The flow-refueling location problem for alternative-fuel vehicles

Beginning with Hodgson (Geogr.Anal.22(1990) 270), several researchers have been developing a new kind of location-allocation model for "flow capturing." Instead of locating central facilities to serve demand at fixed points in space, their models aim to serve demand consisting of origin-destination flows along their shortest paths. This paper extends flow-capturing models to optimal location of refueling facilities for alternative-fuel (alt-fuel) vehicles, such as hydrogen fuel cells or natural gas. Existing flow-capturing models assume that if a flow passes just one facility along its path, it is covered. This assumption does not carry over to vehicle refueling because of the limited range of vehicles. For refueling, it may be necessary to stop at more than one facility in order to successfully refuel the entire path, depending on the vehicle range, the path length, and the node spacing. The Flow Refueling Location Model (FRLM) optimally locates p refueling stations on a network so as to maximize the total flow volume refueled. This paper presents a mixed-integer programming formulation for the nodes-only version of the problem, as well as an algorithm for determining all combinations of nodes that can refuel a given path. A greedy-adding approach is demonstrated to be suboptimal, and the tradeoff curve between number of facilities and flow volume refueled is shown to be nonconvex.