Consider a production line with five work centers in a sequence, with output fro

Question

Consider a production line with five work centers in a sequence, with output from one going to the next. There are buffers between work centers, so each center can work without being blocked by the one downstream (but a work center can be starved by the one upstream, meaning that if the buffer upstream is empty, the work center has to idle). If each work center took exactly ten minutes for each job, then we can have a job done every ten minutes (throughput rate is six per hour, and the throughput time is fifty minutes since there are five work centers - buffers are not really needed). Instead, if the service time at each work center is a random variable, with a mean of 10 minutes and a standard deviation of 2 minutes, then what would happen to the throughput rate and throughput time? In addition, if we limit the buffer to say a size of four units (so if the buffer is full, the upstream machine is blocked until a unit is removed from the buffer), then what would happen to the throughput rate and throughput time? Just state what you think will happen in a qualitative sense based on your intuition (i.e. no need to do any analysis and come up with numerical results)

Explanation / Answer

Let us say that now the service time at each work center is a random variable with mean of 10 minutes and a standard deviation of 2 minutes. This means that the service time at each work station can vary between 8 to 12 minutes.

Therefore, there are three cases that can be formed here.

Now, if we limit the buffer to say a size of four units (so if the buffer is full, the upstream machine is blocked until a unit is removed from the buffer), then the idle time for the upstream machine would increase, thus making the overall throughput time to increase and thus the throughput rate decreases proportionally.

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