Suppose parts arrive in batches of 12 every 396 minutes to a three-station line as a Poisson arrival process (i.e.c^2a= 1 for the batch). All stations can only process one part at each time. The first station has a setup time of 15 minutes and a unit process time (i.e. time to process one part) of 7 minutes, the second sets up in 8 minutes and processes 1 part every 3 minutes, the third requires 12 and 4 minutes for setup and unit processing, respectively.We assume that the machine has no variability in processing time.

(a) What is the utilization of each station? Which is the bottleneck?

(b) What is the cycle time for a part on average if parts are moved 12 at a time (after each station)?

(c) What is the cycle time for the first part (in the 12-part batch) if parts are moved one at a time (after each station)?

(d) What is the cycle time for the 12th part (in the 12-part batch) if parts are moved one at a time (after each station)?

(e) What is the cycle time for a part on average if parts are moved one at a time (after each station)?