Title: Improved total difference method (ITDM): a new approach to solving transportation problem based on modifications of total difference method 1 and integration of total ratio cost matrix

Authors: Muhammad Sam'an; Yosza Dasril; Nazarudin Bin Bujang; Farikhin

Addresses: Department of Informatics, Universitas Muhammadiyah Semarang, Kedungmundu Raya No. 18, Semarang, 50273, Indonesia ' Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia (UTHM), Batu Pahat, Johor, 86400, Malaysia ' Faculty of Technology Management and Business, Universiti Tun Hussein Onn Malaysia (UTHM), Batu Pahat, Johor, 86400, Malaysia ' Department of Mathematics, Universitas Diponegoro, Jl. Prof Soedarto, SH Tembalang, Semarang, 1269, Indonesia

Abstract: In this paper, the initial basic feasible solution is referred to as the initial feasible solution (IFS). There are two phases in solving the transportation problem (TP). An IFS is determined in the first phase by using the least distribution cost, followed by the calculation of the optimal solution through the modification of total difference method (TDM 1), integrated with total ratio cost matrix (TRCM) in the second phase. In some cases, it has been found that TP has equal values of the distribution least costs so that the existing methods generate two or more IFS values. The newly developed algorithm obtains the optimal solution of TP. A total of 26 numerical examples were selected from reputed journals to evaluate the performance of the newly developed algorithm. The computational performances were compared to the existing methods in the literature and the results showed that this algorithm not only solves TP with similar values optimal solution but also produces better minimal solutions than existing methods.

Keywords: transportation problem; IFS; initial feasible solution; optimal solution; total difference method; TRCM; total ratio cost matrix.

DOI: 10.1504/IJCSM.2022.126767

International Journal of Computing Science and Mathematics, 2022 Vol.16 No.1, pp.13 - 23

Received: 21 Jan 2021
Accepted: 19 Mar 2021
Published online: 07 Nov 2022 *

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