Solving the capacitated vehicle routing problem with maximum traveling distance and service time requirements: an approach based on Monte Carlo simulation

This paper presents an approach based on Monte Carlo Simulation (MCS) to solve the Capacitated Vehicle Routing Problem (CVRP) with maximum traveling distance per route and additional costs per service, which introduces additional challenges to the classical CVRP. The basic idea behind our approach is to combine direct MCS with an efficient heuristics --e.g. the Clarke and Wright Savings (CWS) algorithm-- and a divide-and-conquer technique. The CWS heuristics provides a constructive methodology which is improved in two ways: (i) a special random behavior is introduced in the methodology --in this case, a geometric distribution is used for this purpose; and (ii) a divide-and-conquer technique is used to decompose the original problem in smaller sub-problems that are easy to deal with. Our approach is then validated using a set of well-known benchmarks. Finally, the paper discusses some advantages and disadvantages of our approach with respect other existing approaches.