The p-regions problem

Geographical Analysis (2011) ,Volume 43 ,Pages 104-126

Abstract

The p-regions problem involves the aggregation or clustering of n small areas into p spatially-contiguous regions while optimizing some criteria. The main objective of this paper is to explore possible avenues for formulating this problem as a mixed integer programming problem (MIP). The critical issue in formulating this problem is to ensure that each region is a spatially contiguous cluster of small areas. We introduce three MIP models for solving the p-regions problem. Each model minimizes the sum of dissimilarities between all pairs of areas within each region while guaranteeing contiguity. Three strategies designed to ensure contiguity are presented: 1) an adaptation of Miller, Tucker, and Zemlin tour-breaking constraints developed for the traveling salesman problem; 2) the use of ordered-area assignment variables based upon an extension of an approach of Cova and Church for the geographical site design problem; and 3) the use of ow constraints based upon an extension of Shirabe. We test the efficacy of each formulation as well as specify a strategy to reduce overall problem size.

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