Maximum values

y = max{x₁, x₂, ..., x_n} for continuous variables x₁, ..., x_n

• Must know lower and upper bounds

  Li ≤ xi ≤ Ui

  [1.i]

• Introduce binary variables d₁, ..., d_n
  d_i=1 if x_i is the maximum value, 0 otherwise
• MIP formulation

  Li ≤ xi ≤ Ui	[1.i]
  y ≥ xi	[2.i]
  y ≤ xi + (Umax - Li)(1 - di)	[3.i]
  ∑i di = 1	[4]

• See Section General constraints for an alternative formulation via general constraints