Evaluating representation and scale error in the maximal covering location problem using GIS and intelligent areal interpolation

Abstract

A common problem in location-allocation modeling is the error associated with the representation and scale of demand. Numerous researchers have investigated aggregation errors associated with using different scaled data, and more recently, error associated with the geographic representation of model objects has also been studied. For covering problems, the validity of using polygon centroid representations of demand has been questioned by researchers, but the alternative has been to assume that demand is uniformly distributed within areal units. The spatial heterogeneity of demand within areal units thus has been modeled using one of two extremes – demand is completely concentrated at one location or demand is uniformly distributed. This article proposes using intelligent areal interpolation and geographic information systems to model the spatial heterogeneity of demand within spatial units when solving the maximal covering location problem. The results are compared against representations that assume demand is either concentrated at centroids or uniformly distributed. Using measures of scale and representation error, preliminary results from the test study indicate that for smaller scale data, representation has a substantial impact on model error whereas at larger scales, model error is not that different for the alternative representations of the distribution of demand within areal units.

Keywords:

• representation error
• aggregation error
• areal interpolation
• maximal covering location problem

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and criticisms.