Transcript Monte Carlo Simulation in Decision making

Monte Carlo Simulation in
Decision Making
What is Monte Carlo Analysis?
It is a tool for combining distributions, and thereby
propagating more than just summary statistics
It uses random number generation, rather than analytic
calculations. Its core idea is to use random samples of
parameters or inputs to explore the behavior of a
complex system or process
It is increasingly popular due to high speed personal
computers
Since that time, Monte Carlo methods have been applied
to an incredibly diverse range of problems in:
– science, engineering, and finance -- and business
applications in virtually every industry.
Copyright © 2004 David M. Hassenzahl
Background/History
• “Monte Carlo” from the gambling town of the same
name (no surprise)
• First applied in 1947 to model diffusion of neutrons
through fissile materials (scientists at Los Alamos
found problems were too complex for an analytical
solution)
• Limited use because time consuming
• Much more common since late 80’s with more
powerful computers
Copyright © 2004 David M. Hassenzahl
Why Should I Use Monte Carlo Simulation?
• Whenever you need to make an estimate, forecast or
decision where there is significant uncertainty, consider
Monte Carlo simulation –
– if you don't, your estimates or forecasts could be way off the
mark, with adverse consequences for your decisions!
– Dr. Sam Savage, a noted authority on simulation and other
quantitative methods, says "Many people, when faced with
an uncertainty ... succumb to the temptation of replacing the
uncertain number in question with a single average value. I
call this the flaw of averages, and it is a fallacy as
fundamental as the belief that the earth is flat.“
– Or as Milton Freeman said “Don’t cross a river when you are
told the average depth is 4 feet”
Why Should I Use Monte Carlo
Simulation?
• Many business activities, plans and processes are too
complex for an analytical solution -- just like the physics
problems of the 1940s.
• But you can build a spreadsheet model that lets you evaluate
your plan numerically -- you can change numbers, ask 'what
if' and see the results.
– This is straightforward if you have just one or two parameters to
explore.
• But many business situations involve uncertainty in many
dimensions –
– for example, variable market demand, unknown plans of
competitors, uncertainty in costs, and many others -- just like the
physics problems in the 1940s.
• If your situation sounds like this, you may find that the Monte
Carlo method is surprisingly effective for you as well.
How Monte Carlo Simulation Works
• Monte Carlo simulation performs risk analysis by building models of
possible results by substituting a range of values—a probability
distribution—for any factor that has inherent uncertainty.
• It then calculates results over and over, each time using a different set
of random values from the probability functions.
• Depending upon the number of uncertainties and the ranges
specified for them, a Monte Carlo simulation could involve thousands
or tens of thousands of recalculations before it is complete.
– Monte Carlo simulation produces distributions of possible outcome
values.
• By using probability distributions, variables can have different
probabilities of different outcomes occurring.
• Probability distributions are a much more realistic way of describing
uncertainty in variables of a risk analysis.