Intersection of a continuous 1-location problem on a tree network

This study develops the methodology that determines the continuous interval of the potential locations for a single alternative-fuel refueling station on a tree network, with an objective of maximizing the amount of traffic flows in round trips per time unit captured by the station, if the assumption that positive traffic flows are required is relaxed. The set consisting of all intersection vertices is constructed to check the feasible locations of the network, and the properties of the intersection vertex are discussed. Based on these properties, the finite dominating set that guarantees the optimal locations either on the intersection vertex or the endpoint of the segment that identifies all feasible candidate sites of a single refueling station is derived. Then it goes through the computational complexity of the methodology and extends the optimal solution to some interior line segment.