An algorithmic approach to solve unbalanced triangular fuzzy transportation problems

This paper presents problems in fuzzy transportation, which deals with fuzzy costs, fuzzy supplies, and demands of a fuzzy nature on any quantity transported. The paper deals with the minimization of the total fuzzy cost under the fuzzified decision-variables. The proposed method gives better optimum for fuzzy transportation problem (FTP) with unbalance and balance types. The method is intended to obtain a basic feasible solution (or "initial basic feasible solution") (IBFS) of unbalanced fuzzy problems with triangular fuzzy number. A new and simple heuristic approach for obtaining optimum solution of triangular fuzzy unbalanced transportation problem is proposed that reduces the number of iterations in the optimization process. A given triangular fuzzy unbalanced TP is converted into a modified triangular unbalanced FTP by increasing the fuzzy-demand/fuzzy-supply of an origin and a destination, and the same is resolved by new method. Also an illustrative numerical example is discussed for proposed method solving a triangular FTP with m, n origins and destinations, respectively.