John E. Boylan - Intermittent Demand Forecasting

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.

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.

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.

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 four periods with each period showing some demand, as shown in Table 3.6.

How should we define the overall fill rate? There are two possible approaches. The first is to total the satisfied demand (8 units) and divide by the total demand (16 units) to give an overall fill rate of 50%, as shown in Table 3.6. The second approach is to average the fill rates over all four periods, giving an overall fill rate of 56.25%, which is somewhat higher than the first calculation. If all four periods had a fill rate of 50%, then the two calculation methods would agree. The disagreement arises because the average of the fill rates in the second and third periods is 62.5%, whereas only 50% of the total demand over these two periods is fulfilled. The second method can be applied to intermittent demand only if periods with zero demands are excluded from the calculation. For further discussion of this method, please refer to Guijarro et al. (2012). We will base our analysis on the first method, as it is simpler for intermittent demand, and is the standard method in the literature and in practice.

Table 3.6 Fill rates per time period.

To calculate the unit fill rate (FR), we need to evaluate how much demand is satisfied, over a given period of time, as a proportion of the demand over the same period. Equivalently, we can evaluate the average unsatisfied demand per period, as a proportion of the average demand per period, and subtract this ratio from one, as shown in Eq. (3.2).

(3.2)

where represents the stock on hand at the start of time period , after receipt of any orders and dispatch of any outstanding backorders, is demand during time period , and is the number of time periods over which the fill rate is being measured. The superscript indicates a result of zero if the expression in the brackets is negative, and unchanged otherwise. For example, and .

In Eq. (3.2), the expression represents the backorders generated at the end of period as a consequence of demand in that period not being satisfied. If there is sufficient stock ( less than or equal to ), then there are no backorders. If there is insufficient stock ( strictly greater than ), then units are backordered. In the numerator of the ratio in Eq. (3.2), the backorders are summed over all periods and divided by the number of periods ( ) to give the average unsatisfied demand per period. In the denominator, we have the average demand per period. The ratio represents the average unsatisfied demand per period as a proportion of the average demand per period.

For ease of exposition, from this point on, we assume that the review interval is one period ( ). At the end of this section, we return to the more general case when it can be longer.