The p-regions problem

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


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.

+ Publications

An algorithmic approach for simulating realistic irregular lattices

In this paper, we propose an algorithm, RI-Maps, that combines fractal theory, stochastic calculus and computational geometry for simulating realistic irregular lattices with a predefined number of polygons.

Learning outcomes and dropout intentions: An analytical model for Spanish universities

The dropout rate among Spanish university students is very high compared to the European mean, creating a pressing need for the introduction of policies and programmes aimed at increasing rates of persistence.

Propuesta metodologica para la desagregación espacio-temporal de los indicadores de demografía empresarial

Propuesta metodologica para la desagregación espacio-temporal de los indicadores de demografía empresarial

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+ Software and tools

spatially constrained clustering algorithms

Python library with spatially constrained clustering algorithms

Economic multipliers for Colombia

Interactive tool for visualizing the interindustry dynamics in Colombian economy.

Spatial deagregation of multipliers

Interactive tool for visualizing the spatial distribution of economic impacts in Colombian metropolitan areas.

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+ News

RiSE participates in the UN-Habitat Council (Kenya)

RiSE-group was invited to the workshop "The Role of Cities In Creating Improved Economic Opportunities" in the UN-Habitat Governing Council... here are some pictures of the event, Link

The student Oswaldo Zapata awarded

The student of the Master in Economics from the University EAFIT, Oswaldo Zapata, was one of the awarded students by the Government of Antioquia

Noreña's undergraduate thesis published in international book

The thesis of economics student, Miguel Norena, has been published in the book Defining the Regional Spatial Scale in Modern Analysis.

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