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Simulation and Modeling

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
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