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The energy transition in transportation benefits from demand-based models todetermine the optimal placement of refueling stations for alternative fuelvehicles such as battery electric trucks. A formulation known as the refuelingstation location problem with routing (RSLP-R) is concerned with minimizing thenumber of stations necessary to cover a set of origin-destination trips suchthat the transit time does not exceed a given threshold. In this paper weextend the RSLP-R by station capacities to limit the number of vehicles thatcan be refueled at individual stations. The solution to the capacitated RSLP-R(CRSLP-R) avoids congestion of refueling stations by satisfying capacityconstraints. We devise two optimization methods to deal with the increaseddifficulty to solve the CRSLP-R. The first method extends a priorbranch-and-cut approach and the second method is a branch-cut-and-pricealgorithm based on variables associated with feasible routes. We evaluate bothour methods on instances from the literature as well as a newly constructednetwork and find that the relative performance of the algorithms depends on thestrictness of the capacity constraints. Furthermore, we show some runtimeimprovements over prior work on uncapacitated instances.

Optimization methods for the capacitated refueling station location problem with routing