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An Effective Alternative New Approach in Solving Transportation Problems

Received: 15 July 2020     Accepted: 23 January 2021     Published: 30 January 2021
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Abstract

The Transportation problem is one of the most colorful and demanding problems in the history of Operations Research. Many researchers have paid attention to solve the problem using different approaches. In certain approaches focused on finding an initial basic feasible solution and the other to find the optimal solution. It can be noticed that these methods have advantages and disadvantages. Out of all the methods that can be found in the literature, Northwest, Least Cost and Vogel’s Approximation methods are the most prominent and renowned methods in finding an initial basic feasible solution. Also, the Modified Distribution (MODI) Method and Stepping Stone Method are the most acceptable methods in finding the optimal solution to the transportation problem. In this research paper, we propose an alternative method that finds the optimal or nearly optimal solution to the transportation problem. This method which is based on an iterative algorithm can be applied to balance as well as unbalanced transportation problems. It is also to be noticed that this method requires a minimum number of iterations to reach the optimality as compared to the other existing methods. Also, we have developed a new method of finding an optimal solution for both balanced and unbalanced transportation problems.

Published in American Journal of Electrical and Computer Engineering (Volume 5, Issue 1)

This article belongs to the Special Issue Artificial Intelligence in Electrical Power & Energy

DOI 10.11648/j.ajece.20210501.11
Page(s) 1-8
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Transportation Problem, Optimal Solution, Balance, Unbalance and Optimal Solution

References
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[2] S. Akpana, T. Ugbeb, J. Usenc and O. Ajahd. “A Modified Vogel Approximation Method for Solving Balanced Transportation Problems”, American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), 14 (3), 2015, pp. 289-302.
[3] M. M. Ahmed, A. R. Khan, S. Uddin and F. Ahme “A New Approach to Solve Transportation Problems”, Open Journal of Optimization, 5, 2016, pp. 22-30.
[4] M. M. Ahmed, A. R. Khan, F. Ahmed, Md. S. Uddin, “Incessant Allocation Method for Solving Transportation Problems”, American Journal of Operations Research, 6, 2016, pp. 236-244.
[5] A. Charnes, W. W Cooper and A. Henderson, “An Introduction to Linear Programming” John Wiley & Sons, New York. 1953.
[6] G. B. Dantzig, “Linear programming and extensions”. Princeton, NJ: Princeton University press’’, 1963.
[7] N. M. Deshmukh, “An Innovative Method For Solving Transportation Problem”, International Journal of Physics and Mathematical Sciences, Vol. 2 (3), 2012, pp. 86-91.
[8] E. M. U. S. B., Ekanayake, S. P. C., Perera, W. B. Daundasekara, and Z. A. M. S. Juman, “A Modified Ant Colony Optimization Algorithm for Solving a Transportation Problem” Journal of Advances in Mathematics and Computer Science, 2020, 35 (5), 83-101.
[9] L. R. Ford, and D. R. Fulkerson, “Solving the transportation Problem”, The RAND Corporation.1956.
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[12] F. L. Hitchcock, “The distribution of a product from several resources to numerous localities”, J. Math. Phy., 20, 1941, pp. 224-230.
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[14] T. Imam, G. Elsharawy, M. Gomah M, I. Samy, “Solving Transportation Problem”, Using Object-Oriented Model. Int. J. comput. Sci. Netw. Secur. 9 (2), 2009, pp. 353-361.
[15] Z. A. M. S. Juman, M. A. Hoque, “An efficient heuristic approach for solving the transportation problem”, Proceedings of the 2014 International Conference on Industrial Engineering and Operations Management Bali, Indonesia, 2014.
[16] Z. A. M. S. Juman, M. A. Hoque, “An efficient heuristic to obtain a better initial feasible solution to the transportation problem”, Applied Soft Computing 34, 2015, pp. 813-826.
[17] Z, A, M, S. Juman, N. G. S. A. Nawarathne, “An efficient alternative approach to solve a transportation problem. Ceylon Journal of Science 48 (1), 2019, pp. 19-29.
[18] T. C. Koopmans, “Optimum Utiliztion of Transportation System”, Econometrica, Supplement vol 17, 1949.
[19] S. Korukoglu, S. Bali, “A improve Vogel Approximation Method for the transformation Problem”, Mathematical and computational Applications 16 (2), 2011, pp. 370-381.
[20] S. S. Kulkarni, H. G. Datar, “On Solution To Modified Unbalanced Transportation Problem”. Bulletion of the Marathwada Mathematical Society 11 (2), 2010, pp. 20-26.
[21] V. Manisha, M. V. Sarode, “Application of a Dual Simplex method to Transportation Problem to minimize the cost”, International Journal of Innovations in Engineering and Science, 2 (7), 2017.
[22] G. Monge. Mémoire sur la théorie des déblais et des remblais. Histoire de l’Académie Royale des Sciences de Paris, avec les Mémoires de Mathématique et de Physique pour la même année, pages 666–704, 1781.
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Cite This Article
  • APA Style

