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.
What you will learn
- 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
The formulas
- 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
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).
Common 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.