Statistical
Safety stock formula: combine demand volatility and supplier lead-time variance
Size warehouse safety stock for 95% or 99% cycle service levels using Z * SQRT(AvgLeadTime * DemandSD^2 + AvgDemand^2 * LeadTimeSD^2).
Why ignoring supplier lead-time variability causes stockouts
If supplier lead time were 100% fixed, Safety Stock would simply be Z * DemandSD * SQRT(AvgLeadTime). In real supply chains, BOTH daily customer demand AND vendor transit days fluctuate.
Assuming independent daily demand (mean D, std dev SD_D) and lead time in days (mean LT, std dev SD_LT), lead-time demand standard deviation is SQRT(LT * SD_D^2 + D^2 * SD_LT^2). Multiply by one-sided service factor Z (1.28 for 90%, 1.645 for 95%, 2.33 for 99%) and round UP to whole units!
| Input Parameter | Sample Value | Contribution |
|---|---|---|
| Avg Daily Demand (A2) & SD (B2) | 40 units/d, SD = 15 | LT * SD_D^2 = 4 * 225 = 900 |
| Avg Lead Time (C2) & SD (D2) | 4 days, SD = 1 day | D^2 * SD_LT^2 = 1600 * 1 = 1600 |
| Combined Lead-Time SD | SQRT(900 + 1600) | 50.0 units |
| Safety Stock & ROP (Z = 1.645, 95%) | ROUNDUP(1.645 * 50) = 83 units | ROP = 40*4 + 83 = 243 units |
Combined Safety Stock and Reorder Point (ROP) formulas
Round the modeled buffer up to whole units. The approximate one-sided 95% normal factor 1.645 gives 82.25 before rounding, hence 83 units.
=ROUNDUP(E2 * SQRT(C2 * (B2 ^ 2) + (A2 ^ 2) * (D2 ^ 2)), 0)Full Reorder Point (Expected Lead-Time Demand + Safety Stock)
The example reorder point is 243 units of inventory position. If expected demand is fractional and orders require whole units, round the overall threshold appropriately.
=A2 * C2 + ROUNDUP(E2 * SQRT(C2 * (B2 ^ 2) + (A2 ^ 2) * (D2 ^ 2)), 0)Inputs and interpretation
This approximation assumes stationary independent daily demand, lead time independent of demand, and an approximately normal lead-time demand distribution. Cycle service level is not fill rate. Use nonnegative means, standard deviations and Z. Rounding up does not guarantee a service target when assumptions are wrong. Inventory position includes on-hand plus on-order minus backorders; use a consistent continuous-review replenishment policy.
Try the example
Use the original values or change them to test your understanding.