An edge scanning method for the continuous deviation‐flow refueling station location problem on a general network

Abstract

AbstractThis study addresses the continuous deviation‐flow refueling station location problem on a general network. Instead of having a finite number of candidate locations, we consider any point in the network as a candidate location. In addition, vehicles are allowed to deviate from their prescribed (shortest) paths to refuel. At the beginning, we focus on the location of a single refueling facility, which is a relevant problem in the initial stages of development of a refueling infrastructure for alternative fuels in a transportation network. The objective is to maximize the traffic flow covered (in roundtrips per time unit). We propose an exact algorithm that determines the endpoints of all refueling segments on each edge of the network that cover the corresponding origin–destination flows. Then, the set with the best endpoints is shown to be optimal and can be used to determine the entire set of optimal locations. Network reduction rules and a network decomposition procedure are also discussed to reduce the size of the problem and improve the computational efficiency. Later, the entire set of endpoints is used in a set covering model to locate multiple refueling stations under the assumption that every vehicle only needs to refuel once on each way of the round trip. Moreover, we limit the allowed refueling deviation distance from the shortest path. Finally, a numerical example is provided to illustrate the proposed methodology.