Question

Problem 9A-5 Economic Order Quantity; Safety Stock; Just-in-Time Purchasing Impact [LO6]

Imagine It manufactures 3D printers and purchases one of the components used in the printers from a supplier in the U.S. Imagine It uses 4,000 of these components per year at a cost of $160 each.

The components are used evenly in the production process throughout a 360-day production year. The company estimates that it costs $20 to place a single purchase order and about $100 to carry each component in inventory for a year since it must be stored in a climate-controlled unit.

Delivery from the supplier generally takes two days, but it can take as many as six days. The days of delivery time and the percentage of their occurrence are shown in the following tabulation:

Delivery Time (Days)		Percentage of Occurrence
2		75
3		10
4		5
5		5
6		5
		100

Required:
1.Compute the EOQ.

2. Assume that the company is willing to assume a 15% risk of being out of stock. What is the safety stock? The reorder point?

3. Assume that the company is willing to assume only a 5% risk of being out of stock. What is the safety stock? The reorder point?

4. Assume a 5% stock-out risk as stated in (3) above. What is the total cost of ordering and carrying inventory for one year?

5. Refer to the original data. Assume that the company decides to adopt JIT purchasing policies. This change allows the company to reduce its cost of placing a purchase order to only $11.25. Compute the new EOQ.

Answer 1

1. EOQ=√(2*Annual usage*ordering cost per order)/carrying cost

√(2*4000*20)/100=40 UNITS

2. Safety stock=(Expected rate of consumption*expected increase in delivery time)+( Expected rate of consumption*normal reorder period)

=Assuming 15% risk of stock out asper question

4000*15%=600units

Safety stock=600*(2+6)/2=2400 units.

Reorder point=normal usage in units*normal lead time+safety stock

=Normal usage=annual usage/360

4000/360=11.11or11units

Normal lead time=(2+6)/2= 4

Safety stock= 11*4+2400= 2444 units.

3. Assuming stock out risk is 5 percent as per question

Safety stock=(4000*5%)*(2+6)/2=800 units

Reorder level= 11*4+800=844 units

4. Carrying cost and ordering cost remain same as no change in EOQ.

5. √(2*4000*11.25)/100= 300 units when following JIT