A Study on Some Methods for Solving Fuzzy Transportation Problems

Abstract

Cost minimization problem is well known topic of Operations Research. The main aim of cost minimization transportation problem is to find the optimal uantity the product that should be supplied from various sources to various destinations so, that the total transportation cost is minimum. The transportation problems, in which total availability of the product at all the sources and total d emand at all the destination is equal, are said to be a balanced transportation problems otherwise the transportation problem is said to be an unbalanced transportation problems.

In general to find the optimal solution of a transportation problem, it is assumed that the value of each parameter is precisely known. However, in reality, there may exist uncertainty about some or all the parameters of a transportation problem e.g.,the transportation problem between two fixed places varies according to the various situations like traffic jam, weather conditions, road condition etc. Therefore, it is inappropriate to assume that the parameters of transportation problem are precisely known. To handle the impreciseness, various ways have been adopted by the researchers in the literature. One way to handle the same is to represent some/all the parameters of the transportation problem as trapezoidal fuzzy number. In the literature several methods have been proposed to solve fuzzy transportation problems. In this thesis out of these methods, three recently proposed methods [1-3], published in International Journals, are discussed.