COGS variance: purchase price vs usage vs mix

Decompose COGS variance for {period}.

Inputs:
- Actual vs standard costs: {actual_vs_standard_costs}
- Production/volume data: {production_volume}
- Material usage and scrap: {usage_scrap}
- Product mix and sales volumes: {product_mix}
- Inventory changes: {inventory_changes}

Output:
1) Variance decomposition table (PPV, UV, Mix, Yield/Scrap, Other).
2) Key drivers and operational interpretation.
3) Recommended actions and questions for ops/procurement.
4) Suggested KPI tracking to prevent recurrence.

Be explicit about formulas and data requirements.