A Novel Approach for Optimization of Transportation Problem in Chaos Environment

Document Type : Research Paper

Author

Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

Abstract

    Nature is characterized by its chaotic behavior. Mathematics is considered one of the appropriate tools to achieve the best definition of possible its chaos variables and process. Classical mathematics deals with the numbers as static and meaningless, but chaos mathematics deals with it as dynamic evolutionary, and value- added. This paper attempts to introduce the transportation problem representation in chaos environment and also the necessity of the model is investigated. An approach for determining the chaos best solution is proposed briefly. The advantage of the proposed approach is accomplished with the associated ordinary number and the number of iterations arriving to the best solution is reduced. A numerical example is given to illustrate the utility, effectiveness and applicability of the approach for the problem.

Keywords

References

-Ahmed, M., Khan, A., Uddin, M. and Ahmed, F.  (2016) ''A new approach to solve transportation problems'', Open Journal of Optimization, Vol.5, No.1, March 2016, pp.7- 19. Doi: 10.4236/ojop.2016.51003.
-Ammar, E. E. and Khalifa, H. A. (2014) '' Study on multiobjecttive solid transportation problem with fuzzy numbers'', European Journal of Scientific Research, Vol.125, pp.7- 19.
-Anam, S., Khan, A. R., Haque, M. M. and Hadi, R. S. (2012) ''The impact of transportation cost on potato price: A case study of potato distribution in Bangladesh'',  International Journal of Management, Vol.1, pp.1- 12.
-Bit, A. K., Biswal, M. P. and Alam, S. S. (1993) ''Fuzzy programming approach to multi- objective solid transportation problem'', Fuzzy Sets and Systems, Vol. 57, pp. 183- 194.
-Chanas, S. and Kuchta, D. (1996) ''A concept of the optimal solution of the transportation problem with fuzzy cost coefficients'', Fuzzy Sets and Systems, Vol. 82, pp. 299- 305.
-Charnes, A., Cooper, W. W. and Henderson (1953) ''An Introduction to Linear Programming '', John Wiley & Sons, New York.
-Dalman, H. (2018) ''Modeling optimizing of multi- item solid transportation problems with uncertain variables and uncertain entropy function'', Communication in Mathematical Modeling and Applications, Vol. 3, pp. 28- 41.
 
-Dantzig, G. B. (2018) ''Application of the Simplex Method to a Transportation Problem, Activity Analysis of Production and Allocation '', In: Koopmans, T. C., Ed., John Wiley& Sons, New York, 359- 373.
-Das. S. K., Goswami, A. and Alam, S. S. (1999) ''Multi- objective transportation problem with interval cost, source and destination parameters'', European Journal of Operational Research, Vol. 117, pp. 100- 112.
-Dubois, D. and Prade, H. (1980) '' Fuzzy sets and systems: theory and applications”, Academic Press, New York.
-Gabrel, V., Lacroix, M., Murat, C. and Remli, N. (2014) ''Robust location transportation problems under uncertain demands'', Discrete Applied Mathematics, Vol. 164, pp. 100- 111.
-Gupta, G. and Kumari, A. (2017) ''An efficient method intuitionistic fuzzy transportation problem of type-2'', International Journal of Applied Computational Mathematics , Vol. 3, pp.3795-3804.
-Guo, H., Wang, X. and Zhou, S. (2015) ''A transportation problem with uncertain costs and random supplies'', International Journal of e- Navigation and Maritime Economy, Vol. 2, pp.1-11.
-Gutzwiller, M. C. (1991) '' Chaos in Classical and Quantum Mechanics'', Interdisciplinary Applied Mathematics,  Springer, New York, NY.
-Hamdy, A. T. (2007) ''Operations research: An introduction'', 8th Edition, Pearson Prentice Hall, Upper Saddle River.
-Hitchcock, F. L. (1941) ''The distribution of a product from several source to numerous localities'', Journal of Mathematics and Physics, Vol. 20, pp.224-230.
 
