The Intersection of Continuous Mixing Polyhedra and the Continuous Mixing Polyhedron with Flows
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We consider the mixing set with flows: $s+x_t \geq b_t, x_t \leq y_t {\rm for} 1 \leq t \leq n; s \in \R^1_+, x \in \R^n_+, y \in \Z^n_+.$ It models a “flow version” of the basic mixing set introduced and studied by Gu¨nlu¨k and Pochet [Math. Program., 90 (2001), pp. 429-457], as well as the most simple stochastic lot-sizing problem with recourse. More generally it is a relaxation of certain mixed integer sets that arise in the study of production planning problems. We study the polyhedron defined as the convex hull of the above set. Specifically we provide an inequality description, and we also characterize its vertices and rays.