Applying Simulation and Reliability to Vehicle Routing Problems with Stochastic Demands

Vehicle Routing Problems (VRPs) cover a wide range of well-known NP-hard problems where the aim is to serve a set of customers with a fleet of vehicles under certain constraints. Literature contains several approaches -coming from different fields like Operations Research, Artificial Intelligence and Computer Sciencewhich try to get good (near-optimal) solutions for small-, midand large-size instances. The Vehicle Routing Problem with Stochastic Demands (CVRPSD) is a particular case of VRP where demands made by clients are random, which introduces uncertainty in the problem. Thus, a good aprioristic solution may become unfeasible during the delivery phase if total demand in a route exceeds total vehicle capacity. This paper presents a flexible approach for the CVRPSD, which is based on the combined use of Monte Carlo simulation and reliability indices. Our methodology provides a set of alternative solutions for a given CVRPSD instance. These solutions depend on a parameter which controls the probability of suffering route failures during the actual delivering phase. A numerical example illustrates the methodology and its potential applications. Proceedings of the 16th International RCRA workshop (RCRA 2009): Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion Reggio Emilia, Italy, 12 December 2009