Fuzzy Hungarian MODI Algorithm to Solve Fully Fuzzy Transportation Problems

In this paper, a new method is proposed to solve fully fuzzy transportation problems using the approach of the Hungarian and MODI algorithm. The objective of the proposed algorithm, namely, fuzzy Hungarian MODI algorithm, is to obtain the solution of fully fuzzy transportation problems involving triangular and trapezoidal fuzzy numbers. The introduced method together with Yager's ranking technique gives the optimal solution of the problem. It also satisfies the conditions of optimality, feasibility, and positive allocation of cells using the elementwise subtraction of fuzzy numbers. A comparative study of the proposed method with existing procedure reveals that the solution of the proposed method satisfies the necessary conditions of a Transportation Problem (TP) to be an optimal solution in which the other methods do not guarantee. The proposed method is the extension of the Hungarian MODI method with fuzzy values. It is easy to understand and implement, as it follows the standard steps of the regular transportation problems. The method can be extended to other kinds of fuzzy transportation problems, such as unbalanced fuzzy TP, fuzzy degeneracy problem, fuzzy TP with prohibited routes, and many more.