Two Direct Methods in Linear Programming

Abstract In this paper, we introduce two direct methods for solving some classes of linear programming problems. The first method produces the extreme vertex or a neighboring vertex with respect to the extreme point. The second method is based on the game theory. Both these methods can be used in the preparation of the starting point for the simplex method. The efficiency of the improved simplex method, whose starting point is constructed by these introduced methods, is compared with the original simplex method and the interior point methods, and illustrated by examples. Also, we investigate the elimination of excessive constraints.