 # Quantitative Risk Analysis for Project Management

In this article we are going to discuss using Monte Carlo simulation to perform quantitative risk analysis for project management.  The three primary risks to a project are schedule, financial, and technical.  Two of these three risks readily lend themselves to be quantified with Monte Carlo simulation: schedule risk and financial risk.

If you're unfamiliar with Monte Carlo simulation, refer to a previous article on the basics of Monte Carlo simulation.

## Schedule Risk Simulation

Schedule risk is the risk of not completing the project on time.  Quantifying this risk involves simulating project completion time which gives us data to make conclusions.  We can estimate the probability of completion on or before the due data.  We can also look at the minimum and maximum completion dates to understand how much spread is possible.

To simulate, we replace task completion times with a random variable based on an assumed probability distribution.  For schedule risk, this is often the PERT distribution which requires a best case, worst case, and most likely estimate of a task's completion time.  During a simulation, each task's time is sampled from the distribution and the critical path time is calculated based on precedence rules that are built into the spreadsheet model.

#### More Detailed Information

We've covered the risks involved in only using best estimates for completion times here.  There is also an article on how to set up a project network for simulation here.  Finally, check out this article on simulating a critical path.

## Financial Risk Simulation

Financial risk could refer to the project cost, project net present value (NPV), or some other metric.  For financial risk, essentially we build a spreadsheet model that calculates the desired metric.  However, for simulation, we replace items that can vary with a random variable function that samples from an underlying probability distribution.

#### Cost Risk

When building a model for cost risk, we simply enter the various costs in a spreadsheet and sum the costs to get an overall project cost.  Some costs may be fixed such as a purchase contract.  These costs are fixed and do not need to be replaced with a random variable.  Other costs will be estimated, and these need to be replaced with a random variable.

Often, since these estimates are based on opinion, we would use a triangular or trapezoidal distribution.  The triangular distribution requires a best case estimate, worst case estimate, and most likely estimate.  The trapezoidal distribution requires four estimates: worst case, best case, lower most likely, and upper most likely.  The probability is maximum and constant between the lower and upper most likely estimates.  This centers most samples near the lower-upper most likely range while allowing for some outliers in the tails.

If data is available from previous projects, a normal distribution may be more appropriate where the mean and standard deviation of the data defines the distribution.  There are many more possibilities, but the normal distribution will cover the majority of cases.