The daily demand for an item in a store follows a Normal distribution with mean 100 and standard deviation 5. It costs $.024 per day to hold one item in inventory. The fixed cost to make a replenishment order is $30, and the lead time to receive an order is 2 days.
(a) Currently, the inventory policy for this item is to order 300 units whenever the inventory drops to 220 units. Determine the probability of a stock-out under this policy.
(b) Recommend a better inventory policy for the store given that the probability of a stock-out cannot exceed .05. Your policy should include an economic order quantity and a re-order point.