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Monte Carlo Methods - Simulation.   Monte Carlo methods can be used to simulate processes with many varying inputs and outputs.

For a demonstration of a simulation, follow this link.  If it is not installed on your machine, the page will attempt to download Adobe's SVG viewer. 

Whilst Monte Carlo methods can be a valuable aid to decision making, they should not be used without an understanding of the process being modeled.  Typically, in any activity, there are a few critical inputs and it is these which should be the focus of the analysis, not trying to attribute complex distributions to minor variables.  So a Monte Carlo analysis should be preceded by a sensitivity analysis to determine what the important parameters are.

There are many ways of approaching a Monte Carlo analysis, but a good starting point is a flow chart of the processing being modeled.  For the example, we have used a 100m obstacle race.  Five runners with varying combinations of ability to negotiate obstacles and run fast are competing for a trophy.  The coach of Runner D wants to know if a little extra training will increase the probability of his/her protégés chance of winning.

The diagram below shows the flowchart for running a series of races.  By simulating the race many times (say, 1,000 to 1,000,000) it will be possible to estimate the probability of each of the runners winning.  In practice, all runners compete at the same time, however, our computer is simple minded and will treat the race as an event in which one competitor follows another.  The first runner sets the time to beat, if the next runner achieves a faster time, the are treated as the winner until their time is beaten.  The process continues until all runners have completed the race.  The race is then repeated until the set number of simulations has been completed.

For simplicity, it is assumed, that the time each runner takes to complete the course is triangularly distributed.  The time for a given runner to complete the course is determined by selecting a random time, the runner with the lowest time is the winner.

The coach collects data by standing at the trackside and recording the minimum, modal and maximum times of each of the competitors

Athlete	Minimum	Mode	Maximum
Runner A	12.0	13.0	15.0
Runner B	10.0	16.0	20.0
Runner C	11.0	12.5	17.0
Runner D	12.0	13.0	15.0
Runner E	12.0	14.0	18.0

When all the data has been collected, it is fed into the computer program which generates the probabilities of each competitor winning.  This is shown in the graph below:

Runner C is shown to be the strongest competitor, however, Runner D can be as fast and tends not to get tangled up with the obstacles as often as Runner C because his/her maximum times are better.  As the result of a modest change in diet and a little extra effort, Runner D manages to take half a second off his/her minimum modal times and significantly improves his/her chances, as shown in the graph below:

With any form of simulation, it is important to have good data and use it appropriately.  One of the criticisms of simulations is that they don't respond as does the real world, putting aside factors such as poor modeling and programming.  One of the problems is that some input data is subjective.  Taking an example from the oil industry, it is not unknown to use overall success ratios for an area, rather than for a new play that is being proposed.  Thus what in reality is a high risk venture, is treated in the same way as proven (and possibly exhausted) plays.  Thus it is better to have a simple, well calibrated model, than a complex un-calibrated one.

For more information: info@brighton-webs.co.uk