Safety stock protects against uncertainty in demand and lead time. The more variability and the higher the desired service level, the more safety stock is required. This page explains the major formulas used in supply chain analytics and includes multiple numerical examples.

1. Safety Stock with Variable Demand and Fixed Lead Time

\[ \text{Safety Stock} = Z \cdot \sigma_d \cdot \sqrt{L} \]

• \(Z\) = service‑level factor
• \(\sigma_d\) = standard deviation of demand per period
• \(L\) = lead time in periods

Example

• Daily demand std dev = 20
• Lead time = 5 days
• Service level = 95% → \(Z = 1.65\)

\[ 1.65 \cdot 20 \cdot \sqrt{5} = 74 \text{ units} \]

2. Safety Stock with Variable Demand and Variable Lead Time

\[ \text{Safety Stock} = Z \cdot \sqrt{L\sigma_d^2 + D^2\sigma_L^2} \]

• \(D\) = average demand
• \(\sigma_L\) = standard deviation of lead time

Example

• Average demand = 80/day
• Demand std dev = 15
• Lead time = 7 days
• Lead time std dev = 2 days
• Service level = 90% → \(Z = 1.28\)

\[ \text{Safety Stock} = 1.28 \cdot \sqrt{1575 + 25600} = 211 \text{ units} \]

3. Safety Stock Based on Fill Rate (β‑Service Level)

\[ \text{Safety Stock} = \sigma_{DL} \cdot \sqrt{2\ln\left(\frac{1}{1-\beta}\right)} \]

Example

• \(\sigma_{DL} = 50\)
• Fill rate target = 95%

\[ 50 \cdot \sqrt{2\ln(20)} = 122 \text{ units} \]

4. Safety Stock for Intermittent Demand

When demand is sporadic, normal‑distribution formulas fail. Two alternatives:

• Poisson‑based safety stock for low, random demand.
• Croston‑based safety stock using forecast error.

Poisson Example

• Average weekly demand = 4
• Lead time = 3 weeks
• Service factor \(Z = 1.5\)

\[ \text{Safety Stock} = 4 \cdot 3 \cdot (1.5 – 1) = 6 \]

5. Summary Table