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

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  • Hongwei Jiao
  • Yongqiang Chen

Abstract

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.

Suggested Citation

  • Hongwei Jiao & Yongqiang Chen, 2014. "A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:490297
    DOI: 10.1155/2014/490297
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    References listed on IDEAS

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    1. Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, June.
    2. Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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