A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

Abstract

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 $\overline{x}$ is an efficient solution of MOLFPP if $\overline{x}$ is an optimal solution of problem ${\mathrm{\text{M}}\mathrm{\text{a}}\mathrm{\text{x}}}_{x\in X}{\sum }_{i=\mathrm{1}}^k(N_i(x)-Z_i^{\mathrm{*}}{D}_i(x))$, where is $Z_i^{\mathrm{*}}=N_i(x_i^{\mathrm{*}})/D_i(x_i^{\mathrm{*}})$ 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.