Solving Linear Fractional Programming Problem Using Revised and Column Simplex Method

In Operations Research, linear-fractional programming is considered as the generalization of linear programming problem. While in a linear programming the objective function is a linear function, and in a linear-fractional programming the objective function is the ratio of two linear or non-linear functions. The majority of the algorithm used for solving the linear fractional programming problem relies upon the classical simplex method. In this paper, we have proposed a new algorithm for solving a linear fractional programming problem in which the objective function is a combination of linear fractional function, while constraint functions are in the form of linear inequalities. Our proposed algorithm is based on the extension of the method, which is used to solve linear programming problems with linear constraints. The primary intent behind developing this method is that we did not need to transform the linear fractional programming problem into linear programming problem, and also it helps in finding out the feasible region via a sequence of points in the direction that improves the feasibility of the fractional objective function. Numerical examples are given to illustrate the use of these proposed methods. Lastly, to demonstrate the efficacy of the proposed algorithm, we have compared the findings obtained with other approaches to display our algorithm's efficacy.