The p‐Regions Problem. p‐区域问题 |
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| Authors: | Juan C Duque Richard L Church Richard S Middleton |
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| Institution: | 1. Research in Spatial Economics (RiSE), Department of Economics, EAFIT University, Medellin, Colombia;2. Department of Geography, University of California at Santa Barbara, Santa Barbara, CA;3. Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM. |
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| 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 article is to explore possible avenues for formulating this problem as a mixed integer‐programming (MIP) problem. 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 the 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 by Cova and Church for the geographical site design problem; and (3) the use of flow constraints based upon an extension of work by Shirabe. We test the efficacy of each formulation as well as specify a strategy to reduce overall problem size. |
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