SOLVING OF BI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEMS

Abstract

Linear programming and linear fractional program are an optimization problems that use linear equations and inequalities wherein both problems have feasible region. More specifically, the linear programming calculates the policy to seek maximum profit or minimum cost. Whereas the linear fractional pro-gram used to calculate the optimal efficiency ratio between benefit and cost. BOLFPPs optimize two objectives over a feasible region where the two objectives are the ratio of two linear objectives. In more elucidated expression, linear fractional means that the ratio of two linear functions under some technological linear restrictions and the BOPPs that involves such program is known as BOLFPPs. BOLFPPs check the efficiency of a given feasible solution. Harmonic Mean technique is used to solve bi objective linear fractional programming problem. The BOLFPP was first transformed to a single objective linear fractional programming problem (SOLFPP) by using Harmonic Mean technique, thereafter SOLFPP was converted to equivalent LPP using CCT and BAT. The equivalent LPPS has been solved using simplex method and LINDO software. When the two transformations are compared based on number of iterations BAT was better than CCT. Examples have been done for evaluating the efficiency of the proposed optimization technique and theoretical notions have been illustrated in this aspect.