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 (a) the optimal order quantity, (b) the order frequency, and (c) the annual holding and setup cost. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be (d) the new economic order quantity, (e) the order frequency, and (f) annual holding and setup costs? Explain these results.
Annual demand is 175 × 12 = 2100.
(a) Q* = = 273.25; (b) N = = 7.69
(c) TC = ($12 ) + (.27 )($2.50 ) = $92.22 + $92.22 = $184.44
At S = $4:
(d) Q* = = 157.76; (e) N = = 13.31
(f) TC = ($4 ) + (.27 )($2.5 ) = $53.24 + $53.24 = $106.48
The lower order cost encourages smaller, more frequent orders, and it lowers total costs.
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