A Stochastic Model of the Dynamic Vehicle Allocation Problem

The stochastic vehicle allocation problem addresses the movement of vehicles between locations over a given planning horizon. The demand for vehicles to carry loads between locations is uncertain, and vehicles are assumed to be able to handle several loads over the course of the planning horizon. This requires tracking the movement of both loaded and empty vehicles, resulting in a network with stochastic flows. The methodology represents the flows of vehicles over the network explicitly as random variables, taking advantage of the acyclic structure of the time space network. The decision variables are formulated in terms of sending a certain fraction of the supply of vehicles at a node (which is random) over each of the outbound links. The result is a nonseparable objective function with a very simple constraint structure which lends itself readily to the Frank-Wolfe algorithm. Numerical experiments suggest very good computational efficiency.