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Resource Allocation Problems Under Uncertainty in Humanitarian Supply Chains

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Resource Allocation Problems Under Uncertainty in Humanitarian Supply Chains RESOURCE ALLOCATION PROBLEMS UNDER UNCERTAINTY IN HUMANITARIAN SUPPLY CHAINS A Thesis Presented to The Academic Faculty by Melih Celik In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Industrial and Systems Engineering Georgia Institute of Technology August 2014 Copyright c 2014 by Melih Celik RESOURCE ALLOCATION PROBLEMS UNDER UNCERTAINTY IN HUMANITARIAN SUPPLY CHAINS Approved by: Professor Ozlem Ergun, Advisor Professor Eric Feron School of Industrial and Systems School of Aerospace Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Pinar Keskinocak, Advisor Professor Julie Swann School of Industrial and Systems School of Industrial and Systems Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Alan Erera Date Approved: June 19, 2014 School of Industrial and Systems Engineering Georgia Institute of Technology To Mom, Dad, and Simi iii ACKNOWLEDGEMENTS This thesis work could not have been complete without the help and support of many people. It is a great pleasure to express my gratitude to those who have helped me in achieving this goal, and I apologize in advance to the ones whose names are not mentioned in this short space. My advisors, Dr. Ozlem¨ Ergun and Dr. Pınar Keskinocak, have played a signif- icant role not only in supervising this thesis work, but also in shaping up my views on conducting research, teaching, and academic life in general. Their advices and the examples they have set for me will always shed light into my future career. I would also like to acknowledge the contributions of Drs. Julie Swann and Dima Nazzal to various parts of this thesis work. Along with them, the members of my read- ing committee, Dr. Alan Erera and Dr. Eric Feron have provided useful comments and feedback, which have helped improve the quality of the work significantly and provided guidance for future research directions. Working at the Center for Health and Humanitarian Logistics over the last five years has allowed me to collaborate with a number of colleagues. In particular, the experience I gained from working with Alvaro´ Lorca, Ben Johnson, and Kael Stilp has been very valuable. Mallory Soldner has provided significant input for the fourth chapter of the thesis. I am also indebted to the faculty and staff of the Georgia Tech School of Industrial and Systems Engineering for providing a high quality research environment and the opportunity to interact with a diverse group of researchers. I am especially privileged to have met Drs. Dave Goldsman and Craig Tovey, to have been able to share their wisdom and experience, and to have gotten to know them on a personal level. iv My decision to pursue a Ph.D. and an academic career was shaped during my undergraduate and master's level studies at the Industrial Engineering Department of the Middle East Technical University. It gives me great pleasure and excitement to be joining their faculty at the end of my doctoral work. I can never pay back the encouragement and mentoring that my master's thesis advisor, Dr. Haldun S¨ural, has provided ever since my undergraduate sophomore year. Any verbal description of his impact on my academic life would be an understatement. I am also grateful to the fellow Ph.D. students at Georgia Tech ISyE, where I have been able to meet a diverse group of good friends from all over the world and extend my friendship with the ones I had known from before. While mentioning all of their names will not be possible here, I would particularly like to thank Yao-Hsuan Chen, who has been my harshest critic, biggest source of encouragement, and the most patient and understanding listener at the same time; O˘guzhan Ozl¨uand¨ Evren G¨ul,who have always been ready to share even completely random things about life; and Can Oz¨uretmen,with¨ whom I have endured long but mostly enjoyable working hours during the three years we shared an office together. Last but not the least, I would like to express my gratitude to the members of my beloved family. My parents Meral and Salih C¸elik have been able to endure the distance we have been separated with over the last five years, and have never ceased to make me feel their love and support along the way. My brother Semih C¸elik, who is on the verge of obtaining his own doctoral degree, has been my best friend for almost thirty years. Every single achievement I have gained in life is completely devoted to them. v TABLE OF CONTENTS DEDICATION .................................. iii ACKNOWLEDGEMENTS .......................... iv LIST OF TABLES ............................... ix LIST OF FIGURES .............................. x SUMMARY .................................... xiv I INTRODUCTION ............................. 1 1.1 Stochastic Post-Disaster Debris Clearance . .4 1.2 Perishable Commodity Allocation with Multiple Distribution Loca- tions and Demand Types . .6 1.3 Network Design for the Supply Chain of Specialized Nutritious Foods8 II THE POST-DISASTER DEBRIS CLEARANCE PROBLEM UN- DER INCOMPLETE INFORMATION ................ 