Standard Article

Implementing the Simplex Method

  1. Matthew J. Saltzman

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0395

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Saltzman, M. J. 2011. Implementing the Simplex Method. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Clemson University, Department of Mathematical Sciences, Clemson, South Carolina

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The basic simplex method is a simple and straightforward algorithm, but modern efficient implementations represent a tour de force of algorithm engineering and numerical methods designed to exploit opportunities for efficiency wherever they arise. This article surveys the key techniques necessary to implement a robust, efficient simplex code. These techniques support the strategic design principles of minimizing the number of iterations and carrying out the computations in each iteration efficiently and accurately. The primal and dual bounded-variable simplex algorithms are described. Efficient and robust advanced techniques for finding a starting solution, effective pricing, ratio tests and degeneracy management, and sparse linear algebra are covered.

Keywords:

  • linear programming;
  • simplex method;
  • computation;
  • implementation