A location model based on multiple metrics and multiple facility assignment

Two of the most restrictive assumptions of classical network facility location models are that all customers are serviced by their closest facility and that the metric (distance, time or cost) between any two given points is always the same. A median location model based upon relaxations of both these assumptions is developed. This model retains many of the mathematical properties of the well known p-median problem. We show that an optimal solution exists at the nodes of the network, and formulate the problem as an integer linear program. Two very different potential applications are discussed. Solution procedures, optimal and heuristic, are described. The results from several different test data sets indicate that the solution of this new model does not require excessive computation times.