A continuous network location problem for a single refueling station on a tree

• We consider the continuous version of the refueling station location problem on a tree network to maximize the traffic flow covered in round-trips/day.
• Two reduction properties regarding the problem size and some optimality conditions are derived.
• A polynomial algorithm is developed to determine the set of optimal locations for the refueling station.
• A small tree network example is solved to illustrate the algorithm.

This article considers the continuous version of the refueling station location problem on a tree network, which is a common structure in numerous toll roads worldwide, so as to locate a single alternative-fuel refueling station to maximize the traffic flow covered in round trips/day. Two reduction properties regarding the problem size and some optimality conditions are derived. Based on these conditions, an exact polynomial algorithm is developed to determine the set of optimal locations for the refueling station. A small tree network example is solved to illustrate the algorithm.