A computer implementation of the push-and-pull algorithm and its computational comparison with LP simplex method (Q2571997)

The aim of the paper is to test efficiency of the push-and-pull algorithm for solving linear programming problems, which was developed by \textit{H. Arsham} [Initialization of the simplex algorithm: An artificial-free approach, SIAM Rev. 39, No. 4, 736--744 (1997; Zbl 0891.90125)]. It is a new general solution algorithm, which is free from any extraneous artificial variables, artificial objective functions or artificial constraints. A comparison analysis between the new algorithm and the simplex method has been accomplished. The result of this analysis shows that the push-and-pull algorithm is more effective and faster than the simplex method with its usual first phase for obtaining the initial feasible solution. Unlike to the usual phase I procedure of the simplex method, the new algorithm gives an initial feasible solution, which is closer to optimal vertex. A computer implementation of the new algorithm is presented, and an computational comparison of the new algorithm with the usual simplex method is carried out. The advantages of the new algorithm are summarized in the concluding part of the paper.