A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

Abstract

Abstract. This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP) problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

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

“…To solve the multi-objective linear fractional programming model by the linear goal programming method for objective functions that are to be maximized or minimized, Perić and Babić [20] proposed the linearization of the linear fractional objective functions in the following way:…”

“…The complexity of the linearization approaches and problems with orthogonality constraints n k p k = 0, k = 1, 2, …, K will be given in the rest of the paper. In this case we obtain an approximation of the model (2) that gives the week efficient solutions (see more in [9,11,12,19,20]). …”

“…For the linearization of the linear fractional objective functions we can use different methods which do not have the same efficiency. Here we present three linearization methods: 1) Taylor's polynomial linearization approximation [22], 2) the method of variable change ( [9], [11], [12], [18]), and 3) a modification of the method of variable change proposed in [20]. The analysis of the linearization approaches will be done by solving a financial structure optimization problem with respect to efficiency of the obtained results and the difficulties the analysts come upon in preparing the model.…”

“…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.…”

A Distance Based Method for Solving Multi-Objective Optimization Problems

“…Romero (2015) discussed issues related to practical goal programming. Perić, Babić, and Rešić (2014) applied goal programming methods for solving the multi-objective fractional linear programming problems under fuzziness. L. Chen, Qiu, Wei, and Shen (2015) proposed a preference-based multi-objective model for the optimization of best management practices.…”