An iterative algorithm to solve a linear fractional programming problem

Abstract

This paper presents a novel iterative algorithm, based on the ε,δ-definition of continuity, for a linear fractional programming (LFP) problem. Since the objective function is continuous at every point of the feasible region, we construct an iterative constraint by combining our convergence condition and the objective function of the LFP problem. Through this iterative constraint, we construct a new iterative linear programming (LP) problem to obtain the optimal solution of the LFP problem. This iterative LP problem is able to solve all LFP problems that have a bounded feasible region. In order to generate the unbounded solution and the asymptotic solution, we extend our proposed iterative LP problem by adding a new constraint that controls whether the sum of the original decision variables approaches infinity. To demonstrate the efficiency of the proposed method, illustrative numerical examples are provided for all solution cases. Also, we analyse the validity of our algorithm by generating random large-scale production planning test problems.