Lifted inequalities for $$0\mathord {-}1$$ mixed-integer bilinear covering sets

In this paper, we study $$0\mathord {-}1$$ mixed-integer bilinear covering sets. We derive several families of facet-defining inequalities via sequence-independent lifting techniques. We then show that these sets have a polyhedral structure that is similar to that of a certain fixed-charge single-node flow set. As a result, we also obtain new facet-defining inequalities for the single-node flow set that generalize well-known lifted flow cover inequalities from the integer programming literature.