Vehicle routing with stochastic time-dependent travel times

Assigning and scheduling vehicle routes in a stochastic time-dependent environment is a crucial management problem. The assumption that in a real-life environment everything goes according to an a priori determined static schedule is unrealistic. Our methodology builds on earlier work in which the traffic congestion is captured in an analytical way using queueing theory. The congestion is then applied to the VRP problem. In this paper, we introduce the variability in traffic flows into the model. This allows for an evaluation of the routes based on the uncertainty involved. Different experiments show that the risk taking behavior of the planner can be taken into account during optimization. As more weight is given to the variability component, the resulting optimal route will take a slightly longer travel time, but will be more reliable. We propose a powerful objective function that is easily implemented and that captures the trade-off between the average travel time and its variance. The evaluation of the solution is done in terms of the 95th-percentile of the travel time distribution (assumed to be lognormal), which reflects well the quality of the solution in this stochastic time-dependent environment.