| Spatial allocation problems generally involve the aggregation of spatial units into larger groups according to specified criteria. Both geographic information systems (GIS) and mathematical programming techniques have been used to solve these problems, but seldom have those two technologies been integrated in any general manner. This project explores the prospect of establishing that integration by using GIS to cast spatial allocation problems in terms that are amenable to solution by integer programming. It does so by decomposing integer programming models for spatial allocation (IPSA) into elementary components: as data, decision variables, properties, and criteria. It implements these models in a GIS environment and tests their utility. Results indicate that a variety of spatial allocation criteria can be effectively modeled in these terms. They also indicate, however, that spatial properties dependent on the boundaries of geometric objects (e.g., edge roughness or similarity to particular shape) remain difficult, if not impossible, to model. Furthermore, some of the IPSA models generated by the techniques proposed are simply too large and complex to be solved by existing integer programming methods in reasonable time. This tends to occur when allocation criteria involve qualities arising from multiple spatial units, such as compactness. The major implication of this study is that mathematical programming techniques can indeed be used to augment the prescriptive capabilities of geographic information systems in fields such as environmental planning but that such techniques are limited by the inherently complex nature of spatial properties. |
