A Lagrangean Relaxation Method for the Zero-One Facility Location Problem with Uniform Customer Demand and Facility Capacities

Abstract

Consider a capacitated facility location problem in which the demands of customers are all equal and so are the capacities of facilities. Under the restriction that each customers uniform demand be met by exactly one facility, the objective is to select a set of facilities to open, and to assign custormers demand to them so as to minimize the total cost which includes fixed costs of opening facilties as well as variable assignment costs. The problem is modelled as a pure zero-one program which may be viewed as a variant of well-known capacitated facility location problems. The purpose of this study is to develop dfficient computational procedures for solving the pure zero-one facility location problems. Due to the special structure of our zero-one location problem with uniform demand, it can be converted to a location problem. The algorithm is made efficient by employing a device which expliots the special structure of a surrogate constraint. The efficiency of the algorithm is analyzed through computaional experiments with some test problems.