Solution of Unbalanced Assignment Problem using Pentagonal Fuzzy Numbers

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Published: 2025-12-15
Keywords:
Fuzzy Unbalanced Assignment Problem, Pentagonal Fuzzy Number, Hungarian Method, Ranking of Pentagonal Fuzzy Number

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Amit Kumar Nandan
Jitesh Pati Tripathi

Abstract

This paper introduces a solution mechanism for the Unbalanced Assignment Problem with fuzzy costs. Pentagonal fuzzy numbers are used to represent the fuzzy costs. In order to determine the best assignment, we first make the unbalanced assignment problem balanced, and then we use the Ranking of Pentagonal Fuzzy Number (PFN) to turn it into a crisp assignment problem.

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Vol. 29 No. 4 (2025): Table of Content

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Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

1.
Solution of Unbalanced Assignment Problem using Pentagonal Fuzzy Numbers. J. Int. Acad. Phys. Sci. [Internet]. 2025 Dec. 15 [cited 2026 Oct. 23];29(4):185-91. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/640

References

1. H.W. Kuhn; The Hungarian method for the assignment problem, Neval Research Logistics, 2 (1955), 83-97.

2. J. Munkres; Algorithms for the Assignment and Transportation Problems, Journal of the Society for Industrial and Applied Mathematics, 5(1), (1957), 32-38.

3. M. L. Balinski; A competitive (dual) simplex method for the assignment problem, Mathematical Programming, 34 (1986), 125-141.

4. M.S. Hung; A polynomial simplex method for the assignment problem, Operations Research, 31 (1983), 595-600.

5. D. Goldfarb; Efficient dual simplex methods for the assignment problem, Mathematical Programming, 33 (1985), 187-203.

6. M. S. Chen; On a Fuzzy Assignment Problem, Jamkang Journal 22 (1985), 407-411.

7. Long-Sheng Huang, Li-Pu Zhang; Solution Method for Fuzzy Assignment Problem with Restriction of Qualification, Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications (ISDA’06), 2006.

8. A. Khandelwal; A Modified Approach for Assignment Method to Maximize the throughput, International Journal of Pure and Engg. Mathematics (IJPEM), 2(II) (2014), 13-20, ISSN 2348-3881.

9. A. Khandelwal and A. Agarwal; An Amalgamated Approach of Fuzzy Logic and Genetic Algorithm for Better Recruitment Process, TNC Transactions of Network and Communications, 3-3 (2015), 23-31, ISSN: 2054-7420.

10. Amit Kr. Nandan, J. P. Tripathi, V. K. Tiwari, R. K. Shukla; Optimal solution of fuzzy assignment problem using Ranking Technique, International Journal of Scientific Research in Science and Technology (IJSRST), 11-2 (2024), 975-983.

11. Amit Kr. Nandan, J. P. Tripathi, V. K. Tiwari; An optimized approach to solve assignment problems using the fuzzy hungarian method, Engineering and Technology Journal (ETJ), 9-7 (2024), 4458-4461.