 52 Chapter 3. Implicit Modeling: Load Point Based Model 55 3.1. Introduction 55 vii viii CONTENTS 3.2. Load point Based Model 57 3.3. Equivalency of Component and Load Point Based Models 60 3.3.1. Proving sufficient conditions for validity of the implicit model 60 3.3.2. Application to the load point model 66 3.4. Implementation 69 3.5. A Computational Study 72 3.6. Final remarks 74 Chapter 4. Production Scheduling with Flexible Deadline Problem 77 4.1. Introduction 77 4.2. One demand with constant capacity 78 4.2.1. The General Model 79 4.2.2. PSFDP-1C and Lot-sizing with Constant Batches 79 4.2.3. Polyhedral Analysis 83 4.2.4. Example 85 4.2.5. Separation 100 4.2.6. A complete reformulation of PSFDP-1C with only facet-inducing inequalities 102 4.3. One demand with varying capacity 112 4.3.1. Separation 125 4.3.2. A complete reformulation of PSFDP-1V with only facet-inducing inequalities 128 4.4. Multiple demands with constant capacity 137 4.4.1. Example 138 4.4.2. Valid inequalities 140 4.4.3. A sequential procedure for a priori generation of inequalities 145 4.5. Various Arrivals 148 4.5.1. Valid inequalities 150 4.6. Implementation 152 4.7. A Computational Study 153 4.8. Final remarks 156 Chapter 5. Conclusion and Future Work 159 Appendix A. Column Generation 163 Bibliography 167 List of Figures 1.1 Hunter Valley Coal Chain2 1.2 A (simplified) schematic representation of a typical coal export system.5 1.3 Different components are piled beside each other to form a stockpile.6 1.4 Reclaiming direction.6 1.5 P 0 is closer to conv(S) than P 11 1.6 Cutting plain αx ≥ β cuts out optimal solution x∗ 12 2.1 Vessel tonnages 39 2.2 Number of cargoes per vessel 40 2.3 Minimum assembly times for the cargoes of a vessel 40 2.4 Frequency distribution of vessel inter-arrival times 41 2.5 Example of 6-clustering 46 2.6 Number of vessels with delay in each terminal on each day 48 2.7 Number of vessels in queue in each terminal on each day 48 2.8 Tonnage of stockpiles that are being built in each terminal on each day 49 2.9 Tonnage of stockpiles that are being built, held, or reclaimed in each terminal on each day 49 2.10Percentage of stockyard used by the stockpiles that are being built, held, or reclaimed on each day 50 2.11Number of trains unloaded at each terminal on each day 51 3.1 Two ways to assign 8 and 6 train-jobs to c1 and c2 56 3.2 An instance with C not sortable 65 4.1 One demand must be met before its deadline 79 4.2 One demand, D = 9;C = 4; m = 2;T = 4 86 4.3 2-demand, D1 = 4;D2 = 5;C = 3; m = 2;T = 4 139 ix x LIST OF FIGURES 4.4 Various arrivals, D1 = 4;D2 = 5;C = 3; m1 = 1; m2 = 2;T = 4 149 List of Tables 2.1 Model parameters 28 2.2 New model parameters 35 2.3 Terminal characteristics 39 2.4 Minimum total delay incurred by the vessels arriving in the main period 42 2.5 Maximum total delay incurred by the vessels arriving in the main period 42 2.6 Results for different combinations of ∆− and ∆+ 44 2.7 Formulations and strategies results 44 2.8 Average number of vessels and the average delay per vessel 47 3.1 Load point based model parameters 57 3.2 An instance with C not sortable 65 3.3 Component based model results 73 3.4 Load point based model results 73 3.5 Separation 74 4.1 Optimal objective values 154 4.2 Problem size 155 4.3 Violated inequalities 156 xi Abstract The Hunter Valley Coal Chain (HVCC) is the largest coal export operation in the world. It concerns the transport of coal from mines located in the Hunter Valley to the Port of Newcastle in New South Wales, Australia. Approximately 1700 coal vessels are loaded at the Port of Newcastle and more than 150 million tonnes of coal is exported each year. The HVCC is a complex system involving 14 producers operating 35 coal mines, 27 coal load points, 2 rail track owners, 4 above rail operators, 3 coal loading terminals with a total of 8 berths, and 9 vessel operators. The coal export supply chain is managed by the Hunter Valley Coal Chain Co- ordinator (HVCCC). One of the most important and far-reaching decision problems faced by HVCCC is the planning of the long-term capacity. The demand for coal continues to grow and thus the export through the Port of Newcastle is expected to increase in the future. Therefore, the infrastructure needs to be upgraded and the capacities in the system expanded. As upgrading infrastructure and expanding the capacity is extremely expensive, a careful and thorough system analysis is crucial to ensure that investments are made in the right place and at the right time. HVCCC uses an elaborate and detailed simulation model of the HVCC to analyse and assess the throughput of the system, to detect and identify any bottlenecks in the system, and to investigate and explore the benefits of infrastructure upgrades and expan- sions. As the simulation model is very detailed, it takes a considerable amount of time to run, and as a consequence, a few scenarios can be analysed. We develop an integer programming based decision support tool that quickly assesses the throughput of a coal export supply chain for a given level of demand. The tool can be used to rapidly evaluate a number of infrastructures for several future demand scenarios in order to identify a few that should to be investigated more thoroughly using the detailed simulation model.
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