An efficient formulation of the flow refueling location model for alternative-fuel stations

The Flow-Refueling Location Model (FRLM) locates a given number of refueling stations on a network to maximize the traffic flow among origin-destination pairs that can be refueled given the driving range of alternative-fuel vehicles. Traditionally, the FRLM has been formulated using a two-stage approach: the first stage generates combinations of locations capable of serving the round trip on each route, and then a mixed-integer programming approach is used to locate p facilities to maximize the flow refueled given the feasible combinations created in the first stage. Unfortunately, generating these combinations can be computationally burdensome and heuristics may be necessary to solve large-scale networks. This article presents a radically different mixed-binary-integer programming formulation that does not require pre-generation of feasible station combinations. Using several networks of different sizes, it is shown that the proposed model solves the FRLM to optimality as fast as or faster than currently utilized greedy and genetic heuristic algorithms. The ability to solve real-world problems in reasonable time using commercial math programming software offers flexibility for infrastructure providers to customize the FRLM to their particular fuel type and business model, which is demonstrated in the formulation of several FRLM extensions.