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Technical Note—A Counterexample to the Rudimentary Primal Integer Programming Algorithm

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  • S. J. Mathis

    (Office of Emergency Preparedness, Washington, D. C.)

Abstract

This note describes the development of a counterexample to the rudimentary primal integer-programming algorithm. Two examples are given. The first shows the particular sequence of cuts that leads to a cycling process. Then, utilizing the algebraic implications of this sequence of cuts, a second example is developed that does not converge using the usual column-selection rule. A geometric interpretation is provided, and some comments are made on a means to force convergence in these two examples.

Suggested Citation

  • S. J. Mathis, 1971. "Technical Note—A Counterexample to the Rudimentary Primal Integer Programming Algorithm," Operations Research, INFORMS, vol. 19(6), pages 1518-1522, October.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:6:p:1518-1522
    DOI: 10.1287/opre.19.6.1518
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