# Monte Carlo Simulation Technique

The Monte Carlo simulation is a quantitative risk analysis technique which is used to identify the risk level of completing the project on a specific budget/duration. This is one of the most important techniques in risk management; however, you will not see a detailed description of this technique in many PMI-RMP references.

This is a mathematical technique that allows you to account for risks in your decision making process. With the help of this technique you can determine the impact of the identified risks by running simulations many times, and identify a range of possible outcomes in different scenarios.

It involves determining the impact of the identified risks by running simulations to identify the range of possible outcomes for a number of scenarios; random sampling is performed by using uncertain risk variable inputs to generate the range of outcomes with a confidence measure for each outcome. It’s done by establishing a mathematical model and then running simulations using this model to estimate the impact of project risks, and it helps in forecasting the likely outcome of an event and thereby helps in making informed project decisions.

You can use the Monte Carlo simulation to analyze the impact of risks on forecasting models such as cost, schedule estimate, etc. You need this technique here because in these types of decisions, some degree of uncertainty exists. If you don’t use this technique, your outcome will not be sound and the results of your decision may surprise you at a later stage.

This technique gives you a range of possible outcomes and the probabilities that will occur for any choice of action. You can use Monte Carlo simulation to find the best and worst case scenarios of your project, and run simulations to generate most likely outcome for the event . In most situations you will come across a bill-shaped normal distribution pattern for the possible outcomes.

__Example1:__

Let’s discuss the use of the Monte Carlo simulation in determining the project schedule, to perform the Monte Carlo simulation to determine the schedule, you must have duration estimates for each activity.

Let’s say that you have three activities with the following estimates (in months):

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

However, in the best case it will be finished in 16 months, and in the worst case it will be finished in 21 months. Now, if we run the Monte Carlo simulation for these tasks five hundred times, it will show us results like this:

(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 you can see that there is a:

2% chance of completing the project in 16 months

8% chance of completing the project in 17 months

55% chance of completing the project in 18 months

70% chance of completing the project in 19 months

95% chance of completing the project in 20 months

99% chance of completing the project in 21 months

So, you see, this program provides you with a more in-depth analysis of your data which helps you make a better informed decision.

__Example 2: __

Let’s assume you are managing a project involving a creation of an eLearning module, the creation of the eLearning module comprises of three tasks, writing content, creating graphics and Multimedia integration, based on previous projects and expert interviews you determined the best case , most likely and worst case of the activities estimates as follow:

The Monte Carlo simulation randomly selects input values for the different tasks to generate the possible outcomes, assuming the simulation is run 500 times , from the above table we can see that the project can be completed anywhere between 11 and 23 days .

When the Monte Carlo Simulation runs are performed , we can analyze the percentage of times each duration outcome between 11 and 23 is obtained . The following table depicts the outcome of the simulation.

What the previous table and below chart suggests is that , for example , the likelihood of completing the project in 17 days or less is 33% , given this information , it looks much more likely that the project will end up taking anywhere between 19 – 20 Days .

*Key benefits of using Monte Carlo Simulation*

- It’s an easy method for arriving at the likely outcome for an uncertain event and an associated confidence limit for the outcome .
- Simulations are typically useful while analyzing cost and schedule , with the help of monte Carlo Analysis , you can add the cost and schedule risk event to your forecasting model with a greater level of confidence.
- Useful technique for easing decision making based on numerical data to back your decision.
- It can be used to find the likelihood of meeting your project milestones and intermediate goals.

*Steps to follow while performing Monte Carlo Analysis*

**Identification of the project risk variables,**a risk variable is a parameter which is critical to the success of the project and slight variation in its outcome might have a negative impact on the project.

- The project risk variables are typically isolated using the sensitivity and uncertainty analysis.
- Sensitivity Analysis is used for determining the most critical variables in the project.
- Uncertainty Analysis involves establishing the suitability of a result and it helps in verifying the fitness or validity of particular variable,

**Identification of the range limits for the project variables**, This process includes defining the maximum and minimum values for each identified project risk variable , the best way to get this values is using historical data for similar projects , if not , you should rely on expert judgment to determine the most likely values .**Specification of probability weights for the established range values,**It’s the time to allocate the probability of occurrence for the project risk variable, to do so, multi value probability distributions are deployed . Commonly used probability distributions for analyzing risks are normal distribution, uniform distribution, triangle distribution and step distribution.**Establishing the relationships for the correlated values ,**This step involves defining the correlation between the project risk variables , Correlation is the relationship between two or more variables where a change in one variable includes change in other. In Monte Carlo Simulation , input values for the project risk variables are randomly selected to execute the simulation runs , therefor if a certain risk variable inputs are generated that violate the correlation between variables , the output will likely be off the expected value .**Performing Simulation runs ,**This step typically done using a software and ideally 500-1000 runs constitute a good sample size , while executing the simulation runs , random values of risk variables are selected with the specified probability distribution.**Statistical Analysis of the simulation results**, Each simulation run represents the probability of occurrence of risk event, cumulative probability distribution of all the simulation runs is plotted and it can be used to interpret the probability for the result of the project being above or below specific value, this cumulative probability distribution can be used to assess the overall project risk.

__Summary__

- Monte Carlo Simulation is valuable technique for analyzing risks , specifically those related to cost and schedule .
- The fact is based on numeric data gathered by running multiple simulations adds even greater value to this technique, It also helps removing any kind of bias regarding the selection of alternates.
- While preforming Monte Carlo simulation it’s advisable to seek participation of the key project decision-makers and stakeholders, specifically while agreeing on the range values of the project risk variables and probability distributions.
- The reliability of the outputs depends on the accuracy of the range values and the correlation patterns, so that you should practice extreme caution while identifying the correlations and specifying the range values .

__What Questions you shall expect in the PMI-RMP Exam ?__

The figure below shows the results of a Monte Carlo simulation for project schedule Analysis, what’s the probability of the project to finish on time if it is scheduled to finish at 12, Oct?

Choice 1 : 50%

Choice 2 : 60%

Choice 3 : 70%

Choice 4 : 80%

*Solution :*

As per the curve there is 80% probability of the project to finish at October,12

Expect to see 5 or more questions in the PMI-RMP Exam asking you to read the results of the Monte Carlo Simulation software

Choice 4

Good Luck