A Perfect Mathematical Formulation of Fuzzy Transportation Problem Provides an Optimal Solution Speedily

The basic transportation problem was originally developed by Frank Lauren Hitchcock [11], [16]. The transportation problem which transports goods from m sources to n different destinations to minimize total shifting cost. A fuzzy transportation problem is a transportation problem in which the transportation costs, supply and demand quantities are fuzzy quantities. In a fuzzy transportation problem, all parameters are fuzzy number. The aim of Fuzzy transportation is to find the least transportation cost of some commodities through a capacitated network when the supply and demand of nodes and capacity and cost of edges are represented as fuzzy numbers. Fuzzy numbers may be normal or subnormal, Triangular or Trapezoidal or any Fuzzy Russell fuzzy number. Some fuzzy numbers are not directly comparable. In real life case, transportation unit costs have not been precisely determined beforehand, but they are specified by the fuzzy parameters. This paper presents a simple and efficient method that is better than the existing methods, easy to understand and also can give an optimal solution. The proposed method, improved Zero Point Method (IZPM) [10], is used for solving unbalanced fuzzy transportation problems by assuming that a decision maker is uncertain about the precise values of the transportation cost only. In this paper I would like to present, how a fuzzy transportation problem can formulate perfectly forreaching to the optimal solution.