Question

13-11) Ray’s Satellite Emporium wishes to determine the optimal order size for its best-selling satellite dish (Model TS111). Ray has estimated the monthly demand for this model to be 404 units. This model costs Ray $347 to purchase from his supplier. His annual cost to carry inventory is 20% and he estimates that orders cost $42 to process.

a) What is the optimal order quantity?

b) On average, how many satellite dishes are in inventory?

c) What is the annual cost of placing orders for these satellite dishes?

d) What is the total annual cost of holding and ordering these satellite dishes?

e) If Ray used an order quantity of 2000 instead of the optimal order quantity, how much money would he be wasting each year?

Answer 1

Answer a.

Monthly demand = 404 units

Annual demand = 404 * 12
Annual demand = 4,848 units

Cost per unit = $347

Carrying cost per unit = 20% * Cost per unit
Carrying cost per unit = 20% * $347
Carrying cost per unit = $69.40

Ordering cost per order = $42

Economic order quantity = [2 * Annual demand * Ordering cost per order / Carrying cost per unit]^(1/2)
Economic order quantity = [2 * 4,848 * $42 / $69.40]^(1/2)
Economic order quantity = 76.60 or 77 units

Optimal order quantity is 77 units

Answer b.

Average inventory = EOQ / 2
Average inventory = 77 / 2
Average inventory = 38.50 or 39

Answer c.

Number of orders = Annual demand / EOQ
Number of orders = 4,848 / 77
Number of orders = 62.96 or 63

Annual ordering cost = Number of orders * Ordering cost per order
Annual ordering cost = 63 * $42
Annual ordering cost = $2,646

Answer d.

Annual holding cost = Average inventory * Carrying cost per stone
Annual holding cost = 39 * $69.40
Annual holding cost = $2,706.60 or $2,707

Total annual cost = Annual ordering cost + Annual holding cost
Total annual cost = $2,646 + $2,707
Total annual cost = $5,353

Answer e.

Average inventory = Order quantity / 2
Average inventory = 2,000 / 2
Average inventory = 1,000

Number of orders = Annual demand / Order quantity
Number of orders = 4,848 / 2,000
Number of orders = 2.424 or 3

Annual ordering cost = Number of orders * Ordering cost per order
Annual ordering cost = 3 * $42
Annual ordering cost = $126

Annual holding cost = Average inventory * Carrying cost per stone
Annual holding cost = 1,000 * $69.40
Annual holding cost = $69,400

Total annual cost = Annual ordering cost + Annual holding cost
Total annual cost = $126 + $69,400
Total annual cost = $69,526

Therefore, Ray would be wasting $64,173 ($69,526 - $5,353)