Comparative Study of Ranking Methods for Fuzzy Transportation

Abstract

There are several methods that are used to solve the traditional transportation problems whose units of supply, demand quantities, and cost transportation are known exactly. These methods obtain basic solution, and develop it to the best solution through a series of consecutive calculations to obtain the optimal solution.
The steps are more complex with fuzzy variables, so this paper presents the disadvantages of solutions of the traditional ways with existence of variables in the fuzzy form.
This paper also presents a comparison between the results that emerged after using different conversion ranking formulas to convert from fuzzy form to crisp form on the same numerical example with a full fuzzy form. The problem has been then converted into a linear programming model, and the BIG-M method to be later used to find the optimal solution that represents the number of units transferred from processing or supply centers to a number of demand centers based on the known cost of transportation.
Achieving the goal of the problem is by finding the lowest total transportation cost,
while the comparison is based on that value. The results are presented in a
comprehensive table that organizes data and results in a way that facilitates quick
and accurate comparison. An amendment to one of the order formats was suggested,
because it has different results compared to other formulas. One of the ranking
equations is modified, because it has different results compared to other methods..