A note on the continuous mixing set

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Abstract

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.

Original languageEnglish
Pages (from-to)726-733
Number of pages8
JournalOperations Research Letters
Volume36
Issue number6
DOIs
StatePublished - Nov 2008

Keywords

  • Branch-and-cut
  • Mixed-integer programming
  • Polyhedral combinatorics
  • Simple mixed-integer set

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