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Implicit depot assignments and rotations in vehicle routing heuristics

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  • Vidal, Thibaut
  • Crainic, Teodor Gabriel
  • Gendreau, Michel
  • Prins, Christian

Abstract

Vehicle routing variants with multiple depots and mixed fleet present intricate combinatorial aspects related to sequencing choices, vehicle type choices, depot choices, and depots positioning. This paper introduces a dynamic programming methodology for efficiently evaluating compound neighborhoods combining sequence-based moves with an optimal choice of vehicle and depot, and an optimal determination of the first customer to be visited in the route, called rotation. The assignment choices, making the richness of the problem, are thus no more addressed in the solution structure, but implicitly determined during each move evaluation. Two meta-heuristics relying on these concepts, an iterated local search and a hybrid genetic algorithm, are presented. Extensive computational experiments demonstrate the remarkable performance of these methods on classic benchmark instances for multi-depot vehicle routing problems with and without fleet mix, as well as the notable contribution of the implicit depot choice and positioning methods to the search performance. New state-of-the-art results are obtained for multi-depot vehicle routing problems (MDVRP), and multi-depot vehicle fleet mix problems (MDVFMP) with unconstrained fleet size. The proposed concepts are fairly general, and widely applicable to many other vehicle routing variants.

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  • Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2014. "Implicit depot assignments and rotations in vehicle routing heuristics," European Journal of Operational Research, Elsevier, vol. 237(1), pages 15-28.
    • Handle: RePEc:eee:ejores:v:237:y:2014:i:1:p:15-28
    DOI: 10.1016/j.ejor.2013.12.044
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    2. Schmidt, Carise E. & Silva, Arinei C.L. & Darvish, Maryam & Coelho, Leandro C., 2023. "Time-dependent fleet size and mix multi-depot vehicle routing problem," International Journal of Production Economics, Elsevier, vol. 255(C).
    3. Rafael Martinelli & Claudio Contardo, 2015. "Exact and Heuristic Algorithms for Capacitated Vehicle Routing Problems with Quadratic Costs Structure," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 658-676, November.
    4. Rahma Lahyani & Leandro C. Coelho & Jacques Renaud, 2018. "Alternative formulations and improved bounds for the multi-depot fleet size and mix vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(1), pages 125-157, January.
    5. Baozhen Yao & Chao Chen & Xiaolin Song & Xiaoli Yang, 2019. "Fresh seafood delivery routing problem using an improved ant colony optimization," Annals of Operations Research, Springer, vol. 273(1), pages 163-186, February.
    6. Fatih Kocatürk & G. Yazgı Tütüncü & Said Salhi, 2021. "The multi-depot heterogeneous VRP with backhauls: formulation and a hybrid VNS with GRAMPS meta-heuristic approach," Annals of Operations Research, Springer, vol. 307(1), pages 277-302, December.

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