Projecting an extended formulation for mixed-integer covers on bipartite graphs

We consider the mixed-integer version of bipartite vertex cover. This is equivalent to a mixed-integer network dual model, introduced recently, that generalizes several mixed-integer sets arising in production planning. We derive properties of inequalities that are valid for the convex hull of the mixed-integer bipartite covers by projecting an extended formulation onto the space of the original variables. This permits us to give a complete description of the facet-inducing inequalities of the double mixing set and of the continuous mixing set with flows, two mixed-integer sets that generalize several models studied in the literature.