FUTURE AIRCRAFT NETWORKS AND SCHEDULES A Thesis Presented to The Academic Faculty by Yan Shu In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Algorithm, Combinatorics, and Optimization Georgia Institute of Technology August 2011 FUTURE AIRCRAFT NETWORKS AND SCHEDULES Approved by: Dr. Ellis Johnson, Committee Chair Dr. Ozlem Ergun H. Milton Stewart School of Industrial H. Milton Stewart School School of and Systems Engineering Industrial and System Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Ellis Johnson, Advisor Dr. Arkadi Nemirovski H. Milton Stewart School of Industrial H. Milton Stewart School School of and Systems Engineering Industrial and System Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. John-Paul Clarke, CoAdvisor Dr. Barry Smith Daniel Guggenheim School of Barry C Smith LLC Aerospace Engineering and H. Milton Stewart School of Industrial and System Engineering Georgia Institute of Technology Date Approved: June 28, 2011 To myself, iii ACKNOWLEDGEMENTS First of all, I would like to thank my advisors, Dr. Ellis Johnson and Dr. John-Paul Clarke, for their guidance and financial support. They have served as role models to me and given me the freedom to develop myself in my own way. Their brilliant insights and good senses of humor have made working with them enjoyable. I also want to thank the rest of my committee members: Dr. Ozlem Ergun, Dr. Arkadi Nemirovski, and Dr. Barry Smith. In particular, I would like to thank Dr. Barry for his insightful comments. Furthermore, I want to thank Dr. Sergey Shebalov for being the reader of my thesis. In addition, I wish to thank Dr. Robin Thomas for being a responsible director of the Algorithm, Combinatorics, and Optimization (ACO) Program. Thanks for the generous help and great patience from the people of the helpdesk in the math and ISYE departments: Allen Belletti, Justin Filoseta, Matt Hanes, Lew Lefton, May Li, Eric Mungai, and Trey Palmer, to name a few. Thank for the wonderful women that I have met at Georgia Tech. They are Jane Chisholm, Christy Dalton, Karen Hinds, Cathy Jacobson, Sharon McDowel, Dana Randall, Ruth Schowalter, Genola Turner, and Inetta Worthy, to name a few. They show me women's great passion for life. In particular, I would like to thank Cathy and Jane for their great help with my English. I also want to thank Sharon and Genola, from whom I have received all kinds of help and advice. I would also like to thank the all the graduate students that I have met at Georgia Tech. In particular, I wish to thank Doug Altner, Wenwei Chao, You- Chi Cheng, Zhesheng Cheng, Hao Deng, Giang Do, Joshua Griffin, Alex Grigo, Wei iv Guan, Liangda Huang, Brian Knaeble, Yao Li, Nan Lu, David Murphy, Jon Peter- son, Fei Qian, Marc Sedro, Cuizhen Shen, Sangho Shim, Donghyuk Shin, Gustaf S¨oveling, Fatma K´ıl´ın¸c-Karzan, Ke Yin, Chao Wang, Kan Wu, Benjamin Webb, Bo Xu, Mengni Zhang, Kun Zhao, and Peng Zhao. I would also like to extend my thanks to the students in my recitation classes, who made being an instructor enjoyable. Last, but most important of all, I owe my greatest thanks to my parents Fuling Shu and Murong Liu for bringing me into this world and giving me unconditional support at all times. I would also like to thank my aunt, Yaoling Shu, who understands and guides me. v TABLE OF CONTENTS DEDICATION . iii ACKNOWLEDGEMENTS . iv LIST OF TABLES . ix LIST OF FIGURES . xi SUMMARY . xiii I INTRODUCTION . 1 1.1 Overview of Air Transportation Schedule Planning . 2 1.1.1 Background and terminology . 2 1.1.2 Overview of commercial airline schedule planning . 6 1.1.3 Overview of On-demand Schedule Planning . 9 1.2 Statement of Problem . 10 1.3 Statement of Purpose . 13 1.4 Organization of the Thesis . 13 II LITERATURE REVIEW . 15 2.1 Review of the Literature on Passenger Demand Models . 15 2.1.1 Overview of the Discrete Choice Model . 17 2.2 Review of the literature on frequency assignment model . 20 2.3 Review of the Literature on the Fleet Assignment Model . 23 2.4 Review of the Literature on Schedule Design . 25 III THE AIR TRANSPORTATION SYSTEM WITH SMALL AIRCRAFT 30 3.1 Introduction . 30 3.2 Development of Aircraft . 32 3.2.1 New aircraft concepts . 32 3.2.2 Small aircraft . 35 3.3 Business Model of Operating Small Aircraft . 40 vi IV MODELS IN FUTURE AIRCRAFT NETWORK AND SCHEDULE DE- SIGN . 45 4.1 Decomposition Scheme . 45 4.2 Frequency Assignment Model for Scheduled Flights . 47 4.2.1 Introduction . 48 4.2.2 Notations . 49 4.2.3 Passenger path choice model . 51 4.2.4 A formulation of the frequency assignment model . 54 4.3 Frequency Assignment Model for On-demand Flights . 