Question: Consider a factory with two machines A and B; all units must be processed by Machine A first, and then Machine B. Orders (for one unit each) arrive randomly through time and First-In, First-Out (FIFO) scheduling is used at each machine; processing times are variable due to poor maintenance on the machines. An intern has computed actual flow times (including both processing time and queue time) of orders through Machine A and through Machine B; coincidentally, each of these sets of data can be described by a Normal distribution with mean 300 minutes and standard deviation 50 minutes. Also, the flow times are independent.
(a) What is the probability that a new order arriving randomly in time will be completed within 717 minutes? Show work.
(b) Now suppose that the person in charge of each machine must quote a Promised Completion Time such that 95% of the orders would not be tardy. What Promised Completion Time (in minutes) would each person quote? Show work.
(c) Sum your two answers in (b) to obtain a complete job quote time. What is the actual probability that an arriving job will be completed before that complete job quote time?
(d) Suppose the manufacturing process can be reengineered so that units could be processed through the two machines in either order (either A-B or B-A). Describe how you would schedule/sequence work through the factory now. Would this new arrangement produce a smaller average flow time than the original system? Why or why not?