Equity Bicriteria Location Models Using Line Tessellation

This paper examines a model to locate a facility within a given convex polygonal region taking two criteria of equity and efficiency into account. Equity, or rather inequality in the inhabitant-facility distances, is measured by minimizing the sum of the absolute differences between all pairs of squared Euclidean distances from inhabitants to the facility. This measure meets the Pigou-Dalton principle of transfers, and can easily be minimized. Efficiency is measured through Weber-type 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 resulting bicriteria problems. A polynomial procedure is developed to obtain the full bicriteria plot and both trade-off curves.