A New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment
DOI:
https://doi.org/10.24297/ijct.v16i4.6206Keywords:
Optimization; Fuzzy Bi-Objective transportation problem; Ranking function; Triangular fuzzy number; Optimal solution; Improved VAM.Abstract
The present paper attempts to obtain the optimal solution for the fuzzy transportation problem with mixed constraints. In this paper, authors have proposed a new innovative approach for obtaining the optimal solution of mixed constraint fuzzy transportation problem. The method is illustrated using a numerical example and the logical steps are highlighted using a simple flowchart. As maximum transportation problems in real life have mixed constraints and these problems cannot be truly solved using general methods, so the proposed method can be applied for solving such mixed constraint fuzzy transportation problems to obtain the best optimal solutions.
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References
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16. Pandian, P. and Natarajan, G. 2010. A New Method for Finding an Optimal More-For-Less Solution of Transportation Problems with Mixed Constraints. Int. J. Contemp. Math. Sciences. 5, 19, 931 – 942.
17. Pandian, P. and Natarajan, G. 2010. An Approach for solving Transportation Problems with Mixed Constraints. Journal of Physical Sciences. 14, 53 –61.
18. Pandian, P. and Anuradha, D. 2013. Path Method for Finding a More-For-Less Optimal Solution to Transportation Problems. International Conference on Mathematical Computer Engineering. 1, 331–337.
19. George Osuji, A., Opara, J., Anderson Nwobi, C., Onyeze, V. and Andrew Iheagwara, I. 2014. Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics. 2, 10-15.
20. Kavitha, K. and Anuradha, D. 2015. Heuristic algorithm for finding sensitivity analysis of a more for less solution to transportation problems. Global Journal of Pure and Applied Mathematics. 11, 479-485.
21. Joshi, V. D. and Gupta, N. 2012. Identifying more-for-less paradox in the linear fractional transportation problem using objective matrix. Mathematika. 28, 173–180.
22. Adlakha, V. and Kowalski, K. 2000. Technical note, A note on the procedure MFL for a more-for-less solution in transportation problems. Omega. 28, 4, 481–483.
23. Akyar, E., Akyar, H. and Duzce, S. A. 2012. A new method for ranking triangular fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge-based systems. 20, 5, 729-740.
2. Hitchcock, F. L. 1941. The distribution of a product from several sources to numerous localities. Journal of Math. Phys. 20, 224-230.
3. Arora, S. and Khurana, A. 2002. A paradox in an indefinite quadratic transportation problem with mixed constraints. International Journal of Management and Systems. 18(3), 301–318.
4. Lev, B. and Intrator, Y. 1977. Applications of vanishing variables methods to special structured transportation problems. Computers and Operations Research. 4, 21-26.
5. Lev, B. 1972. A non iterative algorithm for tridiagonal transportation problems and its generalization. Journal of Operations Research Society of America. 20,109-125.
6. Arsham, H. 1992. Post optimality analyses of the transportation problem. Journal of the Operational Research Society. 43,121-139.
7. Gupta, A., Khanna, S.and Puri, M. 1993. Paradoxical situation in transportation problems. Cahiers du Centre d’Etudes de RechercheOperationnell. 34, 37-49.
8. Pandian, P. and Natarajan, G. 2010. Fourier method for solving transportation problems with mixed constraints. Int. J. Contemp. Math. Sciences. 5, 28, 1385-1395.
9. Isermann, H. 1979. Solving the transportation problem with mixed constraints. Zeitschrift fur Operations Research. 26, 251-257.
10. Brigden, M. 1974. A variant of transportation problem in which the constraints are of mixed type. Operational Research Quaterly. 25, 3, 437-445.
11. Adlakha, V., Kowalski, K., Lev, B. and Vemuganti, R.R. 2007. More-for-less algorithm for fixed-charge transportation problems. The International Journal of Management Science. 35, 1, 1–20.
12. Adlakha, V., Kowalski, K. and Lev, B. 2006. Solving transportation problems with mixed constraints. International Journal of Management Science and Engineering Management. 1, 1, 47–52.
13. Adlakha, V. and Kowalski, K. 2001. A heuristic method for more-for-less in distribution related problems. International Journal of Mathematical Education in Science and Technology. 32, 61-71.
14. Adlakha, V. and Kowalski, K. 1998. A quick sufficient solution to the More-for-Less paradox in the transportation problem. Omega. 26, 4, 541–547.
15. Pandian, P. and Natarajan, G. 2010. An Optimal More-for-Less Solution to Fuzzy Transportation Problems with Mixed Constraint. Applied Mathematical Sciences. 4, 29, 1405 – 1415.
16. Pandian, P. and Natarajan, G. 2010. A New Method for Finding an Optimal More-For-Less Solution of Transportation Problems with Mixed Constraints. Int. J. Contemp. Math. Sciences. 5, 19, 931 – 942.
17. Pandian, P. and Natarajan, G. 2010. An Approach for solving Transportation Problems with Mixed Constraints. Journal of Physical Sciences. 14, 53 –61.
18. Pandian, P. and Anuradha, D. 2013. Path Method for Finding a More-For-Less Optimal Solution to Transportation Problems. International Conference on Mathematical Computer Engineering. 1, 331–337.
19. George Osuji, A., Opara, J., Anderson Nwobi, C., Onyeze, V. and Andrew Iheagwara, I. 2014. Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics. 2, 10-15.
20. Kavitha, K. and Anuradha, D. 2015. Heuristic algorithm for finding sensitivity analysis of a more for less solution to transportation problems. Global Journal of Pure and Applied Mathematics. 11, 479-485.
21. Joshi, V. D. and Gupta, N. 2012. Identifying more-for-less paradox in the linear fractional transportation problem using objective matrix. Mathematika. 28, 173–180.
22. Adlakha, V. and Kowalski, K. 2000. Technical note, A note on the procedure MFL for a more-for-less solution in transportation problems. Omega. 28, 4, 481–483.
23. Akyar, E., Akyar, H. and Duzce, S. A. 2012. A new method for ranking triangular fuzzy numbers. International Journal of Uncertainty, Fuzziness and Knowledge-based systems. 20, 5, 729-740.
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Published
2017-06-28
How to Cite
Joshi, N., Chauhan (Gonder), S. S., & Raja, R. (2017). A New Approach to Solve Mixed Constraint Transportation Problem Under Fuzzy Environment. INTERNATIONAL JOURNAL OF COMPUTERS &Amp; TECHNOLOGY, 16(4), 6895–6902. https://doi.org/10.24297/ijct.v16i4.6206
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