Application of the Yen's algorithm to the continuous single refueling station location problem on a circuit network

Abstract

Depending on the set of candidate sites, we can classify refueling station location problems as the discrete location problem, where the stations can be located only at the predetermined sites, and the continuous location problem, where they can be placed anywhere along the network. The continuous location problem recently draws attention since it can improve the solution of the discrete counterpart, but this problem is challenging because of the infinite size of the search space. To simplify the problem and find the solution in polynomial time, most recent studies address this problem on tree-like networks. Many road networks, however, have circuits in their structure, and drivers can detour using one of the multiple paths when refueling. In this study, we address the continuous location problem on a general network having circuits to locate a single refueling station. We revise the Yen's algorithm to incorporate the vehicle driving range and the fuel tank levels when finding all detour options. We solve numerical examples to illustrate the proposed method and to verify its performance.