GE Aircraft Engines uses 1200 units of a certain spare part that costs $2500 for each order with
an annual holding cost of $2400/unit. Calculate the total cost for order sizes of 25, 40, 60 and
100. Also compute the economic order quantity and the associated inventory cost.
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To calculate the total cost for each order size, we need to consider both the ordering cost and the holding (or inventory carrying) cost.
Let's start with the ordering cost:
Given that GE Aircraft Engines uses 1200 units of the spare part, and the cost per order is $2500, we can calculate the ordering cost as follows:
Ordering Cost = (Demand in units / Order quantity) * Cost per order
For an order size of 25:
Ordering Cost = (1200 / 25) * $2500
Ordering Cost = 48 * $2500
Ordering Cost = $120,000
Now, let's calculate the holding cost:
The annual holding cost per unit is given as $2400. So, we can calculate the holding cost based on the average inventory level, which is half the order quantity (assuming constant demand throughout the year):
Holding Cost = (Average inventory level) * (Holding cost per unit)
For an order size of 25:
Average inventory level = Order quantity / 2
Average inventory level = 25 / 2
Average inventory level = 12.5
Holding Cost = 12.5 * $2400
Holding Cost = $30,000
Total Cost for an order size of 25 = Ordering Cost + Holding Cost
Total Cost = $120,000 + $30,000
Total Cost = $150,000
Similarly, we can calculate the total cost for order sizes of 40, 60, and 100 using the same process.
For an order size of 40:
Ordering Cost = (1200 / 40) * $2500
Ordering Cost = 30 * $2500
Ordering Cost = $75,000
Average inventory level = 40 / 2
Average inventory level = 20
Holding Cost = 20 * $2400
Holding Cost = $48,000
Total Cost = $75,000 + $48,000
Total Cost = $123,000
For an order size of 60:
Ordering Cost = (1200 / 60) * $2500
Ordering Cost = 20 * $2500
Ordering Cost = $50,000
Average inventory level = 60 / 2
Average inventory level = 30
Holding Cost = 30 * $2400
Holding Cost = $72,000
Total Cost = $50,000 + $72,000
Total Cost = $122,000
For an order size of 100:
Ordering Cost = (1200 / 100) * $2500
Ordering Cost = 12 * $2500
Ordering Cost = $30,000
Average inventory level = 100 / 2
Average inventory level = 50
Holding Cost = 50 * $2400
Holding Cost = $120,000
Total Cost = $30,000 + $120,000
Total Cost = $150,000
Now, let's calculate the economic order quantity (EOQ) and the associated inventory cost. The EOQ can be calculated using the following formula:
EOQ = √((2 * Demand * Ordering Cost) / Holding Cost)
For our given data:
Demand = 1200
Ordering Cost = $2500
Holding Cost = $2400
EOQ = √((2 * 1200 * $2500) / $2400)
EOQ = √((2 * 1200 * $2500) / $2400)
EOQ ≈ 70
To find the associated inventory cost, we can calculate the total cost for the EOQ:
Ordering Cost for EOQ = (1200 / 70) * $2500
Ordering Cost for EOQ ≈ 17.14 * $2500
Ordering Cost for EOQ ≈ $42,857
Average inventory level for EOQ = EOQ / 2
Average inventory level for EOQ ≈ 70 / 2
Average inventory level for EOQ ≈ 35
Holding Cost for EOQ = 35 * $2400
Holding Cost for EOQ ≈ $84,000
Total Cost for EOQ = Ordering Cost for EOQ + Holding Cost for EOQ
Total Cost for EOQ = $42,857 + $84,000
Total Cost for EOQ ≈ $126,857
Therefore, the EOQ for this spare part is approximately 70 units with an associated inventory cost of approximately $126,857.