The facet of Knapsack ploytope, i.e. convex hull of 0-1 points satisfying a givenlinear inequality has been presented in this current paper. Such type of facetsplays an important role in set covering set partitioning, matroidal-intersectionvertex- packing, generalized assignment and other combinatorial problems.Strong covers for facets of Knapsack ploytope has been developed in the first partof the present paper. Generating family of valid cutting planes that satisfyinequality with 0-1 variables through algorithms are the attraction of this paper. پرونده مقاله

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. پرونده مقاله