The following is a simple mixed integer programming problem. Details can be found in Example 3.8 in the "Examples" section.

Example 3.10: Restarting an Integer Program The following example is attributed to Haldi (Garfinkel and Nemhauser 1972) and is used in the literature as a test problem.

It is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable. The proof depends on methods from geometry of numbers.

A new integer programming dual problem is constructed from a reformulation of the integer programming problem. Properties of this integer programming dual problem are developed and it is shown that ...