The p-regions problem
Duque, Juan C.
Church, R. L.
Middleton, R. S.
Duque, Juan C. (email@example.com)
Church, R. L. (firstname.lastname@example.org)
Middleton, R. S. (email@example.com)
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The p-regions problem involves the aggregation or clustering of n small areas into pspatially contiguous regions while optimizing some criteria. The main objective of thisarticle 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 ensurethat each region is a spatially contiguous cluster of small areas. We introduce threeMIP models for solving the p regions problem. Each model minimizes the sum of dis-similarities between all pairs of areas within each region while guaranteeing contigu-ity. Three strategies designed to ensure contiguity are presented: (1) an adaptation ofthe Miller, Tucker, and Zemlin tour-breaking constraints developed for the travelingsalesman problem; (2) the use of ordered-area assignment variables based upon anextension of an approach by Cova and Church for the geographical site design prob-lem; 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 overallproblem size
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