Optimal location of discretionary alternative-fuel stations on a tree-network

Due to global concerns about environmental sustainability in ground logistics, there has been widespread research into alternative-fuel (alt-fuel) vehicles. Compressed natural gas buses have been successfully deployed on a commercial scale in public transportation. Also, sales for electric cars have been gradually increasing. However, uses of other alt-fuel vehicles are in their early stages because developing an infrastructure with refueling stations requires a huge investment. When setting up such an infrastructure, it is necessary to decide the number of refueling stations to be built and where they should be located to cover the maximum traffic flow that can be refueled on a given road network. In this research, we propose a mathematical model to determine optimal locations for a pre-determined number of refueling stations to maximize the traffic flow covered on a tree-network, which is a common structure of toll roads in many states. This model includes four types of constraints to identify number of trips covered for four possible ranges of travel distances between all possible pairs of vehicle origins and destinations.