Question

1. Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas’s faster-moving inventory item has a demand of 6,000 units per year. The cost of each unit is $100, and the inventory carrying cost is $10 per unit per year. The average ordering cost is $30 per order. It takes about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and there are 250 working days per year.)
   1. What is the EOQ?
   2. What is the average inventory if the EOQ is uses?
   3. What is the optimal number of orders per year?
   4. What is the optimal number of days in between any two orders?
   5. What is the annual cost of ordering and holding inventory?
   6. What is the total annual inventory cost, including cost of the 6,000 units?

Answer 1

A. 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