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A decision rule in the simplex method that avoids cycling

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Summary

It is shown that cycling will not occur in the simplex method if the following decision rule is used to solve ties:At each iteration, solve the tie by making a choice that minimizes the number of times the selected basis has appeared in the previous iterations.

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References

  1. Dantzig, George B.: Linear Programming and Extensions. Princeton: University Press 1963.

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  2. Beale, E. M. L.: Cycling in the Dual Simplex Algorithm. Naval Res. Logist. Quart.2, 269–276 (1955).

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Authors and Affiliations

  1. Mathematics Dept., University of Massachusetts, Amherst, Mass., USA

    A. G. Azpeitia & D. J. Dickinson

Authors
  1. A. G. Azpeitia
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  2. D. J. Dickinson
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Azpeitia, A.G., Dickinson, D.J. A decision rule in the simplex method that avoids cycling. Numer. Math. 6, 329–331 (1964). https://doi.org/10.1007/BF01386081

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  • DOI: https://doi.org/10.1007/BF01386081

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