by Henk, Martin, Köppe, Matthias, Weismantel, Robert.

**Series:** 2000-12, Preprints

- MSC:
- 90C11 Mixed integer programming
- 52B11 $n$-dimensional polytopes

**Abstract:**

This paper addresses the question

of decomposing an infinite family of rational polyhedra

in an integer fashion. It is shown that there is

a finite subset of this family that generates the entire family.

Moreover, an integer analogue

of Caratheodory's theorem carries

over to this general setting.

The integer decomposition of a family of polyhedra

has different applications in integer

and mixed integer programming.

**Keywords:**

mixed integer programming, test sets, indecomposable polyhedra, Hilbert bases, rational polyhedral cones