The below figure shows a factory consisting of 6 machines an

The below figure shows a factory consisting of 6 machines and the raw processing times of each machine. Machine 1 receives 4 parts/hour. After processed in Machine 1, 40% of all parts are processed in Machine 2 and 3, and the other 60% are processed in Machine 4 and 5. Finally all parts are processed in Machine 6. Calculate the arrival rates of Machine 2 and 4, and compute the utilization for all 6 machines.

Solution

Here as 40% parts are sent to machine 2, so

arival rate of machine 2 = 0.4 x 4 = 1.6 parts/hour

and accordingly arrival rate of machine 4 = 0.6 x 4 = 2.4 parts/hour

Further we have that utilization factor of a machine = arrival rate/service rate.

So based on given table, utilization factor of machine 1 = 4/0.15 = 26.67

utilization of machine 2 = 1.6/0.5 = 3.2

utilization of machine 3 = 1.6/0.3 = 5.33

utilization of machine 4 = 2.4/0.4 = 6

utilzation of machine 5= 2.4/0.3 = 8

and utilization of machine 6 = 4/0.2 = 8

so total utilization of all machines = 3.2+5.33+26.67+6+8+8

= 57.2

Answer