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

The annual demand is $1,000$ units; the setup or ordering cost is $$10$ per order; and the holding cost per unit per year is $$0\mathrm{.}50.$

Solution

Using these figures, we can calculate the optimal number of units per order:

$$

$*$

$=$

$2$

$$

$$

$$

$$

$*$

$=$

$2$

$($

$1,000$

$)$

$($

$10$

$)$

$0\mathrm{.}50$

$=$

$40,000$

$=$

$200$

units

Insight

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

If D increases to $1,200$ units, what is the new

$$

$*$

$?[$Answer:

$$

$*$

$=$

$219$

units $($approximately$).]$