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Part Three
Planning and control
Table 12.2 Matrix of lead-time and demand-rate probabilities
Lead-time probabilities
1 2 3 4 5
0.1 0.2 0.4 0.2 0.1
110 0.2 110 220 330 440 550
(0.02) (0.04) (0.08) (0.04) (0.02)
Demand-rate probabilities
120 0.3 120 240 360 480 600
(0.03) (0.06) (0.12) (0.06) (0.03)
130 0.3 130 260 390 520 650
(0.03) (0.06) (0.12) (0.06) (0.03)
140 0.2 140 280 420 560 700
(0.02) (0.04) (0.08) (0.04) (0.02)
We can now classify the possible lead-time usages into histogram form. For example,
summing the probabilities of all the lead-time usages which fall within the range 100–199
(all the first column) gives a combined probability of 0.1. Repeating this for subsequent
intervals results in Table 12.3.
Table 12.3 Combined probabilities
Lead-time usage 100–199 200–299 300–399 400–499 500–599 600–699 700–799
Probability 0.1 0.2 0.32 0.18 0.12 0.06 0.02
This shows the probability of each possible range of lead-time usage occurring, but
it is the cumulative probabilities that are needed to predict the likelihood of stock-out
(see Table 12.4).
Table 12.4 Combined probabilities
Lead-time usage X 100 200 300 400 500 600 700 800
Probability of usage
being greater than X 1.0 0.9 0.7 0.38 0.2 0.08 0.02 0
Setting the re-order level at 600 would mean that there is only a 0.08 chance of usage
being greater than available inventory during the lead time, i.e. there is a less than 10 per
cent chance of a stock-out occurring.
Continuous review
Periodic review
Continuous and periodic review
The approach we have described to making the replenishment timing decision is often called
the continuous review approach. This is because, to make the decision in this way, there
must be a process to review the stock level of each item continuously and then place an order
when the stock level reaches its re-order level. The virtue of this approach is that, although
the timing of orders may be irregular (depending on the variation in demand rate), the order
size (Q) is constant and can be set at the optimum economic order quantity. Such continual
checking on inventory levels can be time-consuming, especially when there are many stock
withdrawals compared with the average level of stock, but in an environment where all
inventory records are computerized, this should not be a problem unless the records are
inaccurate.
An alternative and far simpler approach, but one which sacrifices the use of a fixed (and
therefore possibly optimum) order quantity, is called the periodic review approach. Here,
rather than ordering at a predetermined re-order level, the periodic approach orders at a