UC Santa Barbara

Dispersive strategies and outcomes are readily apparent in many geographic contexts. In particular, dispersive strategies can be seen in activities such as: the scattering of military missile silos and ammunition bunkers, center-pivot crop irrigation systems, location of parks, franchise store location, and territorial species den/nest locations. Spatial optimization models represent dispersion where selected facility locations are maximally "packed" or maximally "separated." The Anti-Covering Location Problem, in particular, is one in which a maximum number of facilities are located within a region such that each facility is separated by at least a minimum distance standard from all others. In this context, facilities are "dispersed" from each other through the use of the minimum separation standard. Solutions to this problem are called maximally "packed" as there exists no opportunity to add facilities without violating minimum separation standards.

The Anti-Covering Location Problem (ACLP) can be defined on a continuous space domain, or more commonly, using a finite set of discrete locations. In this dissertation, it is assumed that there exists a discrete set of sites, among which a number will be selected for facility locations, and that this general problem may represent a number of different problems ranging from habitat analysis to public policy analysis. The main objective of this dissertation is to propose a new and improved optimization model for the ACLP when applied to a discrete set of points on a Cartesian plane using a combination of separation conditions called core-and-wedge constraints. This model structure, by its very definition, demonstrates that all planar problems can be defined using at most seven clique constraints for each site. In addition, the use of an added set of facet constraints in reducing computational effort is explored.

Anti-covering location model solutions are maximally packed, providing an "optimistic" estimate of what may be possible in dispersing facilities. But, what if less than optimal sites are employed in a dispersive pattern. That is, to what extent can an optimal maximally packed configuration be disrupted? This possibility is explored through the development of a new model, called the Disruptive Anti-Covering location model.