Disjunctions

Either 5 ≤ x ≤ 10 or 80 ≤ x ≤ 100

• Introduce a new binary variable:
  ifupper: 0 if 5 ≤ x ≤ 10; 1 if 80 ≤ x ≤ 100
• MIP formulation:

  x ≤ 10 + (100 - 10) · ifupper	[1]
  x ≥ 5 + ( 80 - 5) · ifupper	[2]

• Generalization to Either L₁ ≤ ∑_i A_i x_i ≤ U₁ or L₂ ≤ ∑_i A_i x_i ≤ U₂ (with U₁ ≤ L₂)

  ∑i Ai xi ≤ U1 + (U2 - U1) · ifupper	[1]
  ∑i Ai xi ≥ L1 + (L2 - L1) · ifupper	[2]