Question

As a result of many process improvements and IT implementations (like EDI), Big Box-Mart has been able to reduce its order costs from $38.38 to $7.29 when purchasing cases of paper towels from its main paper-products supplier. Annual demand is expected to be 163,000 cases and annual holding costs are $9.38 per case.

Hint #1: This is a purchasing order quantity problem (EOQ), not a production order quantity problem. For this question we are combining a JIT concept (lower ordering costs) with what you learned from a previous chapter (inventory management). If necessary, refer back to that chapter.
Hint #2: Remember to use cell references in all your formulas rather than using a rounded input value from a previous calculation.

Based on this information, what will be the new optimal order quantity (using the reduced ordering cost)? (Display your answer to the nearest whole number.)

When using the reduced ordering cost, as compared to the original ordering cost, by how many cases will the average inventory go down? (Display your answer to the nearest whole number.)

What will be the annual total combined savings to ordering costs and holding costs when using the reduced order cost, as compared to the original ordering cost? (Display your answer to two decimal places.)

Please show your work so I may learn.

Answer 1

	Original Order Cost	Reduced Order Cost	Inventory go down/Savings in cost
Annual Demand	163000	163000
Holding Cost	9.38	9.38
Ordering Cost	38.38	7.29
Optimal order quantity	1155	503
Average Inventory	577	252	326
Order Frequency	141	324
Annual Holding Cost	5416.67	2360.72
Annual Ordering Cost	5416.67	2360.72
Combined Cost	10833.35	4721.43	6111.91

Explanation:

Optimal order quantity = (2*Annual Demand*Ordering Cost/Holding Cost)^0.5

The optimal order quantity is calculated for both the ordering cost

Average Inventory = Optimal Quantitiy/2

The difference of average inventories of both the order cost = 577-252 = 326

When using the reduced ordering cost, as compared to the original ordering cost, the average inventory will go down by 326 cases

Annual holding cost = Average inventory*Holding cost

Annual ordering cost = order frequency*order cost = (Annual demand/optimal quantity)*order cost

Combined cost = Annual holding cost+Annual ordering cost

The annual total combined savings to ordering costs and holding costs when using the reduced order cost, as compared to the original ordering cost is 6111.91.

Excel formula: