A note on the continuous mixing set

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. © 2008 Elsevier B.V. All rights reserved.