Solution of Transportation Problem with South-East Corner Method, North-East Corner Method and Comparison with Existing Method

DOI: 10.4236/oalib.1105377, PP. 1-12

Keywords: Transportation Problem, Initial Basic Feasible Solution (IBFS), Optimal Solution, Transportation Cost, South-East Corner Method (SECM), North-East Corner Method (NECM), Vogel’s Approximation Method (VAM), Modified Distribution Method (MODI)

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Abstract:

Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this paper, two methods are proposed to find an initial basic feasible solution for the transportation problems. The South-East Corner Method (SECM) and the North-East Corner Method (NECM) are adopted to compute the Initial Basic Feasible Solution (IBFS) of the transportation problem. A comparative study is carried out with existing methods like Vogel’s approximation method (VAM) which is to find an initial basic feasible solution and Modified Distribution (MODI) Method which is to find the optimal solution and the methods are also illustrated with numerical examples.

References

[1]	Hitchcock, F.L. (1941) The Distribution of a Product from Several Sources to Numerous Localities. Journal of Mathematics and Physics, 20, 224-230. https://doi.org/10.1002/sapm1941201224
[2]	Dantzig, G.B. (1951) Application of the Simplex Method to a Transportation Problem, Activity Analysis of Production and Allocation. John Wiley and Sons, New York, 359-373.
[3]	Charnes, A., Cooper, W.W. and Henderson, A. (1953) An Introduction to Linear Programming. John Wiley & Sons, New York.
[4]	Hamdy, A.T. (2007) Operations Research: An Introduction. 8th Edition, Pearson Prentice Hall, Upper Saddle River.
[5]	Pandian, P. and Natarajan, G. (2010) A New Approach for Solving Transportation Problems with Mixed Constraints. Journal of Physical Sciences, 14, 53-61.
[6]	Balakrishnan, N. (1990) Modified Vogel’s Approximation Method for Unbalanced Transportation Problem. Applied Mathematics Letters, 3, 9-11. https://doi.org/10.1016/0893-9659(90)90003-T
[7]	Lakshmi, R.A. and Pallavi, P.L. (2015) A New Approach to Study Transportation Problem Using South West Corner Rule. International Journal of Advanced Research Foundation, 2, 1-3.
[8]	Vinoba, V. and Palaniyappa, R. (2014) A Study on North East Corner Method in Transportation Problem and Using of Object Oriented Programming Model (C ). International Journal of Mathematics Trends and Technology, 16, 1-8.
[9]	Asase, A. (2011) The Transportation Problem; Case Study. A Thesis Submitted to the Department of Mathematics Faculty of Physical Science and Technology, Kumasi, 7 June 2011.
[10]	Ndayiragije, F. (2017) South-East Corner Method and a Comparative Study on the North-West Corner, South-East Corner, North-East Corner and South-East Corner Methods. International Journal of Science and Engineering Investigations, 6, 37-39.

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