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 27% per year. Determine the optimal order quantity, order frequency, and the annual cost of inventory management. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be the new economic order quantity, order frequency, and annual inventory management cost? Explain these results

Answer 1

Given that:

Demand (D) = 175 unit per month = 2100 unit per year

Unit cost of towel (C) = $2.5

Ordering cost (O) = $12

Inventory carrying charge (i)=27% per year

Optimal order quantity (Q) = ((2*O*D)/(C*i))^1/2.

Q = ((2*12*2100)/(2.5*.27))^1/2 = 273.25 ( 273 whole number)

Answer:

Optimal order quantity (Q) = 273

Order Frequency = D/O = 2100 / 273 =  7.7 times / year or 8 times per year (whole number)

Annual cost of inventory management = (Q/2)* i*C = (273/2)*.27*2.5 = $92.14

IF due to automation of purchasing process ordering cost reduced to $4:

Optimal order quantity (Q) = ((2*O*D)/(C*i))^1/2.

Q = ((2*4*2100)/(2.5*.27))^1/2 = 157.76 ( 258 whole number)

Optimal order quantity (Q) = 158

Order Frequency = D/O = 2100 / 158 = 13.3 times / year or 13 times per year (whole number)

Annual cost of inventory management = (158/2)* i*C = (273/2)*.27*2.5 = $53.325

Explanation of these results:

If department store order 273 bath towel each time, the total cost which is sum of cost of purchase, ordering cost and holding cost will be minimum per unit.

If new purchase automation adopted the optimal ordering quantity will be reduced to 158. Means department store now order 158 bath towel each time to reduce its total cost.