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.) 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

Raw process time (T0) is the sum of all workstations mean process time. This is only the process time and does not include queuing time.

Raw process time T0 is still the sum of process times.

T0 = 2 + 5 + 10 + 3 = 20 hours.

Critical WIP is also computed the same way.

W0 = rb* T0 = 0,4 * 20 = 8 products.

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