ROUTLEDGE LIBRARY EDITIONS: TRANSPORT ECONOMICS Volume AIRLINE OPERATIONS RESEARCH C\ Taylor & Francis ~Taylor & Francis Group http://tayl ora ndfra n ci s.com AIRLINE OPERATIONS RESEARCH ´ DUŠAN TEODOROVIC First published in 1988 by Gordon and Breach Science Publishers This edition first published in 2017 by Routledge Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 1988 OPA (Amsterdam) B.V All rights reserved No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: ISBN: ISBN: ISBN: 978-0-415-78484-9 978-1-315-20175-7 978-0-415-79224-0 978-1-315-21184-8 (Set) (Set) (ebk) (Volume 3) (hbk) (Volume 3) (ebk) Publisher’s Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original copies may be apparent Disclaimer The publisher has made every effort to trace copyright holders and would welcome correspondence from those they have been unable to trace Airline Operations Research By Dusan Teodorovic GORDON AND BREACH SCIENCE PUBLISHERS New York • London • Paris • Montreux • Tokyo • Melbourne © 1988 by OPA (Amsterdam) B.V All rights reserved Published under license by Gordon and Breach Science Publishers S.A Gordon and Breach Science Publishers Post Office Box 786 Cooper Station New York, New York 10276 United States of America 58, rue Lhomond 75005 Paris France 3-14-9, Okubo Shinjuku-ku, Tokyo Japan Post Office Box 197 London WC2E 9PX England Post Office Box 161 1820 Montreux Switzerland Private Bag Camberwell, Victoria 3124 Australia Library of Congress Cataloging-ln-Publtshing Data Teodorovic D (Dusan) 1951Airline operations research I by Dusan Teodorovic p em.- (Transportation studies; v 10) Translated from Serbo-Croatian (Cyrillic) Bibliography: Includes index ISBN 2-88124-672-9 Aeronautics, Commercial Operations research I Title TL552.T46 1988 367.7'068-dc19 8-21275 CIP No part of this book may be reproduced by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, without permission in writing from the publishers Printed in Great Britain by Billing & Sons Ltd, Worcester Contents ix xi Introduction to the Series Preface TRANSPORTATION DEMAND MODELS 1 Air Transport Demand 1.2 The Supply of Air Transportation Services l A Classification of Demand Estimation Models 1.4 Macroscopic Models of Transportation Demand When Demand is a Function of Time 12 1.5 Macroscopic Models of Transportation Demand When Demand is a Function of Socio-Economic Character is tics 21 Trip Distribution Models • 27 1.6.1 Entropy Trip Distribution Models 29 1.6.2 The Gravity Trip Distribution Hodel 43 1.7 Hultimode Models to Estimate Transportation Demand .• 48 1.8 The Abstract Mode Hodel to Estimate the Number of Passengers on Intercity Traffic 50 Choice Models 56 1.9.1 LOGIT Hodel 62 Calibrating the LOGIT Hodel 66 1.10 Concluding Remarks on Air Transportation Demand 79 ? MATCHING TRANSPORTATION FACILITIES AND PASSENGER DEMAND IN AIR TRAFFIC 81 2.1 Hatching Transportation Facilities and Passenger Demand in Air Traffic 81 v vi CONTENTS 2.2 The Importance of Flight Frequency Determination 82 2.3 The Concept of Passenger Flows and Changes in Their Intensity Over Time 85 2.4 The Passenger Load Factor 88 2.5 Calculating the Number