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Balanced vehicle routing: Polyhedral analysis and branch-and-cut algorithm

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  • Bektaş, Tolga
  • Gouveia, Luis
  • Martínez-Sykora, Antonio
  • Salazar-González, Juan-José

Abstract

This paper studies a variant of the unit-demand Capacitated Vehicle Routing Problem, namely the Balanced Vehicle Routing Problem, where each route is required to visit a maximum and a minimum number of customers. A polyhedral analysis for the problem is presented, including the dimension of the associated polyhedron, description of several families of facet-inducing inequalities and the relationship between these inequalities. The inequalities are used in a branch-and-cut algorithm, which is shown to computationally outperform the best approach known in the literature for the solution of this problem.

Suggested Citation

  • Bektaş, Tolga & Gouveia, Luis & Martínez-Sykora, Antonio & Salazar-González, Juan-José, 2019. "Balanced vehicle routing: Polyhedral analysis and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 273(2), pages 452-463.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:2:p:452-463
    DOI: 10.1016/j.ejor.2018.08.034
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    References listed on IDEAS

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    1. Letchford, Adam N. & Salazar-González, Juan-José, 2015. "Stronger multi-commodity flow formulations of the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 730-738.
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    5. Bektaş, Tolga, 2012. "Formulations and Benders decomposition algorithms for multidepot salesmen problems with load balancing," European Journal of Operational Research, Elsevier, vol. 216(1), pages 83-93.
    6. Augerat, P. & Belenguer, J. M. & Benavent, E. & Corberan, A. & Naddef, D., 1998. "Separating capacity constraints in the CVRP using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 546-557, April.
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    Cited by:

    1. Michiel A. J. uit het Broek & Albert H. Schrotenboer & Bolor Jargalsaikhan & Kees Jan Roodbergen & Leandro C. Coelho, 2021. "Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm," Operations Research, INFORMS, vol. 69(2), pages 380-409, March.
    2. Rodrigo Linfati & Fernando Yáñez-Concha & John Willmer Escobar, 2022. "Mathematical Models for the Vehicle Routing Problem by Considering Balancing Load and Customer Compactness," Sustainability, MDPI, vol. 14(19), pages 1-20, October.
    3. Angel A. Juan & Peter Keenan & Rafael Martí & Seán McGarraghy & Javier Panadero & Paula Carroll & Diego Oliva, 2023. "A review of the role of heuristics in stochastic optimisation: from metaheuristics to learnheuristics," Annals of Operations Research, Springer, vol. 320(2), pages 831-861, January.
    4. Yong Wang & Yingying Yuan & Xiangyang Guan & Haizhong Wang & Yong Liu & Maozeng Xu, 2019. "Collaborative Mechanism for Pickup and Delivery Problems with Heterogeneous Vehicles under Time Windows," Sustainability, MDPI, vol. 11(12), pages 1-30, June.

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