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A branch-and-cut algorithm for the capacitated open vehicle routing problem

Author

Listed:
  • A N Letchford

    (Lancaster University)

  • J Lysgaard

    (Aarhus School of Business)

  • R W Eglese

    (Lancaster University)

Abstract

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.

Suggested Citation

  • A N Letchford & J Lysgaard & R W Eglese, 2007. "A branch-and-cut algorithm for the capacitated open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1642-1651, December.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602345
    DOI: 10.1057/palgrave.jors.2602345
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    References listed on IDEAS

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    1. Manfred W. Padberg & M. R. Rao, 1982. "Odd Minimum Cut-Sets and b -Matchings," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 67-80, February.
    2. Matteo Fischetti & Paolo Toth & Daniele Vigo, 1994. "A Branch-and-Bound Algorithm for the Capacitated Vehicle Routing Problem on Directed Graphs," Operations Research, INFORMS, vol. 42(5), pages 846-859, October.
    3. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    4. D Sariklis & S Powell, 2000. "A heuristic method for the open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(5), pages 564-573, May.
    5. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    6. Tarantilis, C. D. & Diakoulaki, D. & Kiranoudis, C. T., 2004. "Combination of geographical information system and efficient routing algorithms for real life distribution operations," European Journal of Operational Research, Elsevier, vol. 152(2), pages 437-453, January.
    7. Z Fu & R Eglese & L Y O Li, 2005. "A new tabu search heuristic for the open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 267-274, March.
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