of Refused Passengers 90 2.6 Flight Frequency and Air Carrier Competition 97 Flight Frequency and the Quality of Service 101 2.8 Determining Flight Frequency on a Route That Maximizes Air Carrier Profit 104 2.9 An Analysis of the Effects of Flight Frequency on Average Airline Schedule Delay 112 2.10 Determining Flight Frequency on a Route With Competition 126 2.11 Simultaneously Determining Departure Times and Flight Frequency on a Route 131 2.12 Determining Flight Frequencies on a Network That Provide the Highest Quality of Transportation Services with Existing Transportation capacities 145 13 Determining Flight Frequencies on a Network That Minimize the Carrier's Operating Costs 155 2.14 Aircraft Assignment to the Network 160 2.15 Planning Frequency and Traffic Assignment in the Network 165 AIRLINE SCHEDULE DESIGN MODELS 172 3.1 Factors That Influence Airline Schedule Design 172 3.2 Types of Airline Schedules 178 3.3 A Classification of Airline Schedule Design Models 180 CONTENTS vii 3.4 The Sequential Approach to Airline Schedule Design • • • 184 3.5 Determining the Least Number of Aircraft Needed on a Network with Known Departure Times 197 3.6 Method to Determine the Least Number of Aircraft Needed to Service a Network When There are Departure Time Windows •.• 214 3.7 The Effects of Meterological Conditions on Airline Schedule Design • • .• • • • 238 3.8 Designing an Airline Schedule with Maximum Reliability in Relation to Meteorological Conditions 243 3.9 The Influence of the Aircraft Maintenance System on Designing an Airline Schedule 257 3.10 Daily Operational Aircraft Assignment to the Planned Route • 261 3.11 Airline Schedule Perturbations 270 3.12 Designing a New Airline Schedule to Minimize Total Delay When an Aircraft Breaks Down 272 CREW SCHEDULING PROBLEMS 282 4.1 Crew Scheduling 282 4.2 Formulating Crew Scheduling Problems 284 4.3 Crew Scheduling for Long-Haul Flights 290 4.4 Crew Assignments in Short-Haul and MeaiumHaul Traffic as a Set Partitioning Problem 311 Heuristic Set Covering Algorithms for Large Airline Crew Scheduling Problems • • 345 4.6 Crew Scheduling as a Graph Partitioning Problem • • • 348 122 Psaraftis, H.N., "An Exact Algorithm for the Single Vehicle Many-to-Many Dial-A-Ride Problem with Time Windows", Transportation Science, Vol 17, No 3, pp 351-359, 1983 123 Quandt, R.E., Baumol, W.J , "The Demand for Abstract Hodes: Theory and Measurement", Journal of Regional Science, Vol 6, No 2, pp 13-26 1966 124 Quandt, R.E , "The Theory of Travel Demand", Transportation Research, Vol 10, pp 411-413, 1976 125 Rallis, T., Intercity Transport, The MacMillan Press, London, 1977 126 Renard, G., "Competition in Air Transportation : An Econometric Approach", Thesis presented to the Massachusetts Institute of Technology, Cambridge, Massachusetts in 1970, in partial fulfillment of the requirements for the degree of Master of Science 127 Richardson, R., "An Optimization Approach to Routing Aircraft", Transportation Science, Vol 10, No 1, pp 52-71, 1976 128 Richter, R.J., "Optimal Aircraft Rotations Based on Optimal Flight Timing", in Proceedings of the VIII AGIFORS Symposium, 1968 129 Richter, R.J "Experience with the Aircraft Rotation Hodel", in Proceedings of the X AGIFORS Symposium, Terrigal, Australia, 1970 130 Roberts, F.S Applied Combinatories, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1984 131 Rothstein, H., Stone, W., "Passenger Booking Levels", in Proceedings of the VII AGIFORS Symposium, 1967 132 Rothsteien, H., "An Airline Overbooking Hodel", Transportation Science, Vol 5, pp, 180-192, 1971a 133 Rothstein, H , "Airline Overbooking: The State of the Art", Journal of Transoort Economics and Policy, Vol 5, No 1, pp 96-99, 1971b 452 134 Rothstein, H "Airline Overbooking " Fresh Approaches Are Needed", Transportation Science, Vol 9, pp.l69-173, 1975 135 Rothstein, H., "OR and the Airline Overbooking Problem", Operations Research, Vol 33, No 2, pp 237-248, 1985 136 Rubin, J., "Technique for the Solution of Massive Set Covering Problems, with Application to Airline Crew Scheduling", Transportation Science, Vol 7, No 1, pp 34-48, 1973 137 Sasaki, T., "Probabilistic Models for Trip Distribution" in Proceedings of the Fourth International Symposium on tbe Theory of Traffic Flow, Karlsruhe, 1968 138 Scarbrough, J.E., "A Mixed-Integer Programming Model for the Scheduling of Aircraft by Time of Day Within a Network of Airports", Paper presented at the TIHS/ ORSA Joint National Meeting, 1977 139 Scheid, F., Numerical Analysis, McGraw Hill Book Company, New York, 1968 140 Sen, A., Soot, s., Pagitsas, E., "The Loglt Modal Split Model : Some Theoretical Considerations, TransPortation Research, Vol 12, pp 321-324, 1978 141 Simon, J.L "An Almost Practical Solution to Airline Overbooking", Journal of Transport Economics and Policy, Vol 2, No 2, pp 201-202, 1968 142 Simon, J.L., "Airline Overbooking -A Rejoinder", Journal of Transport Economics and Policy, Vol 4, No 2, pp 212-213, 1970 143 Simon, J.L., "Airline Overbooking " The State of the Art - A Reply", Journal of Transport Economics and Policy, Vol 6, NO 3, pp 254-256, 1972 144 Sherali, H.D., Rios, M., "An Air Force Crew Allocation and Scheduling Problem", Journal of Operational Research Society, Vol 35, No 2, pp 91-103, 1984 145 Shlifer, E., Vardi, Y., "An Airline Overbooking Policy", Transportation Science, Vol 9, pp 101-114, 1975 453 146 Simpson, R.W., "A Review of Scheduling and Routing Models for Airline Scheduling", in Proceedings of the IX AGIFORS Symposium, Broadway, England, October, 1969 147 Smith, C.H., Kyle, J.S., "On-Line Flight Schedule Development",in Proceedings of the XII AGIFORS Symoosium Nathanya, Israel, 1972 148 Sommers, A.N., "A Technique for Estimating V/STOL Market Shares", Transportation Science, Vol 3, No 1, pp 1-7, 1969 149 Soumis, F., Ferland, J A , Rousseau, J.H., "HAPUH : A Hodel for Assigning Passengers to a Flight Schedule", Transportation Research, Vol 15A, pp 155-162, 1981 150 Stojkovic, G., "Pregled postojecih teorijskih models i analiza faktora koji opredeljuju putnike za koriscenje aviona na turistickim relacijama" (Review of Theoretical Models and Analysis of Factors Inducing Passengers to Fly on Tourist Routes), Graduation Thesis, Faculty of Transportation and Traffic Engineering, Belgrade, 