You are in charge of inventory control of a highly successfulproduct retailed by your firm. Weekly demand for this itemvaries, with an average of 200 units and a standard devia-tion of 16 units. It is purchased from a wholesaler at a cost of$12.50 per unit. You are using a continuous review system tocontrol this inventory. The supply lead time is 4 weeks. Plac-ing an order costs $50, and the inventory carrying rate peryear is 20 percent of the item’s cost. Your firm operates 5 daysper week, 50 weeks per year.a. What is the optimal ordering quantity for this item?b. How many units of the item should be maintained assafety stock for 99 percent protection against stockoutsduring an order cycle?c. If supply lead time can be reduced to 2 weeks, what is thepercent reduction in the number of units maintained assafety stock for the same 99 percent stockout protection?d. If through appropriate sales promotions, the demand variabil-ity is reduced so that the standard deviation of weekly demandis 8 units instead of 16, what is the percent reduction (com-pared to that in part [b]) in the number of units maintained assafety stock for the same 99 percent stockout protection?
You are in charge of inventory control of a highly successful
product retailed by your firm. Weekly demand for this item
varies, with an average of 200 units and a standard devia-
tion of 16 units. It is purchased from a wholesaler at a cost of
$12.50 per unit. You are using a continuous review system to
control this inventory. The supply lead time is 4 weeks. Plac-
ing an order costs $50, and the inventory carrying rate per
year is 20 percent of the item’s cost. Your firm operates 5 days
per week, 50 weeks per year.
a. What is the optimal ordering quantity for this item?
b. How many units of the item should be maintained as
safety stock for 99 percent protection against stockouts
during an order cycle?
c. If supply lead time can be reduced to 2 weeks, what is the
percent reduction in the number of units maintained as
safety stock for the same 99 percent stockout protection?
d. If through appropriate sales promotions, the demand variabil-
ity is reduced so that the standard deviation of weekly demand
is 8 units instead of 16, what is the percent reduction (com-
pared to that in part [b]) in the number of units maintained as
safety stock for the same 99 percent stockout protection?
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