Journal of the Operations Research Society of Japan
Online ISSN : 2188-8299
Print ISSN : 0453-4514
ISSN-L : 0453-4514
SMALL DEGENERATE SIMPLICES CAN BE BAD FOR SIMPLEX METHODS
Shinji MizunoNoriyoshi SukegawaAntoine Deza
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2017 Volume 60 Issue 4 Pages 419-428

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Abstract

We show that the simplex method with Dantzig's pivoting rule may require an exponential number of iterations over two highly degenerate instances. The feasible region of the first instance is a full dimensional simplex, and a single point for the second one. In addition, the entries of the constraint matrix, the right-hand-side vector, and the cost vector are {0,1,2}-valued. Those instances, with few vertices and small input data length, illustrate the impact of degeneracy on simplex methods.

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© 2017 The Operations Research Society of Japan
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