Polyhedral properties for the intersection of two knapsacks

We address the question to what extent polyhedral knowledge about
individual knapsack constraints suffices or lacks to describe the convex hull of
the binary solutions to their intersection. It turns out that the sign patterns of the
weight vectors are responsible for the types of combinatorial valid inequalities
appearing in the description of the convex hull of the intersection. In partic-
ular, we introduce the notion of an incomplete set inequality which is based
on a combinatorial principle for the intersection of two knapsacks. We outline
schemes to compute nontrivial bounds for the strength of such inequalities w.r.t.
the intersection of the convex hulls of the initial knapsacks. An extension of the
inequalities to the mixed case is also given. This opens up the possibility to use
the inequalities in an arbitrary simplex tableau.