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Approaches to Solving the Express Shipment Service Network Design Problem

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Approaches to Solving the Express Shipment Service Network Design Problem APPROACHES TO SOLVING THE EXPRESS SHIPMENT SERVICE NETWORK DESIGN PROBLEM A Thesis Presented to The Academic Faculty by Leah Josefine Ruckle In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Aerospace Engineering Georgia Institute of Technology August 2018 Copyright c 2018 by Leah Josefine Ruckle APPROACHES TO SOLVING THE EXPRESS SHIPMENT SERVICE NETWORK DESIGN PROBLEM Approved by: Prof. Dimitri Mavris, Advisor Prof. Graeme Kennedy School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Prof. Brian German Dr. Elena Garcia School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Prof. Alejandro Toriello Date Approved: July 9, 2018 School of Industrial & Systems Engineering Georgia Institute of Technology To Rohini Ralby, my Guru. iii ACKNOWLEDGEMENTS Thank you to all the people who have helped me on this journey and made this dissertation possible. First and foremost, thank you to my advisor, Prof. Dimitri Mavris who believed in me before I even set foot on campus. Thank you for all of the things that you have taught, shown, and done for me. A special thank you as well to the members of my doctoral committee, Professors Brian German, Alejandro Toriello and Graeme Kennedy, and Dr. Elena Garcia. I am grateful for your insightful questions, feedback and guidance which undoubtedly made this dissertation richer. Thank you as well to my wonderful boyfriend, Matt Daskilewicz. Finishing this dissertation these past few months would not have been possible without your selfless support. Thank you for being my sounding board, cooking me dinner every night when I worked late, giving me ample hugs, and most of all, being my best friend. I love you, Matthew. I look forward to our future adventures together. Thank you as well to my Guru, Rohini Ralby. You have been with me every step of the way since before I can remember. I so greatly appreciate your steadfast guidance and Love. Thank you so much for your support and daily phone calls these past several months, and all that I have learned from you over the years. It is no exaggeration to say that I would not be where I am today without you. Thank you as well to my parents, Melanie and Keith for encouraging my curiosity about the world and my interest in building things, no matter how many legos you stepped on or pried out of the vacuum cleaner. Finally, thank you to all my friends who have supported and cheered for me along the way, including (but not limited to) Adam Cox, Mallory Rose, David Pate, Xiaofan Fei, Kelly Collett, Erica Feldscher, David Soud, Ian Ralby, and Aaron Ralby. iv TABLE OF CONTENTS DEDICATION .................................. iii ACKNOWLEDGEMENTS .......................... iv LIST OF TABLES ............................... x LIST OF FIGURES .............................. xiii SUMMARY .................................... xv I INTRODUCTION AND MOTIVATION ............... 1 II PROBLEM CHARACTERIZATION ................. 9 2.1 The Express Shipment Problem.................... 10 2.2 Scope of Express Shipment Carriers Today.............. 10 2.2.1 Problem Scope.......................... 12 2.3 Movement of Packages Through the Express Shipment Network... 14 2.3.1 Last Mile Service and Line Haul Service............ 15 2.3.2 Activities............................. 16 2.3.3 Important Activity Times, Cycles and Phases......... 17 2.4 Packages Aggregated as Commodity Flows.............. 18 2.5 Air Fleet Considerations........................ 19 2.6 Air Network Topology.......................... 20 2.7 Data Set................................. 22 2.7.1 Facility Locations........................ 22 2.7.2 Sort Capacity.......................... 24 2.7.3 Product Types and Commit Days............... 24 2.7.4 Commodity Demand...................... 26 2.7.5 Vehicle Fleet and Hull Count.................. 27 2.7.6 Cost............................... 28 2.8 Summary................................. 29 v III EXPRESS SHIPMENT SERVICE NETWORK DESIGN: MOD- ELING THE EXPRESS SHIPMENT PROBLEM ......... 31 3.1 Modeling Logistics Problems as Mixed Integer Programs....... 31 3.2 Network Design Problems........................ 34 3.2.1 Network Design Problem Formulation............. 37 3.2.2 Service Network Design Problem Formulations........ 39 3.3 Express Shipment Service Network Design Problem......... 43 3.3.1 Time-Space Graphs....................... 45 3.3.2 Express Shipment Service Network Design Problem Formulation 46 3.4 Summary................................. 51 IV METHODS FOR SOLVING MIXED INTEGER PROGRAMS, THE ESSND AND RELATED PROBLEMS ................ 