The intersection of continuous mixing polyhedra and the continuous mixing polyhedron with flows

In this paper we investigate two generalizations of the continuous mixing set studied by Miller and Wolsey and Van Vyve: the intersection set and the continuous mixing set with flows, which appears as a strong relaxation of some single-item lot-sizing problems. We give two extended formulations for the convex hull of each of these sets. In particular, for the latter sets the sizes of the extended formulations are polynomial in the size of the original description of the set, thus proving that the corresponding linear optimization problem can be solved in polynomial time.