A Set-Partitioning-Based Model for the Stochastic Vehicle Routing Problem

The objective of the Vehicle Routing Problem (VRP) is to construct a minimum cost set of vehicle routes that visits all customers and satisfies demands without violating the vehicle capacity constraints. The Stochastic Vehicle Routing Problem (SVRP) results when one or more elements of the VRP are modeled as random variables. In this paper, we present a set-partitioning-based modeling framework for the VRP with stochastic demands (VRPSD). The framework can be adapted easily for routing problems with randomness in other problem elements, such as random customers and random travel times. We formulate the VRPSD as a two-stage stochastic program and introduce an extended recourse strategy in which vehicles are allowed to serve additional customers from failed routes prior to returning to the depot or to serve customers from failed routes on a new route after returning to the depot. Computational experiments show that route plans generated using the new recourse function perform quite well, especially for problems with few customers per route, where cost savings of roughly 5% are possible.