Robust alternative fuel refueling station location problem with routing under decision-dependent flow uncertainty

The refueling station location problem with routing (RSLP-R) is defined as a maximal coverage problem that locates alternative fuel refueling stations (AFSs) on a road network to maximize the refueled alternative fuel vehicle flows by considering the limited range of vehicles and the willingness of drivers to deviate from their paths for refueling. In this study, we introduce the robust counterpart of RSLP-R using a decision-dependent polyhedral uncertainty set. We model the flow uncertainty set using a hybrid model that comprises a hose model and individual flow bounds. To take into account the fact that vehicle flows are affected by AFS deployment decisions in their neighborhoods, we incorporate the decision-dependency notion into the flow uncertainty set. We propose two linear mixed integer programming formulations and a Benders reformulation. Our computational experiments on instances based on the road network of Belgium confirm the effectiveness of the reformulation in solving larger instances. We also report the results of experiments to assess the value of incorporating uncertainty and decision-dependency into the problem.