10 2.1 Literature Review . 14 2.2 Problem Description and Model . 18 2.2.1 The Stochastic Debris Clearance Problem (SDCP) . 18 2.2.2 The POMDP Model . 23 2.2.3 Extension to Regional Updates . 29 2.3 Illustrative Examples . 31 2.3.1 An Illustrative Example on Path Networks with Unit Demand 31 2.3.2 An Illustrative Example to Compare Different Solution Ap- proaches to SDCP . 34 2.3.3 Examples on Infinite Paths with Unit Demand . 36 2.3.4 A Continuous Approximation . 39 2.4 Heuristic Approaches . 41 2.4.1 A Heuristic Based On a Continuous-Time Approximation . 41 2.4.2 Heuristics for Approximate Tree Search . 45 2.5 Structural Results on Simple Networks . 46 vi 2.6 Computational Experiments . 57 2.6.1 Instance Generation . 58 2.6.2 Benchmark Approaches . 61 2.6.3 Computational Results . 63 2.7 Conclusions and Further Research Directions . 73 III PERISHABLE COMMODITY ALLOCATION IN HUMANITAR- IAN SUPPLY CHAINS WITH MULTIPLE DEMAND TYPES: EFFECTS OF USAGE POLICY AND CENTRALIZATION .. 75 3.1 Introduction . 75 3.2 Literature Review . 78 3.3 Problem Definition and Models . 83 3.3.1 Characterization of Optimal Allocation Under Prioritization 87 3.3.2 Characterization of Optimal Allocation Under First-Come, First- Served Usage . 91 3.4 Structural Results . 94 3.4.1 Structural Results for a Single Distribution Location and Un- capacitated Warehouse . 94 3.4.2 Relative Performance Comparison for Prioritization and FCFS Usage Policies . 97 3.4.3 Structural Results for Centralized Systems . 100 3.5 Computational Experiments . 107 3.5.1 Instance Generation . 108 3.5.2 Benchmark Approaches . 110 3.5.3 Computational Results . 111 3.6 Conclusions and Further Research Directions . 121 IV A CASE STUDY ON THE SUPPLY CHAIN OF SPECIALIZED NUTRITIOUS FOODS .......................... 123 4.1 Introduction . 123 4.2 A Typical SNF Supply Chain and Challenges in Supply Chain Man- agement . 127 4.2.1 A Typical SNF Supply Chain Structure and Flow of Events . 127 vii 4.2.2 Challenges in SNF Supply Chain Management . 129 4.2.3 An Alternative Network Structure with Intermediate Hubs . 136 4.2.4 Objectives of the Case Study . 138 4.3 Literature Review . 139 4.3.1 Case Studies on Commercial and Humanitarian Food Distri- bution . 140 4.3.2 Multi-Echelon Inventory Management . 141 4.3.3 Joint Transportation and Inventory Management . 142 4.3.4 Joint Facility Location and Inventory Management . 142 4.3.5 Perishable Inventory Management . 143 4.3.6 Optimizing Equity of Allocations . 144 4.3.7 Contributions of the Chapter . 145 4.4 Mathematical Models and Solution Approaches . 145 4.4.1 Models for the Hub System . 146 4.4.2 Models for the District Warehouse System . 152 4.4.3 Models for Equity of Distribution . 157 4.5 Computational Experiments . 160 4.5.1 Instance Generation . 162 4.5.2 Benchmark Approaches . 164 4.5.3 Computational Results . 165 4.6 Conclusions and Further Research Directions . 174 V CONCLUSIONS AND FURTHER RESEARCH DIRECTIONS 177 APPENDIX A | FURTHER COMPUTATIONAL RESULTS FOR RANDOM INSTANCES ......................... 180 APPENDIX B | PROOFS OF STATEMENTS IN CHAPTER 3 183 APPENDIX C | SPECIFICATIONS FOR SPECIALIZED NUTRI- TIOUS FOODS ............................... 195 REFERENCES .................................. 196 viii LIST OF TABLES 1 Notation . 20 2 Number of blocked edges for each instance . 59 3 A summary and comparison of proposed and benchmark heuristics, with ? indicating problem sizes solvable up to 40 blocked roads; ?? up to 100 blocked roads, ??? up to 200 blocked roads, and ???? more than 200 blocked roads . 62 4 Average upper bound gaps and heuristic gaps for POMDP-C along with CPU times (in seconds) . 64 5 Average perfect information gaps of the proposed and benchmark ap- proaches on random instances . 66 6 Average perfect information gaps of the proposed and benchmark ap- proaches on earthquake scenario instances . 67 7 Average CPU times (in seconds) for the proposed and benchmark ap- proaches on random instances . 67 8 Average CPU times (in seconds) for the proposed and benchmark ap- proaches on earthquake scenario instances . 68 9 Summary of the effects of belief structure on solution quality . 69 10 Notation . 85 11 Summary of findings for decentralized, partially centralized, and com- pletely centralized systems under FCFS and prioritization policies . 106 12 Summary of parameters used in the computational experiments, with base case values given in bold . 110 13 The sets, parameters, and decision variables used in the models . 147 14 Parameter settings for the computational experiments . 162 15 Average perfect information gaps for random instances under pij fol- lowing a uniform distribution with parameters U(0:5; 1) and two supply nodes.................................... 181 16 Average perfect information gaps for random instances under pij fol- lowing a uniform distribution with parameters U(0:5; 1) and clearance starting from outside the disaster area .
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