  We consider the bipartite boolean quadric polytope (BQP) with multiple-choice
constraints and analyse its combinatorial properties. The well-studied BQP is
defined as the convex hull of all quadric incidence vectors over a bipartite
graph. In this work, we study the case where there is a partition on one of the
two bipartite node sets such that at most one node per subset of the partition
can be chosen. This polytope arises, for instance, in pooling problems with
fixed proportions of the inputs at each pool. We show that it inherits many
characteristics from BQP, among them a wide range of facet classes and
operations which are facet preserving. Moreover, we characterize various cases
in which the polytope is completely described via the relaxation-linearization
inequalities. The special structure induced by the additional multiple-choice
constraints also allows for new facet-preserving symmetries as well as lifting
operations. Furthermore, it leads to several novel facet classes as well as
extensions of these via lifting. We additionally give computationally tractable
exact separation algorithms, most of which run in polynomial time. Finally, we
demonstrate the strength of both the inherited and the new facet classes in
computational experiments on random as well as real-world problem instances. It
turns out that in many cases we can close the optimality gap almost completely
via cutting planes alone, and, consequently, solution times can be reduced
significantly.
