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.

多站点开放车辆路径问题（MDOVRP）是经典的有能力车辆路径问题的变体，其中车辆可以从不同的站点出发，并且不需要在路线结束时返回站点。本文针对在 VRPSolver 框架内编码的问题提出了一种精确的分支切割和定价算法。为了证明所提出方法的鲁棒性，我们在 24 个 MDOVRP 基准实例上进行了多次计算实验。结果使我们得出两个重要结论。第一个是所提出的算法解决了所有文献实例的最优性，包括迄今为止公开的八个文献实例，而第二个是我们的算法优于以前的最新技术。此外，我们提出了 440 个 MDOVRP 实例，最多 200 个节点，其中 418 个实例通过所提出的方法解决了最优问题。本文的另一个贡献是展示如何针对具有时间窗口约束的 MDOVRP 变体（MDOVRPTW）调整所提出的方法。我们还将我们的方法应用于具有单个仓库的 MDOVRP 和 MDOVRPTW 变体。所有变体的结果表明，我们的方法在合理的计算时间内找到了几乎所有测试实例的最佳解决方案。