Inputs
Example data table
| Scenario | Mean Demand | Demand SD | Lead Time | Lead SD | Service | Safety Stock | Reorder Point |
|---|---|---|---|---|---|---|---|
| Steady lane, moderate volatility | 120 | 35 | 6 | 1.5 | 0.95 | ≈ 391 | ≈ 1,111 |
| Stable lead time, higher demand swings | 200 | 70 | 4 | 0 | 0.98 | ≈ 339 | ≈ 1,139 |
| Long lead time exposure, periodic review | 90 | 25 | 10 | 2 | 0.95 | ≈ 375 | ≈ 1,275 |
Formula used
The calculator models uncertainty during the protection period, which is P = L + R, where L is average lead time and R is the review period.
For fill rate, the calculator uses an expected-shortage approximation: Expected Shortage ≈ σP × L(z), then solves for z such that Fill Rate = 1 − Expected Shortage / Q, where Q is order quantity.
How to use this calculator
- Choose a consistent planning period (day, week, etc.).
- Enter average demand and demand standard deviation per period.
- Enter average lead time and its standard deviation in the same periods.
- Set review period to 0 for continuous review, otherwise enter your review cadence.
- Select service target type: cycle service level or fill rate.
- Enter target level; if fill rate, also enter order quantity.
- Submit to view safety stock, reorder point, and export options.
Service level translates into statistical coverage
Cycle service level targets the probability that on‑hand inventory never hits zero during lead time plus any review gap. The calculator converts the target to a Z value, then multiplies it by the protection‑period standard deviation. For example, moving from 95% to 98% increases Z from about 1.645 to 2.054, often lifting safety stock by roughly 25% for the same variability in practice.
Protection period drives exposure, not calendar time
Protection period equals average lead time plus review period. If you review weekly, you are exposed to both replenishment delay and the time until the next order is placed. A lane with 6 days lead time and a 2 day review period has P = 8 periods, increasing mean demand during protection by 33% versus continuous review at P = 6.
Demand volatility scales with the square root of time
Demand uncertainty grows as σd × √P when lead time is stable. Doubling P does not double the standard deviation; it increases it by √2. This is why compressing lead time from 10 to 6 periods can materially cut safety stock even if demand remains unchanged.
Lead time variability can dominate in constrained networks
When lead time fluctuates, exposure increases by d̄² × σL² inside the variance term. High average demand makes this effect powerful. If d̄ is 200 units and σL is 2 periods, the lead‑time component contributes 160,000 units² to variance, sometimes outweighing demand variance on stable SKUs.
Fill rate needs order quantity context
Fill rate focuses on how much demand is satisfied immediately, so the model uses expected shortage relative to order quantity Q. Larger Q spreads shortage over more units, reducing the Z needed for the same fill rate. If Q is below mean protection demand, reaching aggressive fill rates can require very high safety stock or process changes.
Use outputs to align inventory and transport decisions
Safety stock and reorder point should be reviewed after carrier changes, supplier shifts, or seasonal demand moves. Compare the calculated reorder point to minimum order constraints and warehouse capacity. Track actual stockouts and lead time distributions monthly with discipline, then refresh σd and σL so your service target reflects current network performance always.
FAQs
What is the difference between cycle service level and fill rate?
Cycle service level is the chance of no stockout in the protection period. Fill rate measures the share of demand shipped immediately. Fill rate usually needs order quantity, because shortages are averaged across a replenishment cycle.
Which time unit should I use for demand and lead time?
Use one consistent period everywhere, such as days or weeks. Demand inputs must be per that period, and lead time inputs must be expressed in the same period count.
Why does lead time standard deviation affect safety stock so much?
When lead time varies, demand exposure varies too. The variance term adds average demand squared times lead time variance, which can dominate when volumes are high.
What should I enter for review period?
Enter 0 for continuous review where you reorder as soon as inventory hits the trigger. Enter your review cadence for periodic review, such as 7 for weekly checks in daily units.
How do I choose an order quantity for fill rate mode?
Use your typical replenishment batch, or the quantity set by supplier minimums, container sizes, or economic order logic. If Q is small versus protection demand, targets may require process improvements.
How often should I refresh the inputs?
Update demand and lead time statistics after major changes and at least monthly for fast movers. For stable items, quarterly updates can be sufficient if service performance is monitored.