Islamic Azad University, Rasht BranchIranian Journal of Optimization2588-572306120100901Linear Programming, the Simplex Algorithm and Simple Polytopes567590514145ENDas SashiBhusanDepartment of Mathematics,Balasor college of Engg & Teach. Sergarh, Balasore, Orissa, IndiaBiswal BagabanDepartment of Mathematics F.M.Autonomous College, Balasore, Orissa, IndiaJ.P TripathyDepartment of Mathematics Gurukul Institute of Bhubaneswar,Orissa,IndiaJournal Article20100730<span>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. </span>http://ijo.iaurasht.ac.ir/article_514145_ea1a75142f8b8780dbdd391fe7c2a870.pdf