Gradual cover competitive facility location

A new gradual cover competitive facility location model is proposed and tested. In cover competitive models, it is assumed that up to a certain distance a demand point is attracted to a facility and beyond this distance it is not. The decline in attraction and cover is abrupt. It is either 0 or 1. We propose a gradual decline in attraction from 1 to 0. As the distance increases the attraction and cover decline. The buying power captured by a facility cannot exceed its attraction level, and the total buying power captured by all facilities cannot exceed the buying power available at the demand point. The single-facility location is optimally solved. The largest problem of 1000 demand points is solved in less than one second. The multiple facility version is solved by SNOPT and other solvers.