Question

For product A, a firm has an annual holding cost that is 20% of the item price, an ordering cost of $120 per order, and annual demand of 15,000 units. The product’s discount schedule is given in the following table.

Order Size	Price Per Unit
1 – 250	$30.00
251 – 500	$28.00
501 – 799	$26.00
800 or more	$25.00

-Determine the most cost-effective ordering quantity
-What is the total cost for the order quantity determined in 1).

-Describe inventory policy

Answer 1

Economic order quantity is the quantity at which ordering cost and holding cost are same.

Ordering cost is $120 for each order which is same irrespective of ordering quantity.

Holding cost is 20% of unit cost which is depending upon quantity ordered.

For 1 - 250 = 20% of $30 = $6

For 251 - 500 = 20% of $28 = $5.6

For 501 - 799 = 20% of $26 = $5.2

For 800 and above = 20% of $25 = $5

Cost effective ordering quantity or EOQ formula

= square root of 2 * annual demand * order cost

divided by holding cost per unit

= Square root of [( 2 * 15,000 * 120) / 6]

= Square root of 6,00,000

= 775 units

This is not within the ordering size for respective batch. Batch is within 1 - 250 units. The EOQ quantity is 775 units. Hence not justified.

Similarly for each batch it is to be calculated.

For 251 - 500 = EOQ = 787 units

For 500 - 799 = EOQ = 832 units

For 800 above = EOQ = 848 units

Of all the above only in batch of 800 and more the size batch matches with the answer. Hence correct batch size is 800 and above. And EOQ is 848 units.

For EOQ, cost are as follows -

Total cost = holding cost + ordering cost

Holding cost = 20% of $25 = $5 per unit

Average quantity = 848 units / 2 = 824 units

Holding cost = 424 * 5 = $2,120

Ordering cost = 15,000 / 848 = 18 orders

= 18 * 120 = $ 2,160

The above difference is because of rounding off. The ordering and holding cost are same. Hence total cost = 2,160 * 2 = $4,320

Inventory policy =

Inventory policy should be such the cost occurred are least. The inventory policy by the company is correct of it follows EOQ.

The cost will be less also inventory will be adequate. Inventory should be ordered time to time to avoid rush in hour of need.