A fuzzy goal programming procedure for solving quadratic bilevel programming problems

This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic pro.-ramming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then. at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach. (C) 2003 Wiley Periodicals. Inc.