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.

The EOQ is 509.90

1. Whats the total annual cost including annual fixed ordering cost, inventory holding cost, and stockout cost?
2. If the lead time is normally distributed with a standard deviation of 1 week, whats the ROP?