Quadratic Bi-level Programming Problem Based On Fuzzy Goal Programming Approach

Abstract

This paper presents fuzzy goal programming approach to quadratic bi-level programming problem. In the model formulation of the problem, we construct the quadratic membership functions by determining individual best solutions of the quadratic objective functions subject to the system constraints. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series approximation at the individual best solution point. Since the objectives of upper and lower level decision makers are potentially conflicting in nature, a possible relaxation of each level decisions are considered by providing preference bounds on the decision variables for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing deviational variables. Numerical examples are provided in order to demonstrate the efficiency of the proposed approach.