Capacitated Refueling Station Location Problem with Traffic Deviations Over Multiple Time Periods

In this paper, we consider the problem of locating refueling stations in a transportation network via mathematical programming. The proposed model is applicable for several alternative fuel types and is particularly suitable for hydrogen fuel. We assume that a central planner, a hydrogen manufacturer or a government agency, determines the locations of the refueling stations for a given intra-city transportation network while accounting for multi-period travel demand, nonlinear refueling station operational cost, and the deviations of travelers from their shortest routes to refuel. Incorporating demand patterns over multiple periods allows us to account for both short- and long-term variation in hydrogen refueling demand (the former due to time of day, and the latter future hydrogen fuel cell vehicle growth). It also helps us model the changes in user preferences (station and route choices) and traffic conditions over different periods. To account for refueling station operational cost in making investment decisions, we introduce a staircase marginal cost function. In addition, the model explicitly considers station and route choices of travelers as they may deviate from their original paths to refuel, incurring additional costs and affecting the number and locations of refueling stations. We formulate this problem as a multi-period, mixed-integer model with constant link travel time and staircase operational cost at refueling stations. We applied two well-known solution algorithms, branch-and-bound and Lagrangian relaxation, to solve the problem. Our analysis shows that although we are able to solve the refueling station location problem to optimality with branch-and-bound, the Lagrangian relaxation approach provides very good results with less computational time. Additionally, our numerical example of Mashhad, Iran demonstrates that locating refueling stations with considering multi-period traffic patterns (as opposed to single-period) results in minimum network-wide traffic congestion and lower user and agency costs over a planning horizon.