Abstract Hybrid Routing Models Utilizing Trucks Or
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ABSTRACT Title of dissertation: HYBRID ROUTING MODELS UTILIZING TRUCKS OR SHIPS TO LAUNCH DRONES Stefan Poikonen Doctor of Philosophy, 2018 Dissertation directed by: Professor Bruce Golden R.H. Smith School of Business Technological advances for unmanned aerial vehicles, commonly referred to as drones, have opened the door to a number of new and interesting applications in areas including military, healthcare, communications, cinematography, emergency response, and logistics. However, limitations due to battery capacity, maximum take-off weight, finite range of wireless communications, and legal regulations have restricted the effective operational range of drones in many practical applications. Several hybrid operational models involving one or more drones launching from a larger vehicle, which may be a ship, truck, or airplane, have emerged to help mitigate these range limitations. In particular, the drones utilize the larger vehicle as both a mobile depot and a recharging or refueling platform. In this dissertation, we describe routing models that leverage the tandem of one or more drones with a larger vehicle. In these models, there is generally a set of targets that should be visited in an efficient (usually time-minimizing) manner. By using multiple vehicles, these targets may be visited in parallel thereby reducing the total time to visit all targets. The vehicle routing problem with drones (VRPD) and traveling salesman prob- lem with a drone (TSP-D) consider hybrid truck-and-drone models of delivery, where the goal is to minimize the time required to deliver a set of packages to their re- spective customers and return the truck(s) and drone(s) to the origin depot. In both problems, the drone can carry one homogeneous package at a time. Theoreti- cal analysis, exact solution methods, heuristic solution methods, and computational results are presented. In the mothership and drone routing problem (MDRP), we consider the case where the larger launch vehicle is free to move in Euclidean space (the open seas) and launch a drone to visit one target location at a time, before returning to the ship to pick up new cargo or refuel. The mothership and high capacity drone routing problem (MDRP-HC) is a generalization of the mothership and drone routing problem, which allows the drone to visit multiple targets con- secutively before returning to the ship. MDRP and MDRP-HC contain elements of both combinatorial optimization and continuous optimization. In the multi-visit drone routing problem (MVDRP), a drone can visit multiple targets consecutively before returning to the truck, subject to energy constraints that take into account the weight of packages carried by the drone. HYBRID ROUTING MODELS UTILIZING TRUCKS OR SHIPS TO LAUNCH DRONES by Stefan Poikonen Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2018 Advisory Committee: Professor Bruce Golden, Chair/Advisor Professor Edward Wasil Professor Subramanian Raghavan Professor Denny Gulick Professor Tunay Tunca c Copyright by Stefan Poikonen 2018 Dedication To my family. ii Acknowledgments I owe immeasurable thanks to my advisor, Professor Bruce Golden. His guid- ance has spanned from granular details of papers to strategic and life advice. He helped me to see the light at the end of the long graduate school tunnel when I was still finding myself as a student. It seems just yesterday I was in BMGT831. I hope for many more papers together and four mile walks. I also owe special thanks to Professor Edward Wasil who has worked closely with me on multiple projects. His careful eye and advice have been invaluable, and I deeply appreciate all he has done along the way. I hope to continue collaborating over the coming years. To Rui Zhang, thank you for your sound advice, especially during the job application process. You gave me a more concrete sense of what to expect in the interviewing process, which was extremely helpful. We have worked together on one project so far, but I hope our future proximity in Colorado will lead to others. To Xingyin Wang, I appreciate the time we had to work on a couple projects together and the chances we have had to meet at conferences. Hopefully we can have a chance to meet and collaborate in the future. To other friends in the Saturday research group who have been supportive in a number of ways, thank you. I especially wish to mention Debdatta Sinha Roy, who has been a supportive friend and classmate. To all of you who have helped make this possible through your love, support, and encouragement, thank you. I wish to especially mention my family who have iii consistently supported me in a variety of ways. The work of Chapter 2 