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Journal of Applied Mathematics
Volume 2014, Article ID 490297, 10 pages
Research Article

A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients

1School of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China
2Department of Mathematics, Henan Normal University, Xinxiang 453007, China
3Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Received 11 December 2013; Accepted 24 February 2014; Published 26 March 2014

Academic Editor: Ferenc Hartung

Copyright © 2014 Hongwei Jiao and Yongqiang Chen. 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.


A new linearizing method is presented for globally solving sum of linear ratios problem with coefficients. By using the linearizing method, linear relaxation programming (LRP) of the sum of linear ratios problem with coefficients is established, which can provide the reliable lower bound of the optimal value of the initial problem. Thus, a branch and bound algorithm for solving the sum of linear ratios problem with coefficients is put forward. By successively partitioning the linear relaxation of the feasible region and solving a series of the LRP, the proposed algorithm is convergent to the global optimal solution of the initial problem. Compared with the known methods, numerical experimental results show that the proposed method has the higher computational efficiency in finding the global optimum of the sum of linear ratios problem with coefficients.