Safety Stock Calculation 安全庫存計算
Released已發布Calculate safety stock levels to buffer against demand and lead time uncertainty. Use this skill when the user needs to set inventory buffers, determine service level trade-offs, or optimize safety stock across SKUs — even if they say 'how much buffer inventory', 'stockout prevention', or 'service level calculation'.
演算法技能：Safety Stock Calculation 分析與應用。
Overview概述
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使用時機
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 演算法
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
- Compute demand statistics: average demand (d), demand standard deviation (σ_d)
- Compute lead time statistics: average LT, LT standard deviation (σ_LT)
- Compute combined variability: σ_combined = √(LT × σ²_d + d² × σ²_LT)
- Look up z for target service level
- Safety stock = z × σ_combined
- 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輸出格式
{
"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範例
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注意事項
- 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%.
References參考資料
- For multi-echelon safety stock optimization, see
references/multi-echelon.md - For intermittent demand methods, see
references/intermittent-demand.md