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A Benders Decomposition Approach for the Hybrid Charging Station Location Problem

With the introduction of alternative fuel vehicles into the transportation system, the refueling station location research has been touted in the literature. The flow refueling location problem (FRLP) locates p stations in order to maximize the flow volume that can be accommodated in a road network respecting the range limitations of the vehicles. This paper introduces the hybrid charging station location problem (HCSLP) as an extension of the FRLP. We consider not only the electric vehicles (EVs) but also the plug-in hybrid electric vehicles (PHEVs) when locating the stations. Our objective is to maximize the vehicle-milestraveled (VMT) using electricity and thereby minimize the total cost of transportation under the existing cost structure between electricity and gasoline. This is also indirectly equivalent to maximizing the environmental benefits. We present an arc-cover formulation and a Benders decomposition algorithm as exact solution methodologies to solve the HCSLP. The decomposition algorithm is accelerated using Pareto-optimal cut generation schemes. The structure of the formulation allows us to construct the subproblem solutions, dual solutions and nondominated Pareto-optimal cuts as closed form expressions without having to solve any linear programs. This increases the efficiency of the decomposition algorithm by orders of magnitude and the results of the computational studies show that the proposed algorithm both accelerates the solution process and effectively handles instances of realistic size.