A furnace used in the heat treat operation of cast iron railroad car couplers can hold up to 20 parts. The operation takes an average of 4 hours to process a batch of parts with a standard deviation of 2 hours. The planning department estimates the current demand at 72 parts/day (24-hour day). The parts arrive to the furnace one at a time according to a Poisson stream (i.e., exponential interarrival times).
a) What is the maximum capacity (parts per day) of the heat treat operation?
b) What would be the average cycle time through the operation if we were to use the maximum batch size?
c) What is the minimum batch size that will meet the demand?
d) What would be the average cycle time through the operation if we were to use the minimum feasible batch size?