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Open vehicle routing problem with split deliveries: mathematical formulations and a cutting-plane method

Author

Listed:
  • Efraín Ruiz y Ruiz

    (Tecnológico Nacional de México/Instituto Tecnológico de Saltillo)

  • Irma García-Calvillo

    (Universidad Autónoma de Coahuila)

  • Samuel Nucamendi-Guillén

    (Universidad Panamericana)

Abstract

This study addresses the open vehicle routing problem with split deliveries, a variant of the classical vehicle routing problem that allows open routes and partitioned deliveries for customers (i.e., multiple vehicles may serve one customer). This approach may be beneficial for companies interested in reducing their logistics and distribution costs. This study is motivated by a company in the pharmaceutical industry, that seeks to explore the possibility of splitting their deliveries to improve quality indicators related to on-time deliveries and customer satisfaction. Two mixed-integer formulations of the problem are proposed. Additionally, a cutting-plane method is designed to improve the optimization performance. Computational experiments were conducted to validate the performance of the formulations. The second formulation effectiveness was confirmed by providing optimal solutions for instances of up to 30 nodes in a reasonable computational time. The incorporation of the cutting-plane method improves performance with a substantial reduction in the GAP. In the case study, this new approach shows its effectiveness in economic terms by providing savings of up to 20% of the current distribution costs.

Suggested Citation

  • Efraín Ruiz y Ruiz & Irma García-Calvillo & Samuel Nucamendi-Guillén, 2022. "Open vehicle routing problem with split deliveries: mathematical formulations and a cutting-plane method," Operational Research, Springer, vol. 22(2), pages 1017-1037, April.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:2:d:10.1007_s12351-020-00580-8
    DOI: 10.1007/s12351-020-00580-8
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    References listed on IDEAS

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    1. Araque, J. & Hall, L. & Magnanti, T., 1990. "Capacitated trees, capacitated routing, and associated polyhedra," LIDAM Discussion Papers CORE 1990061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Archetti, Claudia & Savelsbergh, Martin W.P. & Grazia Speranza, M., 2008. "To split or not to split: That is the question," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(1), pages 114-123, January.
    3. P P Repoussis & C D Tarantilis & G Ioannou, 2007. "The open vehicle routing problem with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 355-367, March.
    4. Eduardo Lalla-Ruiz & Christopher Expósito-Izquierdo & Shervin Taheripour & Stefan Voß, 2016. "An improved formulation for the multi-depot open vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 175-187, January.
    5. C. Archetti & M. G. Speranza & A. Hertz, 2006. "A Tabu Search Algorithm for the Split Delivery Vehicle Routing Problem," Transportation Science, INFORMS, vol. 40(1), pages 64-73, February.
    6. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
    7. Gizem Ozbaygin & Oya Karasan & Hande Yaman, 2018. "New exact solution approaches for the split delivery vehicle routing problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 85-115, March.
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