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Degeneracy And Variable Entering/Exiting Rules

  1. István Maros1,2

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0241

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Maros, I. 2011. Degeneracy And Variable Entering/Exiting Rules. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. 1

    Imperial College London, Department of Computing, London, UK

  2. 2

    University of Pannonia, Department of Computer Science and Systems Technology, Veszprém, Hungary

Publication History

  1. Published Online: 14 JAN 2011

Abstract

Degeneracy is a phenomenon in linear programming (LP) that has important implications if the simplex method (SM) is used to solve an LP problem. It can happen that some of the vertices of the convex polyhedron of the feasible solutions (basic solutions) are not uniquely defined. In such a case the SM method may move from one representation of a vertex to another representation of the same vertex, while the value of the objective function remains unchanged. This can lead to a sequence of nonimproving solutions and a return to the first basis in the sequence. If it happens the sequence is repeated infinitely resulting in cycling and the SM does not terminate. There are, however, various theoretical and computational approaches that can prevent the SM from cycling. Even if they may not be able to overcome a long series of nonimproving iterations, called stalling, they still can substantially reduce the number of such iterations. This article gives details of all these phenomena and the indicated remedies.

Keywords:

  • linear programming;
  • simplex method;
  • degeneracy;
  • stalling;
  • cycling