On Solving Linear Fractional Programming Problems

Pandian Ponnaiah,Jayalakshmi Mohan

doi:10.5539/mas.v7n6p90

Abstract

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming problem. The procedures for the proposed methods are illustrated with the numerical examples.

Highlights

Linear fractional programming (LFP) problems are a special type of non-linear programming problems in which the objective function is a ratio of linear functions and the constraints are linear functions
We construct two linear programming problems from the given LFP problem such that one is of maximization type and the other is of minimization type
We prove the following theorem which is used in the proposed method to solve the FFLFP problem

Summary

Introduction

Linear fractional programming (LFP) problems are a special type of non-linear programming problems in which the objective function is a ratio of linear functions and the constraints are linear functions. Jayalakshmi and Pandian (2012) have proposed a method namely, bound and decomposition method to a fully fuzzy linear programming (FFLP) problem to obtain an optimal fuzzy solution. We propose a new method namely, denominator objective restriction method for finding an optimal solution to LFP problems. In this proposed method, we construct two linear programming problems from the given LFP problem such that one is of maximization type and the other is of minimization type. In the decomposition-restriction method, the fuzzy ranking function, the transformation technique and multi-objective non-linear programming technique are not used. Numerical examples are given for better understanding the solution procedures of the proposed methods

Preliminaries

Linear Fractional Programming Problems

D B x 1 x 2 s 1

Fully Fuzzy Linear Fractional Programming Problem

Conclusion