Reorder Point with Safety Stock
Real demand bounces around, so ordering at exactly lead time demand means running out about half the time. Safety stock is a buffer that covers that uncertainty. The reorder point becomes expected lead time demand plus safety stock, sized by the service level you want.
Safety stock and reorder point explained simply
When demand varies, add safety stock to the reorder point: ROP = expected lead-time demand + safety stock, with safety stock = z × σ_d × √L. In the example, 40 units a day, a 9-day lead time and a 95% service level (z = 1.65) give safety stock of about 50 units and a reorder point of about 410.
What this safety stock lesson covers
- Why uncertain demand needs a safety stock buffer
- How service level links to a z score
- How to calculate safety stock from daily demand variability
- How to add safety stock to get the reorder point
Safety stock formulas, explained
- d
- average daily demand
- L
- lead time in days
- SS
- safety stock in units
- z
- z score for the target service level, e.g. 1.65 for about 95%
- σ_d
- standard deviation of daily demand
- L
- lead time in days
How to calculate safety stock step by step (worked example)
Average demand is 40 units a day with a standard deviation of 10 units a day. Lead time is 9 days and the target service level is 95% (z = 1.65). What are the safety stock and reorder point?
- Lead time demand = 40 × 9 = 360 units.
- Standard deviation over lead time = 10 × √9 = 30 units.
- Safety stock = 1.65 × 30 = 49.5 units.
- ROP = 360 + 49.5 = 409.5 units.
Answer: Safety stock is about 50 units and the reorder point is about 410 units (rounded up to whole units).
Service level vs safety stock
| Service level | z | Safety stock | Reorder point |
|---|---|---|---|
| 50% | 0 | 0 | 360 |
| 95% | 1.65 | About 50 | About 410 |
| 99% | 2.33 | About 70 | About 430 |
How much running out can you afford? David's take
A 95% service level means accepting a stock-out in about 1 order cycle in 20. For most items that's a tiny mistake: a customer waits a day. For a critical part that stops a production line, it can be a vital one. My soundbite: the road to success has infinite tiny mistakes, some big mistakes and zero vital mistakes. So don't use one service level for everything. Spend safety stock where running out would be vital, and save it where it wouldn't.
From David's concept: Choose Your Mistakes. This is David's opinion, alongside the standard textbook answer above.
Harder safety stock questions
What does a 99% service level need?
With z = 2.33: safety stock = 2.33 × 30 ≈ 70 units and ROP ≈ 430. Going from 95% to 99% adds about 20 units of stock that sits there all year.
Why multiply by the square root of the lead time?
Daily ups and downs partly cancel out over several days. Variances add up day by day, so the standard deviation over 9 days is 10 × √9 = 30, not 10 × 9 = 90.
Common safety stock questions
What is the formula for reorder point with safety stock?
Reorder point equals average daily demand times lead time, plus safety stock. Safety stock is the extra buffer you hold so you do not run out when demand during the lead time comes in higher than average.
How do you calculate safety stock with a z score?
Multiply the z score for your service level by the standard deviation of demand during the lead time. If you have daily standard deviation and a fixed lead time, the lead time standard deviation is the daily figure times the square root of lead time days.
What z score should I use for a 95% service level?
Use about 1.65 (more precisely 1.645) for a 95% service level. Common others are about 1.28 for 90% and 2.33 for 99%. A higher service level means a bigger z score and more safety stock.
Why multiply by the square root of lead time?
Daily demand swings partly cancel out over several days, so variability grows with the square root of time, not in a straight line. That assumes each day's demand is independent and the lead time is fixed.