Abstract A linear programming, LP, problem is to find a maximum or minimum of a linear function subject to linear inequality constraints. Theoretically every rational LP is solvable in polynomial time by both the ellipsoid method of Khachian and various interior point methods of Karmarker. In practice, very large LPā€™s can be solved efficiently by both the Simplex method and InteriorPoint methods. In 1957, W. M. Hirsch, made a conjecture which says that the diameter of a convex polytope P is bounded by m  n, which imposes bounds on solving and LP problem. That is to say, Simplex Method has although never observed on practical problems, the poor worstcase behavior of the algorithmthe number of iterations may be exponential in the number of unknowns  led to an ongoing search for algorithms with better computational complexity. A few researchers are still looking for the refinement of the simplex method that is polynomial time, the combinatorial method for solving linear programming problems and we try in this thesis to contribute towards a newer refinement.
