A location problem on unicyclic networks: Balanced case

The problem of locating n stations on a unicyclic unidirectional network is considered. The authors formulated the problem as an integer program for the case of a balanced flow matrix, i.e., the total inflow to a station equals the total outflow from that station. The integer programming formulation reduces the problem to a station sequencing problem regardless of the actual station locations on the network. Furthermore, the empirical evidence suggests that the LP solutions to the relaxed IP formulations are optimal.