Techniques that strive to combat the influence of degeneracy in linear programming problems

  • J.H. Nel
  • J.M. Hattingh


Degeneracy can cause enormous problems when solving large scale linear programming problems. This is not only because there is a possibility that the problem can cycle, but also because a large number of iterations can be executed that do not improve the objective. In this article a procedure which utilises derived reduced costs is discussed. The derived reduced cost of a non- basic variable is defined in such a way that it makes the introduction to the non-basic variable into the basis unattractive if such a decision fails to improve the objective. The procedure deliberately strives to combat degeneracy using derived reduced costs, but it also utilises the advantageous properties of the classical gradient methods.


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