Abstract
This paper presents an integer linear programming approach with column generation for the NP-hard Multiple-Depot Vehicle Scheduling Problem (MDVSP) in public mass transit. We describe in detail the basic ingredients of our approach that seem indispensable to solve truly large-scale problems to optimality, and we report on computational investigations that are based on real-world instances of three large German public transportation companies. These instances have up to 25,000 timetabled trips and 70 million integer decision variables. Compared to the results obtained with one of the best planning system currently available in practice, our test runs indicate savings of several vehicles and a cost reduction of about 10%.
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References
Ball, M.O. / Magnanti, T.L. / Monma, C.L. / Nemhauser, G.L. (editors) (1995): Network Routing, volume 8 of Handbooks in Operations Research and Management Science. Elsevier Science B.V.
Bokinge, U. / Hasselström, D. (1980): Improved vehicle scheduling in public transport through systematic changes in the time-table. European Journal of Operational Research, 5:388–395.
Borndörfer, R. / Grötschel, M. / Löbel, A. (1995): Alcuin’s transportation problems and integer programming. Preprint SC 95–27, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Available at www.zib.de. To appear in Butzer, P.L. /Jongen, H.T. / Oberschelp, W. (editors), Charlemagne and his Heritage: 1200 Years of Civilization and Science in Europe, Volume II: The Mathematical Arts, Brepols Publishers.
Bussieck, M. /Winter, T. / Zimmermann, U.T. (1997): Discrete optimization in public rail transport. In Liebling, T.M. /de Werra, D. (editors), Mathematical Programming: A Publication of the Mathematical Programming Society, pages 415–444. Elsevier Science B.V.
Carpaneto, G. / Dell’Amico, M. / Fischetti, M./ Toth, P. (1989): A branch and bound algorithm for the multiple depot vehicle scheduling problem. Networks, 19:531–548.
Chvátal, V. (1980): Linear programming. W. H. Freeman and Company, New York.
CPLEX (1997): Using the CPLEX Callable Library. ILOG CPLEX Division, 889 Alder Avenue, Suite 200, Incline Village, NV 89451, USA. Information about CPLEX available at www.cplex.com.
Daduna, J.R. /Branco, I./ Paixão, J.M.P. (editors) (1995): Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems. Springer Verlag.
Daduna, J.R. / Mojsilovic, M. / Schütze, P. (1993): Practical experiences using an interactive optimization procedure for vehicle scheduling. In Du, D.-Z. /Pardalos, P.M. (editors), Network Optimization Problems: Algorithms, Applications and Complexity, volume 2 of Series on Applied Mathematics, pages 37–52. World Scientific Publishing Co. Pte. Ltd.
Daduna, J.R./ Paixão, J.M.P. (1995): Vehicle scheduling for public mass transit — an overview. In Daduna/Branco/Paixão (1995).
Dell’Amico, M. / Fischetti, M. / Toth, P. (1993): Heuristic algorithms for the multiple depot vehicle scheduling problem. Management Science, 39(1):115–125.
Desrosiers, J. / Dumas, Y. / Solomon, M.M. / Soumis, F. (1995): Time Constrained Routing and Scheduling. In Ball/Magnanti/Monma/Nemhauser (1995), chapter 2, pages 35–139.
Fischetti, M. / Toth, P. (1996): A polyhedral approach to the asymmetric traveling salesman problem. Technical report, University of Bologna. To appear in Management Science.
Fischetti, M./ Vigo, D. (1996): A branch-and-cut algorithm for the resource-constrained arborescence problem. Networks, 29:55–67.
Forbes, M.A. /Holt, J.N. /Watts, A.M. (1994): An exact algorithm for multiple depot bus scheduling. European Journal of Operational Research, 72(1):115–124.
Freling, R./ Paixão, J.M.P. (1995): Vehicle scheduling with time constraint. In Daduna/Branco/Paixão (1995).
Kokott, A./Löbel, A. (1996): Lagrangean relaxations and subgradient methods for multiple-depot vehicle scheduling problems. Preprint SC 96–22, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Available at www.zib.de.
Löbel, A. (1996): Solving large-scale real-world minimum-cost flow problems by a network simplex method. Preprint SC 96–7, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Available at www.zib.de.
Löbel, A. (1997a): Experiments with a Dantzig-Wolfe decomposition for multiple-depot vehicle scheduling problems. Preprint SC 97–16, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Available at www.zib.de.
Löbel, A. (1997b): MCF Version 1.0 — A network simplex implementation. Available for academic use free of charge at www.zib.de.
Löbel, A. (1997c): Optimal Vehicle Scheduling in Public Transit. PhD thesis, Technische Universität Berlin.
Löbel, A. (1997d): Vehicle scheduling in public transit and Lagrangean pricing. Revised Preprint SC 96–26, Konrad-Zuse-Zentrum für Informationstechnik Berlin. Available at www.zib.de.
Ribeiro, C.C. / Soumis, F. (1994): A column generation approach to the multiple-depot vehicle scheduling problem. Operations Research, 42(1):41–52.
Schmidt, V. A. (1997): Auf Sparkurs zum Ziel. Rheinischer Merkur, number 39, page 37, 26th September 1997. In German.
Schrijver, A. (1989): Theory of Linear and Integer Programming. John Wiley & Sons Ltd., Chichester.
Soumis, F. (1997): Decomposition and Column Generation. Chapter 8 in Dell’Amico, M. /Maffioli, F. /Martello, S. (editors), Annotated Bibliographies in Combinatorial Optimization, pages 115–126. John Wiley & Sons Ltd, Chichester.
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Löbel, A. (1999). Solving Large-Scale Multiple-Depot Vehicle Scheduling Problems. In: Wilson, N.H.M. (eds) Computer-Aided Transit Scheduling. Lecture Notes in Economics and Mathematical Systems, vol 471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85970-0_10
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DOI: https://doi.org/10.1007/978-3-642-85970-0_10
Publisher Name: Springer, Berlin, Heidelberg
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