On Modeling Stochastic Travel and Service Times in Vehicle Routing

Vehicle routing problems with stochastic travel and service times (VRPSTT) consist of designing transportation routes of minimal expected cost over a network where travel and service times are represented by random variables. Most of the existing approaches for VRPSTT are conceived to exploit the properties of the distributions assumed for the random variables. Therefore, these methods are tied to a given family of distributions and subject to strong modeling assumptions. We propose an alternative way to model travel and service times in VRPSTT without making many assumptions regarding such distributions. To illustrate our approach, we embed it into a state-of-the-art routing engine and use it to conduct experiments on instances with different travel and service time distributions.