Equity models in planar location

In this paper we investigate planar location models with equity objectives. Two objectives are analyzed: (1) Minimizing the variance of the distances to the facility, and (2) minimizing the range of the distances. The problems are solved using the global optimization technique ‘Big Triangle Small Triangle’. Computational experiments provided excellent results. Solving a problem with 10,000 demand points required less than 5 s of computer time for finding the minimum variance, and less than half that time for finding the minimum range.