The Vehicle Routing Problem with Stochastic Two-Dimensional Items

Abstract

We consider a stochastic vehicle routing problem where a discrete probability distribution characterizes the two-dimensional size (height and width) as well as the weight of a subset of items to be delivered to customers. Although some item sizes and weights are not known with certainty when the routes are planned, they become known when it is time to load the vehicles, just before their departure. If it happens that not all items can be loaded in a vehicle, the items of one or more customers are put aside at a penalty or recourse cost. The objective is to minimize the sum of the routing and expected recourse costs. The problem is modeled as a two-stage stochastic program and solved with the integer L-shaped method. Some new inequalities and lower bounds are proposed. Computational results are reported on test instances specifically generated for this problem, as well as on classical instances for the deterministic case.