Question

The soft goods department of a large department store sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. The store uses an inventory carrying charge of I = 27% per year. Determine:

(3 points) (a) the optimal order quantity,
(1 points) (b) the order frequency,
(1 points) (c) the annual holding and setup cost.

Answer 1

Given are following details :

Annual demand of bath towels = D = 175 /month x 12 months =2100

Order placement cost = Co =$12

Annual unit inventory carrying cost = Ch = 27% of $2.50 = $0.675

Optimal order quantity

= Square root ( 2 x Co x D/ Ch )

= Square root ( 2 x 12 x 2100 / 0.675 )

= 273.25 ( 273 rounded to nearest whole number )

Order frequency = Optimal order quantity / Annual demand x 365 = 274/2100 x 365 = 47.62 days

Annual set up ( order placement) cost

= Ordering cost x Number of orders

= Co x annual demand / Optimal order quantity

= $12 x 2100 / 273

= $92.30

Annual inventory carrying cost

= annual unit inventory carrying cost x Average inventory

= Ch x Optimal order quantity / 2

= $0.675 x 273/2

= $92.13

Annual holding and set up cost = $92.30 + $92.13 = $184.43