Transcript Monte Carlo Simulation

Monte Carlo
Simulation
Presented by Megan Aldrich and
Tiffany Timm
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
Discovery and First Use
 First used by Enrico Fermi in 1930s for
neutron diffusion
 Documented by John von Neumann in
the 1940’s during the Manhattan Project
of World War II
 Popular because gambling was a rising
sport and was coined the name Monte
Carlo by Neumann’s partner Stainslaw
Ulam who loved poker
Pros
 Easy to use
 Can make the complex data simple
 Does not take a lot of time to analyze
 Inexpensive
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
Outline for Monte Carlo
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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.
Our Problem
As the owner of a small grocery store you
have a choice of hiring:
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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.
Our Problem continued
Based on our experience for every one
minute:
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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.
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 > My
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.
Questions
 Under what circumstances would you
use the Monte Carlo Simulation?
 Name three ways you can generate
random numbers.