Q1. Consider a bank with three tellers operating in parallel where tellers take an average of > minutes to serve a customer. a. Assuming tellers are available 100% of the time (i.e., someone else in the bank spells them during breaks and lunches), what is the capacity of the system in customers per hour? b. Assuming that there are no backup tellers and that tellers take two 15 minute breaks and one 30 minute lunch during an 8 hour shift, what is the capacity of the system? C. Using the capacity from part (b), what will be the utilization of the tellers if customers arrive at an average rate of 30 per hour? d. How well do you think tellers will be able to keep up with demand in the scenario of part (c) (i.e., would you expect short or long lines of customers)? Q2. Consider a production line that builds amplifiers in four steps that are carried out at four sequential stations. The average processing times at stations 1, 2, 3, 4 are 10, 24, 40, 18 minutes, respectively. Because some steps are slower than others, some of the stations have more than one machine. The number of (parallel) machines at stations 1, 2, 3, 4 is 1, 2, 6, 2, respectively (see Figure 1). a. What is the capacity of each station in jobs per hour? b. If jobs arrive to the line at a rate of 4 jobs per hour, what is the utilization of each station? Which station is the bottleneck? C. Now suppose that there is a quality check after station 1, which scraps 25% of the amplifiers as defective (see Figure 2). Only non-defective amplifiers move on to station 2 for processing. What is the capacity of each station now? Assuming the arrival rate to the line is still 4 jobs per hour, which station is the bottleneck? 100 4 joby/har - 0 UT 10 min 10 min : n O 24 min 18 min 24 mi 18 min OO 40 min 25% yield loss 40 min Figure 1: Four station serial line with multi-machine stations Figure 2: Four station serial line with multi-machine stations and yield loss