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Visualizing and Constructing Cycles in the Simplex Method

Author

Listed:
  • David Avis

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

  • Bohdan Kaluzny

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

  • David Titley-Péloquin

    (School of Computer Science, McGill University, Montreal, Quebec, Canada H3A 2A6)

Abstract

Most examples of cycling in the simplex method are given without explanation of how they were constructed. An exception is Beale's example built around the geometry of the dual simplex method in the plane [Beale, E. 1955. Cycling in the dual simplex method. Naval Res. Logist. Quart. 2 (4) 269--275]. Using this approach, we give a simple geometric explanation for a number of examples of cycling in the simplex method, including Hoffman's original example [Hoffman, A. 1953. Cycling in the Simplex Algorithm . National Bureau of Standards, Washington, D.C.]. This gives rise to a simple method for generating examples with cycles.

Suggested Citation

  • David Avis & Bohdan Kaluzny & David Titley-Péloquin, 2008. "Visualizing and Constructing Cycles in the Simplex Method," Operations Research, INFORMS, vol. 56(2), pages 512-518, April.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:2:p:512-518
    DOI: 10.1287/opre.1070.0474
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    References listed on IDEAS

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    1. Zhang, Shuzhong, 1999. "New variants of finite criss-cross pivot algorithms for linear programming," European Journal of Operational Research, Elsevier, vol. 116(3), pages 607-614, August.
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    Keywords

    linear programming theory;

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