Consider the plastic bottles demand pattern, A bottling plant uses approximately 3,000 plastic bottles per day (normally distributed), while daily usage has a standard deviation of 55. Order lead time is 3 days (constant). Suppose we plan to set up a periodic review inventory system instead, and we will order this item every 9 days. Order lead time is still the same. This is all one problem.

a. What is the protection interval?

b. What is the average demand during the protection interval? It should be standard deviation of the daily demand x square root of the protection interval.

c. What is the standard deviation of demand during the protection interval? Round your answer to the nearest two decimal points.

d. Using this periodic review system, what order up to level (T) would result in 100 units of safety stock? Show all your work. you would need to correctly find the z-score. Since the situation says the safety stock is 100, you will put that equal to z*s.d. during protection interval, and solve for z. You would then use it to find the corresponding probability from the normal distribution table.

e. What is the predicted service level under this safety stock value? f. What order up to level is needed to provide 99% predicted service level? How much safety stock is associated with this policy? You should be finding the z-score that corresponds to 99%, then use it to find the safety stock amount. Afterwards, you will be able to find the T, which is ADDPI + SS.