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A Branch-and-Price-and-Cut Algorithm for the Vehicle Routing Problem with Two-Dimensional Loading Constraints

Author

Listed:
  • Xiangyi Zhang

    (Civil Flight Service, CAE Inc, Saint-Laurent, Quebec H4T 1G6, Canada)

  • Lu Chen

    (School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Michel Gendreau

    (Département de Mathématiques et de Génie Industriel, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada; Centre Interuniversitaire de Recherche sur les Réseaux d’Entreprise, la Logistique et le Transport, Montreal, Quebec H3C 3J7, Canada)

  • André Langevin

    (Département de Mathématiques et de Génie Industriel, Polytechnique Montréal, Montreal, Quebec H3C 3A7, Canada; Centre Interuniversitaire de Recherche sur les Réseaux d’Entreprise, la Logistique et le Transport, Montreal, Quebec H3C 3J7, Canada)

Abstract

The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) is a practical variant of the classic capacitated vehicle routing problem. A number of algorithms have been developed for the problem, but it is very difficult for the existing exact methods to optimally solve instances featuring with large rectangular items. To address this issue, a branch-and-price-and-cut (BPC) algorithm is proposed in this study. A novel data structure and a new dominance rule are developed to build an exact pricing algorithm that takes the loading constraints into account. Several valid inequalities are used to strengthen the linear relaxation. Extensive computational experiments were conducted on the benchmark instances of the 2L-CVRP, showing that the BPC algorithm outperforms all the existing exact methods for the problem in terms of the solution quality. Fourteen instances are solved to optimality for the first time. In particular, the size of solvable instances with large items is nearly doubled. Moreover, managerial insights about the impact of respecting the last-in-first-out constraint are also obtained.

Suggested Citation

  • Xiangyi Zhang & Lu Chen & Michel Gendreau & André Langevin, 2022. "A Branch-and-Price-and-Cut Algorithm for the Vehicle Routing Problem with Two-Dimensional Loading Constraints," Transportation Science, INFORMS, vol. 56(6), pages 1618-1635, November.
    • Handle: RePEc:inm:ortrsc:v:56:y:2022:i:6:p:1618-1635
    DOI: 10.1287/trsc.2022.1135
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