A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem - Guzel, Nuran (HINDAWI LTD, 2013)
We have proposed a new solution to the Multiobjective Linear Fractional Programming Problem (MOLFPP). The proposed solution is based on a theorem that deals with nonlinear fractional programming with single objective function and studied in the work by Dinkelbach, 1967. As a new contribution, we have proposed that (x) over bar is an efficient solution of MOLFPP if (x) over bar is an optimal solution of problem Max(x is an element of X) Sigma(k)(i=1) (N-i(x) - Z(i)* D-i (x)), where is Z(i)* = N-i(x(i)*)/D-i(x(i)*) for all i. Hence, MOLFPP is simply reduced to linear programming problem (LPP). Some numerical examples are provided in order to illustrate the applications of the proposed method. The optimization software package, namely, WinQSB (Chang, 2001), has been employed in the computations.
Keywords: OPTIMALITY; DUALITY; Mathematics