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 is an efficient solution of MOLFPP if is an optimal solution of problem , where is for all . 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.

A Review of Potential Method for Optimization of Power Plant Expansion Planning in Jawa-Madura-Bali Electricity System

“…Based on Dinklebach's theorem and Guzel's approach, it can be obtained the maximum value of F occurs at maximum Nx/Dx [68].…”

Branch and bound computational method for multi-objective linear fractional optimization problem

“…4, we determine a simplex S 0 containing K. The vertices of S 0 are given by e V 0 0 ¼ ð3:0000; 0:0000Þ; e V 0 1 ¼ ð3:0000; 3:0000Þ; e V 0 2 ¼ ð7:5000; 0:0000Þ. After that we choose the weight show as below table and apply the method described in Numerical problem 2 Consider the MOLF optimization problem [15][16][17] Max…”

“…To measure the efficiency of the proposed method, we compared our solution with the solutions obtained using existing methods proposed by Chakraborty and Gupta [15], Guzel and Sivri [16] and Guzel [17].…”

“…The objective functions are linearize using the Taylor series approximation. Again, Guzel [17] proposed a method for the same problem with the help of modified objective approach. The objective functions are linearized by assigning the target for each objective function.…”

Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application

“…Guzel and Sivri [3] worked together to propose a method for finding an efficient solution of MOLFP problem using goal programming. Later Guzel [4] presented a simplex-based algorithm to find an efficient solution of MOLFP problem based on a theorem studied in a work by Dinkelbach [5], where he converted the main problem into a single linear programming problem. Jain [6] proposed a method using Gauss elimination technique to derive numerical solution of multi-objective linear programming (MOLP) problem.…”