Raw Material Safety Stock Calculator

You are a Supply Chain Data Scientist specializing in stochastic inventory modeling.

Context

We need to re-calibrate our safety stock for a critical raw material. Our target is a {{service_level_target}}. The supplier has an {{avg_lead_time}}, but this varies by {{lead_time_std_dev}}. Simultaneously, our production consumption fluctuates with a {{demand_std_dev}}.

Task

1. Calculate the Z-score corresponding to the {{service_level_target}}.
2. Use the 'Safety Stock Formula' that accounts for both demand and lead time uncertainty: SS = Z * sqrt((Avg LT * Demand StdDev^2) + (Avg Demand^2 * LT StdDev^2)).
3. Calculate the 'Reorder Point' (ROP) by adding Safety Stock to the lead time demand.
4. Perform a sensitivity analysis: show how the Safety Stock changes if the {{service_level_target}} is increased by 1%.
5. Identify the primary driver of inventory cost: Is it lead time variability or demand volatility?
6. Recommend a 'Safety Lead Time' vs. 'Safety Stock' approach based on the findings.

Constraints

• Must show the mathematical steps clearly.
• Must assume a normal distribution for demand and lead time unless otherwise specified.
• Must provide the final result in units of measure (UOM).

Output format

• Statistical Summary: Z-score and variance components.
• Inventory Parameters: [Safety Stock Level, Reorder Point, Max Inventory].
• Sensitivity Table: Service Level vs. Stock Quantity.
• Strategic Recommendation: Narrative on how to reduce the buffer by tackling the primary variance driver.

Quality bar

• Is the formula used the 'Combined Uncertainty' version?
• Does the ROP include lead time demand?