We consider the bilevel programming problem with a special lower level. As a reformulation, we use the optimal value approach which will be the basis for an outer approximation. We establish an algorithm that sequentially improves the approximation in order to solve the bilevel programming problem. Convergence results for both local and global optima are presented.

in this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear bilevel programming (fflblp) problems by representing all the parameters as triangular fuzzy numbers. in the proposed method, the given fflblp problem is decomposed into three crisp linear programming (clp) problems with bounded variables constraints, the three clp problems are solved separately and...

Focus in the paper is on the definition of linear bilevel programming problems, the existence of optimal solutions and necessary as well as sufficient optimality conditions. In the papers [9] and [10] the authors claim to suggest a refined definition of linear bilevel programming problems and related optimality conditions. Mainly their attempt reduces to shifting upper level constraints involvi...

This paper presents a genetic algorithm method for solving convex quadratic bilevel programming problem. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, the bilevel convex quadratic problem is transformed into a single level problem by applying Kuhn-Tucker conditions, and then an effic...

We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially ...

Organizational decision making often involves two decision levels. When the leader at the upper level attempts to optimize hislher objective, the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. Furthermore, such bilevel decision making may involve uncertain parameters which appear either in the objective functions or co...

The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...