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 the mixed integer network dual model, recently introduced in [2], 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.