Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

Abstract

This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1) Taylor’s polynomial linearization approximation, (2) the method of variable change, and (3) a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a) using the optimal value of the objective functions as the decision makers’ aspirations, and (b) the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.