An exact iterative algorithm to solve a linear fractional programming problem

Abstract

The Linear Fractional Programming (LFP) problem that optimizes the ratio of two linear objective functions under linear constraints has a wide range of application areas. Based on the traditional definition of continuity, we developed an exact iterative algorithm that does not depend on big-M coefficients.Removing the nonlinearity in the fractional objective function by converting the objective function into a linear form, an equivalent linear-iterative problem is obtained and a computationally efficient algorithm is proposed. We also analyze the unbounded and asymptotic solution case of the LFP. To demonstrate the efficiency of the proposed method, illustrative numerical examples are provided for all solution cases. Also, we analyze the validity of our algorithm and compare our results with the existing algorithm from the literature by generating random large-scale test problems.