Modified Hungarian Method for Solving Balanced Fuzzy Transportation Problems
Keywords:
Fuzzy Transportation, Hungarian Method, Trapezoidal Fuzzy Number, Robust’s Ranking
Abstract
This paper discusses how to solve balanced transportation problems, with transportation costs in the form of trapezoidal fuzzy numbers. Fuzzy costs are transformed into crisp costs using the Robust’s method as a ranking function. A new approach of modified Hungarian method has been applied to solve the problem of fuzzy transportation. This approach solves the fuzzy transportation problem in one stage of optimization and yields the same results as other methods that solve the problem in two stages.
References
Aini, A. N., Shodiqin, A., & Wulandari, D. (2021). Solving Fuzzy Transportation Problem Using ASM Method and Zero Suffix Method. Enthusiastic: International Journal of Applied Statistics and Data Science, 1(1), 28–35.
Balasubramanian, K., & Subramanian, S. (2018). An Approach for Solving Fuzzy Transportation Problem. International Journal of Pure and Applied Mathematics, 119(17), 1523–1534. Retrieved from http://www.acadpubl.eu/hub/
Bector, C. R., & Chandra, S. (2005). Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer. Berlin.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-Making in a Fuzzy Environment. Management Science, 17(4).
Betts, N., & Vasko, F. J. (2016). Solving the Unbalanced Assignment Problem: Simpler Is Better. American Journal of Operations Research, 06(04), 296–299.
Bisht, D. C. S., & Srivastava, P. K. (2019). One Point Conventional Model to Optimize Trapezoidal Fuzzy Transportation Problem. International Journal of Mathematical, Engineering and Management Sciences, 4(5), 1251–1263.
Dhanasekar, S., Hariharan, S., & Sekar, P. (2016). Fuzzy Hungarian MODI Algorithm to Solve Fully Fuzzy Transportation Problems. International Journal of Fuzzy Systems, 19(5), 1479–1491. Springer Berlin Heidelberg.
Evipania, R., Gandhiadi, G. K., & Sumarjaya, I. W. (2021). Optimalisasi Masalah Penugasan Tidak Seimbang Menggunakan Modified Hungarian Method. E-Jurnal Matematika, 10(1), 26–31.
Farikhin, Sam’an, M., Surarso, B., & Irwanto, B. (2020). Solving of Fuzzy Transportation Problem Using Fuzzy Analytical Hierarchy Process (AHP). Proceedings of the 2nd International Seminar on Science and Technology (ISSTEC 2019) Solving (Vol. 474, pp. 10–15). Retrieved from http://creativecommons.org/licenses/by-nc/4.0/
Hunwisai, D., & Kumam, P. (2017). A Method for Solving a Fuzzy Transportation Problem Via Robust Ranking Technique and ATM. Cogent Mathematics, 4(1), 1–11. Cogent. Retrieved from http://dx.doi.org/10.1080/23311835.2017.1283730
Kar, R., Shaw, A. K., & Mishra, J. (2021). Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problems by Hungarian Method: A New Approach. Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications, 315–333.
Khalifa, H. A. E. W. (2020). Goal Programming Approach for Solving Heptagonal Fuzzy Transportation Problem Under Budgetary Constraint. Operations Research and Decisions, 30(1), 85–96.
Kuhn, H. W. (1955). The Hungarian Method for The Assignment Problem. Naval Research Logistics Quarterly, 2, 83–97.
Kumar, A. (2006). A Modified Method for Solving The Unbalanced Assignment Problems. Applied Mathematics and Computation, 176(1), 76–82.
Malini, S. U., & Kennedy, F. C. (2013). An Approach for Solving Fuzzy Transportation Problem Using Octagonal Fuzzy Numbers. Applied Mathematical Sciences, 7(54), 2661–2673.
Manimaran, S., & Ananthanarayanan, M. (2012). A Study on Comparison Between Fuzzy Assignment Problems Using Trapezoidal Fuzzy Numbers with Average Method. Indian Journal of Science and Technology, 5(4), 2610–2613.
Patil, A., & Chandgude, S. B. (2013). Fuzzy Hungarian Approach for Transportation Model. International Journal of Mechanical and Industrial Engineering, 2(3), 189–192.
Rabbani, Q., Khan, A., & Quddoos, A. (2019). Modified Hungarian Method for Unbalanced Assignment Problem with Multiple Jobs. Applied Mathematics and Computation, 361, 493–498. Elsevier Inc.
Razi, F. A., & Yudiarti, W. W. (2020). Network Optimization of Packaging Water Factory “Aeta” by Using Critical Path Method (CPM) in Tirta Taman Sari Drinking Water Company, Madiun City. Jurnal Varian, 4(1), 11–18.
Sakawa, M. (1993). Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press. New York: Plenum Press.
Srinivasan, R., Karthikeyan, N., Renganathan, K., & Vijayan, D. V. (2020). Method for Solving Fully Fuzzy Transportation Problem to Transform The Materials. Materials Today: Proceedings, 37(2), 431–433. Elsevier Ltd. Retrieved from https://doi.org/10.1016/j.matpr.2020.05.423
Taylor, B. W. (2013). Introduction to Management Science. Pearson Education, Inc. New Jersey.
Yadaiah, V., & Haragopal, V. V. (2016). A New Approach of Solving Single Objective Unbalanced Assignment Problem. American Journal of Operations Research, 06(01), 81–89.
Younis, A. A. A., & Alsharkasi, A. M. (2019). Using of Hungarian Method to Solve The Transportation Problems. EPH - International Journal of Applied Science, 1(1), 834–845. Retrieved from https://ephjournal.org/index.php/as/article/view/1398
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338–353.
