Intermittent Demand Forecasting. John E. Boylan

Table 3.5, the review interval (Week 1) and the lead time (Week 2) are considered separately. In the second column, we exclude the possibility of zero demand, as the measure is restricted to review intervals with non‐zero demand. The values in the fourth column have also changed. In the long run, only half of the weeks have non‐zero demands, according to Table 3.2. Therefore, although only 30% of weeks have a demand of one unit, 60% of weeks with some demand have a demand of one unit. Similarly, 40% of weeks with some demand have a demand of two units. The fifth column uses the same probabilities as in Table 3.2 because the possibility of zero demand is not excluded in Week 2. The final two columns in Table 3.5 are calculated in the same way as in Table 3.3.

Table 3.5 Distribution of total demand over two weeks conditional on non‐zero demand in first week.

Total	Week 1	Week 2	Week 1 Probability	Week 2 Probability	Product	Total Probability
1	1	0	0.6	0.5	0.30	0.30
2	2	0	0.4	0.5	0.20
	1	1	0.6	0.3	0.18	0.38
3	2	1	0.4	0.3	0.12
	1	2	0.6	0.2	0.12	0.24
4	2	2	0.4	0.2	0.08	0.08

Figure 3.1 Comparison of CSL and

.

Now that the conditional probabilities have been calculated, it may be asked if they can be used to estimate . Cardós and Babiloni (2011) pointed out that, strictly speaking, we are interested in the probability that demand over a replenishment cycle does not exceed the stock on hand at the beginning of the cycle. This value would give an exact cycle service level but it is very difficult to calculate and Cardós and Babiloni (2011, p. 64) concluded, ‘The exact method to compute the CSL is not an appropriate procedure to be widely used in a business context’. Consequently, they recommended basing calculations on the cumulative conditional probabilities of demand over the protection interval, in order to estimate the revised cycle service level (). Returning to our example, the results are given in Figure 3.1, and are compared with the original CSL values for different potential OUT levels.

In this example, there is a large difference between the two cycle service level measures, for OUT levels of both one and two units. The difference between the two measures for three units is smaller (96% for CSL, 92% for ) but would lead to a disagreement on the OUT level needed to ensure that a 95% cycle service level target is met. For an OUT level of four units, there is no difference: all demand is satisfied, as the maximum demand over two weeks is for four units (see Table 3.4). It does not matter whether cycles with no demand in the review intervals are excluded or not; there can be no stockouts in either case.

      In our example, the calculations were manageable because the protection interval was only for two periods and the OUT level did not need to exceed four units. The calculations can become more involved for longer protection intervals and higher OUT levels, and approximate formulae have been given to simplify the calculations (Cardós and Babiloni 2011). In Chapter 8, we explain how other formulae can be used if the demand follows certain demand distributions. If no demand distributions can adequately represent the real demand, then another option is to use non‐parametric approaches, to be discussed in Chapter 13.

      3.5.4 Summary

There are two approaches to measuring the cycle service level. These methods produce the same results for non‐intermittent demand. They differ for intermittent items because the second method excludes those cycles with no demand during the review interval. This makes more sense for intermittence, but it complicates the calculation, which depends on combining two different demand distributions, one for the review interval and one for the lead time.

3.6 Calculating Fill Rates

      The unit fill rate is defined as the proportion of demand satisfied directly from stock on hand, as noted earlier. It can be calculated at both aggregate and SKU levels, and can be defined in terms of volume filled or value filled. At SKU level, volume and value fill rates will be the same (unless calculated over a period of time in which there has been a price change) but will usually differ at an aggregate level. In this section, we look at some of the issues that need to be addressed in finding the unit (volume) fill rate, and discuss how demand distributions can be used in its calculation.

      3.6.1 Unit Fill Rates

The basic unit fill rate calculation is straightforward. For example, if in a particular period we satisfy three units out of four demanded directly from stock, then the fill rate is 75%. Let us now consider an example of