# RiskAMP Project

RiskAMP Project is a tool for modeling projects using Monte Carlo simulation. It’s not intended as a project tracking tool; it’s intended as a risk planning and management tool.

## What’s it for?

Imagine you have a project, and you estimate that it will take between 10 and 20 weeks, most likely around 17 weeks.

Now you have to plan around those estimates — allocating resources, scheduling your next project, guaranteeing completion. How do you calculate the risk associated with your project estimates?

For example, what is the probability that you will complete the project within 17 weeks (your most likely estimate)? What is the probability you will complete with 18 or 19 weeks? What impact would that have on resources, bonding, or insurance?

Stochastic modeling using Monte Carlo simulation can help answer these questions. By creating a model incorporating random distributions and your estimates, we can find the risk associated with various outcomes.

## Complex projects

But there’s more to it than that. If all we were trying to do were model your project with a single estimate, we could do it analytically.

Now imagine that you have a project with three separate tasks — let’s refer to the tasks as planning, execution, and completion. We have separate estimates for each of the tasks, based on our experience and expertise.

Task Best Case Worst Case Most Likely
Planning 2 weeks 4 weeks 3 weeks
Execution 12 weeks 18 weeks 16 weeks
Completion 3 weeks 6 weeks 4 weeks

One way to model this project would be to sum up the best case, worst case, and most likely estimates, and base our risk analysis on that. If we did that, the model would look just like the model in the first section (and we could solve it analytically).

But doing that makes an assumption — that these three tasks are perfectly correlated. Meaning that either all the tasks get completed really quickly, or all of them take a long time, or all of them get completed in the most likely time.

In reality, what is more likely to happen is that one task takes a little longer than our estimate, one task completes a little quicker, and another task completes around the estimated time. In other words, the tasks aren’t perfectly correlated. How quickly one task gets completed doesn’t affect how the others are completed.

So what we need to do is model each of these tasks separately, and then look at the combined results.

It turns our that doing that using just math is really complicated (and sometimes impossible). That’s where Monte Carlo simulation comes in. Using Monte Carlo, we can sample each task using a separate distribution, then combine the results, and look at the distribution of outcomes.

Using the example above, if we were to take the simple approach, and just use one set of estimates, the distribution looks like this:

On the other hand, if we model each task separately, the distribution looks like this:

(both of these examples use the PERT distribution to model project outcomes).

Note how the results in the second case are much more clustered around the most likely value. That might not look like much, but if we are trying to understand risk, what is the likelihood that the project will take 25 weeks or more to complete?

Using the simple estimates, the probability is about 25%. Using the composite model, the probability is about 13%. In other words, the risk from the simple model is almost twice that shown in the complex model.