On solving multi-level multi objective linear programming problems through fuzzy goal programming approach

Abstract

In this paper, we propose an alternate technique based on fuzzy goal programming approach for solving multi-level multi objective linear programming problem (ML-MOLPP) which is simpler and requires less computational works than that of proposed algorithm by Baky, I. A. (Applied Mathematical Modelling, 34(2010), 2377–2387). In formulation of FGP model each objective functions at each level are transformed into fuzzy goals. Suitable membership function for every fuzzily described transformed objective functions at each level as well as the control vectors of each level decision makers are defined by determining individual optimal solution of each objective function at each of the decision making level. Then FGP approach is used for achieving highest degree of each of these membership goals by minimizing the sum of negative deviational variables. To avoid decision deadlock, solution preferences by the decision makers at each level are not taken into account of proposed FGP technique. The aim of this paper is to present simple technique to obtain compromise optimal solution of ML-MOLP problems. A comparative analysis based on numerical examples is also carried out to show similarity between two solution methodologies.