A new exact algorithm to solve the multi-trip vehicle routing problem with time windows and limited duration

This article tackles the multi-trip vehicule routing problem with time windows and limited duration. A trip is a timed route such that a succession of trips can be assigned to one vehicle. We provide a two-phase exact algorithm to solve it. The first phase enumerates possible ordered lists of client matching trip maximum duration criterion. The second phase uses a Branch and Price scheme to generate and choose best set of trips to visit all customers. We propose a set covering formulation as the column generation master problem, where columns (variables) represent trips. The sub-problem selects appropriate timing for trips and has a pseudo-polynomial complexity. Computional results on Solomon’s benchmarks are presented. The computional times obtained with our new algorithm are much lower than the ones obtained in the sole exact algorithm previously published on this problem.