An Adjustable Robust Formulation and a Decomposition Approach for the Green Vehicle Routing Problem with Uncertain Waiting Time at Recharge Stations

We investigate the problem of routing a fleet of electric vehicles in an urban area, which must serve a set of customers within predefined time windows. We allow partial battery recharge to any available recharge stations, located in the area. Since the recharge stations could be busy when a driver arrives for charging operations, the time spent can be seen as the sum of recharge times and waiting times. We model the waiting times as uncertain parameters and we assume to do not know their distribution. Hence, we address the problem under the robust optimization framework by modelling the realization of the uncertain parameter with the budget of uncertainty polytope. We propose an adjustable robust formulation, then we implement a rowand-column generation solution approach based on a two-stage reformulation of the problem, to provide a robust routing against infeasibility with respect to time collect requirements. We test the proposed approach on benchmark instances and we analyze the behavior of the considered transportation system with respect to the uncertain parameter. In addition, we investigate the price of robustness and the reliability of the robust solutions obtained.