Question

Our college purchases sweatshirts from a vendor emblazoned with the college name and logo. The vendor sells the sweatshirts to the college for 45 SAR a piece. The cost to the college for placing an order is 175 SAR and the carrying cost is 20% of the average annual inventory value. The college administration estimates that 2,000 sweatshirts will be sold during the year. The vendor has offered the college the following volume discount schedule: Quantity Discount (%) 1 – 299 0% 300 – 499 5% 500 – 799 8% 800+ 12% [5 Marks] The college admin staff wants to determine the optimal order quantity, given the foregoing quantity discount information.

Answer 1

DEMAND = 2000

ORDERING COST = 175

HOLDING COST % = 20 %

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

ANNUAL HOLDING COST = ADJUSTED EOQ / 2 * HOLDING COST PER UNIT

ANNUAL ORDERING COST = (ANNUAL DEMAND / ADJUSTED EOQ) * ORDERING COST

ANNUAL MATERIAL COST = ANNUAL DEMAND * OFFERED PRICE PER UNIT

TOTAL COST OF INVENTORY = ANNUAL(HOLDING + ORDERING + MATERIAL)

OPTIMAL ORDER QUANTITY = 800

ASSOCIATED COST = 82806

NO.	LOWER LIMIT	UPPER LIMIT	PER UNIT PRICE	ADJUSTED HOLDING COST	EOQ	ADJUSTED QUANTITY	ANNUAL HOLDING COST	ANNUAL ORDER COST	ANNUAL MATERIAL COST	TOTAL COST OF INVENTORY
1	0	299	45	9	279	279	279 / 2 = 1255.5	2000 / 279 * 175 = 1254.48	2000 * 45 = 90000	1255.5 + 1254.48 + 90000 = 92510
2	300	499	42.75	8.55	286	300	300 / 2 = 1282.5	2000 / 300 * 175 = 1166.67	2000 * 42.75 = 85500	1282.5 + 1166.67 + 85500 = 87949
3	500	799	41.4	8.28	291	500	500 / 2 = 2070	2000 / 500 * 175 = 700	2000 * 41.4 = 82800	2070 + 700 + 82800 = 85570
4	800	& more	39.6	7.92	297	800	800 / 2 = 3168	2000 / 800 * 175 = 437.5	2000 * 39.6 = 79200	3168 + 437.5 + 79200 = 82806

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