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There are FIVE processesing station in a prodcution system: P1, P2, P3, P4 and P5. The...

There are FIVE processesing station in a prodcution system: P1, P2, P3, P4 and P5. The times taken at each process are as follows 2 minutes, 6 minutes, 4 minutes, 8.6 and 15 minutes. Job request inflow rate is 16 per hour and jobs requests are accepted for six hours only. The systems closes after all accepted jobs have been completed, that is at the closing there are no unfinished jobs in the system.

The system capacity = /hour

The average waiting time in the system in minutes is = minutes

The throughput time of the system is = minutes

The average inventory in the system is = jobs

The average waiting time before P2 = minutes

The average waiting time before P3 = minutes

The average waiting time before P4 = minutes

The average waiting time before P5 = minutes

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Answer #1

Processing time of station P5 is the maximum at 15 minutes.

Therefore, cycle time = 15 minutes

The system capacity = 60/15 = 4 / hour

Total number of jobs accepted in 6 hours = 16*6 = 96

Total time required to process all the jobs = 96/4 = 24 hours

Waiting time for the last job = 24 hours - 6 hours = 18 hours

The average waiting time = (18+0)/2 = 9 hours = 540 minutes

Throughput time of the system = 15*5 = 75 minutes

Average inventory in the system = (96/2)*(1-4/16) = 36 jobs

Inter-arrival time = 60 minutes per hour / arrival rate of 16 jobs per hour = 3.75 minutes

The average waiting time before P2 = 96*(6-3.75)/2 = 108 minutes

The average waiting time before P3 = 96*(4-3.75)/2 = 12 minutes

The average waiting time before P4 = 96*(8.6-3.75)/2 = 232.8 minutes

The average waiting time before P5 = 96*(15-3.75)/2 = 540 minutes

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