Operations Research Batching

You have a two step process for manufacturing tools. The first step is fabrication operation which requires a set-up. The setup time is 15 minutes and the nominal processing time is 0.5 minutes per part. The second process is a batch furnace. The nominal heat treatment time is 2 hours and the furnace can process a maximum of 100 parts per run. However the furnace also breaks down with a mean time to fail of 4 hrs and mean time to repair of 0.5 hrs. The repair time has an exponential distribution. Assuming that the transfer lot size is same the process batch size, and the required production rate is 30 parts per hour with arrival SCV of 1 to the first step, determine the following:

What is availability of each of the two processes?
What is the SCV of process times for each of the two processes?
Assuming that we use the same batch size for both operations, what is the minimum batch size for stable system.
What is the total average cycle time to manufacture a part for a batch size = 2 times the minimum batch size determined in part(a).?

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