If you are involved in risk management, you must be aware of the Monte Carlo simulation. The Monte Carlo simulation is a quantitative risk analysis technique which is used to identify the risk level of completing the project.

This is one of the most important techniques in risk management; however, you will not see a detailed description of this technique in many PMP exam reference books.

Most references will just say that it is a very complex technique that requires a computer’s assistance, and that is it. Consequently, many aspirants don’t dig into it further. The assumption that this technique is very difficult is not true. In fact, this is one of the easiest techniques in the PMBOK Guide.

I assure you that once you read this blog post, you will have the same thoughts as I.

Okay, let’s get started.

### Monte Carlo Simulation

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.

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.

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.

For example, 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.

#### Limitations of the Monte Carlo Simulation

The Monte Carlo simulation has its own set of limitations. Some of these limitations are as follows:

- To run the Monte Carlo simulation, you input three estimates for an activity. If you show some bias in determining the estimates, your result will not give you a correct analysis. Therefore, the results depend on the quality of your estimates.
- The Monte Carlo simulation shows you the probabilities of completing the tasks, it is not the actual time taken to complete the task.
- The Monte Carlo simulation technique cannot be applied to a single task or activity; you need to have all activities, and the risk assessment completed for each activity.
- You will need to buy an add-on or a software program to run the Monte Carlo simulation.

#### Benefits of the Monte Carlo Simulation

The Monte Carlo simulation method has many benefits in project management, such as:

- It helps you evaluate the risk of the project.
- It helps you predict chances of failure, and schedule and cost overrun.
- It converts risks into numbers to assess the risk impact on the project objective.
- It helps you build a realistic budget and schedule.
- It helps you gain management support for risk management.
- It helps you in decision making with the support of objective data.
- It helps you to find out the chances of achieving your project milestones or intermediate goals.

### Summary

The Monte Carlo simulation is a very important tool and technique in the quantitative risk analysis process which helps you make decisions based on an objective data. Although this technique is not used frequently in low and low-medium sized projects, if used it increases the chances of achieving project success within approved baselines.

Here is where this blog post on Monte Carlo Simulation ends. If you have something to say, you can do so through the comments section.

Muhammad Anjum says

Dear Fahad sb,

Assalam o Aleikum,

First of all, Jazak Allah Khair for writing this important blog post explaining technique used in quantitative risk analysis process.

1) In this blog post, I’m not understanding that how does Monte Carlo Simulation actually works and calculate chances of completion (%ages) ?

2) Any mathematical calculation or example or formula ?

Also, which software is required to run this simulation ?

Fahad Usmani says

WaSalaam,

You only come up with your estimates, and input these information into the program. The program will do the calculation for you.

There are many Monte Carlo simulation software available on the net. Just search it on Google and you will get many.

Azaz Ahmed says

Assalam o Aleikum, Brother,

In above example, Activity A will have pert estimate equal to 5 instead of 4.3.

{4+(4×5)+6}/6 = 5

Thank you for sharing . It was very informative.

Fahad Usmani says

The table is corrected.

Mike Delarosa says

Good article!

Fahad Usmani says

Thanks Mike for you visiting and leaving your comment.

Prof Rao says

Nice article…

The way of explanation is very good…

Fahad Usmani says

Thanks Professor.

Ty says

Very simplified to understand. Thanks for the article….

Fahad Usmani says

You are welcome Ty.

Maysara says

I like it. Thank you so much Fahad

Maysara

Fahad Usmani says

You are welcome Maysara.

Ar says

Very good and simple explanation.

Thanks Fahad !!

Fahad Usmani says

I am glad you liked it Ar. Thanks for your visit.

Lcm says

Thank you so much Fahad! Very helpful! I have my exam scheduled on Sept 9th and i am going through all the anxiety to clear this exam

Fahad Usmani says

Thanks Lcm for your comment.

Sunil says

Simple and well explained. Has anyone heard of MC being used in construction projects ?

Fahad Usmani says

It is used on all types of projects.

Praveen says

Good article and expecting Latin Hypercube sampling also

Fahad Usmani says

I have noted your suggestion and I will try to write a post on this topic in future.

Tauseef Qureshey says

How Monte Carlo Simulation help to find out Risk level? Please give examples

Fahad Usmani says

The example is given in the blog post.

Rohit Sunger says

Hi Fahad,

I have a small concern, what would be the inputs that are mandate to run this tool. For example Calculating the schedule we would need all the activity with there estimates, risk assessment done for all the activities and what else that is required.

Please help me on this

Fahad Usmani says

You will need to enter the estimated duration for activities, such as most likely, pessimist and optimistic.

Amro Fadly says

If you are asking about how the Monte Carlo Method is working

It is working by generating random (according to predefined probabilities) samples then calculating the overall probability

For example assume that you have a board and a circle drawn on that board

Let’s throw darts and see how many fell inside or outside the circle

We can calculate the circle area by multiplying the % of darts fell inside by the total area of the board

hamid says

hello dear

I have a question how do we know that 16 =2% is there a method or equation help us to find it correctly

thanx

Fahad Usmani says

In this blog post, this is an assumed data. You will get the real data when you enter correct data in Monte Carlo simulation software.

Anu Raphael says

Thanks for putting this in the most simplest form to understanding the technique..

Fahad Usmani says

You are welcome Anu.