A Comparative Study on Gauss Elimination Method and Simplex Method of Linear Optimization Problem

International Journal of Mathematics Trends and Technology (IJMTT)
© 2017 by IJMTT Journal
Volume-47 Number-1
Year of Publication : 2017
Authors : Rahidas Kumar, Sahdeo Mahto


Rahidas Kumar, Sahdeo Mahto "A Comparative Study on Gauss Elimination Method and Simplex Method of Linear Optimization Problem", International Journal of Mathematics Trends and Technology (IJMTT). V47(1):1-4 July 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

This paper deals a new approach for the solution of linear optimization problem with the help of Gauss Elimination Method of matrix. This method is based on the square matrix which converted into upper triangular matrix by elementary row transformation. This method we get direct solution without any iteration. Also we show that this method is better than Simplex Method.

[1] Dantzig G. B, Linear Programming and Extension. Princenton, University Press, Princenton, NJ
[2] Dantzig G. B., 1951, Maximization of linear function subject to linear inequalities, in T. C. Koopmans(ed.), Activity Analysis OF Production and Allocation, John Wiley & Sons, New York, 339-347.
[3] Bland R. G., 1977. New finite pivoting rules for the simplex method, Mathematics of Operations Research 2, 103- 107
[4] Teukolsky, WH., SA., Vetterling, WT. And Flannery, BP, 2007. NumericalRecipes: The Art of Science Computing(3rd ed.),New York: Cambridge University Press.
[5] Karmakar, N. 1984. A new polynomial time algorithm for linear programming , Combinatorica, 4, 141- 158.
[6] P. Kanniappan and k. Thangavel, 1998 Modified Fourier’s method of solving linear programming problems, Opsearch, 35, 45- 56.
[7] Householder, Alston S., 1975 . The Theory of Matrices in Numerical Analysis, New York; Dover Publications.
[8] Shenoy, G. V. 1998. Linear Programming (Method and Applications), Second Edition, New Age International Publishers.
[9]Horn , Roger A. And Johnson, Charles R., 1985. Matrix Analysis, Cambridge university Press. Section 3.5
[10] Poole, David, 2006, Linear Algebra “A Modern Introduction” (2nd ed.), Canada; Thomson Books/ Cole.
[11] Gupta,R. K., Operations Research, Krishna Prakashan Media (P) Ltd.2013.

Gauss Elimination Method, linear programming problem, system of linear equation, upper triangular matrix, augmented matrix, Simplex Method.