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The energy transition in transportation benefits from demand-based models to determine the optimal placement of refueling stations for alternative fuel vehicles such as battery electric trucks. A formulation known as the refueling station location problem with routing (RSLP-R) is concerned with minimizing the number of stations necessary to cover a set of origin-destination trips such that the transit time does not exceed a given threshold. In this paper we extend the RSLP-R by station capacities to limit the number of vehicles that can be refueled at individual stations. The solution to the capacitated RSLP-R (CRSLP-R) avoids congestion of refueling stations by satisfying capacity constraints. We devise two optimization methods to deal with the increased difficulty to solve the CRSLP-R. The first method extends a prior branch-and-cut approach and the second method is a branch-cut-and-price algorithm based on variables associated with feasible routes. We evaluate both our methods on instances from the literature as well as a newly constructed network and find that the relative performance of the algorithms depends on the strictness of the capacity constraints. Furthermore, we show some runtime improvements over prior work on uncapacitated instances.