MIP — Branch & Bound Unit Commitment

Single-Period · Exact MILP

Single-period unit commitment — one snapshot of demand, no time horizon. Each generator has a binary commitment variable Uᵢ ∈ {0,1} and continuous output pᵢ. LP relaxation at each B&B node computes a lower bound; branches exceeding the incumbent are pruned. Returns proven optimal if fully explored, otherwise best-within-cap.

Generator Fleet

1

P-Min

P-Max

Var $

Start $

2

P-Min

P-Max

Var $

Start $

3

P-Min

P-Max

Var $

Start $

4

P-Min

P-Max

Var $

Start $

Max cap: 200 MW

Optimal Dispatch

Run solver to see dispatch.

Formulation

min Σ (cᵢpᵢ + SᵢUᵢ)

s.t. Σ pᵢ = D

PᵢᵐⁱⁿUᵢ ≤ pᵢ ≤ PᵢᵐᵃˣUᵢ

Uᵢ ∈ {0,1}

LP relaxation: Uᵢ ∈ [0,1] at each node.

Optimal Dispatch Schedule

Run the solver to see optimal dispatch.

B&B Tree

Lower bound vs incumbent per node

Run solver to see B&B tree.