A Hybrid Heuristic for the Probabilistic Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

Abstract

The Probabilistic Capacitated Vehicle Routing Problem (PCVRP) is a generalization of the classical Capacitated Vehicle Routing Problem (CVRP). The main difference is the stochastic presence of the customers, that is, the number of them to be visited each time is a random variable, where each customer associates with a given probability of presence. We consider a special case of the PCVRP, in which a fleet of identical vehicles must serve customers, each with a given demand consisting in a set of rectangular items. The vehicles have a two-dimensional loading surface and a maximum capacity. The resolution of problem consists in finding an a priori route visiting all customers which minimizes the expected length over all possibilities. We propose a hybrid heuristic, based on a branch-and-bound algorithm, for the resolution of the problem. The effectiveness of the approach is shown by means of computational results.