1. Positively Rivet Inc. is a small machine shop that produces sheet metal products. It had one line dedicated to the manufacture of light-duty vent hood shells, but because of strong demand it recently added a second line. The new line makes use of higher-capacity automated equipment but consists of the same basic four processes as the old line. In addition, the new line makes use of one machine per workstation, while the old line has parallel machines at the workstations. The processes, along with their machine rates, number of machines per station, and average times for a lone job to go through a station (not including queue time), are provided below. Over the past 3 months, the old line has averaged 350 parts per day, where one day consists of one 8-hour shift, and has had an average WIP level of 400 parts. The new line has averaged 680 parts per eight-hour day with an average WIP level of 350 parts. Management has been dissatisfied with the performance of the old line because it is achieving lower throughput with higher WIP than the new line, Your job is to evaluate these two lines to the extent possible with the data provided and identify potentially attractive improvement paths for each line by addressing the following questions:
   1. Compute r_b, To, and Wo for both lines. Which line has larger critical WIP? Explain why.
   2. Compute the best case and worst case performance benchmarks for the old and the new line.
   3. Compare the performance of both lines to their corresponding practical worst case. What can you conclude about the relative performance of the two lines compared to their underlying capabilities? Is management correct in criticizing the old line for inefficiency?
   4. If you were the manager in charge of these lines, what option would you consider first to improve the throughput of the old line? Of the new line?

	Old Line
Process	Rate per Machine (parts/hr)	Number of Machines per station	Time (minutes)
Punching	15	4	4.0
Braking	12	4	5.0
Assembly	20	2	3.0
Finishing	50	1	1.2

	New Line
Process	Rate per Machine (parts/hr)	Number of Machines per station	Time (minutes)
Punching	120	1	0.50
Braking	120	1	0.50
Assembly	125	1	0.48
Finishing	125	1	0.48