Discrete scenario-based optimization for the robust vehicle routing problem: The case of time windows under delay uncertainty

Abstract

In this paper we propose a robust optimization strategy for the vehicle routing problem with time windows, where the travel time is considered as uncertain. The objective is to minimize the risk of delay related to the time windows constraint. We first present a robust model in which the uncertain travel time is related to a discrete set of scenarios: each scenario can be viewed as an observation of time required to complete a current route. Such a model is based upon a mixed-integer linear programming that can handle an optimal (solution) value related to the worst observation of the total travel time over all available scenarios. Second, in order to evaluate the effects on the scenario model, a guided neighborhood search-based heuristic is adapted for solving the model and tested on a variety of instances obtained by using Solomon’s standard generator, where a total of 5040 instances are considered. Finally, we study the behavior of the adapted algorithm to solve the robust model and highlight the interaction between the number of scenarios used which are based upon uncertain events and the uncertainty of the problem.