Question

Suppose that the annual demand for a component is approximately 60,000 units. The company orders the component from a supplier who has offered the following quantity discount schedule.

Order Quantity	Price per Unit
0–999	$30
1,000–1,999	$29
2,000–3,999	$28
4,000 or more	$27

If the company’s carrying charge is 15 percent of the item’s price and the cost per order is $150, determine the order quantity that would minimize the total related inventory costs for this component.

Answer 1

DEMAND = 60000

ORDERING COST = 150

HOLDING COST = 15%

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

Q* = ADJUSTED QUANTITY BETWEEN THE UPPER AND LOWER LIMIT AND THE EOQ

AHC = ANNUAL HOLDING COST = (Q* / 2) * HOLDING COST PER UNIT

AOC = ANNUAL ORDERING COST = (DEMAND / Q*) * ORDERING COST

APC = ANNUAL PURCHASING COST = DEMAND * Q*

TCI = TOTAL COST OF INVENTORY =

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT	HOLDING COST	EOQ	Q*	AHC	AOC	APC	TCI
1	1	999	30	4.5	2000	999	(999 / 2) * 4.5 = 2247.75	(60000 / 999) * 150 = 9009.01	60000 * 30 = 1800000	2247.75 + 9009.01 + 1800000 = 1811256.76
2	1000	1999	29	4.35	2034	1999	(1999 / 2) * 4.35 = 4347.83	(60000 / 1999) * 150 = 4502.25	60000 * 29 = 1740000	4347.83 + 4502.25 + 1740000 = 1748850.08
3	2000	3999	28	4.2	2070	2070	(2070 / 2) * 4.2 = 4347	(60000 / 2070) * 150 = 4347.83	60000 * 28 = 1680000	4347 + 4347.83 + 1680000 = 1688694.83
4	4000	OR MORE	27	4.05	2108	4000	(4000 / 2) * 4.05 = 8100	(60000 / 4000) * 150 = 2250	60000 * 27 = 1620000	8100 + 2250 + 1620000 = 1630350

OPTIMAL ORDER QUANTITY = 4000

TOTAL COST OF INVENTORY = 1630350