Question

A provincial government uses massive quantities of computer printer paper, which it buys centrally. The purchasing department calculates an economic order quantity based on an assumed carrying rate of 30% per year. A box of printer paper costs $40, it costs $60 to process an order, and an annual demand is for 36000 boxes of paper.

a) What is the economic order quantity? How much is the total inventory holding and ordering cost?

b) The buyer wishes to determine how sensitive the sum of inventory and ordering costs are to the order quantity. Determine how the costs would change if the order quantity is 50% more than EOQ and 50% less than the EOQ quantity.

Answer 1

Given values:

Carrying rate = 30% per year

Cost of printer paper (C) = $40

Carrying cost (Cc) = Carrying rate x Cost of printer paper

Carrying cost (Cc) = 30% x $40 = $12

Ordering cost (Co) = $60

Annual demand (D) = 36000 boxes

Solution:

(a) Economic Order Quantity (EOQ):

EOQ = SQRT [(2 x D x Co) / Cc]

EOQ = SQRT [(2 x 36,000 x $60) / $12]

EOQ = 600 boxes

Total inventory holding and ordering cost:

Annual inventory holding cost = (EOQ / 2) x Cc

Annual inventory holding cost = (600 / 2) x $12

Annual inventory holding cost = $3,600

Annual ordering cost = (D / EOQ) x Co

Annual ordering cost = (36,000 / 600) x $60

Annual ordering cost = $3,600

Total inventory holding and ordering cost = $3,600 + $3,600

Total inventory holding and ordering cost = $7,200

(b) If the order quantity is 50% more than EOQ:

New order quantity = EOQ + (50% of EOQ)

New order quantity = 600 + (50% of 600)

New order quantity = 900 boxes

Total inventory holding and ordering cost:

Annual inventory holding cost = (Q / 2) x Cc

Annual inventory holding cost = (900 / 2) x $12

Annual inventory holding cost = $5,400

Annual ordering cost = (D / Q) x Co

Annual ordering cost = (36,000 / 900) x $60

Annual ordering cost = $2,400

Total inventory holding and ordering cost = $5,400 + $2,400

Total inventory holding and ordering cost = $7,800

Answer: If the order quantity is 50% more than EOQ, then the total inventory holding and ordering cost will increase.

If the order quantity is 50% less than EOQ:

​​​​​​​New order quantity = EOQ - (50% of EOQ)

New order quantity = 600 - (50% of 600)

New order quantity = 300 boxes

Total inventory holding and ordering cost:

Annual inventory holding cost = (Q / 2) x Cc

Annual inventory holding cost = (300 / 2) x $12

Annual inventory holding cost = $1,800

Annual ordering cost = (D / Q) x Co

Annual ordering cost = (36,000 / 300) x $60

Annual ordering cost = $7,200

Total inventory holding and ordering cost = $1,800 + $7,200

Total inventory holding and ordering cost = $9,000

Answer: If the order quantity is 50% less than EOQ, then the total inventory holding and ordering cost will increase.