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PERIODIC REVIEW MODEL WITH PROBABILISTIC DEMAND 447

a. Lead time is one week and the lead-time demand is normally distributed with a mean of
150 units and a standard deviation of 40 units. What is the reorder point if the pharmacy is
willing to tolerate a 1 per cent chance of stock-out on any one cycle?
b. What safety stock and annual safety stock costs are associated with your
recommendation in part (a)?
c. The order-quantity, reorder point model requires a continuous review system.
Management is considering making a transition to a periodic review system in an
attempt to coordinate ordering for many of its products. The demand during the
proposed two-week review period and the one-week lead-time period is normally
distributed with a mean of 450 units and a standard deviation of 70 units. What is the
recommended replenishment level for this periodic review system if the pharmacy is
willing to tolerate the same 1 per cent chance of stock-out associated with any
replenishment decision?
d. What safety stock and annual safety stock costs are associated with your
recommendation in part (c)?
e. Compare your answers to parts (b) and (d). The pharmacy is seriously considering the
periodic review system. Would you support this decision? Explain.
f. Would you tend to favour the continuous review system for more expensive items? For
example, assume that the drug in the preceding example cost E295 per unit. Explain.

CASE PROBLEM 1 Wagner Fabricating Company

anagers at Wagner Fabricating Company in A one-week lead time is required to obtain the
M Germany are reviewing the economic feasibil- part from the supplier. An analysis of demand during
ity of manufacturing a part that it currently purchases the lead time shows it is approximately normally
from a supplier. Forecasted annual demand for the distributed with a mean of 64 units and a standard
part is 3200 units. Wagner operates 250 days per deviation of ten units. Service level guidelines indi-
year. cate that one stock-out per year is acceptable.
Wagner’s financial analysts established a cost Currently, the company has a contract to pur-
of capital of 14 per cent for the use of funds for chase the part from a supplier at a cost of E18 per
investments within the company. In addition, over unit. However, over the past few months, the com-
the past year E600 000 was the average invest- pany’s production capacity has been expanded. As
ment in the company’s inventory. Accounting a result, excess capacity is now available in certain
information shows that a total of E24 000 was production departments, and the company is
spent on taxes and insurance related to the com- considering the alternative of producing the parts
pany’s inventory. In addition, an estimated E9000 itself.
was lost due to inventory shrinkage, which Forecasted utilization of equipment shows that
included damaged goodsaswellaspilferage. A production capacity will be available for the part
remaining E15 000 was spent on warehouse being considered. The production capacity is avail-
overhead, including utility expenses for heating able at the rate of 1000 units per month, with up
and lighting. to five months of production time available. Man-
An analysis of the purchasing operation shows agement believes that with a two-week lead time,
that approximately two hours are required to proc- schedules can be arranged so that the part can be
ess and coordinate an order for the part regard- produced whenever needed. The demand during
less of the quantity ordered. Purchasing salaries the two-week lead time is approximately normally
average E28 per hour, including employee bene- distributed, with a mean of 128 units and a stand-
fits. In addition, a detailed analysis of 125 orders ard deviation of 20 units. Production costs are
showed that E2375 was spent on telephone, expected to be E17 per part.
paper and postage directly related to the ordering A concern of management is that setup costs will
process. be significant. The total cost of labour and lost

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