Question

The office manager for the Metro Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6500 boxes per year. Annual carrying costs are $3 per box, and ordering costs are $28. The following discount price schedule is provided by the office supply company: ORDER QUANTITY (BOXES) PRICE PER BOX  200–999  $16 1000–2999  14 3000–5999  13 6000+      12 Determine the optimal order quantity and the total annual inventory cost. 13.32 Determine the optimal order quantity and total annual inventory cost for boxes of stationery in Problem 13.31 if the carrying cost is 20% of the price of a box of stationery.

Answer 1

1. DEMAND = 6500

HOLDING COST = 3

ORDERING COST = 28

EOQ = SQRT(2DS/H)

EOQ = SQRT( 2 * 6500 * 28 / 3) = 348

TCI = annual holding cost + annual ordering cost + annual material cost

Annual holding = adjusted quantity / 2 * holding cost

Annual ordering = demand / adjusted quantity * ordering cost

Annual material cost = demand * cost per unit

ADJUSTED Q = EOQ IF EOQ > LOWER LIMIT, < UPPER LIMIT

LOWER LIMIT IF EOQ < LOWER LIMIT

UPPER LIMIT IF EOQ > UPPER LIMIT

NO.	LOWER BRACKET	UPPER BRACKET	PER UNIT	HC	EOQ	Q*	TOTAL COST	FORMULA
1	200	999	16	3	348	348	105044.99	(6500 * 16) + ((348 / 2) * 3) + ((6500 / 348) * 28) = 105045
2	1000	2999	14	3	348	1000	92682	(6500 * 14) + ((1000 / 2) * 3) + ((6500 / 1000) * 28) = 92682
3	3000	5999	13	3	348	3000	89060.67	(6500 * 13) + ((3000 / 2) * 3) + ((6500 / 3000) * 28) = 89061
4	6000	MORE	12	3	348	6000	87030.33	(6500 * 12) + ((6000 / 2) * 3) + ((6500 / 6000) * 28) = 87030

OPTIMAL ORDER QUANTITY = 6000

TOTAL COST OF INVENTORY = 87030

2. If holding cost = 20%

NO.	LOWER BRACKET	UPPER BRACKET	PER UNIT	HC	EOQ	Q*	TOTAL COST	FORMULA
1	200	999	16	3.2	337	337	105079.26	(6500 * 16) + ((337 / 2) * 3.2) + ((6500 / 337) * 28) = 105079
2	1000	2999	14	2.8	361	1000	92582	(6500 * 14) + ((1000 / 2) * 2.8) + ((6500 / 1000) * 28) = 92582
3	3000	5999	13	2.6	374	3000	88460.67	(6500 * 13) + ((3000 / 2) * 2.6) + ((6500 / 3000) * 28) = 88461
4	6000	MORE	12	2.4	389	6000	85230.33	(6500 * 12) + ((6000 / 2) * 2.4) + ((6500 / 6000) * 28) = 85230

OPTIMAL ORDER QUANTITY = 6000

TOTAL COST OF INVENTORY = 85230