A Comparative Study of Two Techniques for Analyzing Optimal Bounds in Fully Fuzzy Transportation Problems Using Parametric Methods

Abstract

This study makes two major contributions: first, it presents a new approach to solving the fuzzy transportation problem (FTP); second, it contrasts two different Parametric methods for analyzing optimal bounds. The first Mechanism is to obtain a fuzzy optimal solution by solving the FTP directly. Then, in order to attain the best crisp outcome, we apply the alpha-cut and parametric function to the fuzzy decision variables and their associated cost values. This produces a sequence of ordinary values for the objective function, and we choose the best one. In the second method, we again employ the alpha-cut and parametric function, but this time we transform all of the Fuzzy transportation problem table components, which are costs, supply, and demand, into crisp numbers. Then we get ordinary TP and solve it to acquire the optimal solution for the objective function. For the values of alpha and beta, we will get a series of crisp solutions this enabling us to determine the best optimal crisp value. This paper offers a thorough analysis of the two approaches, stressing their benefits, drawbacks, and suitability for solving practical issues.