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ISE 580 Fall 2025

Homework #2

Due by 11:59 pm (Pacific) on Friday Sep 26, 2025

Show all your work step by step. Your grade depends on the clarity of solutions and the accuracy of answers.

1. [30 points] Five identical machines operate independently in a small shop. Each machine is up (that is, works) for between 7 and 10 hours (uniformly distributed) and then breaks down. There are two repair technicians available, and it takes one technician between 1 and 4 hours (uniformly distributed) to fix a machine; only one technician can be assigned to work on a broken machine even if the other technician is idle. If more than two machines are broken down at a given time, they form a (virtual) FIFO “repair” queue and wait for the first available technician. A technician works on a broken machine until it is fixed, regardless of what else is happening in the system. All uptimes and downtimes are independent of each other. Starting with all machines at the beginning of an “up” time, simulate this for 160 hours and observe the time-average number of machines that are down (in repair or in queue for repair), as well as the utilization of the repair technicians as a group; put your results in a Text box in your model. Animate the machines when they’re either undergoing repair or in queue for a repair technician, and plot the total number of machines down (in repair plus in queue) over time. (HINT: Think of the machines as “customers” and the repair technicians as “servers” and note that there are always five machines floating around in the model and they never leave.)

2. [30 points] A painting system contains two operations. Parts arrive according to an exponential interarrival-time distribution with mean 5 (all times are in minutes), with the first part’s arriving at time 0. Parts first enter a painting station (there is only one painting resource) that has a triangular operation time with minimum 1, mode 4.5, and maximum 7. Once the part completes the painting operation, it must be allowed to dry for 15 minutes; during this unattended (that is, there’s no resource required) drying time the part is out of the painting station so other parts can be painted, and there is no limit on how many parts can be in their 15-minute drying period at the same time. After drying, the part enters the second operation, which is a finishing operation; this operation has a uniform processing time between 0.5 and 9, and there is only one finishing resource. Run your simulation for a single replication of 24 hours and observe the average total time in system of parts, the time-average number of parts in the system; also observe, for the paint and finishing operations separately, the average time in queue, the time-average number of parts in queue, and the utilizations of the painting and finishing resources. Put a text box in your model with all these output performance metrics. Animate the painting and finishing resources and the queues leading into them, but do not animate the drying operation, and include a plot of each queue length separately on the same axes. Comment briefly on the relationship in your results between the time-average number of parts in system and the sum of the time averages of the number in each of the queues, and what might explain any apparent discrepancies.

3. [40 points] A small manufacturing department contains three serial workstations (that is, parts go through each of the three workstations in order, one workstation after the other). Parts arrive according to an exponential interarrival-time distribution with mean 8 (all times are given in minutes), with the first part’s arriving at time 0. Before a new part can start processing, it must be mounted on a special fixture, and this mounting operation takes 2 minutes (there are four fixtures available, which can be reused, but each fixture can carry only one part at a time). The part remains on the fixture until it completes processing on all the workstations, at which time it is removed from the fixture (this removal operations takes 1 minute), after which the fixture becomes available for another part that might be waiting for it. Processing times at the first workstation follow a triangular operation time with minimum 4, mode 7, and maximum 9. Processing times at the second workstation have a uniform distribution between 5 and 10. Processing times at the third workstation have a triangular operation time with minimum 5, mode 6.5, and maximum 9. Run your simulation for a single replication of length 48 hours, and observe the time-average and maximum total work in process (WIP) in the whole system. At each workstation separately, observe the average and maximum queue lengths, and the resource utilization. Also observe the utilization of the four fixtures as a group, as well as the time-average and maximum number of parts that are waiting for a fixture (before they can even get going into the system for processing). Add a plot for the total WIP and by-workstation queue lengths, all on the same set of axes; add a second plot showing the number of fixtures that are in use. Animate the resources and queues for each of the workstations, and animate the parts waiting for a fixture, but do not animate the fixtures themselves. Put in a text box with the numerical results requested. What appears to be the bottleneck in this system preventing better efficiency? HINT: Remember that an entity can have multiple different resources Seized at the same time, and that the Process module has “Action” options other than the usual Seize-Delay-Release.