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# Economic Order Quantity: Minimizing Ordering and Inventory Costs

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As the production manager, you need to minimize both ordering and inventory costs. You need to provide a recommendation of the optimal order quantity of raw materials to your plant manager. Your objective is to determine the economic order quantity (EOQ). If the annual demand for Ultamyacin at Smitheford is 400,000 units, then the annual carrying cost rate is 15% of the cost of the unit. The product costs \$48/unit to purchase, and the product ordering cost is \$28.00.

-What is the basic EOQ?
-What is the TC (total cost) at the EOQ?
-How much would the TC increase if the order quantity must be 1,000 units?
-How is JIT (just-in-time) ordering methodology different from EOQ methodology?

Explain the concepts of forecasting, system design, capacity planning, quality management and control, supply chain management, inventory management and scheduling, and project management and how they each relate to form an integrated view of production and operations.

#### Solution Preview

"As the production manager, you need to minimize both ordering and inventory costs. You need to provide a recommendation of the optimal order quantity of raw materials to your plant manager. Your objective is to determine the economic order quantity (EOQ). If the annual demand for Ultamyacin at Smitheford is 400,000 units, then the annual carrying cost rate is 15% of the cost of the unit. The product costs \$48/unit to purchase, and the product ordering cost is \$28.00".

Given:
Demand or Annual inventory requirement = 400,000 units
Ordering cost = \$28
Production cost per unit = \$48
Carrying cost = 15% of the cost of the unit = 15% of \$48
= .15* \$48 = \$7.20
The basic EOQ:
EOQ = ? (2SO/C)
Where EOQ = economic order quantity
S = annual inventory requirement
O = cost per order transaction (ordering cost)
C = carrying cost per unit
EOQ = ? [(2) (400,000) (\$28)/\$7.20]
= ? 3111,111.11
EOQ = 1,763.83 or 1764 units

TC (total cost) at the EOQ
Total cost (annual) = ordering cost + carrying (holding cost) (Render et al, 2003).
Annual Ordering cost:
= (Annual demand/ number of units in each order) (ordering cost per order)
= (400,000/1764) (\$28)
= \$6349.21
Annual carrying cost:
= (Average inventory) (carrying cost per unit per year)
Average inventory:
= EOQ/2 = 1764/2
= 882
Annual carrying cost = (882) (\$7.20) = \$6350.40
Total cost at EOQ = \$6349.21 + \$6350.40 = \$12,699.61

TC increase if the order ...

#### Solution Summary

The economic order quantity and total costs for Ultamyacin is found. JIT and EOC are compared and all calculations are shown.

\$2.19

## Economic Order Quantity (EOQ), Ordering Costs, and Average Cycle Stock

Monthly demand for an inventory item currently averages 160 units. The annual carrying cost is \$10 per unit. Ordering cost is \$60 per order. This information applies to all of the questions on this page.

Find the EOQ. Please show the formula (with values) you used.

2.Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.
What is the average cycle stock inventory under this policy? Show your work and clearly label your answer.

3.
Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.
What is the average number of orders per year under this policy? Show your work and clearly label your answer.

4.
Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.
What is the average annual ordering cost under this policy? Show your work and clearly label your answer.

5.
Suppose instead of using the EOQ, we decide to use Q = 200 for the item in the question above.
What is the average annual carrying cost under this policy? Show your work and clearly label your answer.

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