MILP Solver Workflow

Use this skill for binary/integer decisions, linear constraints, and linear or piecewise-linear objectives. It is useful for time-expanded scheduling models with many repeated resource-period constraints.

This is a workflow and implementation guide, not a complete formulation for any one task.

Workflow

1. Parse and normalize data into ordered arrays.
2. Define decision states before coding: status, transitions, continuous quantities, slacks, segments, tiers.
3. Build a deterministic variable map.
4. Add constraints family by family: bounds, linking, balance, time coupling, capacity/ramp limits, cost logic.
5. Solve with an available open-source MILP solver.
6. Extract a candidate solution, rounding binaries only if near integral.
7. Convert internal variables into the report convention.
8. Independently validate extracted arrays.
9. Recompute objective and summaries from extracted arrays.
10. Write final output only after validation passes.

Variable Map Pattern

Use helper functions or dictionaries, not scattered index arithmetic.

offset = {}
n = 0

def alloc(name, shape, lb=0.0, ub=float("inf"), integer=False):
    global n
    size = int(np.prod(shape))
    idx = np.arange(n, n + size).reshape(shape)
    offset[name] = idx
    n += size
    return idx

u = alloc("commitment", (G, T), lb=0, ub=1, integer=True)
start = alloc("startup", (G, T), lb=0, ub=1, integer=True)
dispatch = alloc("dispatch", (G, T), lb=0)
reserve = alloc("reserve", (G, T), lb=0)

Keep variable ownership obvious: type, resource, period, and optional segment/tier.

Sparse Constraint Pattern

Use sparse rows for large time-expanded models:

rows, cols, vals = [], [], []
lb, ub = [], []
row = 0

def add_row(terms, lo, hi):
    global row
    for j, a in terms:
        if abs(a) > 0:
            rows.append(row)
            cols.append(j)
            vals.append(float(a))
    lb.append(float(lo))
    ub.append(float(hi))
    row += 1