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This paper proposes a bi-level linear programming problem with linear constraints, in which the linear objective functions are to be maximized with different rough goals, the suggested approach in this paper is mainly based on the iterative goal programming method of Dauer and Krueger to develop the optimal solution of the bi-level decision- maker, then we uses the concepts of tolerance membership function technique to generate the optimal solution for this problem. An auxiliary problem is discussed as well as an example is presented. [ABSTRACT FROM AUTHOR]

This paper studies a three-level large scale linear programming problem, in which the objective functions at every level are to be maximized. Three-level programming problem can be thought as a static version of the Stackelberg strategy, which is used leader-follower game in which a Stackelberg strategy is used by the leader. This paper proposes a fuzzy approach for solving a three-planner model and a solution method for solving this problem. Each level attempts to optimize its problem separately as a large scale programming problem using a decomposition technique to handle the optimization through a series of sub problems that can be solved easily. This method uses the concept of tolerance membership function to develop a Tchebycheff problem for generating Pareto optimal solution for this problem. Finally, a numerical example is given to clarify the main results developed in this paper. [ABSTRACT FROM AUTHOR]