A branch-and-price approach for a multi-period vehicle routing problem

In this paper, we consider tactical planning for a class of the multi-period vehicle routing problem (MPVRP). This problem involves optimizing daily product collections from several production locations over a given planning horizon. In this context, a single vehicle routing plan for the whole horizon must be prepared, and the seasonal variations in the producers' supplies must be taken into account. The production variations over the horizon are approximated using a sequence of periods, each corresponding to a production season, while the intra-period variations are neglected. We propose a mathematical model that is based on the two-stage a priori optimization paradigm. The first stage corresponds to the design of a plan which, in the second stage, takes the different periods into account. The proposed set-partitioning-based formulation is solved using a branch-and-price approach. The subproblem is a multi-period elementary shortest path problem with resource constraints (MPESPPRC), for which we propose an adaptation of the dynamic-programming-based label-correcting algorithm. Computational results show that this approach is able to solve instances with up to twenty producers and five periods.