Question

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 5, 950 units per year. The cost of each unit is ​$99​, and the inventory carrying cost is ​$9 per unit per year. The average ordering cost is ​$31 per order. It takes about 5 days for an order to​ arrive, and the demand for 1 week is 119 units.​ (This is a corporate​ operation, and there are 250 working days per​ year).

​a) What is the​ EOQ? Q​ = _____  ​(round your response to two decimal​ places).

​b) What is the average inventory if the EOQ is​ used? Average Inventory​ = _____  ​(round your response to two decimal​ places). ​

c) What is the optimal number of orders per​ year? Optimal Number of Orders​ = _____ ​(round your response to two decimal​ places). ​

d) What is the optimal number of days in between any two​ orders? Number of Days Between Two Subsequent Orders​ = _____ ​(round your response to two decimal​ places). ​

e) What is the annual cost of ordering and holding​ inventory? Order Cost​ = ____ ​(round your response to two decimal​ places).

Answer 1

Solution:

(a) Economic Order Quantity (EOQ):

EOQ = SQRT [(2 x D x Co) / Cc]

where,

D = Annual demand

Co = Ordering cost

Cc = Inventory carrying cost

Putting the given values in the above formula,

EOQ = SQRT [(2 x 5,950 x $31) / $9]

EOQ = 202.46

Economic order quantity (EOQ) = 202.46 units

(b) Average inventory:

Average inventory = EOQ / 2

Average inventory = 202.46 / 2

Average inventory = 101.23 units

(c) Number of orders:

Number of orders = (Annual demand / EOQ)

Number of orders = (5,950 / 202.46)

Number of orders = 29.39 orders per year

(d) Number of days between two orders:

Number of days between two orders = (EOQ / Annual demand) x Number of working days per year

Number of days between two orders = (202.46 / 5,950) x 250

Number of days between two orders = 8.51 days

(e) Annual cost of ordering and holding inventory:

​​​​​​​Annual cost of ordering = (Annual demand / EOQ) x Ordering cost

Annual cost of ordering = (5,950 / 202.46) x $31

Annual cost of ordering = $911.04

Annual holding cost = (EOQ / 2) x Holding cost

Annual holding cost = (202.46 / 2) x $9

Annual holding cost = $911.07

Total cost = Annual cost of ordering + Annual holding cost

Total cost = $911.04 + $911.07

Total cost = $1,822.11