Robust Airline Scheduling and Disruption Management

Robust Airline Scheduling and Disruption Management Sophie Kenrick Dickson Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy Department of Mathematics and Statistics THE UNIVERSITY OF MELBOURNE November 2013 Copyright c 2013 Sophie Kenrick Dickson All rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilm or any other means without written permission from the author. Abstract IRLINE scheduling is traditionally concerned with developing a plan that is most A profitable, and is usually done under conditions that are assumed to be known. In reality, however, airline operations are subject to uncertainty such as weather, traffic and equipment failure which cause disruption to passengers. In this thesis, we explore ways to design schedules that are robust to disruption as well as approaches for recovering once disruption has occurred. We formulate these problems as Integer Programming models. Most of these models are difficult to solve and require specialised IP solution approaches to solve them in a reasonable time frame. For both the robust schedule design and recovery problems, computational results are presented to explore the computational efficiency of the solution approaches developed, as well as results demonstrating the quality of the solutions obtained. Using the robust schedule design methodology developed, we analyse the resulting schedules to generate insights into where slack time is best allocated to maximise its effectiveness. For both problems, we also investigate the underlying structure of the Integer Programs to understand the conditions under which an integer valued optimum will be obtained when solving the linear relaxation. The thesis consists of two main components: Part II which presents our approach to solving the robust airline scheduling problem and Part III which presents our approach for solving the recovery problem. The remaining parts, I and IV, form the introduction and conclusion to the work, providing the motivation for the work contained within the thesis and drawing the links between Parts II and Part III. iii Declaration This is to certify that 1. the thesis comprises only my original work towards the PhD, 2. due acknowledgement has been made in the text to all other material used, 3. the thesis is less than 100,000 words in length, exclusive of tables, maps, bibliogra- phies and appendices. Sophie Kenrick Dickson, November 2013 v Acknowledgements There is a large and important cast of people without whom this thesis would not have been possible. To my supervisors: Heng-Soon Gan, Natashia Boland and Mark Wallace, thank you for your time, guidance, ideas, feedback, insights, and providing me with the opportunity to learn more about the topics in this thesis than I ever thought possible. I am also grateful to Ian Evans and Paul Hyland (CTI Pty Ltd) for their ongoing support and guidance on a variety of practical airline related issues and for numerous technical suggestions and in- sightful feedback that improved the content and exposition of this work. This research was supported by the Australian Research Council Linkage Project LP0668076 and by CTI Pty Ltd. The experience of completing this research has been greatly enhanced by the opportu- nities I have been afforded to apply my academic knowledge in a practical setting. Many thanks to Chris Davies, Gerry Turner, Mark Dal Pra and Gavin Richardson for making this possible. You have all provided me with great insights into how airlines operate, and what managers and executives are concerned with when it comes to airline operations management. To my comrades in the trenches: Emily, Liv and Kerem thank you for your friendship. Emily, an extra thank you for your joyful energy in the office and the endless supply of mo- tivating techniques (bricks, lollies, a balloon, rocks), productivity generators (ITWE, dashes, TODO lists), and occasional productivity dampeners (tea breaks, horoscopes, FML). To all of my parents, thank you for being role models in the way you live your life, and providing me with the love, encouragement and education to make almost anything possible. To my grandparents, Doomie, Mark, Lettie and Bill, thank you for giving me the type of love that helps me believe almost anything is possible! Maddy, thank you for vii allowing me to maintain a healthy perspective by reminding me that I have been writing “just a really long essay” and for always listening when I just needed to be heard. Dave, thank you for your enthusiasm and your willingness to explore, discuss and debate ideas (I am sure it keeps my brain healthy!). And of course, to James, my first, my last, my everything. I am so incredibly fortunate to have you in my life. viii Preface The following sections of this thesis are substantially based upon work published or submitted for publication, or include collaborative work. 1. The MIP described in Section 7.4, which forms the basis of the approach in Chap- ter 8, was originally developed as an entrant into the 2008/9 ROADEF Challenge, a collaborative project with Wenkai Li and Olivia Smith (Dickson et al. [57]). The collaboration focused on developing the MIP formulation, with the remainder of the work, including the strategies to solve the MIP, the code development and testing and the written report being completed by the author of this thesis. 