A vehicle routing problem with flexible time windows

In this paper, we introduce the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW), in which vehicles are allowed to deviate from customer time windows by a given tolerance. This flexibility enables savings in the operational costs of carriers, since customers may be served before and after the earliest and latest time window bounds, respectively. However, as time window deviations are undesired from a customer service perspective, a penalty proportional to these deviations is accounted for in the objective function. We develop a solution procedure, in which feasible vehicle routes are constructed via a tabu search algorithm. Furthermore, we propose a linear programming model to handle the detailed scheduling of customer visits for given routes. We validate our solution procedure by a number of Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances. We highlight the costs involved in integrating flexibility in time windows and underline the advantages of the VRPFlexTW, when compared to the VRPTW.