To illustrate how safety stock is calculated, we assume company ABC has a part (e.g, a special screw) in its inventory. Company ABC buys screws from its supplier and resells them to customers. The following table shows the quantity of screws purchased from company ABC in past months. The column header "demands" refers to the quantity of screws.
| Month | Demands |
|---|---|
| 1 | 35 |
| 2 | 45 |
| 3 | 67 |
| 4 | 55 |
| 5 | 23 |
| 6 | 61 |
| 7 | 78 |
| 8 | 32 |
| 9 | 77 |
| 10 | 81 |
| 11 | 55 |
| 12 | 76 |
We calculate the standard deviation of monthly demand (STD), e.g., using Excel spreadsheet formula, STDEV().
| Standard Deviation of Demand (STD = STDEV()) | 19.8 |
When company ABC places an order of the part with the supplier, it will take 45 days to receive it. Thus, the lead time is 45 days.
| Lead Time in Days (LT) | 45 |
The future monthly demand from customers is alaways fluctuating. We assume that company ABC wants to achieve the demand satisfaction (DS) or fill rate of 95%. Safety stock is the cushion of inventory that satisfies the DS given the random nature of future demands. It is commonly calculated using the following equation:
| Safety Stock (SS) = Norminv (DS)*sqrt(LT/30)*STD |
Norminv(DS) is the inverse of the standard normal cumulative distribution function. In Excel spreadsheet, the function is referred to as norminv(). In python, the function is called norm.ppf(DS). As DS approaches 100%, the value of norminv increases drastically as shown in the chart below. In practice, DS is capped at 99%.
Let's further assume that the unit cost of the part for company ABC to buy from the supplier is $5.
| Unit Cost | $5.00 |
The following table summarizes how safety stock and its costs are calculated.
| Lead Time in Days (LT) | 45 |
| Standard Deviation of Demand (STD = STDEV()) | 19.8 |
| Demand Satisfaction (DS) or Fille Rate | 95% |
| Safety Stock : FLOOR(NORMINV(DS,0,1)*SQRT(LT/30)*STD,1). To convert days to months, LT is divided by 30. Floor function rounds down a real number to an integer. | 39 |
| Unit Price | $5.00 |
| Cost of Safety Stock | $195.00 |
In calculating safety stock, it is a common practice to round down the float number into an integer. This is accomplished by Excel function Floor().
1. Readers may use our online safety stock calculator here.
2. A free Excel spreadsheet can be downloaded here. A user fills the numbers in cells highlighted in green and safety stock and its cost will be calculated automatically as shown below.
