On the exact solution of the multi-depot open vehicle routing problem

The multi-depot open vehicle routing problem (MDOVRP) is a variant of the classical capacitated vehicle routing problem, where the vehicles can depart from different depots and they do not need to go back to the depot at the end of the route. This paper presents an exact branch-cut-and-price algorithm for the problem that is coded within the VRPSolver framework. In order to prove the robustness of the proposed method, we present several computational experiments over 24 MDOVRP benchmark instances. The results allow us to draw two important conclusions. The first one is that the proposed algorithm solves to the optimality all literature instances including eight that were open so far while the second one is that our algorithm outperforms the former state-of-art. Besides, we propose 440 MDOVRP instances with up to 200 nodes, where 418 of them are solved to the optimality by the proposed method. Another contribution of this paper is to show how to adapt the proposed method for the MDOVRP variant with time windows constraints (MDOVRPTW). We also apply our approach to MDOVRP and MDOVRPTW variants with a single depot. The results for all variants show that our method find the optimal solution for almost all tested instances in reasonable computational times.