An Average Based Method for Finding the Basic Feasible Solution for the Fuzzy Transportation Problems

Abstract

Fuzzy transport problems are another special type of transport problem (TP). In a transportation problem, what is primarily considered is how to carry out the relevant process while reduce the total cost of the transporting the goods to different destinations. This objective is also valid for fuzzy TP. However, the supply quantity, demand, and unit cost values cannot be determined precisely, and those values are represented by "fuzzy number sets." There, the relevant solution value is obtained as a basic solution or an optimal solution. Thus, various researchers have proposed various algorithms to obtain an efficient initial solution or an optimal solution (OS) to fuzzy transportation problems. Accordingly, in this research article, we have presented another method to obtain an basic feasible solution (BFS) value for fuzzy transportation problems. It is prepared by creating a new value for each cell based on Yager's robust ranking method. In obtaining these values, the average of the crisp values of the columns and rows of the relevant column or row was basically considered. After that, the algorithm was used to solve mathematical problems. In here, the proposed method is primarily considered for triangular and trapezoidal fuzzy transportation problems. Also, the basic solution obtained from those solutions was that algorithm and the current approach are compared, and the efficiency and correctness of the proposed method were tested. Based on the analysis of the obtained data, the new method can be shown as an easy method to understand the efficiency that can be used to obtain the BFS to fuzzy transportation problems.