in this dissertation is derived from joint work with Xingyin Wang and Bruce Golden, some of which appeared in the journal Optimiza- tion Letters and some of which appeared in the journal Networks. The work of Chapter 3 in this dissertation is derived from joint work with Bruce Golden and Edward Wasil, which will appear in the INFORMS Journal on Computing. The work of Chapters 4 and 5 in this dissertation are derived from joint work with Bruce Golden. iv Table of Contents Dedication ii Acknowledgements iii List of Tables ix List of Figuresx List of Abbreviations xiii 1 Introduction1 1.1 Background on Drones..........................1 1.2 Academic Literature Review.......................6 1.2.1 Drone Routing..........................6 1.2.2 Hybrid Truck-and-Drone Models................8 1.3 Main Contributions............................ 10 2 The Vehicle Routing Problem with Drones 12 2.1 Problem Definition............................ 12 2.2 Extensions: Cost Issues, Other Metrics, and Limited Battery Life.. 16 2.2.1 Limited Battery and Maximum Savings............. 17 2.2.2 Truck and Drones Utilizing Different Metrics.......... 19 2.2.3 Economic Savings......................... 22 2.3 Extension to CEV RP ∗ .......................... 25 2.3.1 VRPD: An Intermediate Problem................ 26 2.3.2 V RP D in the Limit....................... 27 2.4 Conclusions and Future Work...................... 30 3 Exact and Heuristic Methods for the Traveling Salesman Problem with a Drone 32 3.1 Introduction................................ 32 3.2 Literature Review............................. 33 3.3 Defining the TSP-D and Notation.................... 37 v 3.3.1 TSP-D: Problem Definition................... 37 3.4 Branch-and-bound Approach....................... 39 3.4.1 Nodal Structure and Branching Procedure........... 39 3.4.2 Lower Bound Evaluation for a Node............... 41 3.4.3 Exploration, Upper Bounds, and Terminating the Algorithm. 43 3.4.4 Example of the Branch-and-Bound Approach......... 46 3.4.5 Reduction to O(Cn2)....................... 47 3.5 Additional Heuristics for the TSP-D.................. 48 3.5.1 Boosted Lower Bound Heuristic................. 48 3.5.1.1 Linear Boost Heuristic................. 49 3.5.1.2 Quadratic Boost Heuristic............... 50 3.5.2 Divide-and-Conquer Heuristic.................. 51 3.6 Computational Results.......................... 53 3.6.1 Branch-and-Bound Results for Different Tree Exploration Ra- tio Values............................. 54 3.6.2 Solution Quality and Computation Time Results for Five TSP- D Solution Methods....................... 59 3.6.3 Linear and Quadratic Boost Heuristics Tradeoff........ 60 3.6.4 Divide-and-Conquer Heuristic Tradeoff............. 61 3.6.5 Effect of Drone Battery Duration and Speed on the TSP-D Solutions.............................. 62 3.6.6 The Effect of Distance Metrics on the TSP-D Solutions.... 63 3.7 Conclusions and Future Work...................... 65 4 The Mothership and Drone Routing Problem 67 4.1 Introduction................................ 67 4.2 Literature Review............................. 68 4.3 Defining the Problem........................... 70 4.4 Exact Solution Method.......................... 73 4.4.1 Second Order Cone Program for a Fixed Sequence....... 73 4.4.2 Branch-and-Bound: Finding the Best Sequence........ 76 4.5 Heuristics for MDRP........................... 82 4.5.1 Greedy Sequence......................... 82 4.5.2 Greedy Sequence with Local Search............... 82 4.5.3 Partial Solve with Greedy Insert................. 85 4.6 MDRP Computational Results...................... 86 4.6.1 Comparing Solution Methods for MDRP............ 87 4.6.2 Analysis of MDRP Computational Results........... 90 4.7 The Mothership and High Capacity Drone Routing Problem..... 91 4.7.1 Concepts: Drone Subtours and Compositions......... 92 4.7.2 Second Order Cone Program for a Fixed Composition..... 94 4.7.3 Finding the Best Composition.................. 97 4.7.3.1 Branch-and-bound: An Exact Approach....... 98 4.7.3.2 Greedy Sequence Exact Composition Heuristic... 98 4.7.3.3 Greedy Sequence and Greedy Composition...... 99 vi 4.7.3.4 Greedy Sequence and Greedy Composition with Slack100 4.8 MDRP-HC Computational Results................... 101 4.8.1 Analysis of MDRP-HC Computational Results......... 103 4.9 Variants, Conclusions, and Future Work................ 104 4.9.1 Variants.............................. 104 4.9.2 Conclusions............................ 104 4.9.3 Future Work............................ 106 4.10 Insert A: Computing the best composition for a given input sequence 107 4.11 Insert B: Variants of MDRP....................... 108 4.12 Insert C: Variants of MDRP-HC..................... 113 5 The Mothership and Drone Problem: