Advances in Operations Research
Volume 2009 (2009), Article ID 212040, 10 pages
doi:10.1155/2009/212040
Research Article

A BSSS Algorithm for the Location Problem with Minimum Square Error

Jafar Fathali,1 Mehdi Zaferanieh,2 and Ahmad Nezakati1

1Department of Mathematics, Shahrood University of Technology, University Blvd., Shahrood 36199 95161, Iran
2Department of Mathematics, Tarbiat Moallem University of Sabzevar, Tovhid Town, Sabzevar 9617976487, Iran

Received 7 May 2009; Revised 17 September 2009; Accepted 15 October 2009

Academic Editor: Khosrow Moshirvaziri

Copyright © 2009 Jafar Fathali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let n weighted points be given in the plane R2. For each point a radius is given which is the expected ideal distance from this point to a new facility. We want to find the location of a new facility such that the sum of the weighted errors between the existing points and this new facility is minimized. This is in fact a nonconvex optimization problem. We show that the optimal solution lies in an extended rectangular hull of the existing points. Based on this finding then an efficient big square small square (BSSS) procedure is proposed.