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Journal of Applied Mathematics
Volume 2013, Article ID 276245, 7 pages
Research Article

A Global Optimization Algorithm for Sum of Linear Ratios Problem

Institute of Information & System Science, Beifang University of Nationalities, Yinchuan 750021, China

Received 31 January 2013; Accepted 8 May 2013

Academic Editor: Farhad Hosseinzadeh Lotfi

Copyright © 2013 Yuelin Gao and Siqiao Jin. 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.


We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.