Application of integer and mixed-integer programming on the facility location problem with equal capacities

This study introduces mathematical models for solving real location problems of two transportation networks with 59 and 120 nodes by applying integer and mixed-integer programming. The aim is to determine the number and locations of overhaul facilities and to minimize the weighted distance between potential clients and overhaul facilities. The solutions are compared by combining the following requirements: all clients need to be fully serviced; the capacity of overhaul facilities must not be exceeded; each overhaul facility must provide at least minimum working capacity (75%); partial servicing is allowed (clients from the same node can be serviced by more than one overhaul facility). It is assumed that all overhaul facilities have the same equipment and that the servicing needs are known. The experiments have shown that the solutions of the models are provided in less time using mixed-integer programming in comparison to integer programming.