Kasana, H. S. and Kumar, K. D.(2005) '' Introductory Operations Research: Theory and Applications '', Springer International Edition, New Delhi.
-Kaur, L., Rakshit, M. and Singh, S. (2018) '' A new approach to solve multi- objective transportation problem'', Applications and Applied Mathematics: An International Journal (AAM) Vol. 13, pp. 150- 159.
Etata, C., Satish, M. G. and Islam, M. R. (2006) '' Chaos numbers'', International Conference on Computational Intelligence for Modelling Control and Automation(CIMCA) IEEE, Sydney, Australia.
-Khan, A. R. (2011) ''A resolution of the transportation problem: An algorithm approach '', Jahangirnagar University Journal of Science, Vol. 34, pp. 49- 62.
-Kumar, R., Edalatpanah, S.A., Jha, S. and Sing,R. (2019) '' A pythagorean fuzzy approach to the transportation problem '', Complex & Intelligent Systems, Vol. 5, pp. 255- 263.
-Kundu, P., Kar, S. and Maiti, M. (2014) '' Fixed charge transportation problem with type-2 type variables '', Information Sciences, Vol. 255, pp. 170- 186.
-Li, L. and Lai, K. K. (2002) ''A fuzzy programming to the multi- objective transportation problem'', Computers and Operations Research, Vol. 27, pp. 43- 57.
-Liu, P., Yang, L., Wang, L.and Li,S. (2014) '' A solid transportation problems with type-2 fuzzy variables '', Applied Soft Computing, Vol. 24, pp. 543- 558.
-Mahewan, U. P. and Garesan, K. (2018) '' Solving fully fuzzy transportation problem using pentagonal fuzzy numbers'', National Conference on Mathematical Techniques and its Applications, (1000) 012014.
-Maity, G., Roy, S. K. and Verdegay, J. L. (2016) ''Multi- objective transportation problem with cost reliability under uncertain environment'', International Journal of Computational Intelligence Systems, Vol. 9, pp. 839- 849.
-Omar, M S. and Samir, S. S. (2003) ''A parametric study on transportation problem under fuzzy environment, '' The Journal of Fuzzy Mathematics, Vol. 11, pp. 115- 124.
-OTT, E. (2002) ''Chaos in dynamical systems'', 2nd Edition, Cambridge University Press, Cambridge.
-Pandian, P. and Natarajan, G. (2003) '' A new approach for solving transportation problems with mixed constraints'', Journal of Physical Sciences, Vol. 14, pp. 53- 61.
-Peitgen, H-O., Jurgens, H. and Saupe, D. (2004) ''Chaos and Fractals'', 2nd Edition, Springer, New York, NY.
-Rashid, A., Ahmed, S. S. and Uddin, Md. S. (2013) ''Development of a new heuristic for improvement of initial basic feasible solution of a balanced transportation problem'', Jahangirnagar University Journal of Mathematics and Mathematical Sciences, Vol. 28, pp. 105- 112.
-Roy, S. K. (2016) ''Transportation problem with multi- choice cost and demand and stochastic supply'', Journal of the Operations Research Society of China, Vol. 4, doi: 10. 1007/ s40305- 016-0125-3.
-Shenoy, G. V., Srivastava, U. K. and Sharma, S. C. (1991) ''Operations research for management'', 2nd Edition, New Age International (P) Limited Publishers,, New Delhi.
-Strogatz, S. H. (2001) ''Nonlinear dynamics and chaos: with applications to physics'', Piology, Chemistry and Engineering, Peruses Books Group, New York, NY.
-Tada, M. and Ishii, H. (1996) ''An integer fuzzy transportation problem'', Computers & Mathematics with Applications, Vol. 31, pp. 71- 87.
-Vidhya, V. and Ganesan, K. (2018) ''Different approaches for the solution of multi- objective fuzzy transportation problems'', International Journal of Pure and Applied Mathematics, Vol. 119, pp. 373- 383.
-Zhang, B., Peng, J., Li, S. and Chen, L. (2016) '' Fixed charge solid transportation problem in uncertain environment and its algorithm'', Computers and Industrial Engineering, Vol. 102, pp. 186- 197.

Files

Share

How to cite

Statistics