Question

(20) A flow line has two stations. The first station has a processing time of 6 minutes, and it has 3 servers. The second has a processing time of 11 minutes, and it has 4 servers. There is a constant arrival rate of jobs to the line What is the maximum utilization at each station? What assumptions do you need to ensure that maximum utilization is achieved? It turns out that the non-bottleneck station is very expensive, so management would like to maximize its utilization without reducing throughput. What change to the system should be made?

Answer 1

Solution:

1)

Capacity of the first station = Number of servers / Processing time

= 3/6

= 0.5 per minute

Capacity of the second station = 4/11

= 0.364 per minute

Capacity of the second station is lesser. Therefore, it is the bottleneck.

Maximum utilization of the first station = 0.364/0.5

= 72.73 %

Maximum utilization of the second station = 0.364/0.364

= 100 %

The assumption for maximum utilization is that line is capacity constrained, which means the arrival rate is greater than or equal to the capacity of the bottleneck (second) station

2)

In order to maximize the utilization of the non-bottleneck (first) station, number of servers must be reduced to 2 and the processing time must be decreased to 5.5 minutes. By doing this, the capacity of first station = 2/5.5 = 0.364 per minute

This will ensure 100% utilization of the first station