1984 151 Swan, W.H , "A Systems Analysis of Scheduled Air Transportation Networks",Report FTL-R79-5, Massachusetts Institute of Technology, 1979 152 Taha, H., Operations Research, MacMillan Publishing Company, Inc., New York, 1982 153 Taneja, N.K., The Commercial Airline Industry, Lexington Books, Lexington, Massachusetts, 1978 154 Teodorovic, D., Acimovic-Raspopovic, v., "Primena entropijskog modela srednje duzine putovanja na ocenu intenzitet putnickih tokova u jugoslovenskom unutrasnjem vazdusnom saobracaju" (Application of the Entropic Hodel of Medium Haul Flights to Estimate Passenger Flows in Yugoslav Domestic Air Traffic), Collection of Paoers from the Faculty of Transportation and Traffic Engineering, no 5, pp 123-133, 1981 155 Teo:iorovic, D., "Flight Frequency Determination", Journal of Transportation Engineering, Vol 109, No 5, pp 747-757, 1983 454 156 D., Tosi~, V., Jovanovi~, T., "Prognoza putnickih tokova u domacem vazdusnom saobracaju na linijama is SR Slovenije" (Passenger Flow Forecast for Domestic Flights from SR Slovenia), Saobracaj, year XXXI, no 2, pp 10-21, 1984a Teodorovi~, 157 Teodorovic, D., Guberinic, s., "Optimal Dispatching Strategy on an Airline Network After a Schedule Perturbation", Eurooean Journal of Operational Research, Vol 15, No 2, pp 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Mathematical Statistics Problems), Faculty of Transportation and Traffic Engineering, Belgrade, 1981 170 Wang, K., "Optimum Seat Allocation for Multi-Leg Flights with Multiple Fare Types", in Proceedings of the XXIII AGIFORS Symposium, Olive Branch, Mississippi, 1983 170a Williamson, W.G., "Computer Programs for Fleet and Schedule Planning", in Proceedings of the VII AGIFORS Symposium, 1967 171 Young, D.R , "Scheduling a Fixed-Schedule, Common Carrier Passenger Transportation System", Transportation Science, Vol 4, No 3, pp 243-269, 1970 456 I NDE X Abara Abstract mode model 50, 79, 158 Acimovic-Raspopovic 42 Air ~arri~rs Agard 81-85, 89, 97-99, 104, 109, 110, 118, 126, 130, 147, 148, 156, 160, 170, 171-175, 1771 1781 211, 2131 2331 2391 2431 252, 257-260, 2621 2701 271, 2821 283, 2851 289, 292, 293, 302, 305, 306, 311, 3121 314, 3451 3601 362, 383, 390-394-, 396, 399, 4061 414, 4161 4171 4231 4271 430, 433-4351 4371 438 365 Aggregated models 49 Aircraft assignment models Aircraft routing models 159 183 183 184 Airline network 81 290 Airline schedule 11 102 152 172-174 176-185 187, 188, 193-195, 198, 2111 2131 2151 238-2411 243, 244, 246, 249, 255, 257-262, 270-273, 2821 2841 2901 3111 3121 3631 382 Airline schedule perturbation Airport 270 1 19, 20, 34, 79, 132, 174-176, 185, 188, 190, 196, 223, 238, 240, 241, 251, 257, 260, 2661 416, 4171 421 422 Air transpnrtation 1 4, 8, 11, 12 14, 84, 132, 133 1371 1791 1841 282 Air lr.JH: ;portation demand Anderson Antosik Arabeyre 4, 11 48 79 80 391 413 414 365 367 369 371 373 312 314 457 Abara Abstract mode model 50, 79, 158 Acimovic-Raspopovic 42 Air carriers Agard 81-85, 89, 97-99, 104, 109, 110, 118, 126, 130, 147, 148, 156, 160, 170, 171-175, 177, 178, 211, 213, 233, 239, 243, 2521 257-2601 2621 2701 2111 2821 2831 2851 2891 