A heat-treatment operation takes 6 hours to process a batch of parts with a standard deviation of 3 hours. The maximum that the oven can hold is 125 parts. Currently, there is demand for 160 parts per day (16-hour day), which arrive at the heat-treatment operation one at a time according to a Poisson stream (i.e., ca = 1).

(a) What is the maximum capacity of the heat-treatment operation in terms of an average number of parts per day?

(b) If the maximum batch size from part (a) is used, what is the average cycle time through the operation?

(c) What is the minimum batch size required for the stability of the system while meeting demand?

(d) If the minimum batch size from part (c) is used, what is the average cycle time through the operation?