## Monte Carlo Simulation

The Project Management Body of Knowledge (PMBOK Edition 6) advocates the use of Monte Carlo simulation for performing quantitative risk analysis.

In the project management discipline, Monte Carlo method, or probability simulation, is a computer-based mathematical technique used to understand the impact of risk and uncertainty. Its most common use is in the creation of the project schedule and the determination of the project end date. The Monte Carlo method was invented by scientists working on the atomic bomb project in the 1940s. They named the method after the city in Monaco famed for its casinos and games of chance.

Monte Carlo simulation provides a number of advantages over *deterministic, *or single-point estimates:

- Helps to evaluate the overall risk in the project.
- Converts uncertainty on the project into tangible numbers to assess the overall impact to the project.
- It can be applied to assess the impact on the schedule or the cost.
- Provides the answer in a range of probabilities or a curve.
- The answer can give you, quite accurately, the probability of completing the project with a specific cost, or a specific date.

Consider a project critical path that consists of only three sequential tasks:

We also estimate the minimum and maximum expected time (based on our experience, others’ experience and expertise, or historical information) to produce a quantitative range of possible outcomes:

In the Monte Carlo simulation, we randomly generate values for each of the tasks, then calculate the total time to completion. The simulation will be run at least 500 times. Based on the results of the simulation, we will be able to describe some of the characteristics of the risk in the model.

To test the likelihood of a particular result, we count how many times the model returned that result in the simulation. In this case, we want to know how many times the result was less than or equal to a particular number of weeks.

The original estimate for the “most likely”, or expected case, was 14 weeks. From the Monte Carlo simulation, however, we can see that out of 500 trials using random values, the total time was 14 weeks or less in only 34% of the cases. Put another way, in the simulation there is only a 34% chance – about 1 out of 3 – that any individual trial will result in a total time of 14 weeks or less. On the other hand, there is a 79% chance that the project will be completed within 15 weeks. Further, the model demonstrates that it is extremely unlikely, in the simulation, that we will ever fall at the absolute minimum or maximum total values.

After running the simulations, we would not normally want to pick the end date that has a 50-50 chance of success. The Monte Carlo analysis will tell us the date that we have an 80 percent chance to achieve, or a 90 percent chance, depending on how safe we need to be.

Like any forecasting model, the simulation will only be as good as the estimates we make. It’s important to remember that the simulation only represents probabilities and not certainty. Nevertheless, Monte Carlo simulation can be a valuable forecasting tool. Here’s another example:

Let us assume that the simulation is run 500 times. From the above table, we can see that the project can be completed anywhere between 11 to 23 days. When the Monte Carlo simulation runs are performed, we can analyse the percentage of times each duration outcome between 11 and 23 is obtained. The following table depicts the outcome of a possible Monte Carlo simulation:

What the above table and chart suggest is, for example, that the likelihood of completing the project in 17 days or less is 33%. Similarly, the likelihood of completing the project in 19 days or less is 88%, etc. Note the importance of verifying the possibility of completing the project in 17 days, as this, according to the Most Likely estimates, was the time you would expect the project to take. Given the above analysis, it looks much more likely that the project will end up taking anywhere between 19 – 20 days.

Thus, Monte Carlo simulation is a valuable technique for analysing project risks, specifically those related to cost and schedule. The fact that it is based on numeric data gathered by running multiple simulations helps in removing any kind of project bias regarding the selection of alternatives while planning for risks.

While running the Monte Carlo simulation, it is advisable to seek active participation of the key project decision-makers and stakeholders, specifically while agreeing on the range values of the project risk variables and the probability distribution patterns to be used. This will go a long way in building stakeholder confidence in your overall risk-handling capability for the project. Moreover, this serves as a good opportunity to make them aware of the entire risk management planning being done for the project.

You will need to buy an add-on or a software program to run the Monte Carlo simulation. Some software to perform the Monte Carlo simulation:

**GoldSim**– Premier Monte Carlo simulation software solution for dynamically modeling complex systems in business, engineering and science. GoldSim supports decision and risk analysis by simulating future performance while quantitatively representing the uncertainty and risks inherent in all complex systems.**Excel Solver**– Risk Solver Pro offers lightning fast Monte Carlo simulation and powerful Decision Tree capabilities all in one easy to use product.**Crystal Ball**and**@RISK**perform risk analysis using Monte Carlo simulation to show us many possible outcomes in our Microsoft Excel spreadsheet and tells us how likely they are to occur. This means we can judge which risks to take and which ones to avoid.

While not as sophisticated or accurate as Monte Carlo simulations, the comparatively simplistic PERT (Expected duration = (O + 4M + P) / 6) still gives us a pretty good estimate for most projects, although there is no getting around the triple-entry required to make both tools work. A particular advantage of using Monte Carlo simulation is that it will evaluate all the paths through the project network diagram (not just the critical path) and the resulting normal curve created by the Central Limit Theorem can help us see what-if scenarios from every angle. But most project estimates do not require this level of rigour, and however we derive our estimates, remember that an “exact estimate” remains an oxymoron.