# Production systems modeling 3 | Operations Management homework help

Question1

A painting system contains two operations. Part arrive according to an exponential interarrival-time distribution with mean 5 (all times are in Minuets), 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.

Question2

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 not that there are always five machines floating around in the model and they never leave.)

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