Safety Stock: worked example
| Service level | 95 percent |
|---|---|
| Daily demand standard deviation (units) | 20 |
| Lead time (days) | 9 |
| Average daily demand (units) | 100 |
| Safety stock (units) | 98.7 |
| Reorder point (units) | 998.7 |
Safety Stock: formula
Common error: Multiplying by the lead time instead of its square root. That treats each day's variation as perfectly linked and overstates the buffer for longer lead times.
Service level is entered as a z-score: 1.28 for about 90%, 1.645 for 95% and 2.33 for 99%. Daily demand standard deviation measures how much demand varies from day to day, computed from sales history, and lead time is the days between order and delivery. Average daily demand is used for the reorder point.
The formula assumes demand varies but lead time is fixed.
Safety Stock: changing Daily demand standard deviation (units)
| Daily demand standard deviation (units) | Safety stock (units) | Reorder point (units) |
|---|---|---|
| 16 | 79 | 979 |
| 18 | 88.8 | 988.8 |
| 20 (example) | 98.7 | 998.7 |
| 22 | 108.6 | 1,008.6 |
| 24 | 118.4 | 1,018.4 |
Safety Stock: compare input ranges
| Input | Tested from | To | Safety stock (units): low input | Safety stock (units): high input | Swing |
|---|---|---|---|---|---|
| Service level | 90 percent | 99 percent | 76.9 | 139.6 | 62.7 (64%) |
| Daily demand standard deviation (units) | 18 | 22 | 88.8 | 108.6 | 19.7 (20%) |
| Lead time (days) | 8 | 10 | 93 | 104 | 11 (11%) |
| Average daily demand (units) | 90 | 110 | 98.7 | 98.7 | 0 |
Safety Stock: individual input comparisons
| Input | Value | Safety stock (units) | Reorder point (units) |
|---|---|---|---|
| Service level | 90 percent | 76.9 | 976.9 |
| 95 percent | 98.7 | 998.7 | |
| 97.5 percent | 117.6 | 1,017.6 | |
| 99 percent | 139.6 | 1,039.6 | |
| Daily demand standard deviation (units) | 16 | 79 | 979 |
| 18 | 88.8 | 988.8 | |
| 20 | 98.7 | 998.7 | |
| 22 | 108.6 | 1,008.6 | |
| 24 | 118.4 | 1,018.4 | |
| Lead time (days) | 7 | 87 | 787 |
| 8 | 93 | 893 | |
| 9 | 98.7 | 998.7 | |
| 10 | 104 | 1,104 | |
| 11 | 109.1 | 1,209.1 | |
| Average daily demand (units) | 80 | 98.7 | 818.7 |
| 90 | 98.7 | 908.7 | |
| 100 | 98.7 | 998.7 | |
| 110 | 98.7 | 1,088.7 | |
| 120 | 98.7 | 1,178.7 |
Safety Stock: combined input changes
| Daily demand standard deviation (units) / Lead time (days) | 7 | 9 | 11 |
|---|---|---|---|
| 16 | 69.6 | 79 | 87.3 |
| 18 | 78.3 | 88.8 | 98.2 |
| 20 | 87 | 98.7 | 109.1 |
| 22 | 95.7 | 108.6 | 120 |
| 24 | 104.4 | 118.4 | 130.9 |
Safety Stock: which assumptions move the result?
Safety Stock: values and definitions
| Quantity and definition | Value used |
|---|---|
| Service level — The chance of not running out during the lead time. | 95 percent |
| Daily demand standard deviation (units) | 20 |
| Lead time (days) | 9 |
| Average daily demand (units) | 100 |
| Safety stock (units) | 98.7 |
| Reorder point (units) | 998.7 |
The formula assumes demand is normally distributed and independent from day to day, and it ignores variation in lead time, which is often the larger risk. Intermittent or seasonal items need other methods. Historical variation may not represent the future, and forecasting errors are different from raw demand variation.
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Safety stock buys protection against demand that runs higher than average while you wait for a delivery. The buffer grows with the variation in demand, with the square root of the lead time and with the service level you want. With daily demand varying by 20 units, a 9 day lead time and a 95 percent target, the buffer is about 99 units, and the reorder point is about 999.
Base the standard deviation on real demand history over the same unit of time as the lead time. A guess makes the whole buffer a guess.
Use the result in the reorder point calculator, and compare the cost of holding it with the inventory carrying cost page. The economic order quantity calculator sets the order size, and the inventory turnover calculator shows whether stock is moving. Review the parameters every quarter.
What service level should I choose?
It depends on the cost of a stockout. Many businesses use 95%, higher for critical items, and lower for cheap or easily substituted ones.
Why does safety stock rise with the square root of lead time?
Because variation adds up over days, and independent daily variations grow with the square root of the number of days, not directly with the days.
Does supplier reliability matter?
Yes. If lead time varies, add that variation to the calculation, or your safety stock will be too low.