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An Improved Branch-and-Cut Algorithm for the Capacitated Vehicle Routing Problem

Author

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  • N. R. Achuthan

    (Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Western Australia 6845)

  • L. Caccetta

    (Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Western Australia 6845)

  • S. P. Hill

    (Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, Western Australia 6845)

Abstract

The capacitated vehicle routing problem (CVRP) deals with the distribution of a single commodity from a centralized depot to a number of specified customer locations with known demands. The CVRP considered in this paper assumes common vehicle capacity, fixed or variable number of vehicles, and an objective to minimize the total distance traveled by all the vehicles. This paper develops several new cutting planes for this problem, and uses them in an exact branch-and-cut algorithm. Two of the new cutting planes are based on a specified structure of an optimal solution and its existence. Computational results are reported for 1,650 simulated Euclidean problems as well as 24 standard literature test problems; solved problems range in size from 15–100 customers. A comparative analysis demonstrates the significant computational benefit of the proposed method.

Suggested Citation

  • N. R. Achuthan & L. Caccetta & S. P. Hill, 2003. "An Improved Branch-and-Cut Algorithm for the Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 37(2), pages 153-169, May.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:2:p:153-169
    DOI: 10.1287/trsc.37.2.153.15243
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    References listed on IDEAS

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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. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm," European Journal of Operational Research, Elsevier, vol. 248(1), pages 33-51.
    3. Boshuai Zhao & Kai Wang & Wenchao Wei & Roel Leus, 2024. "The Dial-a-Ride Problem with Limited Pickups per Trip," Papers 2408.07602, arXiv.org, revised Aug 2024.
    4. Qiuping Ni & Yuanxiang Tang, 2023. "A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research," Sustainability, MDPI, vol. 15(9), pages 1-37, April.
    5. Çetinkaya, Cihan & Karaoglan, Ismail & Gökçen, Hadi, 2013. "Two-stage vehicle routing problem with arc time windows: A mixed integer programming formulation and a heuristic approach," European Journal of Operational Research, Elsevier, vol. 230(3), pages 539-550.
    6. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2011. "A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery," European Journal of Operational Research, Elsevier, vol. 211(2), pages 318-332, June.
    7. Leggieri, Valeria & Haouari, Mohamed, 2017. "Lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 263(3), pages 755-767.
    8. Karaoglan, Ismail & Altiparmak, Fulya & Kara, Imdat & Dengiz, Berna, 2012. "The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach," Omega, Elsevier, vol. 40(4), pages 465-477.
    9. Uchoa, Eduardo & Pecin, Diego & Pessoa, Artur & Poggi, Marcus & Vidal, Thibaut & Subramanian, Anand, 2017. "New benchmark instances for the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 845-858.

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