2921 2931 3021 3051 3061 3111 3121 3141 3451 3601 3621 3831 390-394-1 3961 39914061 414141614171 4231 4271 430, 433-4351 4371 438 365 Aggregated models 49 Aircraft assignment models Aircraft routing models 159 183 183 184 Airline network 81 290 Airline schedule 11 102 152 172-174 176-185 187 1881 193-1951 1981 2111 2131 2151 238-2411 2431 2441 2461 2491 2551 257-262, 270-2731 282, 2841 2901 3111 3121 363, 382 Airline schedule perturbation Airport 270 1 19, 20 34, 79, 132, 174-176, 185 188, 190 196, 2231 2381 2401 2411 2511 2571 2601 2661 4161 4171 421, 422 Air transportation 1, 3, 4, 11 12, 14 84 132, 133, 137, 1791 184, 282 Air transportation demand Anderson Antosik Arabeyre 4, 51 8, 11 48, 79, 80 391, 413 414 365, 367, 369, 371, 373 312, 314 458 Ashford 176 Babic 240, 241, 260 Baker 312, 346, 362 Brt 11 28 41 28 51 312 344 3481 349 J 52 J 56 358 365 Baumol 50, 53 Behbehani 25 Bipartite graph Bjorkman 199, 204 - 206, 210, 216, 218, 266 20 Bornemann 382 Branr.h- and-bound Brown Bnhr Carter Chang 215, 220, 226, 259, 275, 277, 281, 311, 343 25, 26 365, 366, 369, 372, 378, 379-381 155 167 Chnir.e function 56, 58, 59, 61, 65, 74, 78 Choice models Christofides 59-61, 65-67, 72, 75, 78, 167 312 Combinatorial programming 215, 259, 264, 275, 318, 326 Crew rostering 289 Crew scheduling 282-284, 288, 290, 318, 344, 345, 350, 363, 365, 371 Cumulative density function Darby-Dowman 403 312 Dead heading crews 175 459 Deckwitz 181 Demand scheduling de Neufville Desrosiers 177, 180 83, 99, 100, 146 215 Deterministic choice models De Vany 104 Disaggregated models 49, 70, 75 Dynamic airline schedule Dynamic programming Entropy 58, 60 179 133, 215, 249, 251, 259, 326, 434 29-31 Entropy model 29, 31, 79 Etcheberry 312 Etschmaier 100, 180, 258, 260, 270 Falkson Fisher 391, 394 141 Fleet planning models Flight frequency Frequency share 183 3, 4, 81-84, 86, 88, 90, 95-97, 99, 101 - 106 109-114, 117-119, 124-126, 130-133, 137-139 145-1471 149-151, 153-160, 163, 165-172, 180, 185, 232 100, 159, 164 Gaballa 382, 384, 385, 389 Gagnon 87, 91 Garges 104 Gasco 144, 145, 391 460 Gelerman 83, 99, 100 Gerbracht Ghobrial 160, 312, 313, 363, 364, 391, 396, 403, 407 83, 112, 165, 167-170 Giannessi 363 Gillett 141 Glanert 365, 369 Gompertz curve Gordon 15, 16 67, 146, 182, 186 Graph partitioning problem Griesshaber 312, 391, 423 Grilihes 19 Grulovic 24, 25 Guberinic 270 Haydon 382-385, 389 Gerring 56, 58 Heuristic procedure Holst 181, 215, 230, 281, 344, 362, 367, 368 263, 265, 267, 269 Hungarian algorithm Hwang 138, 145 Hyman 87, 182, 186 Integer programming Jaikumar Jaw 344, 347, 349 298, 300, 304 158, 216 141 215 Johnston 82 461 Kanafani Kedic 11, 25, 59, 78, 165, 167 49 King 99 Konig 160, 263, 264 Korman 312, 315 Kuhn 298 Kyle 181 Lagrangian function 31, 32, 39, 148, 151 Lagrange multiplier 31, 148, 151 Laplace function Lasky 94, 130, 411 312, 314, 326, 327, 342 Lease squares method Lee 14-16, 47, 65 263, 264 Lemke 312 Levin 56, 58, 141, 215, 220, 222 Linear programming Littlewood 312, 391, 423, 425, 427 Load factor Lof 158, 159, 164, 215, 220, 221 88-90, 93, 97, 102, 103, 105, 107, 118, 138, 1471 152, 160, 161, 1671 110, 171 - 