ISE 580 Fall 2025
Homework #4
Show all your work step by step. Your grade depends on the clarity of solutions and the accuracy of answers.
1. [50 points] Stacks of paper arrive at a trimming process with interarrival times of EXPO(10); all times are in minutes and the first stack arrives at time 0. There are two trimmers, a primary and a secondary. All arrivals are sent to the primary trimmer. If the queue in front of the primary trimmer is shorter than five, the stack of paper enters that queue to wait to be trimmed by the primary trimmer, an operation of duration TRIA(9, 12, 15). If there are already five stacks in the primary queue, the stack is balkedtothe secondary trimmer (which has an infinite queue capacity) for trimming, of duration TRIA(17, 19, 22). After the primary trimmer has trimmed 25 stacks, it must be shut down for cleaning, which lasts EXPO(30). You need to define a failure in the failure data module similar to the one shown in Figure 1.
Figure1 - Primary Trimmer Failure
During this time, the stacks in the queue for the primary trimmer wait for it to become available. Animate and run your simulation for a single replication of 5,000 minutes. Collect statistics, by trimmer, for cycle time, resource utilization, number in queue, and time in queue. Put a text box in your Arena file with, separately for each of the two trimmers, the average time in system (a.k.a. cycle time) for stacks of paper that go through that trimmer, the resource utilization, the time-average number of stacks in that queue, and the average time of stacks in that queue.
2. [50 points] Develop a model of a three-workstation serial production line with high reject rates: 7% after each workstation. Parts rejected after the first workstation are sent to scrap. Parts rejected after the second workstation are returned to the first workstation where they are reworked, which requires a fresh “draw” from the processing-time distribution but increased by 50% from the distribution of the original operation. (This penalty factor of 1.5 applies only at workstation 1 and not at workstation 2 when the part returns to it.) Parts rejected at the third workstation are returned to the second workstation where they are reworked, with a 50% penalty there (but not on its revisit to workstation 3). The operation times are TRIA(5, 9, 12), TRIA(5, 8.5, 13), and TRIA(6.5, 8.9, 12.5) for workstations 1, 2, and 3 respectively (all times are in minutes). Part interarrival times to the system are UNIF(6, 14). Run the model for 20,000 minutes, collecting statistics on the average number in queue at each workstation, the number of scrapped parts, workstation utilizations, and average and maximum cycle times for all parts. Also, collect statistics on the number of times a part was rejected. Hint: You can assign the service times of parts as an attribute to each part before the process module. This approach provides the flexibility needed to handle rejected parts effectively.