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 $104, and the inventory carrying
cost is $11 per unit per year. The average ordering cost is $29 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 the
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 cost of the
6,000 units?
Annual demand (D) = 5950 units
Ordering cost (S) = $29 per order
Carrying cost (H) = $11
Number of days per year = 250 days
A) Economic order quantity (Q) = sqrt of (2DS / H)
= sqrt of [(2 x 5950 x 29)/11]
= 177 units
B) Average inventory = Q/2 = 177/2 = 88.5
C) Number of orders per year = D/Q = 5950/177 = 33.62
D)Time between orders = (Q/D) number of days per year
= (177/5950)250
= 7.44 days
E) Annual ordering cost = (D/Q) S = (5950/177)29 = $974.86
Annual holding cost = (Q/2)H = (177/2)11 = $973.5
Annual cost of ordering and holding inventory = $974.86+$973.5 = $1948.36
F) Cost of the 6000 units = 6000 x cost per unit = 6000 x $104 = $624000
Total annual inventory cost = Ordering cost + Holding cost + product cost = $974.86+$973.5+$624000 = $625948.36
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