ABSTRACT
Many problems in location theory deal with the placement of facilities on a network so as to minimize some function of the distances between facilities or between facilities and other nodes of the network [1]. Such problems model the placement of “desirable” facilities such as warehouses, hospitals, and fire stations. However, there are situations in which facilities must be located so as to maximize a given function of the distances. Such location problems are referred to as dispersion problems [2] as they model situations in which proximity of facilities is undesirable. One example of such a situation involves placing “obnoxious” (also called “undesirable”) facilities such as nuclear power plants, oil storage tanks, and ammunition dumps [2,3]. These facilities need to be spread out to the greatest possible extent so that an accident at one of the facilities does not damage any of the others. Another example in which dispersion problems arise is in the distribution of business franchises in a city [2,4]. In this case, separation of business units is desirable to minimize the competition for customers among the units. In these examples, the facilities to be dispersed are assumed to be of the same type. Applications involving multiple types of facilities (e.g., incinerators, landfills) have also been considered in the literature [3].
