Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother's hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year.

a. How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost?

b. How many orders per year would be placed? What would the annual ordering cost be?

c. What would the average inventory be? What would the annual holding cost be?

a) Order size = 20,000 units

b) No of orders = 5.

Annual ordering cost = $50

c) Average inventory = 10,000 units

Annual holding cost = $50

Explanation:

To minimize total inventory cost, the company would have to place order equal to the Economic Order Quantity (EOQ)

EOQ = √2 * Co * D/Ch

EOQ - economic order quantity, Co - ordering cost per order, Ch - carrying cost per unit per year, D - Annual demand

EOQ = √ (2 * 10 * 100,000) / 0.005 = 20,000 units

No of orders to place = Annual demand/EOQ

= 100,000 / 20,000

= 5 orders

Annual ordering cost = 5 * $10 = $50

Average inventory = Minimum stock + order quantity/2

= 20,000/2 = 10,000 units

Annual holding cost = average inventory * holding cost per unit

= 10,000 * 0.005 = $50

Order size = 20,000 units

No of orders = 5.

Annual ordering cost = $50

Average inventory = 10,000 units

Annual holding cost = $50