Using GIS and K = 3 central place lattices for efficient solutions to the location set-covering problem in a bounded plane

Abstract

One of the simplest location models in terms of its constraint structure in location-allocation modeling is the location set-covering problem (LSCP). Although there have been a variety of geographic applications of the set-covering problem (SCP), the use of the SCP as a facility location model is one of the most common. In the early applications of the LSCP, both potential facility sites as well as demand were represented by points discretely located in geographic space. The advent of geographic information systems (GIS), however, has made possible a greater range of object representations that can reduce representation error. The purpose of this article is to outline a methodology using GIS and K = 3 central place lattices to solve the LSCP when demand is continuously distributed over a bounded area and potential facility sites have not been defined a priori. Although, demand is assumed to exist over an area, it is shown how area coverage can be accomplished by the coverage of a point pattern. Potential facility site distributions based on spacings that are powers of one-third the coverage distance are also shown to provide more efficient coverage than arbitrarily chosen spacings. Using GIS to make interactive adjustments to an incomplete coverage also provides an efficient alternative to smaller spacings between potential facility sites for reducing the number of facilities necessary for complete coverage. © 2010 Blackwell Publishing Ltd.