On solving transportation problems with triangular fuzzy numbers: Review with some extensions

In conventional transportation problems it is assume that the decision maker has exact information about the coefficients belonging to the problem. In real world applications, values of transportation cost, supply and demand of the product may not be known precisely due to uncontrollable factors. To deal with such situations, fuzzy set theory is applied in literature to solve the transportation problems. In this paper, some existing methods for solving fuzzy transportation problem (FTP) are reviewed. Moreover, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, a new method is proposed for finding that kind of FTP in which the transportation costs and values of supplies and demands are represented by non-negative triangular fuzzy numbers. The FTP is converted into three crisp transportation problems and these crisp problems are solved with the standard transportation simplex algorithms. The advantages of the proposed method over the existing methods are discussed by an application example. The obtained results show that the method proposed in this study is simpler and computationally more efficient than some existing methods commonly used in the literature.

Computational complexity Fuzzy transportation problem Transportation simplex algorithm