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
Homework Answers
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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