Question

In: Operations Management

Special Purpose EOQ Model: Price-break model Problem information: Annual Forecast: 12,000 units Order processing cost: $125/order...

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?

Solutions

Expert Solution

Annual inventory cost has 2 components :

Annual ordering cost
Annual inventory holding cost

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

keosha answered 1 year ago

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