On Fuzzy Three Level Large Scale Linear Programming Problem

This paper suggests an algorithm to solve a three level large scale linear programming problem with fuzzy numbers, where all coefficients of the objective functions are symmetric trapezoidal fuzzy numbers. A three-level programming problem can be thought as a static version of the Stackelberg strategy. The suggested algorithm uses a linear ranking function at each level to define a crisp model which is equivalent to the fuzzy number, then all decision makers attempts to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.