# 10.5.4 Safety Demand Calculation for Various Planning Periods

### Intended learning outcomes: Identify variables for safety demand calculations. Explain expected value and standard deviation with continuous demand. Describe expected value and standard deviation over n statistical periods.

A planning period represents the time span between “today” and the point in time of the last demand that was included in a specific planning consideration.

Figure 10.5.4.1 provides a few definitions required for the following discussion.

Fig. 10.5.4.1      Definitions of variables for safety calculations.

In a forecast calculation, we determine expected value and standard deviation for a particular statistical period, for example, the SP. In materials management, however, it is necessary to have values for various planning periods. If, for example, the planning period is the lead time, then we have to take the total forecast demand during the lead time into consideration. Usually this is up until the receipt of the production or procurement order.[note 1013]

We can infer the formulas shown in Figure 10.5.4.2 on the basis of the models developed in Section 10.5.2; the formulas are also valid for the non-integral proportions of PP:SP.

Fig. 10.5.4.2      Expected value and standard deviation with continuous demand.

In a nonstationary process, different expected values or standard devia­tions arise for various time periods in the future. Assuming independent forecast values in individual periods, the expected values and variances of demand can be added during the planning period. For n statistical periods, this produces the formulas shown in Figure 10.5.4.3.

Fig. 10.5.4.3      Expected value and standard deviation over n statistical periods.

We can also use these formulas for certain periods, usually in the near future, where the demand has been established deterministically, that is, through customer orders, for examp­le. The demand for these periods demonstrates a 0 variance. Similarly, a linear interpolation of the expected value and variance is used to determine intermediate values during a period.