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Vehicle Scheduling in Public Transit and Lagrangean Pricing

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  • Andreas Löbel

    (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustraße 7, D-14195, Berlin, Germany)

Abstract

This paper investigates the solution of the linear programming (LP) relaxation of the multi-commodity flow formulation of the multiple-depot vehicle scheduling problems arising in public mass transit. We develop a column generation technique that makes it possible to solve the huge linear programs that come up there. The technique, which we call Lagrangean pricing, is based on two different Lagrangean relaxations. We describe in detail the basic ingredients of our approach and give computational results for large-scale test data (with up to 70 million variables) from three German public transportation companies. Because of these results, we propose Lagrangean pricing as one of the basic ingredients of an effective method to solve multiple-depot vehicle scheduling problems to proven optimality.

Suggested Citation

  • Andreas Löbel, 1998. "Vehicle Scheduling in Public Transit and Lagrangean Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1637-1649, December.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-1:p:1637-1649
    DOI: 10.1287/mnsc.44.12.1637
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    References listed on IDEAS

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    1. Mauro Dell'Amico & Matteo Fischetti & Paolo Toth, 1993. "Heuristic Algorithms for the Multiple Depot Vehicle Scheduling Problem," Management Science, INFORMS, vol. 39(1), pages 115-125, January.
    2. Forbes, M. A. & Holt, J. N. & Watts, A. M., 1994. "An exact algorithm for multiple depot bus scheduling," European Journal of Operational Research, Elsevier, vol. 72(1), pages 115-124, January.
    3. Pamela H. Vance & Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser, 1997. "Airline Crew Scheduling: A New Formulation and Decomposition Algorithm," Operations Research, INFORMS, vol. 45(2), pages 188-200, April.
    4. Celso C. Ribeiro & François Soumis, 1994. "A Column Generation Approach to the Multiple-Depot Vehicle Scheduling Problem," Operations Research, INFORMS, vol. 42(1), pages 41-52, February.
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    Cited by:

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    5. Karabuk, Suleyman, 2009. "A nested decomposition approach for solving the paratransit vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 448-465, May.

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