Assignment

Exercise 1

Suppose that a simulation model is built for a manufacturing system consisting of a large number of machines in series separated by buffers (queues). Since the computer execution time of the model is excessive, it is decided to divide the model into two submodels. The first submode! is run and the departure time of each part (and any other required attributes) is written to a file. The second submodel is executed by driving it with the information stored in the file. Discuss the legitimacy of this modeling approach.

Exercise 2

Stacks of paper arrive at a trimming process with interarrival times of EXPO(10); all times are minutes and the first stack arrives at time 0. There two trimmers, a primary and a secondary. All arrivals are sent to the primarytrimmer. If the queuein front of the primary trimmer is shorter than five, the stack of paper enters that he 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 balked to the secondary trimmer (which has an infinite queue capacity) for trimming, of duration TRIA (l 7, 19, 22). After the primary trimmer has trimmed 25 stacks, it must be shut down for cleaning, which lasts EXP0(30). 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.

Exercise 3

Develop a model of a three-workstation seral 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 number in queue at each workstation, the number of scrapped parts, workstation utilizations, and average and maximum cycle times for parts that are not rejected at any workstation and for parts that are rejected at least once. Also, collect statistics on the number of times a part was rejected.