Special Purpose EOQ Model: Price-break model Problem information: Annual Forecas
ID: 349974 • Letter: S
Question
Special Purpose EOQ Model: Price-break model
Problem information:
Annual Forecast: 12,000 units
Order processing cost: $125/order
Inventory Carrying rate: 20% per year
Unit Price
Price levels
1 to 999 units/order
$510
1000 to 2999 units/order
$500
3000+ units/order
$490
1. Calculate EOQ at each price-break
2. Determine Q at each price-break
3. Plug the Q value into the total cost annual cost function to determine the total cost for each order quantity
a. TAIC = RC + (R/Q)S + (Q/2)kC
4. What is the optimal order quantity?
5. What is the total annual inventory cost at the optimal order quantity?
Unit Price
Price levels
1 to 999 units/order
$510
1000 to 2999 units/order
$500
3000+ units/order
$490
Explanation / Answer
Annual inventory cost has 2 components :
Let optimal order quantity = Q
Annual demand = D
Cost of placing an order = Co
Annual unit inventory holding cost = Ch
Therefore ,
Annual ordering cost
= Cost of placing an order x Number of orders in a year
= Cost of placing an order x Annual demand / Optimal order quantity
= Co x D/Q
Annual inventory holding cost
= Annual unit inventory holding cost x Average inventory
= Annual unit inventory holding cost x
= Cost of placing an order x Optimal order quantity / 2
= Ch x Q/2
Total annual inventory cost at optimal order quantity
= Annual ordering cost + Annual inventory holding cost
= Co x D/Q + Ch x Q/2
TOTAL ANNUAL INVENTORY COST AT OPTIMAL ORDER QUANTITY = Co x D/Q + Ch x Q/2
TOTAL ANNUAL INVENTORY COST AT OPTIMAL ORDER QUANTITY = Co x D/Q + Ch x Q/2
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