Finite dominating sets for the refueling station location problem in fleet operations

This study considers a set of routes used by public transportation vehicles and dedicated distribution fleets in a general network. We aim to optimally locate alternative fuel refueling stations in the network to serve these dedicated routes. Deviations from prescribed routes for refueling purposes are allowed. Unlike most related literature, our approach considers all points in the network as candidate refueling station locations. We derive coverage constraints for any candidate location to serve a given route. Then we develop an exact algorithm to establish a finite dominating set (FDS) of candidate locations guaranteed to include an optimal solution to the problem. This set can be used in a mathematical model to minimize the number of stations required to cover all flows in the network. Numerical experiments on realistic networks are presented to illustrate the proposed methodology and to demonstrate its scalability and sensitivity to changes in parameter values.