Solution approach to multi-objective linear fractional programming problem using parametric functions

In this paper, an iterative technique based on the use of parametric functions is proposed to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem. The decision maker ascertains own desired tolerance values for the objectives as termination constants and imposes them on each iteratively computed objective functions in terms of termination conditions. Each fractional objective is transformed into non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively computed and ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-constraint method is used to obtain the pareto (weakly) optimal solutions in each step. The computations get terminated when all the termination conditions are satisfied at a pareto optimal solution of an iterative step. A numerical example is discussed at the end to illustrate the proposed method and fuzzy max–min operator method is applied to validate the obtained results.