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A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen

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Abstract

We address a variant of the vehicle routing problem with time windows that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to visit this customer. In addition, the objective function consists of minimizing a weighted sum of the total number of routes, number of deliverymen and traveled distance. These characteristics make this variant very challenging for exact methods. To date, only heuristic approaches have been proposed for this problem, and even the most efficient optimization solvers cannot find optimal solutions in a reasonable amount of time for instances of moderate size when using the available mathematical formulations. We propose a branch-price-and-cut method based on a new set partitioning formulation of the problem. To accelerate the convergence of the method, we rely on an interior-point column and cut generation process, a strong branching strategy and a mixed-integer programming-based primal heuristic. Additionally, a hierarchical branching strategy is used to take into account the different components of the objective function. The computational results indicate the benefits of using the proposed exact solution approach. We closed several instances of the problem and obtained upper bounds that were previously unknown in the literature.

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Acknowledgements

We would like to thank the two anonymous referees, who have made valuable comments and certainly improved the content of this paper.

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Authors and Affiliations

  1. Production Engineering Department, Federal University of Sao Carlos, Rodovia Washington Luis Km 235, Sao Carlos, SP, Brazil

    Pedro Munari & Reinaldo Morabito

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  1. Pedro Munari
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  2. Reinaldo Morabito
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Correspondence to Pedro Munari.

Additional information

This research has been supported by FAPESP (Sao Paulo Research Foundation, Brazil) under project numbers 2014/00939-8 and 2016/01860-1 and CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brazil) under project numbers 482664/2013-4 and 479328/2013-7.

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Munari, P., Morabito, R. A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen. TOP 26, 437–464 (2018). https://doi.org/10.1007/s11750-018-0481-8

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