Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 5,800 units per year. The cost of each unit is $98, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $30 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 116 units. (This is a corporate operation, and the are 250 working days per year.)

A) What is the EOQ?
B) What is the average inventory if the EOQ is used?
C) What is the optimal number of orders per year?
D) What is the optimal number of days in between any two orders?
E) What is the annual cost of ordering and holding inventory?
F) What is the total annual inventory cost, including cost of the 5,800 units?

Answer 1

DEMAND = 5800
ORDERING COST = 30
HOLDING COST = 8
COST PER UNIT = 98
LEAD TIME = 5
WORKING = 250

1. EOQ = SQRT(2 * ANNUAL DEMAND * ORDERING COST / HOLDING COST PER UNIT) = SQRT(2 * 5800 * 30 / 8) = 209

2. AVERAGE INVENTORY = EOQ / 2 = 209 / 2 = 104.5

3. ORDER FREQUENCY = DEMAND / EQQ = 5800 / 209 = 27.75

4. CYCLE TIME = EOQ / (ANNUAL DEMAND / WORKING) = 209 / (5800 / 250) = 9.01

5. ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST PER UNIT = (209 / 2) * 8 = 836

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (5800 / 209) * 30 = 832.54

TOTAL COST OF MANAGING INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST = 836 + 832.54 = 1668.54

6. ANNUAL MATERIAL COST = ANNUAL DEMAND * PRICE PER UNIT = 5800 * 98 = 568400

TOTAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL MATERIAL COST = 836 + 832.54 + 568400 = 570068.54

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