Big-M and two-phase methods
General · Mathematics
Study notes
Q: Why need Big-M for max x+y s.t. x+y ≥ 2? Set up Phase I. Surplus: x+y-s₁ = 2: no basic feasible (s₁ = -2)! Add artificial a₁: x+y-s₁+a₁ = 2. Big-M: max x+y-Ma₁ (M huge: drives a₁ → 0!). Two-phase: Phase I min a₁; if 0: feasible, drop a₁, Phase II. (Artificial variables: jump-start!)