ISE 403: Homework Lab #5, Fall 2013

Due: Wednesday, October 30 at 11:59pm


  1. Airline Service:  An airline ticket counter has two customer queues, one for regular customers, who are served by four agents, and one for frequent flyer membership customers, who are served by one agent.  Approximately 2 out of every 10 customers have frequent flyer memberships.  Customers arrive with an exponential interarrival time of two minutes from 8 a.m. to 4 p.m., and 4 minutes from 4 p.m. to closing at midnight.  During the second shift (4 p.m. to closing), all customers use the first counter with four agents.  During the first shift, if an arriving frequent flyer membership customer observes that the regular customer queue has two or fewer people while the frequent flyer agent is busy, the customer will enter the regular customer queue.  Service time for regular customers is normally distributed with a mean of 10 minutes and a standard deviation of 4 minutes.  Service time of frequent flyer customers is also normally distributed with a mean 7 minutes and a standard deviation of 2 minutes.

    a. Simulate for five, 16-hour days (five replications of 16 hours each), collect and report 95% confidence interval statistics on the queue sizes and utilization of agents along with the flow times of each customer type.  Also count the number of times a frequent flyer customer decides to enter the regular customer queue during the first shift.  Turn these in as a table.

    b. If your model is a valid representation of the ticket counter, do you have any concerns about the operation, based on your review the statistics produced by the simulation?  (state your concerns in three or fewer sentences)

Notes:  If the original arrival process is Poisson (exponential interarrival times), and arrivals are randomly removed, then the “thinned” process remains Poisson, but with a different mean.  For example, if the mean interarrival time is 2 minutes, and 50% are removed randomly the mean interarrival time becomes 4 minutes with an exponential intearrival distribution. Remember that conditions can contain multiple relationships, such as NQ(Regular Flyer.Queue) <= 2 && NR(FreqFlyerAgent) == 1, where NQ() is the number in queue and NR() is the number busy.  TNOW is current simulation time

Submit model file (.doe) you developed and call it yournameLAB5p1.doe (no animation required). Submit also yournameLAB5p1 with a table of confidence intervals and counts (a) and provide a short discussion for (b).

  1. Machine Operation: Parts for an order are produced in automatic bar stocking machines from metal bars that are manually loaded in the machine and automatically fed into cutters within the machine.  Finished parts drop into a tray beside the machine.  A machine operator is assigned a fixed number of automatic bar stocking machines in a factory.  When a machine finishes processing, the operator removes the tray of finished parts, places an empty tray, loads new bar stock in the machine if needed, adjusts the machines cutting tools, and restarts the machine.  The machine operates without requiring the operator until it finishes the number of parts for the order. The time the operator requires to remove the finished parts, load the bar stock into the machine, adjusts the machine, and starts it up is Lognormally distributed with a mean (LogMean) of 18 minutes and a standard deviation (LogStd) of 3 minutes.  The job processing time (which is a function of the number of parts for an order) is described by an Erlang distribution whose exponential mean is 24 minutes and whose order k is 3.  You may assume that bar stock is always available for making parts.  Run until the machines have produced parts for 500 orders. Do five replications. 

a. The simulation should produce output (including 95% confidence intervals) for: the number of machines waiting for the operator, the time machines spend waiting for the operator, the utilization of the operator, and the time it takes to produced the parts for the 500 orders. 

b. Create a table (not from Arena) that shows these mean performance measures if 4, 5, 6, or 7 machines are assigned to an operator (report means, not confidence intervals).

c. In your opinion, what number of machines should be assigned to an operator and why do you make this recommendation?  (write no more than three sentences to answer this).

Notes:  Carefully think about your conceptual model relative to what the entities will represent.  There is generally no need to model something that is not in limited supply.  You can stop the simulation based on a "terminating condition" in Run/Run Setup/Replication Parameters.  Observe that NC() is the Arena variable for current count.  Use a Variable for the number of machines assigned to an operator, so you can change it easily.

Submit model file (.doe) you developed and call it yournameLAB5p2.doe (no animation required). Submit also yournameLAB5p2 with a table of confidence intervals for (a), a table of values for (b), and provide a short discussion for (c).