Question

A manufacturer of automotive components purchases a particular part for use in its manufacturing process from a supplier for 23.0 per unit. The annual demand for the part is 33,053 units per year. The manufacturer has estimated that the ordering cost is 187 per order. The annual holding charge is 24 percent of the unit purchase cost. The supplier has a lead time of 37 days. Recently, the supplier has offered a purchase discount. The supplier will reduce the unit purchase cost by 5.0 percent if the manufacturer uses an order quantity of 4,653 units per order. What is the total annual inventory and purchasing cost if the manufacturer uses an order quantity of 4,653 units per order? Use at least 4 decimal places.

Answer 1

The total annual inventory and purchasing cost for the automotive components manufacturer using an order quantity of 4,653 units per order, after accounting for the discount, ordering, and holding costs is $9,856.26.

Step-by-step explanation:

To determine the total annual inventory and purchasing cost with the new order quantity of 4,653 units per order, we need to calculate both the purchasing cost and the holding cost with the discounted unit price. The discounted unit price is 23.0 units per order minus 5 percent, which is 23 × 0.95 = 21.85 per unit.

The total annual purchasing cost is the annual demand multiplied by the new unit price, so 33,053 × 21.85 = $$7",309.05. The total number of orders needed annually is the annual demand divided by the order quantity, so 33,053 / 4,653 ≈ 7.1043 orders per year. The ordering cost per year is 7.1043 × 187 = $$1,328.50.

The annual holding cost is calculated using the average inventory level, which is half the order quantity, and the holding charge rate. The average inventory level is 4,653 / 2 = 2,326.5 units. With a holding charge of 24 percent, the holding cost per unit is 21.85 × 0.24 = $$5.2440. Therefore, the total holding cost is 2,326.5 × 5.2440 = $$1",1$$8.71.

Finally, to get the total annual cost, we sum the purchasing cost, ordering cost, and holding cost: $7,309.05 (purchasing cost) + $1,328.50 (ordering cost) + $1,218.71 (holding cost) = $9,856.26.