Intermittent Demand Forecasting. John E. Boylan

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zero.

      This is a natural assumption for demand itself, although it is not appropriate for ‘net demand’, which is found by subtracting returns from demand (Kelle and Silver 1989). This is relevant in closed‐loop supply chains where items are returned for refurbishment or remanufacturing.

      3.5.2 Cycle Service Levels Based on All Cycles

      In Chapter 2, we indicated why the distribution of demand over the whole protection interval () is needed to determine OUT levels in periodic review systems. To recap, suppose that the stock on hand is at the OUT level just after a review and no order is triggered. In that case, the stock must last not just until the time of the next review (an interval of R time units), but until any stock is received after that review. This necessitates a further delay of L time units, to allow for the supplier's lead time. Care is needed in counting the length of the lead time. The use of an protection interval assumes that an order placed at the end of period arrives in time to satisfy demands of period . If it arrives in time to satisfy the demands of period , then the effective lead time is and, for review intervals of length one period, the protection interval is of length rather than (Teunter and Duncan 2009).

Suppose that the demand distribution in Table 3.2 accurately represents the probabilities of future demand values over a single week, and that demand is independent and identically distributed. We are using a periodic review system, with a review interval of one week and a lead time of one week. Therefore, the protection interval is two weeks, and the distribution of demand over two weeks is shown in Table 3.3.

Table 3.3 Probability distribution of total demand over two weeks.

Total	Week 1	Week 2	Week 1	Week 2	Product	Total
0	0	0	0.5	0.5	0.25	0.25
1	1	0	0.3	0.5	0.15
	0	1	0.5	0.3	0.15	0.30
2	2	0	0.2	0.5	0.10
	1	1	0.3	0.3	0.09
	0	2	0.5	0.2	0.10	0.29
3	2	1	0.2	0.3	0.06
	1	2	0.3	0.2	0.06	0.12
4	2	2	0.2	0.2	0.04	0.04

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, denotes demand over the review interval (Week 1), demand over the lead time (Week 2), and

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