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 acomprehensive table that organizes data and results in a way that facilitates quickand accurate comparison. An amendment to one of the order formats was suggested,because it has different results compared to other formulas. One of the rankingequations is modified, because it has different results compared to other methods..
Highlights
Transportation problem is classified as an important linear programming model which is solving means finding the optimal solution that represents the final optimum value of the total cost of transportation problems
The aim of this study is to compare between various ranking formulas to obtain the optimal solution in order find the minimum value of total cost of transportation.The data and results that placed in the table for comparison and analysis, columns A-D are trapezoidal fuzzy numbers for numerical example, columns E-K represent the results of applying ranking formulas, column L
Data and results that are obtained by applying the fifth formula are not accepted depending on the nature of the model of transportation as they are out of the limits
Summary
Transportation problem is classified as an important linear programming model which is solving means finding the optimal solution that represents the final optimum value of the total cost of transportation problems. The transportation model "classic model" represents the known data in the problem which is the cost of transportation of one unit from supply center to demand center This model is solved by many different methods to find an optimal solution, such as lower cost LCM, north-west corner NWM, Vogel approximated method VAM, and stepping stone method SSM [4]. All these famous methods looking for an optimal distribution way to transport unites among cells of the model table with lowest total cost value
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