Question

Economic order quantity (EOQ).

​ Tinnendo, Inc. believes it will sell 4 million​ zen-zens, an electronic​ game, this coming year. Note that this figure is for annual sales. The inventory manager plans to order​ zen-zens 50 times over the next year. The carrying cost is ​$0.04 per​ zen-zen per year. The order cost is $513 per order. What are the annual carrying​ cost, the annual ordering​ cost, and the optimal order quantity for the​ zen-zens? Verify your answer by calculating the new total inventory cost.

What is the annual carrying cost for the​ zen-zens?

​( ) $  (Round to the nearest​ dollar.)

Answer 1

If the inventory manager orders 50 inventory times over the next year, the following would be his costs:

Annual Ordering Costs = 513 * 50 = $25,650 (513 per order for 50 orders)

Annual Holding Cost = (4,000,000/50) * (1/2) * 0.04 = $1,600

Since 50 orders will be placed, the quantity ordered per order would be 80,000 units (4,000,000/50)

This means, that the average inventory in stock through the year would be 80,000/2 = 40,000 units

Carrying cost per zen zen per year is 0.04. Thus total carrying cost is $1,600

The total cost of inventory here is = 25,650 + 1,600 = $27,250

Calculating the Economic Order Quantity

Formula is as follows:

Q = (2AO/C)^1/2

Q = Economic Order Quantity

A = Annual Demand

O = Ordering Cost per order

C = Carrying cost per unit per annum

Q = (2*4,000,000*513/0.04)^1/2

=320,312.35 units.

Optimal ordering quantity per order would be 320,312.35 units.

This means number of orders would be 4,000,000/320,312.25 = 12.49 orders.

Here, the ordering costs = 12.49 * 513 = $6,407

Carrying Costs = (320,312.35) * (1/2) * 0.04 = $6,406

Total inventory costs = $12,813

Thus, we can see how adopting EOQ would reduce the annual costs by $14,437 (27750 - 12813)