Mathematical formulations for the multi-period alternative fuel refueling station location problem with routing under decision-dependent flow dynamics

The refueling station location problem with routing considers vehicles' ranges and drivers' preferences about their routes to improve the alternative fuel station infrastructure. Comprehensive planning is necessary for developing a mature infrastructure to overcome budgetary constraints and spatial limitations. Hence, adopting a multi-period planning approach becomes crucial when taking into account the evolving demand for alternative fuel vehicles over time. The evolution of demand can be dependent on exogenous and endogenous factors. Although it is typical to account for exogenous demand growth in multi-period planning, a few studies also take into account an endogenous factor which is the refueling opportunity of drivers on their paths. In this study, in addition to the refueling opportunities, we consider the proximity of each individual station to the flow-based demands. We draw attention to the significance of considering the effects of individual station locations on demand evolution, as these strategic locations can play an important role in reducing the drivers' range anxiety and increasing their acceptance of the technology. Hence, we introduce a multi-period alternative fuel refueling station location problem with routing under different vehicle flow evolution dynamics that employ various weights for the factors where the natural growth rate is exogenous and the decisions of station locations and flow coverage are endogenous to the problem. We propose three mixed integer linear programming formulations for different evolution dynamics. We carry out computational experiments on the real road networks of Belgium, California, and Turkey and present our findings on the performances of the proposed mathematical models and the gains that can be obtained by considering multi-period planning and incorporating the effects of decisions into the vehicle flow evolution.