Three stages algorithm for finding optimal solution of balanced triangular fuzzy transportation problems

Abstract

In the literature, the fuzzy optimal solution of balanced triangular fuzzy transportation problem is negative fuzzy number. This is contrary to the constraints that must be non-negative. Therefore, the three stages algorithm is proposed to overcome this problem. The proposed algorithm consist of segregated method with segregating triangular fuzzy parameters into three crisp parameters. This method avoids the ranking technique. Next, total difference method is used to get initial basic feasible solution (IBFS) value based on segregating triangular fuzzy parameters. While, modified distribution algorithm is used to determine optimal solution based on IBFS velue. In order to illustrate the proposed algorithm is given the numerical example and based on the result comparison, the proposed algorithm equality to the two existing algorithms and better then the one existing algorithm. The proposed algorithm can solve in the fuzzy decision-making problems and can also be extended to an unbalanced fuzzy transportation problem.