A NEW PROCESS FOR SOLVING LINEAR FRACTIONAL PROGRAMMING PROBLEM

Author Name: Dr. A. Anna Sheela

Volume/Issue: 02/03

Country: India

DOI NO.: 08.2020-25662434 DOI Link: https://www.doi-ds.org/doilink/09.2021-12498469/UIJIR

Affiliation:

Department of Mathematics, Saradha Gangadharan College, Affiliated to Pondicherry University Puducherry- 605 004

ABSTRACT

There is a need for generalizing the simplex technique for linear programming to the ratio of linear functions or the ratio of quadratic functions and in such a situation, all the problems are fragments of a general class of optimization problems, termed in the literature as fractional programming problems. The linear fractional programming problem arise when there appears a necessity to optimize the efficiency in other activities also, for example, profit gained by company per unit of expenditure of labor, cost of production per unit of produced goods etc. Nowadays, because of deficit of natural resources, the use of such specific criteria becomes more and more topical and relevant. Linear Fractional problems arises in management decision making, research, finance, production, Health care and Hospital Planning and transportation etc., In this paper, a new process has been introduced for solving linear fractional programming problem. The main purpose of this method is to reduce the number of iterations in order to save time. By using the numerical examples, we suggest that the optimality of this method arises in a few numbers of iteration than the existing Simplex method for solving linear fractional programming problem. Also, in certain cases, the same number of iterations is maintained for the optimality.

Key words: Basic feasible solution, optimum solution, alternative simplex method, linear programming problem, linear fractional programming problem.