Improved Segregated Advancement (I-SA): a new method for solving full triangular fuzzy transportation problems

ABSTRACT In this paper, triangular fuzzy numbers (TFN) are used to represent the uncertainty of data in the transportation problems (TP), which are referred to as fuzzy transportation problems (FTP). The main issues in the FTP are the lack of information, error of the basic trading rules, incomplete fuzzy data, and the limitations of the existing fuzzy-ranking functions which is failed to compare two TFN. Segregated advancement (SA) is a separation approach where the TFN represented by low, middle, and upper are solved part by part. The flaw of SA is that it uses the classical algorithms which are NWC, LCM, and VAM. Therefore, we proposed the improvement based on the combination of total ratio cost matrix and total difference method by column without using classical ranking functions. The first and second examples illustrate the existing methods without using the SA approach. The results show that the proposed method obtained the optimal solution of FTP, whereas the existing methods produced infeasible solution. The third example presents the limitation of existing methods along with the SA approach. The results show that the proposed method is capable in solving the third example whereas the existing approach failed to solve the said example.