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COGS variance: purchase price vs usage vs mix

Breaks COGS variance into purchase price, usage/efficiency, and mix components. Useful for manufacturing/retail and product businesses.

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.

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