Product values

y = x · d for one continuous variable x, one binary variable d

• Must know lower and upper bounds

  L ≤ x ≤ U

• MIP formulation:

  Ld ≤ y ≤ Ud	[1]
  L(1 - d) ≤ x - y ≤ U(1 - d)	[2]

Product of two binaries: d₃ = d₁ · d₂

• MIP formulation:

  d3 ≤ d1

  d3 ≤ d2

  d3 ≥ d1 + d2 -1