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 5,850 units per year. The cost of each unit is $98, and the inventory carrying cost is ​$11 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 117 units.​ (This is a corporate​ operation, and there are 250 working days per​ year).

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

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

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

​d) What is the optimal number of days in between any two​orders? days ​(round your response to two decimal​places).

​e) What is the annual cost of ordering and holding​ inventory? per year ​(round your response to two decimal​places).

​f) What is the total annual inventory​ cost, including the cost of the ​units? per year ​(round your response to two decimal​places).

Answer 1

Annual Demand D = 5850 units

Unit Price P = 98

Holding Cost H = 11

Ordering cost S = 31

Working Days = 250

Daily Demand d = 5850/250 = 23.40

a)

EOQ = (2DS/H)^(1/2)

EOQ = (2*5850*31/11)^(1/2)

EOQ = 181.58 units

b)

Average Inventory = EOQ/2 = 181.58/2 = 90.79

c)

Number of Orders = D/EOQ = 5850/181.58 = 32.22

d)

Days between orders = EOQ/d = 181.58/23.40 = 7.76 days

e)

Annual Ordering & Holding Cost = (D/EOQ)*S + (EOQ/2)*H

Annual Ordering & Holding Cost = (5850/181.58)*31 + (181.58/2)*11 = 1997.42

f)

Total cost = Annual Ordering & Holding Cost + P*D

Total Cost = 1997.42 + 5850*98

Total Cost = 575297.42