Question

Consider the following inventory information and relationships for the F. M. Beaner Corporation:
1. Orders can be placed only in multiples of 100 units.
2. Annual unit usage is 300,000.
3. The carrying cost is 30% of the purchase price of the goods.
4. The purchase price is $10 per unit.
5. The ordering cost is $50 per order.
6. The desired safety stock is 1000 units. (This does not include delivery- time stock.)
7. Delivery time is 2 weeks.   

a. What is the optimal EOQ level?
b. How many orders will be placed annually?
c. At what inventory level should a reorder be made?
d. What is the total cost of EOQ based system? Don’t forget Safety stock.   
e. What happens to EOQ if the carrying cost rises? Explain.

Answer 1

Solution:

Part a – Optimal EOQ Level

Economic Order Quantity (EOQ) = ((Annual Demand x Ordering Cost per order) / Carrying

Cost per unit per annum))1/2

Here,

Annual Demand = 300,000

Ordering Cost per order = $50

Carrying Cost per unit per annum = Purchase Price $10 * 30% = $3

EOQ = ((300,000*50) / 3)1/2

= 2,236 Units (Rounded to Zero decimal places)

Optimal EOQ Level = 2,236 Units

Part b –

Number of orders to be placed Yearly = Annual Demand / Optimal EOQ level

= 300,000 / 2,236

= 134 Orders (rounded to zero decimal place)

Part c –

Re-Order Level = Safety Stock + Lead time consumption

Here.

Safety Stock = 1,000 Units (given)

Lead Time Consumption = Delivery Time 2 weeks * Weekly Consumption (300,000 / 52 weeks)

= 11,538 Units

Re-Order Level = 1,000 Units + 11,538 Units = 12,538 Units

Part d –

Total Cost of EOQ based system = Total Material Cost + Total Ordering Cost + Total Carrying Cost

	$$
Total Material Cost (300,000 Units * Purchase Price 10)	$1,000,000
Total Ordering Cost (134 Orders * $50)	$6,700
Total Carrying Cost (Refer Note 1)	$6,354
Total Cost	$1,013,054

Note 1 -

Total Carrying Cost = Average Inventory * Carrying Cost per unit per annum

Average Inventory = ½ EOQ 2,236 + safety stock 1,000 = 1,118 + 1,000 = 2,118 Units

Total Carrying Cost = Average Inventory 2,118 * $3 = $6,354

Part e –

If the carrying cost rises, the EOQ level decreases.

For example, current carrying cost in the question is $3 and if it rises to $5, the EOQ level would be

EOQ = ((300,000*50) / 5)1/2

= 1,732 Units (Rounded to Zero decimal places)

It means if carrying cost rises the EOQ level decrease.

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