Locating multiple facilities in a planar competitive environment

We investigate the location of one or more facilities anywhere in an area in which several competing facilities already exist. The attractiveness of each facility is modeled by a utility function. Each customer selects the facility with the greatest utility function value. The objective is to find the locations for one or more facilities which attract the maximum buying power. We generate a set of candidate locations and solve the single facility problem by evaluating the buying power attracted to the new facility at each candidate location. We then solve the location of multiple facilities by converting the problem to a maximum covering problem. The solution procedure is illustrated on an example problem with 100 demand points and seven existing facilities. As a case study we find the best locations of new convenience stores in the city of Seto, Japan.