This paper proposes a local branching matheuristic for the vehicle routing problem with stochastic demands (VRPSD). The problem is cast in a two-stage stochastic programming model, in which routes are planned in the first stage and executed in the second stage. In this setting, a failure may occur if a vehicle does not have sufficient capacity to serve the realized demand of a customer, which is revealed only upon arrival at a customer’s location. In the event of a failure, a recourse action is performed by having the vehicle return to the depot to replenish its capacity and resume its planned route at the point of failure. Thus, the objective of the VRPSD is to minimize the sum of the planned routes cost and of the expected recourse cost. We propose a local branching matheuristic to solve the multi-VRPSD. We introduce an intensification procedure applied at each node of the local branching tree. This procedure is embedded in a multi-descent scheme for which we propose a diversification strategy. Extensive computational results demonstrate the effectiveness of our matheuristic.

中文翻译：

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具有随机需求的多车辆路径问题的局部分支数学

本文提出了具有随机需求的车辆路径问题的局部分支数学方法（VRPSD）。该问题是在两阶段随机规划模型中提出的，该模型在第一阶段规划路线并在第二阶段执行路线。在这种情况下，如果车辆的容量不足以满足客户的实际需求，则可能会发生故障，只有在到达客户的位置时才会显示出来。如果发生故障，则通过使车辆返回仓库以补充其容量并在故障点恢复其计划路线来执行补救措施。因此，VRPSD的目标是使计划路线成本和预期追索成本之和最小。我们提出了一种局部分支数学方法来解决多VRPSD问题。我们介绍了在本地分支树的每个节点上应用的强化过程。该程序嵌入到多下降方案中，为此我们提出了多元化策略。大量的计算结果证明了我们数学的有效性。