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

6 comma 0006,000

units per year. The cost of each unit is

$102102,

and the inventory carrying cost is

$99

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

120120

units. (This is a corporate operation, and there are

250250

working days per year).

a) What is the EOQ?

196.64196.64

units (round your response to two decimal places).

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

98.3298.32

units (round your response to two decimal places).

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

30.5130.51

orders (round your response to two decimal places).

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

8.198.19

days (round your response to two decimal places).

e) What is the annual cost of ordering and holding inventory?

$1769.75 .1769.75.

per year (round your response to two decimal places).

Answer 1

Demand = 6,000

Holding cost = $ 9

Ordering cost = 29

EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

ANNUAL HOLDING COST = (EOQ / 2) * HOLDING COST

ANNUAL ORDERING COST = (DEMAND / EOQ) * ORDERING COST

EXPECTED NUMBER OF ORDERS = DEMAND / Q   

TIME BETWEEN ORDERS = EOQ / DAILY DEMAND

DAILY DEMAND = DEMAND / NO. OF WORKING DAYS

A. EOQ = SQRT(2 * 6000 * 29 / 9) = 196.64

B. AVERAGE INVENTORY = EOQ / 2 = 196.64 / 2 = 98.32

C. NUMBER OF ORDERS = 6000 / 196.64 = 30.51

D. DAYS BETWEEN ORDERS = 250/30.51 = 8.19

E. ANNUAL HOLDING COST = (196.64 / 2) * 9 = 884.88

ANNUAL ORDERING COST = (6000 / 196.64) * 29 = 884.87

TOTAL COST = AHC + AOC = 884.88 + 884.87 = 1769.75