Problem 7-9 (Algo)

Ergonomics Incorporated sells ergonomically designed office chairs. The company has the following information:

Average demand = 30 units per day

Average lead time = 37 days

Item unit cost = $57 for orders of less than 270 units

Item unit cost = $56 for orders of 270 units or more

Ordering cost = $32

Inventory carrying cost = 20%

The business year is 250 days.

How many chairs should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time.

What will the firms average inventory be under each alternative?

What will be the annual ordering and holding costs for each alternative?

Explanation

The EOQ and TAC at the $57 price is:

EOQ=27,500units/year$32/order$57/unit0.20=205.1957=206unitsEOQ=27,500units/year$32/order$57/unit0.20=205.1957=206units

Average inventory = 206 units/2 = 103.0 units

TAC of ordering 206 units

Annual ordering cost = $32 (7,500 units/206 units) = $1,165.05

Holding costs = $57 0.20 (206 units/2) = $1,174.20

Annual product cost = $57 7,500 units = $427,500

Total cost = $429,839.25

The EOQ at the $56 price is:

EOQ=27,500units/year$32/order$56/unit0.20=207.0197=208unitsEOQ=27,500units/year$32/order$56/unit0.20=207.0197=208units

Since 270 units must be ordered to obtain this price:

Average inventory = 270 units/2 = 135 units

TAC of ordering 270 units

Annual ordering cost = $32 (7,500 units/270 units) = $888.89

Holding costs = $56 0.20 (270 units/2) = $1,512.00

Annual product cost = $56 7,500 units = $420,000

Total cost = $422,400.89

The firm should order 270 chairs each time. It will save $7,438.36 each year.