Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Degeneracy

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_223

The situation in which a linear-programming problem has a basic feasible solution with at least one basic variable equal to zero. If the problem is degenerate, then an extreme point of the convex set of solutions may correspond to several feasible bases. As a result, the simplex method may move through a sequence of bases with no improvement in the value of the objective function. In rare cases, the algorithm may cycle repeatedly through the same sequence of bases and never converge to an optimal solution. Anticycling rules, and perturbation and lexicographic techniques prevent this risk, but usually at some computational expense.  Bland's anticycling rules;  Linear programming;  Simplex method.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA