Vehicle Routing with Stochastic Demands: Models & Computational Methods

Abstract

In this paper we provide an overview and modeling details regarding vehicle routing in situations in which customer demand is revealed only when the vehicle arrives at the customer’s location. Given a fixed capacity vehicle, this setting gives rise to the possibility that the vehicle on arrival does not have sufficient inventory to completely supply a given customer’s demand. Such an occurrence is called a route failure and it requires additional vehicle trips to fully replenish such a customer. Given a set of customers, the objective is to design vehicle routes and response policies which minimize the expected delivery cost by a fleet of fixed capacity vehicles. We survey the different problem statements and formulations. In addition, we describe a number of the algorithmic developments for constructing routing solutions. Primarily we focus on stochastic programming models with different recourse options. We also present a Markov decision approach for this problem and conclude with a cha llenging conjecture regarding finite sums of random variables.