Monte Carlo Simulation

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Monte Carlo Simulation

• Presented by Megan Aldrich and Tiffany Timm

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What is Monte Carlo?

• Uses random numbers to generate a simulation to
  mimic real data
• Helps find statistics for data that is really
  messy
• Use of a computer is required

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Discovery and First Use

• First used by Enrico Fermi in 1930s for neutron
  diffusion
• Documented by John von Neumann in the 1940s
  during the Manhattan Project of World War II
• Popular because gambling was a rising sport and
  was coined the name Monte Carlo by Neumanns
  partner Stainslaw Ulam who loved poker

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Pros

• Easy to use
• Can make the complex data simple
• Does not take a lot of time to analyze
• Inexpensive

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Cons

• Original expense to develop and operate
  simulations can be high
• Not sufficient in dealing with small numbers and
  usually has the operator estimating when this
  happens

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Outline for Monte Carlo

• List all possible outcomes for each event.
• Determine the probability of each outcome.
• Determine subsets of the integers which have the
  same relative frequencies as the probabilities.
• Set up a correspondence between the outcomes and
  the subsets.
• Select a random number.
• Using each random number to represent the
  corresponding event, perform the experiment and
  note the outcome.
• Repeat until desired confidence.

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Our Problem

• As the owner of a small grocery store you have a
  choice of hiring
• Two cashiers who do their own bagging, and each
  of whom can check out a shopper in two minutes,
  or
• One cashier and one bagboy who, working as a
  team, can check out a shopper in one minute.
• We want to find the best scenario.

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Our Problem continued

• Based on our experience for every one minute
• Zero people get in line 30 of the time
• One person gets in line 40 of the time
• Two people get in line 30 of the time
• Using this system we can find the expected wait
  time per customer and the expected line length
  they will encounter.

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Problem analysis

• We generated random numbers in Excel and used a
  program written by Tiffany to run the experiment
• We want to explore
• Ho Mx My
• H1 Mx gt My

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Results

• We reject the null hypothesis in favor of the
  alternative hypothesis. This shows that the
  average wait time for a one-lane system is longer
  than a two-lane system.
• Therefore, we would choose a two-lane system to
  effectively lower the wait time for customers.

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Questions

• Under what circumstances would you use the Monte
  Carlo Simulation?
• Name three ways you can generate random numbers.