An optimal approach for a set covering version of the refueling-station location problem and its application to a diffusion model

This article deals with the refueling-station location problem for alternative fuel vehicles in a traffic network. Alternative fuel vehicles can be characterized by the vehicle range that limits the travelable distance with fuel at full capacity. I propose an efficient formulation of the refueling-station location problem using an optimal property and prove that the problem is NP(Non-deterministic Polynomial)-complete in the strong sense. I consider a special case of the refueling-station location problem in which the construction costs are equal for all nodes. In this case, the problem is to determine refueling station locations to minimize the total number of stations, while making the possible multiple predetermined origin–destination round-trips. I propose an optimal algorithm applicable when no refueling stations currently exist in a traffic network and a dynamic programming based algorithm applicable when a set of refueling stations already exists. I apply the algorithms to a traffic network to study the diffusion of refueling stations and predict the speed and range of station establishment. The computational experiments show that the speed of diffusion depends on the vehicle range and the sequence of the origin–destination demands considered in the diffusion process.