173, 180, 391, 392, 424, 439 141, 215 Logistic curve LOGIT model 15-17, 19 62, 66, 75, 78, 79, 166, 169-171 Macroscopic models Harchettini 11, 12, 21, 22, 26, 79 365, 369, 382 462 77, 7B, 1!3, 97, 99, 164 MiHkf't shiHf' Marsten 283, 312, 315, 343, 344 Martinez 391, 409 Matching 353-354, 356, 357, 399-361 Hathaisel 180 Maximum likelihood method Hayer 391, 423, 427 Mean trip length model Microscopic models Miler 38, 39, 42, 43, 79 11, 12, 79 87, 141 Hi tchell Mitra 65, 66 382 312 Modal split 7, 8, 79, 83 Modified exponential curve Mondria 15, 16 290, 310 Morlok 155 Multicriteria decision making Multimode models 8, 11, 48, 49, 79 Multiple regression technique Nagarajan 391, 439 Nicoletti 363, 365, 382 Niederer Odier 138, 145 23, 55, 65 181 312 463 Oliver 40 Overbooked passengers Pearl-Reed curve Pierce 395, 397, 439 15, 16 312, 314, 315, 317, 325, 326, 337, 342 Pollack Potts 197, 215, 230 40 Powell 86, 99, 129 Probability density function Proportional model Psaraftis 31, 33, 35, 36, 39, 79 215 Quandt 50, 53 Renard 83, 99 Reno 60, 62, 93, 102, 112, 113, 116, 127-129, 406, 413, 425, 428, 437 263, 264 Reservation level 394, 396-398, 403-405, 408, 409, 414-418, 422, 423, 427, 428 Roberts 284, 285, 298, 312, 344, 348, 349, 353, 357, 359, 365 Rothstein Rubin 258, 260, 270, 391, 394, 423 312 Sadoulet Sanchez Sasaki 78 391, 409 39 Schedule delay Scheid 102, 107, 109, 112-114, 116, 118, 119, 146, 148, 149, 154, 160 74 464 Seat allocation Seat hours 424, 435, 436 147, 150, 151, 153 Set covering problem 215, 221, 288, 346, 347, 349 Set partitioning problem Shepardson Shlifer 283, 312, 315, 343, 344 391, 409, 413-416 Shuttle service Simon 137, 143, 145 391, 394 Simpson Smith 84, 87, 159, 179, 182, 215 181 Sommers 56, 58 Sorensen Soumis 263, 265, 267, 269 87, 91, 93 Space-time diagram 141, 201, 206, 211, 216, 217, 218, 226229, 236, 278 Stochastic choice models Stochastic delay Stojkovic Stone Swan 288, 313, 344, 346, 351 58, 60-62 103, 107, 109, 154 49 391 86-88, 93, 106, 107, 109, 111, 112 Taha 220 Taneja 177 Teodorovic Titze 33, 35, 42, 87, 112, 113, 119, 123, 138, 140, 149, 243, 249, 252, 270 391, 423 465 Tomlin 39 Tosic 240, 241 Traffic assignment 165, 167 Transportation network Travel costs Travel time 29, 30, 112, 131, 146, 165, 198, 201 215, 230, 239, 252 3, 59, 76 2, 8, 11, 28, 45, 51, 52, 56, 59, 84, 132, 165, 169 Trip assignment 7, Trip distribution 7, 8, 27-29, 43, 79 Trip generation Trip length Vickrey 391, 394 391, 423, 435, 438 Watkins 25, 26 Williamson Yoon 38, 42 391, 409, 413-416 Vardi Wang 7, 181 138, 145 466 ...ROUTLEDGE LIBRARY EDITIONS: TRANSPORT ECONOMICS Volume AIRLINE OPERATIONS RESEARCH C\ Taylor & Francis ~Taylor & Francis Group http://tayl ora ndfra n ci s.com AIRLINE OPERATIONS RESEARCH ´... further development of operations research methods in the field of air transportation Air carrier problems are also of interest to some universities When writing Airline Operations Research my primary... Camberwell, Victoria 3124 Australia Library of Congress Cataloging-ln-Publtshing Data Teodorovic D (Dusan) 195 1Airline operations research I by Dusan Teodorovic p em.- (Transportation studies; v 10)