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Equity-Efficiency Bicriteria Location with Squared Euclidean Distances

Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba 305-8573, Japan
Railway Technical Research Institute, Kokubunji 185-8540, Japan
MOSI, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium
osawa{at}sk.tsukuba.ac.jp
ozaki{at}rtri.or.jp
frank.plastria{at}vub.ac.be

A facility must be located within a given region taking two criteria of equity and efficiency into account. Equity is sought by minimizing the inequality in the facility-inhabitant distances, as measured by the sum of the absolute differences between all pairs of squared Euclidean distances from inhabitants to the facility. This measure meets the Pigou-Dalton condition of transfers and can easily be minimized. Efficiency is measured through optimizing the sum of squared inhabitant-facility distances, either to be minimized or maximized for an attracting or repellent facility, respectively. Geometric localization results are obtained for the whole set of Pareto-optimal solutions for each of the two resulting bicriteria problems within a convex polygonal region. A polynomial procedure is developed to obtain the full bicriteria plot, both trade-off curves, and the corresponding efficient sets.

Subject classifications: facilities planning; equity continuous location; programming; bicriteria.
History: Received March 2005; revision received May 2006; accepted May 2006.