This paper presents a new primal dual simplex method and investigates the duality formation implying in classical simplex methods. We reviews classical simplex methods for linear programming problems and give a detail discussion for the relation between modern and classical algorithms. The two modified versions are present. The advantages of the new algorithms are simplicity of implementation, low computational overhead and surprisingly good computational performance. they always proved to be more efficient than classical simplex methods on our test problems.
3,School of Information and Mathematics, Yangtze university, Jingzhou, Hubei, China, and School of Mathematics and Statistics, Wuhan university, China. 2004.10.04.