Problem 3. (chapter 9: Inventory Policy Decisions) Suppose that an auto part in a manufacturer's inventory has the following characteristics:

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Forecast of demand Forecast= 1,250 cases per week

error, std. dev.= 475 cases per week

Lead time= 2.5 weeks

Carrying cost = 30% per year

Purchase price, delivered= $56 per case

Replenishment order cost=$40 per order

Stockout cost= $10 per case

Probability of being in stock during the lead time =80%

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Assume the manufacturer uses ROP method to control the inventory of this item.

1. What is the economic order quantity?
2. What is the reorder point?
3. What's the expected number of units out of stock annually?
4. What is the annual service level?
5. What's the total annual costs excluding purchasing costs? (Note that the annual purchasing
6. costs equal to the purchasing price per case multiplied by the annual purchasing quantity in cases. Regardless of the replenishment order size per time, the annual purchasing costs should be the same since the annual purchasing quantity is stable. Therefore, we usually do not need to include purchasing costs in the total annual costs. )
7. If the lead time is normally distributed with a standard deviation of 0.5 weeks, what's the ROP?