The Boolean polynomial polytope with multiple choice constraints

We propose a polytope to study multiple choice polynomial programming (MCPP). It is the convex hull of $0$-$1$ vectors satisfying multiple choice constraints and production constraints both of which are associated with a hypergraph. With the help of the decomposability property, we obtain an explicit half-space representation of the MCPP polytope when the underlying hypergraph is α-acyclic by induction on the number of hyperedges. We also present a necessary and sufficient condition for the inequalities lifted from the facet-inducing ones for the multilinear polytope to be still facet-inducing for the MCPP polytope.