The continuous mixing polyhedron
(2005) Mathematics of operations research — Vol. 30, n° 2, p. 441-452 (2005)
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- We analyze the polyhedral structure of the sets P-CMIX = {(s, r, Z) is an element of R x R-+(n) x Z(n) vertical bar s + r(j) + z(j) >= f(j), j = 1,..., n} and P-+(CMIX) = P-CMIX n (s >= 0). The set P-CMIX is a natural generalization of the mixing set studied by Pochet and Wolsey [15, 16] and Gunluk 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 0(n) x 0(n 2) variables and constraints and indicate how to separate over conv(P-CMIX) in O(n(3)) time. Finally, we show how the mixed integer rounding (MIR) inequalities of Nernhauser and Wolsey [14] and the mixing inequalities of Gunluk and Pochet [8] constitute special cases of the cycle inequalities.
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Van Vyve, M. (2005). The continuous mixing polyhedron. Mathematics of operations research, 30(2), 441-452. https://doi.org/10.1087/moor.1040.0130 (Original work published 2005)