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Monte Carlo Analysis

Updated on Sep 2, 2025
 
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Risk analysis is part of every decision we make. We are constantly faced with uncertainty, ambiguity, and variability. And even though we have unprecedented access to information, we can’t accurately predict the future. Monte Carlo simulation (also known as the Monte Carlo Method) lets you see all the possible outcomes of your decisions and assess the impact of risk, allowing for better decision making under uncertainty.

Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. The technique is used by professionals in such widely disparate fields as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the climate & environment control.

The Monte Carlo simulation was invented by an atomic nuclear scientist named Stanislaw Ulam in 1940, and it was named Monte Carlo after the town in Monaco which is famous for its casinos.

We can use the Monte Carlo simulation to analyze the impact of risks on forecasting models such as cost, schedule estimate, etc. in a project scenario. We need this technique here because some degree of uncertainty exists in these types of decisions. This technique gives us a range of possible outcomes and the probabilities that will occur for any choice of action.

An Example:

We must have duration estimates for each activity to perform the Monte Carlo simulation to determine the schedule.

Suppose that we have three activities with the following estimates (in months):

Activity

Optimistic

Mostly Likely

Pessimistic

PERT Estimate

A

5

4

6

4.5

B

5

6

7

6

C

6

7

8

7

Total

16

17

21

17.5

From the above table we can deduce that according to the PERT estimate, these three activities will be completed in 17.5 months.

However, in the best case, it will be finished in 16 months, and in the worst case, it will be completed in 21 months.

Now, if we run the Monte Carlo simulation for these tasks five hundred times, it will show us results such as:

Duration(in months)

Changes of Completion

16

2%

17

8%

18

55%

19

70%

20

95%

21

100%

(Please note that the above data is for illustration purpose only, and is not taken from an actual Monte Carlo simulation test result.)

From the above table we can see that there is a:

  1. 2% chance of completing the project in 16 months.
  2. 8% chance of completing the project in 17 months.
  3. 55% chance of completing the project in 18 months.
  4. 70% chance of completing the project in 19 months.
  5. 95% chance of completing the project in 20 months.
  6. 100% chance of completing the project in 21 months.

So, we can see, this program provides us with a more in-depth analysis of the data which helps us make a better-informed decision.

Conclusion

The Monte Carlo Analysis is an important method adopted by managers in estimation process to calculate the many possible project completion dates and the most likely budget required for the project. Using the information gathered through the Monte Carlo Analysis, project managers are able to give senior management the statistical evidence for a more reliable timeline and budget required to complete a project with a greater chance of success.

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