Question

A large law firm uses an average of 80 boxes of copier paper a day. The firm operates 300 days a year. Storage and handling costs for the paper are $2 a year per box, and it costs approximately $12 to order and receive a shipment of paper.

1. What order size would minimize the sum of annual ordering and carrying costs?

2. Compute the total annual cost using your order size from the previous part.

3. Except for rounding, are annual ordering and carrying costs always equal at the EOQ?

4. The administrative director is currently ordering batches of 200 packages. The partners of
the company expects the office to be managed effectively. Do you believe that the
director should use the optimal order size rather than batches of 200 packages?
Justify your answer.

Answer 1

ANNUAL DEMAND = 24000
ORDERING COST = 12
HOLDING COST = 2

1. EOQ = SQRT(2 * ANNUAL DEMAND * ORDERING COST / HOLDING COST PER UNIT) = SQRT(2 * 24000 * 12 / 2) = 537

2. ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST PER UNIT = (537 / 2) * 2 = 537

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (24000 / 537) * 12 = 536.31

TOTAL COST OF MANAGING INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST = 537 + 536.31 = 1073.31

3. NO, THEY ARE NOT ALWAYS EQUAL, HOWEVER, THEY ARE ALWAYS CLOSE TO EACH OTHER.

4. FOR VALUE OF 200 UNITS:
ANNUAL HOLDING COST = (ORDER QUANTITY / 2) * HOLDING COST = (200 / 2) * 2 = 200
ANNUAL ORDERING COST = (ANNUAL DEMAND / QUANTITY) * ORDERING COST = (24000 / 200) * 12 = 1440
TOTAL COST OF MANAGING = 200 + 1440 = 1640
SAVINGS = 1640 - 1073.31 = 566.69

YES, ORDERING THE EOQ IS BETTER BECAUSE OF THE LOWER MANAGING COST

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