Company X stocks a certain type of containers, each of which occupies 4 square feet of warehouse
space. The warehouse space currently available for storing this type of container is limited
to 3000 square feet. Demand for the container is 12,000 units per year. The fixed ordering
cost is $30 per order and the holding cost per unit is $2 per year.
(a) What is the optimal order size that minimizes the total ordering cost and holding cost? Canwe accommodate the calculated optimal order quantity in our warehouse?
(b) Now suppose that some storage space has to be used for other purposes,leaving only 2000
square feet available for storing this type of container. The holding cost per unit remains
$2 per year. What is the optimal order size in this case? Explain why (no more than two
sentences).
To find the optimal order size that minimizes the total ordering cost and holding cost, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula calculates the order quantity that minimizes the total cost by balancing the cost of ordering and the cost of holding inventory.
(a) The EOQ formula is given by:
EOQ = sqrt(2DS/H)
Where:
D = demand per year
S = ordering cost per order
H = holding cost per unit per year
Plugging in the given values:
D = 12,000 units/year
S = $30/order
H = $2/year
EOQ = sqrt(2 * 12,000 * 30 / 2) = sqrt(12,000 * 30) ≈ 207
Therefore, the optimal order size that minimizes the total cost is approximately 207 units.
To check if we can accommodate the calculated optimal order quantity in our warehouse, we need to calculate the total space required by the order:
Total space required = EOQ * space occupied per unit
Plugging in the values:
EOQ = 207 units
Space occupied per unit = 4 square feet
Total space required = 207 * 4 = 828 square feet.
Since the total space required is 828 square feet and the available warehouse space is only 3000 square feet, we can accommodate the calculated optimal order quantity in our warehouse.
(b) If the available warehouse space is reduced to 2000 square feet, the calculation for the optimal order size remains the same using the EOQ formula. The only change is that we need to consider the reduced warehouse space in the calculation of the maximum order quantity.
Using the same values as before, the total space required is 207 * 4 = 828 square feet, which exceeds the available warehouse space of 2000 square feet.
Therefore, in this case, it is not possible to accommodate the calculated optimal order quantity in the reduced warehouse space of 2000 square feet.