Question

The owner of the Beachcomber Hair Salon in Galveston, Texas, orders bottles of professional shampoo from a local beauty care distributor. Based on the store's popularity, the owner is considering adding two more chairs to accommodate more customers each day. To make room for the new chairs, however, the owner must reduce the size of the storage area used for all of the supplies. Specically, she estimates that there will only be space to store 20 bottles at a time. The store currently uses approximately 45 bottles of shampoo per month, and the owner estimates that the new chairs will increase this usage to 60 per month. The bottles of shampoo cost the store $32.73 each. The distributor charges a shipping fee of $35 per order, and the owner estimates that each order costs the store an additional $5 to process and place. The store uses an annual holding cost rate of 34% to make its inventory decisions.

a. If the store can only accommodate a maximum inventory of 20 bottles of shampoo after the expansion, determine the extra inventory costs that it will incur each year compared to its cost-minimizing order quantity.

b. One way to make smaller orders more economical would be to reduce the ordering cost. Determine the ordering cost that would make an order quantity of 20 bottles optimal for the store.

c. Suggest one practical way to reduce the ordering cost to the level determined in Part b.

Answer 1

Given:

Annual Demand	A	12*60 = 720
Purchase Cost	P	$32.73
Holding rate	I	0.34
Annual holding charge	H = P*I	$11.13
Ordering cost	S	$35.00

Items	Formula	EOQ plan	Current Plan
Order Size (units)	Q* = ?(2AS/(H))	?(2*720*35/(11.13)) = 67	20
Annual Ordering cost	AOC = A/Q x S	720/67*35 = $374.45	$1,260.00
Annual Holding Cost	AHC = Q/2 x H	67/2*11.13 = $374.45	$111.28
Total Inventory cost	TIC = AHC + AOC	$748.91	$1,371.28
Savings		1371.28-748.91 = $622.38

Savings = TIC with EOQ plan – TIC with Q = 20 units = $1371.28 - $748.91 = $622.38

b.

Let,

EOQ = 20 units

New ordering cost = S*

Q = ?(2AS*/(H))

S* = Q²H/(2A)

S* = 20² x 11.13/(2 x 720) = $3.02

ordering cost that would make an order quantity of 20 bottles optimal for the store = $3.02