Monte Carlo Simulation in Decision Making

Copyright © 2004 David M. Hassenzahl

What is Monte Carlo Analysis?It is a tool for combining distributions, and thereby

propagating more than just summary statisticsIt 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

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.