Maximum penalty method to solve transportation problem

Kumbhar, S. M.; Dinde, H. T.

doi:10.47974/JSMS-1495

Open Access Research Article

Maximum penalty method to solve transportation problem

^*S. M. KumbharCorresponding authorsnlkumbhar3@gmail.comDepartment of MathematicsShivaji UniversityKolhapur, Maharashtra, 416004, India0009-0003-5790-967XView full profile → , H. T. Dindedrhtdmaths@gmail.comDepartment of MathematicsShri Shiv-Shahu MahavidyalayaSarud, Maharashtra, 416214, India0009-0006-6081-186XView full profile →

* Corresponding author · click or hover a name for details

pp. 355–363Vol. 29Issue 4April 2026DOI: 10.47974/JSMS-1495XML

Received:: 08 Apr 2025
Published Online:: 08 Jan 2026
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1495
Pages:: 355–363

Abstract

In this present article, we have proposed a method to obtain an Initial Basic Feasible Solution (IBFS) for the Transportation Problem. It is based on Maximum penalty where row penalty and column penalty is obtained by the average of Maximum and Minimum element of newly formed Transportation Table. Proposed method is illustrated with numerical examples and compared results with existing well known methods.

Keywords

IBFS Average Penalty Transportation cost

Subject Classifications

90B06

References

[1] R. Agarwal, R. P. Chaturvedi, A. Mishra, S. Asthana, and M. Parashar, “An approach for determining the best solution for intuitionistic fuzzy transportation problem,” Journal of Information and Optimization Sciences, vol. 45, no. 7, pp. 1867–1879 (2024), doi: 10.47974/JIOS-1739.
[2] A. A. Alsaraireh, “Optimality solution of transportation problem in a new method (summation and ratio method),” International Journal of Membrane Science and Technology, vol. 10, no. 4, pp. 46–52 (2023).
[3] C.-J. Lin and W.-T. Lin, “A systematic weighted Hungarian algorithm for optimization and postoptimal analysis of transportation problem,” Journal of Statistics and Management Systems, vol. 26, no. 4, pp. 843–866 (2023), doi: 10.47974/JSMS-936.
[4] V. Joshi, S. S. Naharwar, J. Singh, and K. Nisar, “A new solution procedure for multi-objective linear fractional transportation problem with rough parameters,” Journal of Interdisciplinary Mathematics, vol. 26, pp. 121–132 (2023), doi: 10.47974/JIM-1651.
[5] V. Joshi, S. S. Naharwar, J. Singh, and K. Nisar, “An improved solution approach for solving multi-objective linear and linear fractional transportation problem,” Journal of Interdisciplinary Mathematics, vol. 26, pp. 133–143 (2023), doi: 10.47974/JIM-1652.
[6] F. H. Thanoon, “Proposed method for solving transportation problems,” Wasit Journal for Pure Sciences, vol. 1, no. 3 (2022).
[7] M. M. Hossain and M. M. Ahmed, “A comparative study of initial basic feasible solution by a least cost mean method (LLCM) of transportation problem,” American Journal of Operation Research, vol. 10, pp. 122–131 (2020).
[8] S. Rekha, B. Srividhya, and S. Vidya, “Transportation cost minimization: Max–min penalty approach,” IOSR Journal of Mathematics (IOSR-JM), vol. 10, no. 2, pp. 6–8 (2014).
[9] S. Raigar and G. Modi, “An effective methodology for solving transportation problem,” International Journal of Scientific and Innovative Mathematical Research (IJSIMR), vol. 5, no. 10, pp. 23–27 (2017).
[10] S. Kumbhar and H. T. Dinde, “A comparative study of IBFS for solving transportation problem: Average of cost approach,” Panamerican Mathematical Journal, vol. 35, no. 4S, pp. 180–189 (2025).
[11] S. Duraphe and S. Raigar, “A new approach to solve transportation problems with the max–min total opportunity cost method,” International Journal of Mathematics Trends and Technology (IJMTT), vol. 51, no. 4 (2017).
[12] Y. Kacher and P. Singh, “A comprehensive literature review on transportation problems,” International Journal of Applied and Computational Mathematics, vol. 7, Art. no. 206 (2021).

Views: 130Downloads: 66Citations: 0