III. Factory Dynamics (30 points): Consider a balanced serial line with three si
ID: 452102 • Letter: I
Question
III. Factory Dynamics (30 points): Consider a balanced serial line with three single-machine stations and exponentially distributed process times. Let t and rb denote, respectively, the average process time per job at each station and the bottleneck production rate. [Use specific values of t and rb, if useful. For example, if each of the stations was like those in Penny Fab One, t = 2 hours and rb = 0.5 jobs per hour. You should get the same answers no matter what t and rb you choose, as long as rb = 1/t (as required in single-machine stations).] Suppose the line utilization is 75 percent (i.e., THactual = 0.75 rb) and the line runs under the CONWIP protocol, i.e., a new job enters when an old completed job leaves.
Calculate the practical worst case cycle time as a percentage or multiple of T0, the raw process time (If CT = 2 T0, cycle time is two times or 200% of T0)
Explanation / Answer
Utilization = arrival rate / effective production rate = 75%
TH actual = 0.75 rb
Suppose t = 2 and rb = 0.5 , N= 3
therefore t0 = N* t = 3 * 2 = 6
where N is the three single-machine stations
Then w0 = t0 * rb = 6 * 0.5 = 3
Law Worst-Case Performance): The worst case cycle time or a given WIP level w is given by
CT = 2 * T0 = 12 = w * T0
Or w = 2
the practical worst case cycle time as a percentage or multiple of T0, for a given WIP level w is given by
CT pwc = T0 + ( w-1) /Rb
= 6 + (2-1) /0.5 = 6+ 2 = 8
Where t is the average process time per job at each station
Rb is the bottleneck production rate