EFFICIENCY OF THE SIMPLEX METHOD: A SURVEY.

The purpose of this paper is to survey the body of knowledge on the efficiency of the Simplex Method, from both practical and theoretical points of view. Adopting the number of iterations (pivot steps) as the yardstick for efficiency, we survey four aspects of the issue: (1) Reports on practical experience of the method's performance on real-life LP problems. (2) Results on controlled (Monte-Carlo) experiments solving LP problems which were randomly generated according to some predetermined distributions. (3) Complexity results, including theoretical analyses on both upper and lower bounds for the performance of the Simplex as well as non-Simplex algorithms for LP. (4) Results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the Simplex Method. We discuss the consequences and limitations of the various studies.