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For the current batch size of 100 wafers, how long would it take to produce 50 wafers? assume that the batch needs to stay together during deposition and patterning (i.e., the firm does not work with transfer batches that are less than the production batch). however, the 50 wafers can leave the process the moment all 50 wafers have passed through the etching stage. recall that a setup can only be started upon the arrival of the batch at the machine.
c. for what batch size is step 3 (etching) the bottleneck?
d. suppose jcl inc. came up with a new technology that eliminated the setup time for step 1 (deposition), but increased the processing time to 0.45 min./unit. what would be the batch size you would choose so as to maximize the overall cap

Answer :

meerkat18

c. if batch size is B, then activity time of step 3 is 20 + 0.20B which is always lesser than the activity time of step 2, 30 + 25B for a positive value of B. Hence step 3 can never be the bottleneck.

d. Under the new technology, the process capacity of step 1 is no longer dependent on batch size and is equal to (1/0.45 min/unit) * (60 min/hr) = 133.33 units/hr. This is clearly the maximum overall process capacity that can be targeted.

Given that step 3 can never be the bottleneck, the maximum overall process capacity of 133.33 units/hour can be achieved by choosing a batch size for which step 1 is the bottleneck. So if B is the batch size for which step 1 is the bottleneck, then we have B/(30 + 0.25B) >= 1/0.45. Solving for B, we get B >= 150

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