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Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem

Author

Listed:
  • Dominik Goeke

    (School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany)

  • Roberto Roberti

    (Department of Information, Logistics and Innovation, VU Amsterdam, 1081 HV Amsterdam, Netherlands)

  • Michael Schneider

    (School of Business and Economics, RWTH Aachen University, 52062 Aachen, Germany)

Abstract

Providing consistent service by satisfying customer demands with the same driver (driver consistency) at approximately the same time (arrival-time consistency) allows companies in last-mile distribution to stand out among competitors. The consistent vehicle-routing problem (ConVRP) is a multiday problem addressing such consistency requirements along with traditional constraints on vehicle capacity and route duration. The literature offers several heuristics but no exact method for this problem. The state-of-the-art exact technique to solve VRPs—column generation (CG) applied to route-based formulations in which columns are generated via dynamic programming—cannot be successfully extended to the ConVRP because the linear relaxation of route-based formulations is weak. We propose the first exact method for the ConVRP, which can solve medium-sized instances with five days and 30 customers. The method solves, via CG, a formulation in which each variable represents the set of routes assigned to a vehicle over the planning horizon. As an upper bounding procedure, we develop a large neighborhood search (LNS) featuring a repair procedure specifically designed to improve the arrival-time consistency of solutions. Used as stand-alone heuristic, the LNS is able to significantly improve the solution quality on benchmark instances from the literature compared with state-of-the-art heuristics.

Suggested Citation

  • Dominik Goeke & Roberto Roberti & Michael Schneider, 2019. "Exact and Heuristic Solution of the Consistent Vehicle-Routing Problem," Transportation Science, INFORMS, vol. 53(4), pages 1023-1042, July.
  • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:4:p:1023-1042
    DOI: 10.1287/trsc.2018.0864
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    3. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    4. Soriano, Adria & Vidal, Thibaut & Gansterer, Margaretha & Doerner, Karl, 2020. "The vehicle routing problem with arrival time diversification on a multigraph," European Journal of Operational Research, Elsevier, vol. 286(2), pages 564-575.
    5. Díaz-Ríos, Daniel & Salazar-González, Juan-José, 2024. "Mathematical formulations for consistent travelling salesman problems," European Journal of Operational Research, Elsevier, vol. 313(2), pages 465-477.
    6. Mohsen Emadikhiav & David Bergman & Robert Day, 2020. "Consistent Routing and Scheduling with Simultaneous Pickups and Deliveries," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1937-1955, August.
    7. Daniel Y. Mo & H. Y. Lam & Weikun Xu & G. T. S. Ho, 2020. "Design of Flexible Vehicle Scheduling Systems for Sustainable Paratransit Services," Sustainability, MDPI, vol. 12(14), pages 1-18, July.
    8. Quirion-Blais, Olivier & Chen, Lu, 2021. "A case-based reasoning approach to solve the vehicle routing problem with time windows and drivers’ experience," Omega, Elsevier, vol. 102(C).
    9. Xuming Wang & Jiaqi Zhou & Xiaobing Yu & Xianrui Yu, 2023. "A Hybrid Brain Storm Optimization Algorithm to Solve the Emergency Relief Routing Model," Sustainability, MDPI, vol. 15(10), pages 1-31, May.
    10. Liu, Chuanju & Zhang, Junlong & Lin, Shaochong & Shen, Zuo-Jun Max, 2023. "Service network design with consistent multiple trips," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 171(C).
    11. Mancini, Simona & Gansterer, Margaretha & Hartl, Richard F., 2021. "The collaborative consistent vehicle routing problem with workload balance," European Journal of Operational Research, Elsevier, vol. 293(3), pages 955-965.
    12. Rodríguez-Martín, Inmaculada & Yaman, Hande, 2022. "Periodic Vehicle Routing Problem with Driver Consistency and service time optimization," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 468-484.
    13. Nolz, Pamela C. & Absi, Nabil & Feillet, Dominique & Seragiotto, Clóvis, 2022. "The consistent electric-Vehicle routing problem with backhauls and charging management," European Journal of Operational Research, Elsevier, vol. 302(2), pages 700-716.
    14. Yang, Meng & Ni, Yaodong & Song, Qinyu, 2022. "Optimizing driver consistency in the vehicle routing problem under uncertain environment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    15. Zhou, Lin & Zhen, Lu & Baldacci, Roberto & Boschetti, Marco & Dai, Ying & Lim, Andrew, 2021. "A Heuristic Algorithm for solving a large-scale real-world territory design problem," Omega, Elsevier, vol. 103(C).

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