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 5,8505,850 units per year. The cost of each unit is $9696, and the inventory carrying cost is $88 per unit per year. The average ordering cost is $2929 per order. It takes about 55 days for an order to arrive, and the demand for 1 week is 117117 units. (This is a corporate operation, and there are 250 working days per year).

a) What is the EOQ?

205.94 units (round your response to two decimal places).

b) What is the average inventory if the EOQ is used?

102.97 units (round your response to two decimal places).

c) What is the optimal number of orders per year?

28.41 orders (round your response to two decimal places).

d) What is the optimal number of days in between any two orders?

8.80 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).

Answer 1

Annual demand (D) = 5850 units

Carrying cost (H) = $8

Ordering cost (S) = $29

Number of days per year = 250

Average daily demand (d) = D/Number of days per year = 5850/250 = 23.4 units

a) Economic order quantity (EOQ) = √(2DS/H)

= √[(2 × 5850 × 29) / 8]

= √(339300/8)

= √42412.5

= 205.94 units

b) Average inventory = EOQ/2 = 205.94/2 = 102.97 units

C) Number of orders per year = D/EOQ = 5850/205.94 = 28.41

D) Optimal number of days between order = (EOQ/D) Number of days per year = (205.94/5850) 250 = 8.80 days

E) Annual ordering cost = (D/EOQ) S =(5850/205.94) 29 = $823.78

Annual holding cost = (EOQ/2) H = (205.94/2) 8 = 823.76