2. Parts of Chapters 7 and 8 form the basis of a multi-authored paper (Dickson et al. [59], under review). The other authors are Wenkai Li, Mark Wallace and Natashia Boland. While working on this paper, Mark Wallace and Wenkai Li contributed significantly to a literature review that forms the basis of Section 7.2; Wenkai Li contributed the formulation of the alternative MIP described in Section 7.4.2; and Natashia Boland contributed to the written explanation of the various models, as well as the strength- ening constraints in Section 8.1.2. 3. The model of Chapter 3 and preliminary results from Chapter 5 were originally presented at the 20th ISMP in Chicago (Dickson and Boland [58]). ix Contents I Introduction and Background 1 1 Introduction 3 1.1 Background and Motivation . .3 1.2 Airline Planning and Operations . .6 1.2.1 Airline Schedule Planning . .6 1.2.2 Schedule Recovery and Disruption Management . .9 1.3 Problem Description and Research Methodology . 11 1.3.1 Robust scheduling framework: integrating design and recovery . 11 1.3.2 A simplified problem assuming push-back recovery . 14 1.3.3 The isolated recovery problem . 15 1.4 Terminology, Abbreviations etc . 16 1.5 Outline of the Thesis . 16 1.5.1 Outline of Part II - Robust Airline Scheduling . 16 1.5.2 Outline of Part III - Disruption Management . 17 1.6 Contribution of the Thesis . 18 1.6.1 Contribution of Part II - Robust Airline Scheduling . 18 1.6.2 Contributions of Part III - Disruption Management . 19 1.7 Background Mathematical Theory . 20 II Robust Airline Scheduling 21 2 Robust Airline Scheduling: A Review 25 2.1 Introduction . 25 2.1.1 Definition of Robustness . 26 2.1.2 Robust Airline Scheduling Terminology and Notation . 28 2.2 Literature Summary . 30 2.2.1 Optimisation Under Uncertainty . 30 2.2.2 Robust Scheduling . 32 2.2.3 Robust Airline Scheduling . 34 2.3 Approaches for Reducing Propagated Delay . 35 2.3.1 Overview of models for reducing propagated delay . 35 2.3.2 Robust Aircraft Maintenance Routings (Lan et al. [110]) . 38 2.3.3 Single Layer Model and Multi Layer Model (Ahmadbeygi et al. [9]) . 39 2.3.4 Probability of Delay Propagation (PDP) (Borndorfer et al. [61]) . 42 2.3.5 Other models . 44 xi 2.4 Limitations of existing models . 45 2.4.1 Independence of Primary and Propagated delay . 45 2.4.2 Objective Based on Average or Total Delay . 48 2.4.3 Retime or reroute only . 50 3 Delay Transition Model: A new model for Robust Airline Schedule Design 51 3.1 Delay Transition Concepts and Theory . 52 3.1.1 Continuous Delay Transition Function . 53 3.1.2 Discrete Propagated Delay Transition Function . 57 3.1.3 Discrete Recovery Transition Function . 60 3.1.4 Discrete Total Delay Transition Function . 63 3.2 Estimated On Time Performance . 65 3.2.1 OTP-MOD Inputs . 65 3.2.2 Methodology . 67 3.2.3 Applications . 68 3.3 Delay Transition Model (DTM) . 70 3.3.1 Retiming and Rerouting (DTM-RTN) . 71 3.3.2 Retiming Only (DTM-T) . 76 3.3.3 Rerouting Only (DTM-R) . 76 3.4 Reformulated Delay Transition Model (DTM-RTA) . 76 3.5 Discussion . 78 3.5.1 Budget Total Slack . 78 3.5.2 Minimize expected delay . 79 3.5.3 Include w in objective . 79 3.5.4 Additional transition point . 79 3.5.5 Crew and Maintenance Feasibility . 80 3.6 Computational Results . 83 3.6.1 Test Data Sets . 83 3.6.2 Computational Environment . 84 3.6.3 Optimality . 86 3.6.4 Schedule Improvement . 88 3.6.5 Model Comparison . 89 3.6.6 Preliminary Conclusion . 90 4 Delay Transition Model: Parameter Setting 95 4.1 Estimating Delay Transition Function from Historical Data . 96 4.1.1 Delay Reasons . 96 4.1.2 Identifying Primary versus Propagated Delay Using Delay Code Data 98 4.1.3 Identifying Primary versus Propagated Delay Using Departure Time Data ...................................... 98 4.1.4 Transition Classifications . 102 4.1.5 Estimating Transition Function . 102 4.2 Sample Size and Transition Probability Confidence Intervals . 103 4.3 Selecting Delay Categories . 105 4.3.1 Delay profile control . 106 4.3.2 w-error . 107 4.3.3 Sample Size Error . 109 xii 4.4 Identifying Transition Classifications .

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