# 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

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 (i.e., not including queue time), are given for’ each line in the following table: Over the past three months, the old line has averaged 315 parts per day, where one day consists of one eight-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 above data and identify potentially attractive improvement paths for each line by addressing the following questions. (a) Compute rb, T0 and W0 for both lines. Which line has the larger critical WIP? Explain why. (b) Compare the performance of the two lines to the practical worst case in terms of throughput. What can you conclude about the relative performance of the two lines compared to their underlying capabilities? 2.  Consider a balanced line consisting of five single-machine stations with exponential process times (hint: this means it is a kind of practical worst case). Suppose the utilization is 75 percent and the line runs under the CONWIP protocol (i.e., a new job is started each time a job is completed). (a) What is the WIP level in the line? (b) What is the cycle time as a percentage of T0