Table 3.4 Cumulative distribution of total demand over two weeks.
| Demand | Probability | Cumulative probability |
|---|---|---|
| 0 | 0.25 | 0.25 |
| 1 | 0.30 | 0.55 |
| 2 | 0.29 | 0.84 |
| 3 | 0.12 | 0.96 |
| 4 | 0.04 | 1.00 |
In Table 3.3,
To find the probabilities in Table 3.3, we first consider all the possible ways of achieving the demand values over two weeks. For example, a total demand of two can be achieved in three ways (two in Week 1, zero in Week 2; or one in Week 1, one in Week 2; or zero in Week 1 and two in Week 2). The full listings are given in the second and third columns of Table 3.3.
The probabilities in the fourth and fifth columns are taken directly from Table 3.2. The product of these probabilities in the sixth column represents the chance of a particular sequence of demands in Weeks 1 and 2 (assuming independence of demands). In the final column, the probabilities are summed appropriately, for each potential value of total demand over two weeks. For example, the probability of having a total demand of two is the sum of 0.10, 0.09, and 0.10, giving a value of 0.29. Now that the probabilities of demand over two weeks have been calculated, we can find the cumulative probability distribution, which represents the probabilities of observing particular demand values, or less than those values, as shown in Table 3.4.
The cumulative distribution of total demand over the protection interval is often used as an approximation to the cycle service level in
3.5.3 Cycle Service Levels Based on Cycles with Demand
The CSL measure is appropriate for non‐intermittent demand but suffers from some drawbacks for intermittent demand. Cardós et al. (2006) gave the example of a product, without any stock at all, facing a demand once every 10 weeks. Even with no stock, there would be no stockouts in 90% of the weeks because there is no demand in 90% of the weeks. If the replenishment cycle is one week, then this would mean that the CSL is 90%. However, as the authors commented, with no stock, there is no service!
Examples such as this motivate the development of a revised method of calculating the cycle service level for intermittent demand items. Instead of looking at all replenishment cycles, we focus on those replenishment cycles that contain some demand. In this book, the revised cycle service level will be denoted as
1 The probability of demand over the review interval, conditional on this demand being strictly positive.
2 The (unconditional) probability of demand over the lead time.
These calculations are illustrated in Table 3.5.
The notation in Table 3.5 is the same as in Table 3.3. The probability in the fifth column is unconditional, and may be written as
In