DB pie operates a conventional stock control system based on re-order levels and economic order quantities. The various control levels were set originally based on estimates which did not allow for any uncertainty and this has caused difficulties because, in practice, lead times, demands and other factors do vary.

As part of a review of the system, a typical stock item, part No. X206, has been studied in detail as follows:

Note: It can be assumed that the demands would apply for the whole of the appropriate lead time.
DB pie works for 240 days per year and it costs Re 0.15 p.a. to carry a unit of X 206 in stock. The re-order level for this part is currently 150,000 units and the re-order cost is Rs 1,000.
You are required to

(a) calculate the level of buffer stock implicit in a re-order level of 150,000 units;

(b) calculate the probability of a stockout;

(c) calculate the expected annual stockouts in units;

(d) calculate the stockout cost per unit at which it would be worthwhile raising the re-order level to 175,000 units.

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Data for part No. X206 Lead Times 15 working days 20 working days Probability 0.2 0.5 25 working days Demand per working day 5,000 units 7,000 units 0.3 Probability 0.5 0.5