Abstract
There are well-known examples of cycling in the linear programming simplex method having basis size two and requiring only six pivots. We prove that any example having basis size two for the network simplex method requires at least ten pivots. We also present an example that achieves this lower bound. In addition, we show that an attractive variant of Cunningham's noncyling method does admit cycling.
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References
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Research supported in part by a grant from N.S.E.R.C. of Canada and by Bell Laboratories. On leave at Institut für Operations Research. Universität Bonn, supported by SFB 21 (DFG).
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Cunningham, W.H., Klincewicz, J.G. On cycling in the network simplex method. Mathematical Programming 26, 182–189 (1983). https://doi.org/10.1007/BF02592054
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DOI: https://doi.org/10.1007/BF02592054