Simulation Exam

Practice Exam

1. Customers arriving to a bank wait in line to perform their transactions with a single bank teller on duty.  Data on service times collected over the course of a week are summarized in the histogram below (x-axis is in minutes).  What might explain the look of this histogram? Based on your explanation, discuss how you would model the service time in a simulation model of this bank.  

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1. A bank with two ATMs in its lobby has noticed long lines in front of them and has received some customer complaints.  Mike is conducting a simulation class project to help the bank decide whether to install an extra ATM machine.  He sits there with his stop-watch and records interarrival times of customers who line up for the ATMs (there is a single line feeding the ATMs) as well as the times customers spend doing their transactions.  He then fits input distributions to the interarrival times and service times, runs the baseline model with the two ATMs, and find that the usual output measures (e.g, wait times, utilization) of the model match well with the actual system measures.  To help the bank understand what would happen if a third ATM were installed, he goes into the Resource module of Arena, changes the number of ATM resources from 2 to 3, and then re-runs the model under that scenario.  I marks points off and tell him “besides increasing the number of ATM resources from 2 to 3, there is something else you should have considered.”  What important aspect do you think Mike missed?  

1. Custom Tee Shirts is planning to print and sell specially designed tee shirts for the Stanley Cup Finals (SCF).  The shirts cost $5 to produce and are sold for $21 each during the SCF.  The demand for tee shirts during the SCF depends on how many games it lasts.  The table below gives the probability the SCF lasts for 4, 5, 6, or 7 games (the finals are over when the first of the two opposing teams wins 4 games).  Assume the demand for tee shirts during the SCF is normally distributed with average = 2000*games and standard deviation = .20*average.  In the three months after the SCF is over, the price for the tee shirts is $10, and demand for the tee shirts during these three months is normally distributed with average = 4000 and standard deviation = 800.  After this three month period, any remaining t-shirts are given away for free.

Because of production lead times, the company has one opportunity to decide how many tee shirts to produce, which would be ready by the time the SCF starts.

Table: Probability the SCF lasts 4, 5, 6, or 7 games

Develop and analyze an @Risk model to justify your recommendation of how many tee shirts Custom Tee Shirts should produce.

1. A bomber is attempting to destroy an ammunition depot.  As shown in the figure below, the depot is represented as a circle centered at the origin with a radius of 400 meters.  A bomber flying in the East-West direction drops a bomb.  The point of contact in the East-West direction is normally distributed: the bomb is expected to hit at 0 meters in the East-West direction with a standard deviation of 300 meters.  The point of contact in the North-South direction is also normally distributed: the bomb is expected to hit at 0 meters in the North-South direction with a standard deviation of 250 meters.  The entire depot is destroyed if a bomb falls anywhere on it.  

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1. Develop an @Risk model to estimate the probability that the depot is destroyed.

Enter your estimate below, justified by the results of your model.