TY - JOUR
T1 - A note on the continuous mixing set
AU - Zhao, M.
AU - de Farias, I. R.
N1 - Funding Information:
We gratefully acknowledge the support of the NSF and IBM to this work through grants CMMI-0121495 and CMMI-0620755 and an IBM Faculty Award to de Farias, respectively. We are also grateful to the editors and two anonymous referees, whose careful review, criticism, and suggestions improved the paper substantially.
PY - 2008/11
Y1 - 2008/11
N2 - The continuous mixing set is S = {(s, r, z) ∈ ℜ × ℜ+n × Zn : s + rj + wj zj ≥ fj, j = 1, ..., n}, where w1, ..., wn > 0 and f1, ..., fn ∈ ℜ. Let m = | {w1, ..., wn} |. We show that when w1 | ⋯ | wn, optimization over S can be performed in time O (nm + 1), and in time O (n log n) when w1 = ⋯ = wn = 1.
AB - The continuous mixing set is S = {(s, r, z) ∈ ℜ × ℜ+n × Zn : s + rj + wj zj ≥ fj, j = 1, ..., n}, where w1, ..., wn > 0 and f1, ..., fn ∈ ℜ. Let m = | {w1, ..., wn} |. We show that when w1 | ⋯ | wn, optimization over S can be performed in time O (nm + 1), and in time O (n log n) when w1 = ⋯ = wn = 1.
KW - Branch-and-cut
KW - Mixed-integer programming
KW - Polyhedral combinatorics
KW - Simple mixed-integer set
UR - http://www.scopus.com/inward/record.url?scp=54249086085&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2008.08.001
DO - 10.1016/j.orl.2008.08.001
M3 - Article
AN - SCOPUS:54249086085
VL - 36
SP - 726
EP - 733
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 6
ER -