An approach for unbalanced fully rough interval transportation problem

Year 2023, Volume: 52 Issue: 5, 1408 - 1424, 31.10.2023

S. Shivani Deepika Rani Ali Ebrahimnrjad

https://doi.org/10.15672/hujms.980108

Cited By: 1

Abstract

In this study, we consider an unbalanced fully rough interval transportation problem, where all the parameters and decision variables are represented by rough interval numbers. A method named as split and separation method has been proposed in the literature to find the optimal solution of balanced fully rough interval transportation problem. As per our knowledge, no method exists in the literature to solve an unbalanced fully rough interval transportation problem. Therefore, a new method is proposed in this study to solve such problem. Using proposed methodology, firstly the unbalanced problem is converted into a balanced one and then the optimal solution of the balanced problem is obtained. To show the applicability of the proposed methodology, a numerical example is solved. Finally, the study’s conclusions and future research directions are discussed.

Keywords

Transportation problem, Rough interval coefficient, Unbalanced fully rough interval transportation problem, Optimal solution.

References

• [1] A.Y. Adhami and F. Ahmad, Interactive Pythagorean-hesitant fuzzy computational algorithm for multi-objective transportation problem under uncertainty, Int. J. Manag. Sci. Eng. Manag. 15 (4), 288-297, 2020.
• [2] M.M. Ahmed, A.R. Khan, M.S. Uddin and F. Ahmed, A new approach to solve transportation problems, Open J. Optim. 5, 22-30, 2016.
• [3] A. Akilbasha, G. Natarajan and P. Pandian, Finding an optimal solution of the interval integer transportation problems with rough nature by split and separation method, Int. J. Pure Appl. Math. 106 (6), 1-8, 2016.
• [4] B. Amaliah, C. Fatichah and E. Suryani, A supply selection method for better feasible solution of balanced transportation problem, Expert Syst. Appl. 203, 1-9, 2022.
• [5] P. Anukokila, B. Radhakrishnan and A. Anju, Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters, RAIRO Oper. Res. 53, 157-178, 2019.
• [6] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1), 87-96, 1986.
• [7] M. Bagheri, A. Ebrahimnejad, S. Razavyan, F. Hosseinzadeh Lotfi and N. Malekmohammadi, Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem, Oper. Res. 22, 1479-1509, 2022.
• [8] A. Baidya, U.K. Bera and M. Maiti, Multi-stage multi-objective solid transportation problem for disaster response operation with type-2 triangular fuzzy variables, Hacet. J. Math. Stat. 45 (5), 1485-1518, 2016.
• [9] S. Bera, P.K. Giri, D.K. Jana, K. Basu and M. Maiti, Multi-item 4D-TPs under budget constraint using rough interval, Appl. Soft Comput. 71, 364-385, 2018.
• [10] D. Chauhan, and A. Yadav, Optimizing the parameters of hybrid active power filters through a comprehensive and dynamic multi-swarm gravitational search algorithm, Eng. Appl. of Artif. Intell. 123 (Part C), 1-36, 2023.
• [11] D. Chauhan, and A. Yadav, A competitive and collaborative-based multilevel hierarchical artificial electric field algorithm for global optimization, Inf. Sci. 648, 1-35, 2023.
• [12] N.T.A Chilwal, An optimal controlled selection procedure for sample coordination problem using linear programming and distance function, Hacet. J. Math. Stat. 44 (1), 215-228, 2014.
• [13] A. Das, U.K. Bera and M. Maiti, A profit maximizing solid transportation model under a rough interval approach, IEEE Trans. Fuzzy Syst. 25 (3), 485-498, 2016.
• [14] H. Garg and R.M. Rizk-Allah, A novel approach for solving rough multi-objective transportation problem: development and prospects, Comput. Appl. Math. 40 (4), 1-24, 2021.
• [15] S. Ghosh, S.K. Roy, A. Ebrahimnejad and J.L. Verdegay, Multi-objective fully intuitionistic fuzzy fixed-charge solid transportation problem, Complex Intell. Syst. 7, 1009-1023, 2021.
• [16] A. Gupta, A. Kumar and A. Kaur, Mehar’s method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems, Optim. Lett. 6, 1737-1751, 2012.
• [17] F.L. Hitchcock, The distribution of a product from several sources to numerous localities, J. Math. Phys. 20 (1-4), 224-230, 1941.
• [18] Y. Kacher and P. Singh, Fuzzy harmonic mean technique for solving fully fuzzy multiobjective transportation problem, J. Comput. Sci. 63, 1-14, 2022.
• [19] K. Karagul and Y. Sahin, A novel approximation method to obtain initial basic feasible solution of transportation problem, J. King Saud Univ. Eng. Sci. 32 (3), 211-218, 2020.
• [20] S. Korukoglu and S. Balli, An improved vogel’s approximation method for the transportation problem, Math. Comput. Appl. 16 (2), 370-381, 2011.
• [21] A. Kumar and A. Kaur, Application of classical transportation methods to find the fuzzy optimal solution of fuzzy transportation problems, Fuzzy Inf. Eng. 3 (1), 81-99, 2011.
• [22] B. Liu and B. Liu, Theory and Practice of Uncertain Programming, 239, Springer, 2009.
• [23] S. Mahajan and S. Gupta, On fully intuitionistic fuzzy multi objective transportation problems using different membership functions, Ann. Oper. Res. 296, 211-241, 2021.
• [24] A. Mahmoodirad, T. Allahviranloo and S. Niroomand, A new effective solution method for fully intuitionistic fuzzy transportation problem, Soft Comput. 23 (12), 4521-4530, 2019.
• [25] D. Mardanya, G. Maity, S.K. Roy and V.F. Yu, Solving the multi-modal transportation problem via the rough interval approach, RAIRO Oper. Res. 56 (4), 3155-3185, 2022.
• [26] S. Midya and S.K. Roy, Multi-objective fixed-charge transportation problem using rough programming, Int. J. Oper. Res. 37 (3), 377-395, 2020.
• [27] S. Muthuperumal, P. Titus and M. Venkatachalapathy, An algorithmic approach to solve unbalanced triangular fuzzy transportation problems, Soft Comput. 24, 18689- 18698, 2020.
• [28] Z. Pawlak, Rough sets, Int. J. Comput. Inf. Sci. 11, 341-356, 1982.
• [29] D. Rani, T. Gulati and A. Kumar, A method for unbalanced transportation problems in fuzzy environment, Sadhana 39, 573-581, 2014.
• [30] M. Rebolledo, Rough intervals-enhancing intervals for qualitative modeling of technical systems, Artif. Intell. 170 (8-9), 667-685, 2006.
• [31] S.K. Roy and S. Midya, Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment, Appl. Intell. 49, 3524-3538, 2019.
• [32] S.K. Roy, S. Midya and V.F. Yu, Multi-objective fixed-charge transportation problem with random rough variables, Int. J. Uncertain. Fuzziness Knowlege-Based Syst. 26 (06), 971-996, 2018.
• [33] Shivani, D. Rani and A. Ebrahimnejad, On solving fully rough multi-objective fractional transportation problem: development and prospects, Comput. Appl. Math. 42 (6), 1-27, 2023.
• [34] J. Xu and Z. Tao, Rough Multiple Objective Decision Making, Chapman and Hall/CRC, 2019.
• [35] L. Zadeh, Fuzzy sets, Inf. Control. 8 (3), 338-353, 1965.