In: Operations Management
Cesar Rego Computers, a Mississippi chain of computer hardware and software retail outlets, supplies both educational and commercial customers with memory and storage devices. It currently faces the following ordering decision relating to purchases ofdisks:
D |
37,000 disks |
S |
$23 |
I |
23% |
Purchase price |
$0.88 |
Discount price |
$0.82 |
Quantity needed to qualify for the discount = 5,900 disks.
What is the EOQ?
EOQ = ___ units (round your response to the nearest wholenumber).
Since the total cost with discounted volume is (greater than or equal to/ less than?) the total cost at the EOQ volume, Cesar Rogo should (take or not take)
the discount, provided other factors such as storage space, etc. permits.
DEMAND = 37000
ORDERING COST = 23
HOLDING COST = 0.2024
COST PER UNIT = 0.88
EOQ = SQRT(2 * ANNUAL DEMAND * ORDERING COST / HOLDING COST PER UNIT) = SQRT(2 * 37000 * 23 / 0.2024) = 2900
ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST PER UNIT = (2900 / 2) * 0.2024 = 293.48
ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST = (37000 / 2900) * 23 = 293.45
ANNUAL MATERIAL COST = ANNUAL DEMAND * PRICE PER UNIT = 37000 * 0.88 = 32560
TOTAL COST OF INVENTORY = ANNUAL HOLDING COST + ANNUAL ORDERING COST + ANNUAL MATERIAL COST = 293.48 + 293.45 + 32560 = 33146.93
USING 5900 UNITS AS ORDERING QUANTITY
ANNUAL HOLDING COST = (5900 / 2) * 0.1886 = 556.37
ANNUAL ORDERING COST = (37000 / 5900) * 23 = 144.24
TOTAL COST OF PURCHASING = 37000 * 0.82 = 30340
ANNUAL TOTAL COST = ANNUAL HOLDING COST + ANNUAL ORDERING COST +
ANNUAL COST OF MATERIAL = 556.37 + 144.24 + 30340 = 31040.61
OPTIMAL ORDER QUANTITY = 5900 UNITS
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