Zimmermann, H. J. (1978). Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and Systems, 1(1), 45–55.
Balasubramanian, K., & Subramanian, S. (2018). An Approach for Solving Fuzzy Transportation Problem. International Journal of Pure and Applied Mathematics, 119(17), 1523–1534. Retrieved from http://www.acadpubl.eu/hub/
Bector, C. R., & Chandra, S. (2005). Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer. Berlin.
Bellman, R. E., & Zadeh, L. A. (1970). Decision-Making in a Fuzzy Environment. Management Science, 17(4).
Betts, N., & Vasko, F. J. (2016). Solving the Unbalanced Assignment Problem: Simpler Is Better. American Journal of Operations Research, 06(04), 296–299.
Bisht, D. C. S., & Srivastava, P. K. (2019). One Point Conventional Model to Optimize Trapezoidal Fuzzy Transportation Problem. International Journal of Mathematical, Engineering and Management Sciences, 4(5), 1251–1263.
Dhanasekar, S., Hariharan, S., & Sekar, P. (2016). Fuzzy Hungarian MODI Algorithm to Solve Fully Fuzzy Transportation Problems. International Journal of Fuzzy Systems, 19(5), 1479–1491. Springer Berlin Heidelberg.
Evipania, R., Gandhiadi, G. K., & Sumarjaya, I. W. (2021). Optimalisasi Masalah Penugasan Tidak Seimbang Menggunakan Modified Hungarian Method. E-Jurnal Matematika, 10(1), 26–31.
Farikhin, Sam’an, M., Surarso, B., & Irwanto, B. (2020). Solving of Fuzzy Transportation Problem Using Fuzzy Analytical Hierarchy Process (AHP). Proceedings of the 2nd International Seminar on Science and Technology (ISSTEC 2019) Solving (Vol. 474, pp. 10–15). Retrieved from http://creativecommons.org/licenses/by-nc/4.0/
Hunwisai, D., & Kumam, P. (2017). A Method for Solving a Fuzzy Transportation Problem Via Robust Ranking Technique and ATM. Cogent Mathematics, 4(1), 1–11. Cogent. Retrieved from http://dx.doi.org/10.1080/23311835.2017.1283730
Kar, R., Shaw, A. K., & Mishra, J. (2021). Trapezoidal Fuzzy Numbers (TrFN) and its Application in Solving Assignment Problems by Hungarian Method: A New Approach. Fuzzy Intelligent Systems: Methodologies, Techniques, and Applications, 315–333.
Khalifa, H. A. E. W. (2020). Goal Programming Approach for Solving Heptagonal Fuzzy Transportation Problem Under Budgetary Constraint. Operations Research and Decisions, 30(1), 85–96.
Kuhn, H. W. (1955). The Hungarian Method for The Assignment Problem. Naval Research Logistics Quarterly, 2, 83–97.
Kumar, A. (2006). A Modified Method for Solving The Unbalanced Assignment Problems. Applied Mathematics and Computation, 176(1), 76–82.
Malini, S. U., & Kennedy, F. C. (2013). An Approach for Solving Fuzzy Transportation Problem Using Octagonal Fuzzy Numbers. Applied Mathematical Sciences, 7(54), 2661–2673.
Manimaran, S., & Ananthanarayanan, M. (2012). A Study on Comparison Between Fuzzy Assignment Problems Using Trapezoidal Fuzzy Numbers with Average Method. Indian Journal of Science and Technology, 5(4), 2610–2613.
Patil, A., & Chandgude, S. B. (2013). Fuzzy Hungarian Approach for Transportation Model. International Journal of Mechanical and Industrial Engineering, 2(3), 189–192.
Rabbani, Q., Khan, A., & Quddoos, A. (2019). Modified Hungarian Method for Unbalanced Assignment Problem with Multiple Jobs. Applied Mathematics and Computation, 361, 493–498. Elsevier Inc.
Razi, F. A., & Yudiarti, W. W. (2020). Network Optimization of Packaging Water Factory “Aeta” by Using Critical Path Method (CPM) in Tirta Taman Sari Drinking Water Company, Madiun City. Jurnal Varian, 4(1), 11–18.
Sakawa, M. (1993). Fuzzy Sets and Interactive Multiobjective Optimization. Plenum Press. New York: Plenum Press.
Srinivasan, R., Karthikeyan, N., Renganathan, K., & Vijayan, D. V. (2020). Method for Solving Fully Fuzzy Transportation Problem to Transform The Materials. Materials Today: Proceedings, 37(2), 431–433. Elsevier Ltd. Retrieved from https://doi.org/10.1016/j.matpr.2020.05.423
Taylor, B. W. (2013). Introduction to Management Science. Pearson Education, Inc. New Jersey.
Yadaiah, V., & Haragopal, V. V. (2016). A New Approach of Solving Single Objective Unbalanced Assignment Problem. American Journal of Operations Research, 06(01), 81–89.
Younis, A. A. A., & Alsharkasi, A. M. (2019). Using of Hungarian Method to Solve The Transportation Problems. EPH - International Journal of Applied Science, 1(1), 834–845. Retrieved from https://ephjournal.org/index.php/as/article/view/1398
Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338–353.
Zimmermann, H. J. (1978). Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and Systems, 1(1), 45–55.
Published
2022-04-30
How to Cite
[1]
F. Allung Blegur and N. Dethan, “Modified Hungarian Method for Solving Balanced Fuzzy Transportation Problems”, Jurnal Varian, vol. 5, no. 2, pp. 161 - 170, Apr. 2022.
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