The Mixing Set with Flows

We consider here the mixing set with flows: s + xt amp;#8805; bt, xt amp;#8804; yt for 1 amp;#8804; t amp;#8804; n; s E IR, x E IR, y E Z. It models the flow version of the basic mixing set introduced and studied by Guuml;nluuml;k 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