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April 19, 2014

April 19, 2014

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

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 12:56pma. 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

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