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Models for the single-vehicle preemptive pickup and delivery problem

Author

Listed:
  • H. L. M. Kerivin

    (Université Blaise-Pascal–Clermont-Ferrand II, Complexe Scientifique des Cézeaux
    Clemson University)

  • M. Lacroix

    (Université Blaise-Pascal–Clermont-Ferrand II, Complexe Scientifique des Cézeaux
    LAMSADE, CNRS UMR 7024)

  • A. R. Mahjoub

    (Université Blaise-Pascal–Clermont-Ferrand II, Complexe Scientifique des Cézeaux
    LAMSADE, CNRS UMR 7024)

Abstract

In this paper, we study a variant of the well-known single-vehicle pickup and delivery problem where the demands can be unloaded/reloaded at any node. By proving new complexity results, we give the minimum information which is necessary to represent feasible solutions. Using this, we present integer linear programs for both the unitary and the general versions. We then show that the associated linear relaxations are polynomial-time solvable and present some computational results.

Suggested Citation

  • H. L. M. Kerivin & M. Lacroix & A. R. Mahjoub, 2012. "Models for the single-vehicle preemptive pickup and delivery problem," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 196-223, February.
    • Handle: RePEc:spr:jcomop:v:23:y:2012:i:2:d:10.1007_s10878-010-9349-z
    DOI: 10.1007/s10878-010-9349-z
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    References listed on IDEAS

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    1. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
    2. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    3. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
    4. Grunert, Tore & Sebastian, Hans-Jurgen, 2000. "Planning models for long-haul operations of postal and express shipment companies," European Journal of Operational Research, Elsevier, vol. 122(2), pages 289-309, April.
    5. M. W. P. Savelsbergh & M. Sol, 1995. "The General Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 29(1), pages 17-29, February.
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    Cited by:

    1. Salazar-González, Juan-José & Santos-Hernández, Beatriz, 2015. "The split-demand one-commodity pickup-and-delivery travelling salesman problem," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 58-73.

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