52 4.1 A Brief Overview of Solution Approaches for Mixed Integer Programs 52 4.1.1 Linear Programming Solution Methods............ 53 4.1.2 Monolithic Solution Methods for Mixed Integer Programming 54 4.1.3 Decomposition Solution Methods for Mixed Integer Program- ming............................... 61 4.1.4 Heuristic and Metaheuristic Solution Methods for Mixed In- teger Programming....................... 64 4.2 Express Shipment Service Network Design Problem Analysis and So- lution Approaches............................ 67 4.2.1 Collaboration Between MIT and UPS............. 67 4.2.2 ESSND Problem Solution Methods.............. 70 4.2.3 ESSND Problem Analysis.................... 74 4.3 Solution Approaches for Related Problems.............. 77 4.3.1 Relevant Survey Papers..................... 77 4.3.2 Lettermail/Postal Package Delivery Problems......... 78 4.3.3 Passenger Airline Problems................... 79 4.3.4 Less-Than-Truckload Problems................. 83 4.3.5 Other Transportation Planning & Logistics Problems.... 85 vi 4.3.6 Other Network Design Problems................ 87 4.4 Summary................................. 90 V RESEARCH PLAN ............................ 91 5.1 Solution Methods............................ 91 5.2 Heuristic Decomposition-Based Research Questions.......... 95 5.2.1 Discipline Definition....................... 97 5.2.2 Discipline Arrangement..................... 99 5.2.3 Improvements to the Sequential Algorithm.......... 101 5.3 Benders Decomposition-Based Research Questions.......... 104 5.4 Experimental Testbed.......................... 106 5.5 Summary................................. 109 VI SOLVING THE ESSND PROBLEM USING A MONOLITHIC APPROACH ................................. 111 6.1 Creation of the Time-Space Graph................... 112 6.1.1 Network Creation in the Literature.............. 112 6.1.2 Network Creation for the Express Shipment Problem..... 113 6.2 Defining Commodity Routing Options................. 118 6.3 Generating Vehicle Movement Options................. 121 6.4 Results.................................. 122 6.4.1 Computational Testbed..................... 122 6.4.2 Baseline Problem Instance................... 123 6.4.3 Unreduced Problem Instance.................. 126 6.5 Sensitivity Studies............................ 127 6.5.1 Number of Airports....................... 128 6.5.2 Product Set........................... 129 6.5.3 Temporal Scope......................... 130 6.5.4 Consolidation Opportunities.................. 131 6.5.5 Secondary Sort Threshold.................... 133 6.5.6 Formulation Relaxations.................... 135 vii 6.6 Summary................................. 138 VII HEURISTIC DECOMPOSITION ................... 139 7.1 Research Questions for the Development of the Heuristic Decomposi- tion Approach.............................. 140 7.2 Discipline Definition........................... 145 7.2.1 Physical Decomposition: Temporal............... 147 7.2.2 Physical Decomposition: Spatial................ 150 7.2.3 Functional Decomposition.................... 155 7.2.4 Refinement of the Discipline Definition Hypothesis...... 162 7.3 Discipline Arrangement......................... 163 7.3.1 Fixed-Point Iteration-Based Solution Generation Approach. 166 7.3.2 Package Routing with Aircraft Problem............ 170 7.3.3 Basic Sequential Algorithm................... 177 7.4 Collapsed Product Set Sequential Algorithm............. 182 7.4.1 Collapsed Product Set Package Routing Problem....... 182 7.4.2 Collapsed Product Set Sequential Algorithm......... 188 7.4.3 Collapsed Product Set Sequential Algorithm with Flexible De- ferred Volume.......................... 197 7.5 Improved Sequential Algorithm..................... 200 7.5.1 Phase-Based Hull Count Constraint.............. 200 7.5.2 Improved Sequential Algorithm with the Phase-Based Hull Count Constraint........................ 206 7.5.3 Sort-Centric Balance Constraint................ 209 7.5.4 Improved Sequential Algorithm with the Sort-Centric Balance and Phase-Based Hull Count Constraints........... 212 7.6 Sensitivity Studies............................ 215 7.6.1 Sort Capacity.......................... 215 7.6.2 Fleet Size............................. 218 7.6.3 Airport Subsets......................... 224 7.6.4 Different Days of the Week................... 226 viii 7.6.5 Temporal Scope......................... 229 7.7 Summary................................. 233 VIII BENDERS DECOMPOSITION .................... 235 8.1 Benders Reformulation and Decomposition.............. 237 8.1.1 Formulation of ESSND Problem for Benders Decomposition. 241 8.2 Relevant Applications of Benders Decomposition in the Literature. 242 8.2.1 Applications to Airline Problems................ 243 8.2.2 Applications to other Transportation and Network Design Prob- lems...............................
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