55 4.3.1 Introduction . 55 4.3.2 Notations . 56 4.3.3 Passenger mode choice model . 57 4.3.4 Frequency assignment model . 60 4.4 Rough Fleet Assignment Model . 61 4.4.1 Rough timeline network . 61 4.4.2 Notations . 63 4.4.3 Itinerary-based rough fleet assignment model . 64 4.5 Timetable Model with Time Windows . 65 4.5.1 Network for a timetable model with time windows . 65 4.5.2 Notations . 68 4.5.3 Mathematical formulation . 69 V IMPLEMENTATION OF FUTURE AIRCRAFT NETWORK AND SCHED- ULE DESIGN . 70 5.1 Data Analysis . 70 5.1.1 Fleet . 70 5.1.2 Passenger demand . 72 5.1.3 Airports . 73 5.1.4 Parameters for the path choice model . 75 5.1.5 Parameters for the mode choice model . 76 vii 5.2 Implementation of the Frequency Assignment Model for Scheduled Flights . 78 5.2.1 Overall network structure . 79 5.2.2 Iterative algorithm for frequency assignment problem . 82 5.3 Implementation of the Frequency Assignment Model for On-Demand Flights . 92 5.4 Implementation of the Rough Fleet Assignment Model . 96 5.4.1 Leg-based rough fleet assignment model . 96 5.4.2 Decomposition scheme . 96 5.4.3 Formulation of leg-based rough fleet assignment models . 99 5.5 Implementation of the timetable model . 113 VI ANALYSIS OF FUTURE AIRCRAFT NETWORKS AND SCHEDULES 121 6.1 Comparison with the Schedules and the Networks of the Airlines in the United States . 121 6.2 New Aircraft Network and Schedules in Different Scenarios . 128 6.3 Implication of Using New fleets in the Aircraft Network and Schedule132 VII CONCLUSION AND FUTURE RESEARCH . 136 REFERENCES . 141 VITA . 148 viii LIST OF TABLES 1 An example of an airline flight schedule . 3 2 List of selected VLJs [1] . 38 3 Characteristics of fleets used in scheduled flights . 71 4 Characteristics of new fleets for scheduled flights . 71 5 Characteristics of fleets used in on-demand services . 72 6 Parameter estimation of the travel logit model (from Adler et al. [32]) 76 7 Parameter estimation in the mode choice model (from Baik et al. [35]) 78 8 A summary of instances of the frequency assignment problem created in this thesis . 82 9 Computational result 1 of instances of two relaxation problems of the initial subproblem . 86 10 Computational result 2 of instances of two relaxation problems of the initial subproblem . 87 11 Computational result of the iterative algorithm on instances of the frequency assignment problem . 90 12 Comparison 1 of the two iterative algorithms on the instances of the frequency assignment problem . 92 13 Comparison 2 of the two iterative algorithms on the instances of the frequency assignment problem . 93 14 Comparison of the computational results of the frequency assignment problem with different link parameters γ . 94 15 A summary of instances of the rough fleet assignment problem created in this section . 106 16 Computational result of instances of the time-slot assignment subproblem107 17 Computational result 1 of instances of the fleet assignment subproblem 108 18 Computational result 2 of instances of the fleet assignment subproblem 109 19 Computational result 1 of instances of the fleet assignment problem . 111 20 Computational result 2 of instances of the fleet assignment problem . 112 21 A summary of instances of the timetable problem created in this section115 ix 22 A summary of instances of the time-category subproblem created in this section . 116 23 Computational result 1 of instances of the timetable problem . 118 24 Computational result 2 of instances of the timetable problem . 119 25 Computational result 3 of instances of the timetable problem . 120 x LIST OF FIGURES 1 Illustration of two types of flight itineraries (based on a graph in Lewe et al. [64]) . 4 2 A hub-and-spoke network and a spoke-to-spoke network . 5 3 Scheduling planning process . 6 4 A connection network . 24 5 A timeline network . 25 6 Illustration of a new type of flight itineraries (based on a graph in Lewe et al. [64]) . 44 7 Flow chart . 48 8 Rough timeline network . 62 9 Illustration of a connecting bank at a hub . 66 10 Comparison of the timelines of Stations A and B . 66 11 Illustration of a timeline network with connection arcs . 67 12 Illustration of one sample of passenger demand . 74 13 Illustration of one sample of leisure passenger demand . 75 14 Illustration of one sample of business passenger demand . 76 15 Illustration of one sample of passenger volume at each airport . 77 16 Illustration of the capacity of 35 selected airports . 77 17 Illustration of the geological structure of the 200 selected airport . 80 18 Illustration of one sample of passenger demand in each market .