The mixing set with flows

We consider here the mixing set with flows: s + xt >= bt, xt <= yt for 1 <= t <= n; s [belongs] R+exp.1+, ˙ [belongs] R+exp.n, y [belongs] Z+exp.n. It models the "flow version" of the basic mixing set introduced and studied by Gunluk and Pochet, as well as the most simple stochastic lot-sizing problem with recourse, and more generally is a relaxation of certain mixed integer sets that arise in the study of production planning problems. We study the polyhedron obtained by convexifying the above set. Specifically we provide a system of inequalities that gives its external description and characterize its vertices and rays.)