Linear edge costs and labeling algorithms: The case of the time-dependent vehicle routing problem with time windows

In this paper we implement a branch-price and cut algorithm for a time dependent vehicle routing problem with time windows in which the goal is to minimize the total route duration. The travel time between two customers is given by a piecewise linear function on the departure time and, thus, it need not remain fixed along the planning horizon. We discuss different alternatives for the implementation of these linear functions within the labeling algorithm applied to solve the pricing problem. We also provide a tailored implementation for one of these alternatives, relying on efficient data structures for storing the labels, and show several strategies to accelerate the algorithm. Computational results show that the proposed techniques are effective and improve the column generation step, solving all instances with 25 customers, 49 of 56 with 50 customers, and many instances with 100 customers. Furthermore, heuristic adaptations are able to find good quality solutions in reasonable computation times.Fil: Lera Romero, Gonzalo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad Torcuato Di Tella; ArgentinaFil: Miranda Bront, Juan Jose. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Soulignac, Francisco Juan. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentin