Construction Heuristics for the Airline Taxi Problem

211 Pages·2013·4.87 MB·English

Construction Heuristics for the
Airline Taxi Problem
Ian Michael Dougal Campbell
A thesis submitted to the Faculty of Engineering and the Built Environment, Uni-
versity of the Witwatersrand, Johannesburg, in fulfilment of the requirements for
the degree of Doctor of Philosophy.
Johannesburg, October 2013
Declaration
I declare that this thesis is my own, unaided work, except where otherwise acknowl-
edged. ItisbeingsubmittedforthedegreeofDoctorofPhilosophyintheUniversity
of the Witwatersrand, Johannesburg. It has not been submitted before for any de-
gree or examination at any other university.
Signed this day of 20
Ian Michael Dougal Campbell.
i
Acknowledgements
Firstly, I would like to thank my parents, my sister and my brothers for many years
of love and support.
Secondly, special thanks to my supervisor, Prof. M.M. Ali, for his unwavering and
motivational guidance and support, as well as his patience in wading repeatedly
through this tome and his resulting comments and corrections.
Thirdly, many thanks to Margaret Campbell and Prof. Robert Reid for their com-
prehensive proof reading and valuable corrections.
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Abstract
A literature review of vehicle routing problems (VRPs) in general, and specifically
airline scheduling problems and the airline taxi problem, is provided. A real-world
airline taxi scheduling problem is described as experienced by a tourist airline oper-
ating in the Okavango Delta, Botswana. In this problem, a daily schedule is drawn
up manually by a team of experienced schedulers a few days before the day in ques-
tion. In this research, a slightly relaxed version of the problem is considered in order
to develop heuristics and modelling methods which will be useful for general cases.
Various methods and heuristics are proposed for the problem and tested on a small
versionoftheproblemaswellasthefull-sizedversion. Themostpromisingmethods
are demonstrated and solutions provided. One of the methods was applied to the
actual problem to demonstrate the practical usefulness. In this case a schedule with
a cost 12% lower than the manual schedule cost was achieved. All the heuristics and
methods are applicable to certain other VRPs, particularly real-world or highly-
constrained VRPs. An example is provided of a solution method for a real-world
instance of the multi-vehicle capacitated vehicle routing problem (MVCVRP). An-
other example is provided of a standard, benchmark instance from the internet of a
capacitated vehicle routing problem with time windows (CVRPTW).
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Contents
Declaration i
Acknowledgements ii
Abstract iii
Contents iv
List of Figures ix
List of Tables x
1 Introduction 1
1.1 Scheduling in Commercial Scheduled Airlines . . . . . . . . . . . . . 1
1.2 On-Demand Airline Scheduling . . . . . . . . . . . . . . . . . . . . . 2
1.3 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Objectives 5
3 Literature Review 6
3.1 Vehicle Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1.1 Types of Vehicle Routing Problems . . . . . . . . . . . . . . . 6
iv
3.1.2 Solving VRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Airline Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Scheduled Airlines . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2 Charter Airlines . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 On-Demand Air Transportation . . . . . . . . . . . . . . . . . 41
3.3 Solving large MIP problems . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Conclusions from Literature Review . . . . . . . . . . . . . . . . . . 46
4 Methodology 47
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Small-Scale Benchmark Airline Taxi Problem . . . . . . . . . . . . . 49
4.3 Sefofane Air Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Application to Other VRPs . . . . . . . . . . . . . . . . . . . . . . . 50
5 The Sefofane Air Scheduling Problem Description 52
5.1 Sefofane Air Operations . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Problem Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6 Multi-Commodity Network Flow ILP with Time Discretisations 59
6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7 Heuristics for Problem Size Reduction 64
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.2 Group Aggregation Heuristic . . . . . . . . . . . . . . . . . . . . . . 65
7.2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
v
7.2.2 Aggregation Validation . . . . . . . . . . . . . . . . . . . . . 66
7.3 Geographic Heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.3.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7.3.2 Evaluation of Geographic Heuristic Effect . . . . . . . . . . . 68
7.4 MCNFP Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.4.1 Small Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.4.2 Full Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8 Agent Routing Variable Generation 76
8.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
8.2 Observations and Results . . . . . . . . . . . . . . . . . . . . . . . . 83
8.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
9 Composite Variable Formulation 88
9.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
9.2 Observations and Results . . . . . . . . . . . . . . . . . . . . . . . . 93
9.2.1 Small Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 93
9.2.2 Full Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
9.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
10 The Sefofane Air Scheduling Problem 97
10.1 Constrained Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
10.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 100
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11 Other VRPs 102
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
11.2 Multi Vehicle CVRP (MVCVRP) . . . . . . . . . . . . . . . . . . . . 102
11.2.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . 102
11.2.2 Exact ILP Formulation . . . . . . . . . . . . . . . . . . . . . 103
11.2.3 Composite Variable Formulation . . . . . . . . . . . . . . . . 106
11.2.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
11.2.5 Observations and Results . . . . . . . . . . . . . . . . . . . . 109
11.2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
11.3 CapacitatedVehicleRoutingProblemwithTimeWindows(CVRPTW)110
11.3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . 110
11.3.2 Variable Generation . . . . . . . . . . . . . . . . . . . . . . . 111
11.3.3 Observations, Results and Discussion . . . . . . . . . . . . . . 116
12 Conclusions 117
13 Recommendations 120
REFERENCES 121
APPENDIX A Sefofane Air Problem Data 134
APPENDIX B Manual Schedule 140
APPENDIX C Aggregation Heuristic Result 145
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APPENDIX D Agent Routing MATLAB Code - Airline Taxi Prob-
lem 148
D.1 Attractiveness Parameters . . . . . . . . . . . . . . . . . . . . . . . . 148
D.2 Agent Routing Function . . . . . . . . . . . . . . . . . . . . . . . . . 148
APPENDIX E Agent-Generated Variable Schedule 169
APPENDIX F Automated Composite Schedule 172
APPENDIX G MVCVRP Data 175
G.1 Problem Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
G.2 Supplied Delivery Lists . . . . . . . . . . . . . . . . . . . . . . . . . . 180
G.2.1 List for Day 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
G.2.2 List for Day 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
G.2.3 List for Day 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
APPENDIX H Agent Routing MATLAB Code - CVRPTW 190
APPENDIX I CVRPTW Data 196
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List of Figures
3.1 An Insertion Heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 A Savings Heuristic. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 2-Opt Exchange Move . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Multi Agent Cooperative Search . . . . . . . . . . . . . . . . . . . . 23
3.5 GPDP Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Time-Space Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.7 Time-Space Network with Time Discretisations . . . . . . . . . . . . 38
5.1 Cessna C206 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Cessna C208 Grand Caravan . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Map of the Okavango Delta Area . . . . . . . . . . . . . . . . . . . . 56
7.1 Geographic Heuristic . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.1 Agent Routing Method Modelling Process . . . . . . . . . . . . . . . 84
9.1 Linking of Two Flight Variables (Dual Linking) . . . . . . . . . . . . 89
9.2 Composite Variable Modelling Method . . . . . . . . . . . . . . . . . 91
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