Given a 3 step process in which all processes require setup, how does the batch size affect the bottleneck?

Question

I came across this textbook problem today, in which we are given three steps as below

The question asks, "for what batch size is step 3 (etching) the bottleneck?"

Now, I am aware that you can calculate the capacity of a process that has setup time by using the formula

Capacity for Batch Size = Batch Size / (Setup Time + (Batch Size * Processing Time) )

I did this for all three in excel and my point is, the batch size is irrelevant in this case, as the third process will always have the lowest capacity. I encountered the same question in the last problem and had the same conclusion.

Am I forgetting something here?

Answer 1

The third process does not always have lowest capacity. In fact, it never does. Ask yourself the following question: for what batch size does etching take less total time (setup plus processing) than patterning takes?