Safety Stock Calculation

Overview

Safety stock is buffer inventory held to protect against demand and lead time variability. Formula: SS = z × √(LT × σ²_d + d² × σ²_LT) where z=service factor, LT=lead time, σ_d=demand std dev, d=avg demand, σ_LT=lead time std dev. Directly trades inventory cost against stockout risk.

When to Use

Trigger conditions:

• Setting inventory buffers for variable-demand items
• Choosing target service levels and computing required safety stock
• Optimizing safety stock across a portfolio of SKUs

When NOT to use:

• When demand is deterministic (use EOQ without safety stock)
• For one-time purchase decisions (use newsvendor model)

Algorithm

IRON LAW: Safety Stock Is a TRADE-OFF, Not a Target
More safety stock = fewer stockouts but higher holding cost.
The relationship is non-linear: going from 95% to 99% service level
roughly DOUBLES safety stock. Going from 99% to 99.9% doubles it
again. Always quantify the cost of each service level increment.
z-values: 90%→1.28, 95%→1.65, 99%→2.33, 99.9%→3.09.

Phase 1: Input Validation

Collect: historical demand data (weekly/monthly), lead time data (average and variability), target service level, unit cost and holding rate. Gate: Minimum 12 periods of demand data, lead time estimates available.

Phase 2: Core Algorithm

1. Compute demand statistics: average demand (d), demand standard deviation (σ_d)
2. Compute lead time statistics: average LT, LT standard deviation (σ_LT)
3. Compute combined variability: σ_combined = √(LT × σ²_d + d² × σ²_LT)
4. Look up z for target service level
5. Safety stock = z × σ_combined
6. Reorder point = d × LT + SS

Phase 3: Verification

Simulate: using historical demand, would the computed SS have prevented stockouts at the target service level? Gate: Simulated service level matches target (±2%).

Phase 4: Output

Return safety stock with cost impact and service level analysis.

Output Format

{
  "safety_stock": 250,
  "reorder_point": 850,
  "service_level": 0.95,
  "annual_holding_cost": 5000,
  "metadata": {"avg_demand_weekly": 120, "demand_cv": 0.3, "avg_lead_time_weeks": 5}
}

Examples

Sample I/O

Input: Weekly demand: avg=100, σ=30. Lead time: avg=4 weeks, σ=1 week. Target: 95%. Expected: σ_combined = √(4×900 + 10000×1) = √(3600+10000) = √13600 = 116.6. SS = 1.65 × 116.6 = 192 units.

Edge Cases

Input	Expected	Why
Zero demand variability	SS from LT variability only	σ_d = 0, only lead time risk remains
Zero lead time variability	SS from demand variability only	σ_LT = 0, standard formula simplifies
Very long lead time	High SS	More uncertainty accumulates over longer periods

Gotchas

• Normal distribution assumption: Formula assumes normally distributed demand. Highly intermittent demand (many zeros) needs different approaches (Poisson, negative binomial).
• Demand forecast error, not demand variability: If you use a forecast, SS should buffer forecast ERROR (σ_error), not raw demand variability.
• Service level definition: Cycle service level (probability of no stockout per cycle) ≠ fill rate (fraction of demand met from stock). Companies often mean fill rate but calculate cycle SL.
• Lead time data quality: Lead time variability is often poorly tracked. Underestimating σ_LT leads to insufficient safety stock.
• ABC segmentation: Don't apply the same service level to all SKUs. A-items (high revenue) deserve 99%; C-items may be fine at 90%.

Scripts

Script	Description	Usage
scripts/safety_stock.py	Compute safety stock and reorder point with combined demand/lead-time variability	python scripts/safety_stock.py --help

Run python scripts/safety_stock.py --verify to execute built-in sanity tests.

References

• For multi-echelon safety stock optimization, see references/multi-echelon.md
• For intermittent demand methods, see references/intermittent-demand.md