Simulation and Modeling
Exercises: For this laboratory assignment, you are expected to do the following three exercises. Make sure you address all parts of the question and provide appropriate answers to the questions as stated. Attach a coversheet to your Assignment, with your full name and student number clearly indicated. Each question is worth 15 marks, for a total mark out of 45. This assessment is worth 10% of your mark for ENGG953 in total. Ensure you show your system design, including parameter settings, results and your analysis of the results relative to system performance. You must submit both a hardcopy of the Assignment with your written solutions (aim, design, implementation settings, results, analysis, conclusions and recommendations) as well as a CD that contains your Arena (.doe) files. Your lecturer will be running your Arena models, so ensure they are complete and properly labelled. Question 1 (15 marks). Five identical machines operate independently in a small shop. Each machine is up (i.e. works) for between six and ten hours (uniformly distributed) and then breaks down. There are two repair technicians available, and it takes one technician between one and three 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. 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. Show your system design and provide comments about its performance and parameters that you established in the model. 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. Analyze the results obtained from running the simulation.
Question 2 (15 marks). Parts arrive at a single machine system according to an exponential interarrival distribution with a mean 20 minutes; the first part arrives at time 0. Upon arrival, the parts are processed at a machine. The processing-time distribution is TRIA(11,16,18) minutes. The parts are inspected and about 25% are sent back to the same machine to be reprocessed (same processing time). Run the simulation for 20,000 minutes to observe the average and maximum number of times a part is processed, the average number of parts in the machine queue and the average part cycle time (time from a part’s entry to the system to its exist after however many passes through the machine system are required). Analyze the results obtained from running the simulation. Question 3 (15 marks). A production system consists of four serial automatic workstations. The first part arrives at time zero, and then (exactly) every 9.8 minutes thereafter. All transfer times are assumed to be zero and all processing times are constant. There are two types of failures; major and jams. The data for this system are given in the table below (all times are in minutes). Use exponential distributions for the uptimes and uniform distributions for repair times (for instance, repairing jams at Workstation 3 is UNIF(2.8, 4.2). Run your simulation for 10,000 minutes to determine the percent of time each resource spends in the failure state and the ending status of each workstation queue (tabulate your results). Workstation Number Process Time Major Failure Means Uptimes Major Failure Means Repair Jam Means Uptime Jam Means Repair 1 8.5 475 20, 30 47.5 2, 3 2 8.3 570 24, 36 57 2.4, 3.6 3 8.6 665 28, 42 66.5 2.8, 4.2 4 8.6 475 20, 30 47.5 2, 3 End of Assignment 1.
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