INetflix Almost all brick-and-mortar DVD stores have disappeared in last few years due to online streaming and mail order DVD rental companies such as Netflix. One of the key decisions at Netflix is to determine how many copies of newly released titles cach regional warehouse should purchase. Whern making inventory decisions, one factor Netflix needs to be concemed with is the variability of rent cycle time (from the time that a DVD is placed in a mail until the time that it is returned, processed, and ready to be shipped again). In an ideal world where the rent cycle time is perfectly predictable and is the same for every customer, Netflix can easily figure out how many turn around the DVDs fast while others hold onto them for weeks. This variability is the reason that Netflix becomes interested in tracking the total rent cycle time and utilize the information in their stocking decision. (FYI, Netflix also utilizes a tactic to buy some time by sending a DVD from the customer's queue instead of making them wait for a specific DVD) The total rent cycle time can be decomposed in four components: Total rent cycle time(T) copies it needs to stock. However, in reality, some customers Home Delivery Time(H) + Time that a DVD stays with a customer(D) +Return Delivery Time(R) + Return processing and restocking time(S) -H+D+R+S After several rounds of lean implementation and process innovation, Netflix can process the return and restock in 1 day with certainty (S1). On the other hand, delivery times (both from and to the Warehouse)-H and R-are random and so is the time that a DVD stays with a customer (D). After looking at the histograms of past transactions, the one-way delivery time (both home and return deliveries) seems to approximately follow a normal distribution with mean of 1.5 days and standard deviation of 0.5 days. A further study shows that home delivery time and return delivery time are Historical data also shows that for most new releases, the time that a DVD stays with a customer (D) is normally distributed with mean 7 of days and standard deviation of 2.5 days. For the purpose of analysis, you can assume that Netflix and the Postal Service work 24 hours a day and 7 days a week (so that you do not have to round each number). Also, for the purpose of your analysis, you can assume that all of four time components are independent of each other