An Approach to Fuzzy Transportation Problem Using Different Ranking Methods

Abstract

The Transportation Problem is a well-known optimization problem in the field of Operations Research that is used to model and solve real-world transportation and logistics problems. It involves determining how to transport a certain quantity of goods from a set of sources to a set of destinations at minimum cost, subject to constraints on the supply and demand of the goods. Many times dealing with Transportation planning, decision problems, input data and related parameters, such as available supply and forecast demand, are often vague/fuzzy because some information is unavailable or incomplete. At the same time, decision makers have to deal with the conflicting goals of managing the use of limited resources within the organization. newlineThe idea of a fuzzy set was first proposed by Zadeh in the year 1965, as a mean of handling uncertainty that is due to imprecision rather than randomness. Crisp transportation problem is converted to fuzzy transportation problem using various fuzzy numbers like central triangular fuzzy number, triangular fuzzy number, trapezoidal fuzzy number etc. Taking distance d (central fuzzy triangular number) from the center of crisp number x to obtained fuzzy transportation problem and determine the error in transportation problem which is the difference between cost of fuzzy and crisp transportation problem. Furthermore, the crisp transportation problem is converted into the fuzzy transportation problem solved by applying the methods Fuzzy North West Corner Method, Fuzzy Least Cost Method (MMM) and Fuzzy VAM method. newlineThe fuzzy number cannot be ordered but partially ordered. Using different ranking method to ordered triangular and trapezoidal method we obtained the optimum solution to fuzzy transportation problem. The solution of fuzzy transportation problem is discussed by taking various cases. First all solution variables are fuzzy, after that coefficient of objective function are fuzzy and in next case the right hand side limit are fuzzy. Applying different ranking method to ordered fuzzy num