Logical AND

d = min {d₁, d₂} for two binary variables d₁, d₂, or equivalently
d = d₁ · d₂ (see Section Product values), or
d = d₁ AND d₂ as a logical expression

• IP formulation

  d ≤ d1	[1.1]
  d ≤ d2	[1.2]
  d ≥ d1 + d2 - 1	[2]
  d ≥ 0	[3]

• Generalization to d = min {d₁, d₂, ..., d_n}

  d ≤ di	[1.i]
  d ≥ ∑i di - (n - 1)	[2]
  d ≥ 0	[3]

  Note: equivalent to d = d₁ · d₂ · ... · d_n
  and (as a logical expression): d = d₁ AND d₂ AND ... AND d_n
• See Section Boolean variables for an alternative formulation via Boolean variables