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

S. J. Mathis
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S. J. Mathis: Office of Emergency Preparedness, Washington, D. C.

Operations Research, 1971, vol. 19, issue 6, 1518-1522

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.

Date: 1971
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