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

Hongwei Jiao | Zendy; Yongqiang Chen | Zendy

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

Author(s) -

Hongwei Jiao,

Yongqiang Chen

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/490297

Subject(s) - mathematics , relaxation (psychology) , linear programming , mathematical optimization , linear programming relaxation , upper and lower bounds , linear system , branch and bound , value (mathematics) , mathematical analysis , statistics , psychology , social psychology

A new linearizing method is presented for globally solving sumof linear ratios problem with coefficients. By using the linearizing method, linear relaxationprogramming (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 coefficientsis put forward. By successively partitioning the linear relaxation of the feasible region andsolving a series of the LRP, the proposed algorithm is convergent to the global optimalsolution of the initial problem. Compared with the known methods, numerical experimentalresults show that the proposed method has the higher computational efficiency in finding theglobal optimum of the sum of linear ratios problem with coefficients

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