A note on the continuous mixing set

M. Zhao; I. R. de Farias

doi:10.1016/j.orl.2008.08.001

A note on the continuous mixing set

M. Zhao, I. R. de Farias

Industrial Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The continuous mixing set is S = {(s, r, z) ∈ ℜ × ℜ₊ⁿ × Zⁿ : s + r_j + w_j z_j ≥ f_j, j = 1, ..., n}, where w₁, ..., w_n > 0 and f₁, ..., f_n ∈ ℜ. Let m = | {w₁, ..., w_n} |. We show that when w₁ | ⋯ | w_n, optimization over S can be performed in time O (n^{m + 1}), and in time O (n log n) when w₁ = ⋯ = w_n = 1.

Original language	English
Pages (from-to)	726-733
Number of pages	8
Journal	Operations Research Letters
Volume	36
Issue number	6
DOIs	https://doi.org/10.1016/j.orl.2008.08.001
State	Published - Nov 2008

Keywords

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

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title = "A note on the continuous mixing set",

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.",

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AU - de Farias, I. R.

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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

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JF - Operations Research Letters

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