Joint location/sizing maximum profit covering models

The problem of locating an endogenously determined number of facilities to maximize the total profit obtained by all facilities is addressed. Revenues are derived from the sale of a product at demand points distributed throughout the region. Costs are incurred in locating facilities and in transporting goods to customers. A facility may only sell the product at those locations that are sufficiently close to the facility site. The basic model simultaneously locates facilities and determines the appropriate level of investment at each site. The level of investment determines the area in which the facility may sell the product. A number of variations of the problem are formulated as integer linear programming problems. In particular, the maximum covering location problem is shown to be a special case of this model. Sample results are presented. Qualitative conclusions regarding the locational trends identified by the model are discussed. Model extensions and applications of the model are outlined.