Problem 3. (Chapter 9: Inventory Policy Decisions) Suppose that an auto part in a manufacturers inventory has the following characteristics:

Forecast of demand = 1000 cases per week

Forecast error, std. dev. = 250 cases per week

Lead time = 4 weeks

Carrying cost = 30% per year

Purchase price, delivered = $60 per case

Replenishment order cost = $45 per order

Stockout cost = $14 per case

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

The manufacturer uses ROP method to control the inventory of this item. The manufacturer operates 52 weeks a year.

1. What is the economic order quantity?

2. What is the reorder point?

3. Whats the expected number of units out of stock annually?

4. What is the annual service level?

5. Whats the total annual cost including annual fixed ordering cost, inventory holding cost, and stockout cost?

6. If the lead time is normally distributed with a standard deviation of 1 week, whats the ROP?