A local branching matheuristic for the multi-vehicle routing problem with stochastic demands

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.