A fuzzy measure of vulnerability for the optimisation of vehicle routing problems with time windows

Abstract

In a vehicle routing problem (VRP) with time windows, the start of service needs to take place within the customer time window. Due to uncertainty on travel times, vehicles might arrive late at a customer’s site. A VRP is mostly solved to minimize a total cost criterion (travel time, travel distance, fixed and variable vehicle costs). But the dispatcher might also take into consideration the risk of non-conformance with the service agreement to start service within the time window. Therefore, a measure of risk, called “vulnerability of a solution,” is developed to serve as a second criterion. This chapter develops such a measure based on a distance metric and investigates its strengths and weaknesses.