A Unified Model for Dispersing Facilities

摘要

One of the important classes of facility dispersion problems involves the location of a number of facilities where the intent is to place them as far apart from each other as possible. Four basic forms of the p-facility dispersion problem appear in the literature. Erkut and Neuman present a classification system for these pur classic constructs. More recently, Curtin and Church expanded upon this framework by the introduction of "multiple types" of facilities, where the dispersion distances between specific types are weighted differently. This article explores another basic assumption found in all four classic models (including the multitype facility constructs of Curtin and Church): that dispersion is accounted for in terms of either distance to the closest facility or distances to all facilities (from a given facility), whether applied to a single type of facility or across a set of facility types. In reality, however, measuring dispersion in terms of whether neighboring facilities to a given facility are dispersed rather than whether all facilities are dispersed away from the given facility often makes more sense. To account for this intermediate measure of dispersion, we propose a construct called partial-sum dispersion. We propose four "partial-sum" dispersion problem forms and show that these are generalized forms of the classic set of four models codified by Erkut and Neuman. Further, we present a unifying model that is a generalized form of all four partial-sum models as well as a generalized form of the original four classic model constructs. Finally, we present computational experience with the general model and conclude with a few examples and suggestions for future research.