A combination of TDM and KSAM to determine initial feasible solution of transportation problems
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Abstract
In case of the Transportation Problem (TP), it was found that TP had equal the smallest so that the existing methods will be generated two or more IFS values. The newly developed algorithm is generated through a combination of Total Difference Method (TDM) and Karagul-Sahin Approximation Method (KSAM) algorithm, is capable to determine the initial feasible solution of TP. Based on the numerical illustration of TP example to evaluate the performance of the new proposed algorithm. The computational performances have been compared to the existing methods (TDM1 and KSAM) and the results shown this algorithm achieved better performance than the existing methods for TP example.
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References
D. Aprilianto, “SVM optimization with correlation feature selection based binary particle swarm optimization for diagnosis of chronic kidney disease,” J. Soft Comput. Explor., vol. 1, no. 1, pp. 24–31, 2020.
R. H. Saputra and B. Prasetyo, “Improve the accuracy of c4.5 algorithm using particle swarm optimization ( pso ) feature selection and bagging technique in breast cancer diagnosis,” J. Soft Comput. Explor., vol. 1, no. 1, pp. 47–55, 2020.
I. E.Tiffani, “Optimization of naïve bayes classifier by implemented unigram, bigram, trigram for sentiment analysis of hotel review,” J. Soft Comput. Explor., vol. 1, no. 1, pp. 1–7, 2020.
A. Khan, “A Re-solution of the Transportation Problem: An Algorithmic Approach,” Jahangirnagar Univ. J. Sci., vol. 34, pp. 49–62, 2011.
M. A. Islam, M. M. Haque, and M. S. Uddin, “Extremum difference formula on total opportunity cost: a transportation cost minimization technique,” Prime Univ. Journa, vol. 6, no. 2, pp. 125–130, 2012.
M. Ashraful Babu, M. Abu Helal, M. S. Hasan, and U. K. Das, “Lowest Allocation Method (LAM): a new approach to obtain feasible solution of transporta-tion model,” Int. J. Sci. Eng. Res., vol. 4, no. 11, 2013.
U. Kanti Das, M. Ashraful Babu, A. Rahman Khan, and D. Sharif Uddin, “Advanced Vogel’s Approximation Method (AVAM): a new approach to determine penalty cost for better feasible solution of transportation problem,” Int. J. Eng. Res. Technol., vol. 3, p. 182, 2014.
A. R. Khan, V. Adrian, N. Sultana, and S. S. Ahmed, “Determination of initial basic feasible solution of a transportation problem: a TOCM-SUM approach,” Bul. Institutului Politeh. Din Iasi, vol. 61, pp. 39–49, 2015.
T. Can, “Tuncay Can’s Approximation method to obtain initial basic feasible solution to transport problem,” Appl. Comput. Math., vol. 5, no. 2, p. 78, 2016, doi: 10.11648/j.acm.20160502.17.
M. M. Ahmed, A. R. Khan, F. Ahmed, and M. S. Uddin, “Incessant Allocation Method for Solving Transportation Problems,” Am. J. Oper. Res., vol. 06, no. 03, pp. 236–244, 2016, doi: 10.4236/ajor.2016.63024.
M. M. Ahmed, A. R. Khan, M. S. Uddin, and F. Ahmed, “A new approach to solve transportation problems,” Open J. Optim., vol. 05, no. 01, pp. 22–30, 2016, doi: 10.4236/ojop.2016.51003.
E. Hosseini, “Three new methods to find initial basic feasible solution of transportation problems,” Appl. Math. Sci., vol. 11, pp. 1803–1814, 2017, doi: 10.12988/ams.2017.75178.
Y. Harrath and J. Kaabi, “New heuristic to generate an initial basic feasible solution for the balanced transportation problem,” Int. J. Ind. Syst. Eng., vol. 30, no. 2, p. 193, 2018, doi: 10.1504/ijise.2018.10016216.
S. M. Abul Kalam Azad and M. Kamrul Hasan, “An effective algorithm to solve cost minimising transportation problem,” Int. J. Math. Oper. Res., vol. 15, no. 4, pp. 434–445, 2019, doi: 10.1504/IJMOR.2019.103005.
Z. H. Radthy, F. H. Maghool, and A. H. Khaleel, “Application the linear programming according to transportation problem on real data,” Int. J. Sci. Technol. Res., vol. 8, no. 1, pp. 100–102, 2019.
B. Amaliah, C. Fatichah, and E. Suryani, “Total opportunity cost matrix – Minimal total: A new approach to determine initial basic feasible solution of a transportation problem,” Egypt. Informatics J., vol. 20, no. 2, pp. 131–141, 2019, doi: 10.1016/j.eij.2019.01.002.
B. Amaliah, C. Fatichah, E. Suryani, and A. Muswar, “Total opportunity cost matrix - Supreme cell: A new method to obtain initial basic feasible solution of transportation problems,” in ACM International Conference Proceeding Series, 2020, pp. 151–156, doi: 10.1145/3411174.3411198.
K. Karagul and Y. Sahin, “A novel approximation method to obtain initial basic feasible solution of transportation problem,” J. King Saud Univ. - Eng. Sci., vol. 32, no. 3, pp. 211–218, 2020, doi: 10.1016/j.jksues.2019.03.003.
Z. U. Rizqi, “Zack algorithm: A heuristic approach to solve transportation problem,” in Proceedings of the International Conference on Industrial Engineering and Operations Management, 2019, pp. 1127–1131.
L. Kaur, M. Rakshit, and S. Singh, “An alternate approach for finding the initial basic feasible solution of transportation problem,” Int. J. Sci. Technol. Res., vol. 8, no. 9, pp. 442–447, 2019.
P. Sumathi and C. V. Sathiya Bama, “An innovative route to acquire least cost in transportation problems,” Int. J. Eng. Adv. Technol., vol. 9, no. 1, pp. 5368–5369, 2019, doi: 10.35940/ijeat.A3070.109119.
B. Mallia, M. Das, and C. Das, “A New Algorithm for Bottleneck Transportation Problem,” Int. J. Innov. Technol. Explor. Eng., vol. 8, no. 8, pp. 419–423, 2019.
R. Murugesan and T. Esakkiammal, “Determination of best initial basic feasible solution of a transportation problem: A TOCM-ASM approach,” Adv. Math. Sci. J., vol. 9, no. 7, pp. 4563–4577, 2020, doi: 10.37418/amsj.9.7.25.
R. Murugesan and T. Esakkiammal, “An improved ASM method for the transportation problem,” Adv. Math. Sci. J., vol. 9, no. 10, pp. 8259–8271, 2020, doi: 10.37418/amsj.9.10.55.
R. Murugesan and T. Esakkiammal, “TOCM-VAM method versus asm method in transportation problems,” Adv. Math. Sci. J., vol. 9, no. 6, pp. 3549–3566, 2020, doi: 10.37418/amsj.9.6.34.