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## Q. 12.EX.3

FINDING THE OPTIMAL ORDER SIZE AT SHARP, INC.. Sharp, Inc., a company that markets painless hypodermic needles to hospitals, would like to reduce its inventory cost by determining the optimal number of hypodermic needles to obtain per order.
APPROACH $\blacktriangleright$ The annual demand is 1,000 units; the setup or ordering cost is $10 per order; and the holding cost per unit per year is$.50.

## Verified Solution

SOLUTION $\blacktriangleright$ Using these figures, we can calculate the optimal number of units per order:

$Q^* = \sqrt{\frac{2DS}{H}}$

$Q^* = \sqrt{\frac{2(1,000)(10)}{0.50}} = \sqrt{40,000} =$ 200 units

INSIGHT $\blacktriangleright$ Sharp, Inc., now knows how many needles to order per order. The firm also has a basis for determining ordering and holding costs for this item, as well as the number of orders to be processed by the receiving and inventory departments.

LEARNING EXERCISE $\blacktriangleright$ If D increases to 1,200 units, what is the new $Q^*$? [Answer: $Q^*$ = 219 units.]

RELATED PROBLEMS $\blacktriangleright$ 12.7, 12.8, 12.9, 12.10, 12.11, 12.14, 12.15, 12.17, 12.29 (12.31, 12.32, 12.33a, 12.35a are available in MyOMLab)
EXCEL OM Data File Ch12Ex3.xls can be found in MyOMLab.
ACTIVE MODEL 12.1 This example is further illustrated in Active Model 12.1 in MyOMLab.