Question

The Metropolitan Book Company purchases paper from the Atlantic Paper Company. Metropolitan produces magazines and paperbacks that require 1,215,000 pounds of paper per year. The cost per order for the company is $1,200; the cost of holding 1 pound of paper in inventory is $0.08 per year. Determine the following: a) The economic order quantity b) The minimum total annual cost c) The optimal number of orders per year d) The optimal time between orders.

	TOTAL ANNUAL INVENTORY COST
	SUMMARY
	Q = ORDER QUANTITY =
	AVERAGE INVENTORY =
	NUMBER OF ORDERS =
	CARRYING COST =
	ORDERING COST =
	TOTAL COST
	OPTIMAL TIME BETWEEN ORDERS =

Answer 1

Annual demand, A = 1,215,000 pounds of paper
Ordering cost per order, O = $1,200
Holding cost per pound of paper per annum, H = $0.08

Economic order quantity, EOQ = (2 * A * O / H)^(1/2)
Economic order quantity, EOQ = (2 * 1,215,000 * $1,200 / $0.08)^(1/2)
Economic order quantity, EOQ = 36,450,000,000^(1/2)
Economic order quantity, EOQ = 190,918.83 pounds of paper

Average inventory = EOQ / 2
Average inventory = 190,918.83 / 2
Average inventory = 95,459.415 pounds of paper

Number of orders = Annual demand / Economic order quantity
Number of orders = 1,215,000 / 190,918.83
Number of orders = 6.363961

Carrying cost = Average inventory * Holding cost per pound of paper per annum
Carrying cost = 95,459.415 * $0.08
Carrying cost = $7,636.75

Ordering cost = Number of orders * Ordering cost per order
Ordering cost = 6.363961 * $1,200
Ordering cost = $7,636.75

Total cost = Carrying cost + Ordering cost
Total cost = $7,363.75 + $7,636.75
Total cost = $15,000.50

Optimal time between orders = 365 / Number of orders
Optimal time between orders = 365 / 6.363961
Optimal time between orders = 57.35 days