Consider a balanced serial line with three single-machine stations and exponenti

Question

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.

1.) How would you expect the line’s PWC cycle time and actual cycle time to change if a machine was added to the middle station # 2, ceteris paribus (all else remaining unchanged)?

Explanation / Answer

Since the new machine is added at middle station, first and tge third station remains the bottleneck stations. rb will remain same in this case.

Considering the case of penny fab where cycle time is 2 hrs and rb is 1/t = 0.5

In this case even if a extra machine is added at any stage the time gap between two output will remain unchaned as it will be decided by the bottleneck machine. Cycle time of both first and third machine will be the cycle time of the line.

Hence actual cycle time will not change.

PWC means Practical worst case performace and

CTpwc= T0 + (w-1)/rb

Here T0 is total process time

In first case when there was no extra machine at station 2 T0 was 3t (sum of time spent at each machine) but when extra machine is added then T0 is 2.5t (as time spent at station 2 will be 0.5t as compared to t in earlier case since capacity has been doubled)

Using CTpwc= T0 + (w-1)/rb where w = WIP which in this case is 1 as the process is ConWIP

Hence replacing w = 1

CTpwc old = T0 = 3t

CTpwc new = 2.5t

Hence there is a difference of 0.5t in case of PWC cycle time while actual cycle time does not change with the addition of a new machine.

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