Ben Parker, Executive Producer for Epic Productions Film Company, is trying to decide when to reorder the 35 millimeter film his photographers use for publicity photos. 35 mm film is used by the Epic photographers at a fairly constant rate, with an average demand during leadtime of 75 rolls and a variance of 25 rolls. (Ben would agree that the daily usage of 35 mm film seems to be normally distributed.) The leadtime on an order of 35 mm film is 5 days, and there are 250 working days in the year.

a. Suppose Ben decides to reorder 35 mm film when there are 86 rolls left in stock. How much safety stock is implied by this reorder point?

b. What is the service level implied by Ben’s reorder point of 86 rolls? 

c. If a publicity photographer runs out of film, it is usually impossible to arrange a future photo session with the movie stars who are being photographed. Keeping this in mind, Ben Parker decides that he wants a service level of 97.72% for his 35 mm film inventory policy. What is his reorder point for 35 mm film?

d. If Ben decides to have extra 4 rolls of 35 mm as safety stock, what is the ROP? And what is the probability of stock-out?