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IJSTR >> Volume 3- Issue 2, February 2014 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Logical Development Of Vogel's Approximation Method (LD-VAM): An Approach To Find Basic Feasible Solution Of Transportation Problem

[Full Text]

 

AUTHOR(S)

Utpal Kanti Das , Md. Ashraful Babu, Aminur Rahman Khan, Md. Abu Helal, Dr. Md. Sharif Uddin

 

KEYWORDS

Index Terms: Transportation Problem (TP), LD-VAM, VAM, LPP, Penalty, Transportation Cost.

 

ABSTRACT

Abstract: The study in this paper is to discuss the limitation of Vogel’s Approximation Method (VAM) and developed an improved algorithm after resolving this limitation for solving transportation problem. Vogel’s Approximation Method (VAM) is the more efficient algorithm to solve the transportation problem but it has some limitations when highest penalty cost appear in two or more row or column. For that case VAM does not give any logical solution. In this paper we stand a logical approach for this problem and developed an algorithm named by “Logical Development of Vogel’s Approximation Method (LD-VAM)” where feasible solution from this method are very close to optimal solution more than VAM.

 

REFERENCES

[1] Hamdy A. Taha. Operation Research: An Introduction, Eighth Edition, ISBN-13: 978-0132555937,

[2] P. Rama Murthy. Operation Research, Second Edition, ISBN (13): 978-81-224-2944-2

[3] Hamdy A Taha. TORA Optimizing System Software.

[4] Hillier, F. S. and G. J. Lieberman. 1995. Introduction to Operations Research, 6th ed. New York: McGraw-Hill, Inc.

[5] A. Edward Samuel and M. Venkatachalapathy. “Modified Vogel’s Approximation Method for Fuzzy Transportation Problems”, Applied Mathematical Sciences, Vol. 5, 2011, no. 28, 1367 – 1372.

[6] Nagraj Balakrishnan,Tulane University. Modified Vogel’s Approximation Method for the Unbalanced Transportation Problem. Appl. Math. Lett. Vol. 3, No. 2, pp. S11, 1990

[7] M.A. Hakim, An Alternative Method to find Initial Basic Feasible Solution of a Transportation problem. Annals of Pure and Applied Mathematics, Vol. 1, No. 2, 2012, pp. 203-209, ISSN: 2279-087X (P), 2279-0888(online)

[8] Ramakrishnan, G.S., An improvement to Goyal's modified VAM for the unbalanced transportation problem, Journal of Operational Research Society, 39(6) (1988) 609-610

[9] Md. Amirul Islam, Aminur Rahman Khan, M. Sharif Uddin and M. Abdul Malek. Determination of Basic Feasible Solution of Transportation Problem: A New Approach. Jahangirnagar University Journal of Science, Vol. 35, No. 1, pp. 101 – 108, ISSN 1022-8594 (2012).

[10] Korukoğlu, S. and S. Balli. An Improved Vogel’s Approximation Method for the transportation problem. Mathematical and Computational Applications, Vol. 16, No. 2, pp. 370-381, 2011

[11] Aminur Rahman Khan. A Re-solution of the Transportation Problem: An Algorithmic Approach. Jahangirnagar University Journal of Science, Vol. 34, No. 2, pp. 49-62 ISSN 1022-8594 (2011).

[12] Mathirajan, M. and B. Meenakshi, Experimental Analysis of some Variants of Vogel’s Approximation Method, Asia-Pacific Journal of Operational Research 21(4) (2004) 447-462.

[13] Shimshak, D.G., J.A. Kaslik and T.D. Barclay, A modification of Vogel's approximation method through the use of heuristics, INEOR, 19 (1981) 259-263.

[14] Reinfeld, N.V. and W.R. Vogel, Mathematical Programming, Prentice-Hall, Englewood Gliffs, New Jersey (1958).