    Ekanayake E. M. U. S. B., Perera S. P. C., Daundasekara W. B., Juman Z. A. M. S. (2021). An Effective Alternative New Approach in Solving Transportation Problems. American Journal of Electrical and Computer Engineering, 5(1), 1-8. https://doi.org/10.11648/j.ajece.20210501.11

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    ACS Style

    Ekanayake E. M. U. S. B.; Perera S. P. C.; Daundasekara W. B.; Juman Z. A. M. S. An Effective Alternative New Approach in Solving Transportation Problems. Am. J. Electr. Comput. Eng. 2021, 5(1), 1-8. doi: 10.11648/j.ajece.20210501.11

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    AMA Style

    Ekanayake E. M. U. S. B., Perera S. P. C., Daundasekara W. B., Juman Z. A. M. S. An Effective Alternative New Approach in Solving Transportation Problems. Am J Electr Comput Eng. 2021;5(1):1-8. doi: 10.11648/j.ajece.20210501.11

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  • @article{10.11648/j.ajece.20210501.11,
      author = {Ekanayake E. M. U. S. B. and Perera S. P. C. and Daundasekara W. B. and Juman Z. A. M. S.},
      title = {An Effective Alternative New Approach in Solving Transportation Problems},
      journal = {American Journal of Electrical and Computer Engineering},
      volume = {5},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.ajece.20210501.11},
      url = {https://doi.org/10.11648/j.ajece.20210501.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajece.20210501.11},
      abstract = {The Transportation problem is one of the most colorful and demanding problems in the history of Operations Research. Many researchers have paid attention to solve the problem using different approaches. In certain approaches focused on finding an initial basic feasible solution and the other to find the optimal solution. It can be noticed that these methods have advantages and disadvantages. Out of all the methods that can be found in the literature, Northwest, Least Cost and Vogel’s Approximation methods are the most prominent and renowned methods in finding an initial basic feasible solution. Also, the Modified Distribution (MODI) Method and Stepping Stone Method are the most acceptable methods in finding the optimal solution to the transportation problem. In this research paper, we propose an alternative method that finds the optimal or nearly optimal solution to the transportation problem. This method which is based on an iterative algorithm can be applied to balance as well as unbalanced transportation problems. It is also to be noticed that this method requires a minimum number of iterations to reach the optimality as compared to the other existing methods. Also, we have developed a new method of finding an optimal solution for both balanced and unbalanced transportation problems.},
     year = {2021}
    }
    

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    DO  - 10.11648/j.ajece.20210501.11
    T2  - American Journal of Electrical and Computer Engineering
    JF  - American Journal of Electrical and Computer Engineering
    JO  - American Journal of Electrical and Computer Engineering
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    UR  - https://doi.org/10.11648/j.ajece.20210501.11
    AB  - The Transportation problem is one of the most colorful and demanding problems in the history of Operations Research. Many researchers have paid attention to solve the problem using different approaches. In certain approaches focused on finding an initial basic feasible solution and the other to find the optimal solution. It can be noticed that these methods have advantages and disadvantages. Out of all the methods that can be found in the literature, Northwest, Least Cost and Vogel’s Approximation methods are the most prominent and renowned methods in finding an initial basic feasible solution. Also, the Modified Distribution (MODI) Method and Stepping Stone Method are the most acceptable methods in finding the optimal solution to the transportation problem. In this research paper, we propose an alternative method that finds the optimal or nearly optimal solution to the transportation problem. This method which is based on an iterative algorithm can be applied to balance as well as unbalanced transportation problems. It is also to be noticed that this method requires a minimum number of iterations to reach the optimality as compared to the other existing methods. Also, we have developed a new method of finding an optimal solution for both balanced and unbalanced transportation problems.
    VL  - 5
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Author Information
  • Department of Physical Sciences, Faculty of Applied Sciences, Rajarata University of Sri Lanka, Mihinthale, Sri Lanka

  • Department of Engineering Mathematics, Faculty of Engineering, University of Peradeniya, Peradeniya, Sri Lanka

  • Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka

  • Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka

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