Objective
Safety stock (SS) is based on:
The forecast error is modeled by using a gamma distribution:
Service level target can be expressed using:
The impact of key drivers on inventory are:
The following table shows target service level and z factors.
| Target Service Level | Z Factor |
|---|---|
| 50% | 0.000000 |
| 60% | 0.253347 |
| 70% | 0.524401 |
| 75% | 0.674490 |
| 80% | 0.841621 |
| 85% | 1.036433 |
| 90% | 1.281552 |
| 91% | 1.340755 |
| 92% | 1.405072 |
| 93% | 1.475791 |
| 94% | 1.554774 |
| 95% | 1.644854 |
| 96% | 1.750686 |
| 97% | 1.880794 |
| 98% | 2.053749 |
| 99% | 2.326348 |
| 99.9% | 3.090232 |
| 99.99% | 3.719016 |
In the following figure, the forecast for standard deviation impacts the width of the distribution.
The following example shows a scenario with PBR = 1, a lead time of 0, a demand of 100 plus/minus 25, and a service level of 95%.
The initial on-hand value is 41 units, and the target inventory position (TIP) is calculated according to the formula given in the figure.
Next, the missing values for period 2 are derived.
 Demand Variability with Instantaneous Lead Time_image.png "The figure describes the Demand and Service Level.")
The steps are repeated for periods 3 and 4, and the average is calculated.
 Demand Variability with Instantaneous Lead Time_image.png "The figure describes the Demand and Service Level.")
Assume the distributions in two consecutive periods is given in the following figure.
.png "The figure describes the Risk Pooling Opportunity")
Risk pooling can reduce the total risk and insecurity by combining different individual risks and insecurities, as shown in the following figure.
.png "The figure describes the Risk Pooling Opportunity .")
The following example shows a scenario with PBR = 1, LT = 2, NSP = 95%, and a demand of 100 plus/minus 25. The value for target inventory position (TIP) is calculated as shown in the figure.
 Demand Variability_image.png "The figure describes the Safety Stock and Inventory Position")
The initial on-hand value is 72 units and the initial planned receipts is 100 + 100 units. The values for the subsequent periods are calculated according to the table in the figure.
 Demand Variability_image.png "The figure describes the On-Hand Inventory.")
The values for the different subsequent periods are calculated by repeating the steps. Finally, an average is determined.
 Demand Variability_image.png "The figure describes the Demand and Replenishment.")
To further characterize and define safety stock, two questions are important:
How often do situations occur in which the safety stock is needed at all?
In how many of these cases is the amount of safety stock not sufficient to satisfy the requirement?
