Question

Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chainwithacentralinventoryoperation. Thomas?sfastest-movinginventoryitemhasademand 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.)

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

Answer 1

Demand per year (D) = 6000 units

Cost of each unit = $100

Inventory carrying cost (H) = $10 per unit per year

Ordering cost (S) = $30 per order

Lead time = 5 days

Demand for 1 week = 120 units.

Number of weeks = 6000/120 = 50

250 working days per year. Hence one week = 250/50 = 5 days

Question – a:

We have to find the Economic Ordering Quantity.

We know that,

EOQ =

Here,

D = 6000

S = $30 per order

H = $10 per unit per year.

Hence,

EOQ =

=

= √36000

= 189.74

= 190

Hence EOQ = 190

Question – b:

In EOQ, the average inventory = EOQ/2

Here EOQ = 190 units.

Hence average inventory = 190/2 = 95 units

Average Inventory = 95 units.

Question – c:

Optimal Number of orders per year = Annual demand/EOQ = 6000/190 = 31.57

Number of orders cant be in fraction.

Hence,

Optimal number of orders = 32

Question – d:

Optimal Number of days in between two orders:

Number of days between orders can also be defined as total number of days divided by number of orders.

= 250/32 = 7.81 (or 8 days)

Question – e:

Annual cost of ordering = number of orders*per order ordering cost = 32*30 = $960

Inventory holding cost = average inventory*per unit per year holding cost = (EOQ/2)*10 = (190/2)*10 = $950

Total ordering and holding cost = $960 + $950 = $1910

Question – f:

The total annual inventory cost, including the cost of the 6,000 units = total ordering and holding cost + cost of 6000 units

Cost of one unit = $100

Cost of 6000 units = 6000*100 = $600000

Hence total cost of 6000 units = $600000 + $1910 = $601910

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