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A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem

Author

Listed:
  • Letchford, Adam N.

    (Department of Management Science)

  • Lysgaard, Jens

    (Department of Business Studies)

  • Eglese, Richard W.

    (Department of Management Science)

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

  • Letchford, Adam N. & Lysgaard, Jens & Eglese, Richard W., 2006. "A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem," CORAL Working Papers L-2006-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbls:2006-006
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    File URL: http://www.hha.dk/bs/wp/log/L_2006_06.pdf
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    References listed on IDEAS

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    1. C D Tarantilis & G Ioannou & C T Kiranoudis & G P Prastacos, 2005. "Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 588-596, May.
    2. Brandao, Jose, 2004. "A tabu search algorithm for the open vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 552-564, September.
    3. 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.
    4. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    5. 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.
    6. 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.
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    Citations

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    Cited by:

    1. Liu, Ran & Jiang, Zhibin, 2012. "The close–open mixed vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 220(2), pages 349-360.
    2. T Bektaş & Seda Elmastaş, 2007. "Solving school bus routing problems through integer programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1599-1604, December.
    3. U Derigs & K Reuter, 2009. "A simple and efficient tabu search heuristic for solving the open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1658-1669, December.
    4. Fung, Richard Y.K. & Liu, Ran & Jiang, Zhibin, 2013. "A memetic algorithm for the open capacitated arc routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 50(C), pages 53-67.
    5. D Aksen & Z Özyurt & N Aras, 2007. "Open vehicle routing problem with driver nodes and time deadlines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1223-1234, September.
    6. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    7. Zhen, Lu & Tan, Zheyi & Wang, Shuaian & Yi, Wen & Lyu, Junyan, 2021. "Shared mobility oriented open vehicle routing with order radius decision," Transportation Research Part A: Policy and Practice, Elsevier, vol. 144(C), pages 19-33.
    8. Abdelkader Sbihi & Richard W. Eglese, 2007. "The Relationship between Vehicle Routing & Scheduling and Green Logistics - A Literature Survey," Working Papers hal-00644133, HAL.

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