Question

2 ) Warren W. Fisher Computer Corporation purchase 8000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per year. Fisher operates his business 200 days per year and finds that deliveries from his supplier generally take 5 working days.

1. What is the optimal order quantity?

2. What is the expected number of orders placed each year?

3. What is the expected time between orders?

4. What is the total annual inventory cost?

Answer 1

Warren W. Fisher Computer Corporation purchase 8000 transistors each year as components in minicomputers. The unit cost of each transistor is $10, and the cost of carrying one transistor in inventory for a year is $3. Ordering cost is $30 per year. Fisher operates his business 200 days per year and finds that deliveries from his supplier generally take 5 working days.

Number of transistors purchased, D = 8000

Unit cost of each transistor, C = $10

Carrying cost, H = $3

Ordering cost, S = $30

1. What is the optimal order quantity?

Optimal order quantity, Q* = sqrt ( 2DS / H )

Q* = sqrt ( 2 * 8000 * 30 / 3 ) = sqrt ( 160000 )

Q* = 400 units

Optimal order quantity = 400 units

2. What is the expected number of orders placed each year?

Expected number of orders, N = D / Q*

N = 8000 / 400 = 20 units

Expected number of orders placed = 20 units

3. What is the expected time between orders?

Expected time between orders, T = working days per year / N

Fisher operates his business 200 days per year

T = 200 / 20 = 10 days

Expected time between orders = 10 days

4. What is the total annual inventory cost?

Total annual inventory cost, TC = DC + DS / Q* + HQ* / 2

DC : Annual purchase cost

DC = 8000 * 10 = $80000

DS / Q* : Annual ordering cost

DS / Q* = 8000 * 30 / 400 = $600

HQ* / 2 : Annual Holding Cost

HQ* / 2 = 3 * 400 / 2 = $600

Total annual inventory cost, TC = 80000 + 600 + 600 = $81200

Total annual inventory cost = $81200