A Fuzzy Approach for Solving a Three–Level Large Scale Linear Programming Problem

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.