Question

Wohl's Discount Stores stocks toy race cars. Recently, the store has been given quantity discount schedules for these cars. This quantity schedule is shown in the table below. Thus, the normal cost for toy race car is $5.00 for orders between zero and 999 units. The unit cost drops to $4.80 for orders between 1,000 to 1,999, and the unit cost is only $4.75 for orders that are as large as 2,000 and more. Further, ordering cost is $49.00 per order, annual demand is 5,000 race cars, and inventory carrying cost rate, i, as a percentage of cost, is 20% or 0.20. Discount number Discount quantity Discount price 0 to 999 1,000 to 1,999 2,000 and over $5.00 $4.80 $4.75 a. What order quantity will minimize the total annual inventory cost? b. What is the minimum total annual inventory cost?

Answer 1

DEMAND = 5000

ORDERING COST = 49

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 = 1000

ASSOCIATED COST = 24725

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	999	5	1	700	700	(700 / 2) * 1 = 350	5000 / 700 * 49 = 350	5000 * 5 = 25000	350 + 350 + 25000 = 25700
2	1000	1999	4.8	0.96	714	1000	(1000 / 2) * 0.96 = 480	5000 / 1000 * 49 = 245	5000 * 4.8 = 24000	480 + 245 + 24000 = 24725
3	2000	& MORE	4.75	0.95	718	2000	(2000 / 2) * 0.95 = 950	5000 / 2000 * 49 = 122.5	5000 * 4.75 = 23750	950 + 122.5 + 23750 = 24823

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