Posted by **Jackson** on Monday, September 20, 2010 at 8:19am.

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s fastest moving inventory item has a demand of 6000 units per year. The cost of each unit is $100.00, and the inventory carrying cost is $10.00 per unit per year. The average ordering cost is $30.00 per order. It takes about 5 days for an order to arrive, and demand for 1 week is 120 units (this is a corporate operation, there are 250 working days per year).

a. What is the EOQ?

b. What is the average inventory if the EOQ is used?

c. What is the optimal number of orders per year?

d. What is the optimal number of days in between any two orders?

e. What is the annual cost of ordering and holding and holding inventory?

f. What is the total annual inventory cost, including cost of the 6,000 units?

- Business -
**Gin**, Wednesday, March 30, 2011 at 12:56pm
a. What is the EOQ? = 189.74 units

Step (1): Determine the Annual Set-up Cost

*Annual set-up cost = (# of orders placed per year) x (Setup or order cost per order)

= Annual Demand

# of units in each order ¡Á (Setup or order cost per order)

= (D/Q) ¡Á(S)

= (6000/Q) x (30)

Step (2): Annual holding cost = Average inventory level x Holding cost per unit per year

= (Order Quantity/2) (Holding cost per unit per year)

= (Q/2) ($10.00)

Step (3):

Optimal order quantity is found when annual setup cost equals annual holding cost:

(D/Q) x (S) = (Q/2) x (H)

(6,000/Q) x (30) = (Q/2) (10)

=(2)(6,000)(30) = Q2 (10)

Q2 = [(2 ¡Á6,000 ¡Á30)/($10)] = 36,000

Q = ¡Ì([(2 ¡Á6,000 ¡Á30)/(10)]) = ¡Ì36,000

Q = 189.736 ¡Ö 189.74 units

EOQ = 189.74 units

b. What is the average inventory if the EOQ is used?

Average inventory level = (Order Quantity/2)

= (189.74) /2 = 94.87

Average Inventory level =94.87 units

c. What is the optimal number of orders per year?

N= ( Demand/ order quantity) = (6000/ 189.736)=31.62

N = 31.62

The optimal number of orders per year = 31.62

d. What is the optimal number of days in between any two orders?

T = (Number of Working Days per year) / (optimal number of orders)

T = 250 days per year / 31.62 = 7.906

T= 7.91

The optimal number of days in between any two orders = 7.91

e. What is the annual cost of ordering and holding inventory?

(Q) x (H)

(189.736 units) x ($10) =$1,897.36

¡Ö $1,897

The annual cost of ordering and holding the inventory = $1,897

f. What is the total annual inventory cost, including cost of the 6,000 units?

TC = setup cost + holding cost

TC = (Dyear/Q) (S) + (Q/2) (H)

TC = (6,000/189.74) ($30.00) + (189.74/2) ($10.00)

TC = $948.67 + $948.7

TC = 1,897.37 ¡Ö $1,897

Purchase cost = (6,000 units) x ($100/unit) = $600,000

Total annual inventory cost = $600,000 + $1,897 = $601,897

Total annual inventory cost = $601,897

## Answer this Question

## Related Questions

- math - You manage inventory for your company and use a continuous review ...
- Business Math - As a newly hired staff accountant for Jordan Designs, you have ...
- Quantitative methods. - INVENTORY MODEL The demand for a particular item is 10 ...
- math - A sporting goods company has a distribution center that maintains ...
- Math - Tracy Company, a manufacturer of air conditioners, sold 100 units to ...
- Stats - Consider the Avionic Manufacturing Company that wishes to meet a demand ...
- operations management - A company requires 5,000 units of a product in a single ...
- business - At the end of January, Mineral Labs had inventory of 725 units, which...
- Quantitative Methods - The reorder point [see equation 14.6] is defined as the ...
- math - Eddings Company had a beginning inventory of 400 units of Product XNA at ...

More Related Questions