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The Continuous Mixing Polyhedron

Center of Operations Research and Econometrics (CORE), Université catholique de Louvain, 34, Voie du Roman Pais, 1348 Louvain-la-Neuve, Belgium
vanvyve{at}core.ucl.ac.be

We analyze the polyhedral structure of the sets P^CMIX = {(s, r, z) R x R₊ⁿ x Zⁿ | s + r_j + z_j f_j, j = 1, ..., n} and P₊^CMIX = P^CMIX {s 0}. The set P₊^CMIX is a natural generalization of the mixing set studied by Pochet and Wolsey [15, 16] and Günlük and Pochet [8] and recently has been introduced by Miller and Wolsey [12]. We introduce a new class of valid inequalities that has proven to be sufficient for describing conv(P^CMIX). We give an extended formulation of size O(n) x O(n²) variables and constraints and indicate how to separate over conv(P^CMIX) in O(n³) time. Finally, we show how the mixed integer rounding (MIR) inequalities of Nemhauser and Wolsey [14] and the mixing inequalities of Günlük and Pochet [8] constitute special cases of the cycle inequalities.

Key Words: mixed integer rounding; mixing; convex hull proof; lot sizing
History: Received: October 28, 2003; revision received: May 18, 2004;revision received: August 6, 2004;

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