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

Pedro Munari (munari***at***dep.ufscar.br)
Reinaldo Morabito (morabito***at***dep.ufscar.br)

Abstract: We address a variant of the vehicle routing problem with time windows (VRPTW) 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 (BPC) 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 (MIP)-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.

Keywords: vehicle routing, multiple deliverymen, time windows, column generation, branch-price-and-cut, interior point, city logistics

Category 1: Applications -- OR and Management Sciences (Transportation )

Category 2: Integer Programming

Category 3: Combinatorial Optimization

Citation: Munari, P.; Morabito, R. A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen. Technical Report, Production Engineering Department, Federal University of São Carlos, Rod. Washington Luís, km 235 - SP-310, São Carlos - SP - CEP: 13565-905, Brazil. January, 2016.

Download: [PDF]

Entry Submitted: 01/16/2016
Entry Accepted: 01/17/2016
Entry Last Modified: 09/17/2017

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