A Comparative Analysis of Various Optimization Methods for Solving Fully Fuzzy Transportation Problems

This study investigates the solution of a Trapezoidal Fuzzy Transportation Problem (FTP) using Basirzadeh’s Fuzzy Ranking Approach through various optimization methods. The FTP was drawn from Pandian and Natarajan’s 2010 article in Applied Mathematical Sciences. They used the Fuzzy Zero Point Method to solve the FTP. However, the fact that this method has eleven steps, each requiring fuzzy operations, makes it a compelling process. To point out this complexity and to illustrate how easy to get the result, Basirzadeh’s method has been adopted in this study. In this method, the fuzzy data is converted into crip data, and a transportation matrix is created. Then it can be solved by any transportation method and the results may remain crisp or they might be fuzzified. In this study, firstly, the FTP has been solved using the Fuzzy Zero Point Method. Not only the initial cost table and final allocation table have been shared with readers, but also all intermediate steps of the fully fuzzy solution have been demonstrated. Subsequently, some common optimization methods used in transportation problems such as Northwest Corner, Least Cost, Russel, and Vogel’s methods, have been applied to Basirzadeh’s method and the results have been compared. Russel’s Method seems to be the best among these methods because it yielded the lowest transportation cost.