Intermittent Demand Forecasting. John E. Boylan

      where is the demand over the protection interval () and is the long‐run average demand per (single) period. We shall refer to this as the traditional fill rate calculation.

      As we shall see later, this traditional fill rate calculation suffers from some drawbacks, whether demand is intermittent or not. However, it is often used in practice, and so it is important to understand its calculation, including its flaws and how they can be rectified.

To illustrate the traditional calculation of fill rates, we now look at another example. The review interval is set as one week and the lead time as two weeks. The distribution of demand is similar to the example in Table 3.2, except that it is lumpier, with a spike of demand at four units, as shown in Table 3.7.

Table 3.7 Distribution of lumpy demand over one week.

Demand	Probability
0	0.5
1	0.3
4	0.2
5 or more	0.0

Table 3.8 Traditional fill rate calculation (

and

;

).

Demand	Probability	Not satisfied	Expected	Not satisfied	Expected
	)
1	0.225	0	0.000	0	0.000
2	0.135	0	0.000	0	0.000
3	0.027	0	0.000	0	0.000
4	0.150	0	0.000	0	0.000
5	0.180	0	0.000	0	0.000
6	0.054	0	0.000	0	0.000
8	0.060	1	0.060	0	0.000
9	0.036	2	0.072	1	0.036
12	0.008	5	0.040	4	0.032
		Total	0.172	Total	0.068
		Fill rate ()	84.4%	Fill rate ()	93.8%

Continuing this example, we summarise in Table 3.8 the probabilities of demand over a protection interval of three weeks (first two columns) and traditional fill rate calculations for OUT levels of seven units (middle two columns) and eight units (final two columns).

      The first column of Table 3.8 lists all of the possible total demands over three weeks, given possible demands of zero, one, and four units in one week. The possibility of zero demand over the whole three weeks has not been included. It is not relevant from a fill rate perspective because there is no demand to be fulfilled. Some demand values are omitted, such as seven, as there is no combination of three weeks of demand, in this example, that can give this number. The detailed calculations for the second column are not given but they follow exactly the same approach as in Table 3.3, where all combinations of demands are identified, and probabilities are calculated accordingly.

The third and fifth columns of Table