National Center for Geographic Information and Analysis

There has been considerable interest in the development of analysis techniques for Geographical Information Systems (GIS). This includes such normative spatial models as vehicle routing models, districting and turfing models for dividing up land into territories for schools, sales/service, and voting, and location models for identifying sites or patterns of sites to provide service accessibility. The GIS system may provide a unique data base for application and analysis. This paper discusses several problems associated with the integration of a normative location model into a GIS. A number of specifics associated with the p-median model are given. These include: demand zone definition, facility site definition, and solution algorithm selection and development. Within the context of selecting a solution process, we show that such a selection is not necessarily an easy one to make. We demonstrate that the best such solution technique may have some potential drawbacks in application. We present the results of several test applications and a glimpse of the pathology of the final solutions. This discussion raises a major, but often ignored, issue involving the application of a location heuristic: namely, how often should we restart a heuristic to help ensure that the best solution found is optimal or near-optimal. We propose and test a dynamic stopping rule that can be used to help ensure that the best solution is identified. The results of this analysis can be of great, practical value in the successful application of location models within a GIS framework.