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

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.