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PERIODIC REVIEW MODEL WITH PROBABILISTIC DEMAND 439
Figure 10.14 Probability Distribution of Demand During the Review Period and Lead
Time for the Dollar Discounts Problem
Mean = 250
Standard Deviation = 45
115 160 205 250 295 340 385
Demand
In the periodic review model, the order quantity at each review period must
be sufficient to cover demand for the review period plus the demand for the
following lead time. That is, the order quantity that brings the inventory position
up to the replenishment level M must last until the order made at the next
review period is received in inventory. The length of this time is equal to the
review period plus the lead time. Figure 10.14 shows the normal probability
distribution of demand during the review period plus the lead-time period for
one of the Dollar Discounts products. The mean demand is 250 units, and the
standard deviation of demand is 45 units. Given this situation, the logic used to
establish M is similar to the logic used to establish the reorder point in Section
10.7. Figure 10.15 shows the replenishment level M with a 1 per cent chance that
demand will exceed that replenishment level. In other words, Figure 10.15 shows
the replenishment level that allows a 1 per cent chance of a stock-out associated
with the replenishment decision. Using the normal probability distribution table
in Appendix A, we see that a value of M that is 2.33 standard deviations above
the mean will allow stock-outs with a 1 per cent probability. Therefore, for the
assumed normal probability distribution with ¼ 250 and s ¼ 45, the replenish-
ment level is determined by:
EXCEL file
M ¼ 250 þ 2:33ð45Þ¼ 355
PERIODIC
Figure 10.15 Replenishment Level M that Allows a 1 per cent Chance of a Stock-Out
for the Dollar Discounts Problem
No Stock-Out Stock-Out
(demand M ) (demand > M )
99% 1%
M
115 160 205 250 295 340 385
Demand
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