# Monte Carlo simulation

# [edit] Introduction

A **Monte Carlo simulation** is a computational risk analysis tool applied to situations that are uncertain or variable. It is a mathematical way of predicting the outcomes of a situation or set of circumstances by giving a range of possible outcomes and assessing the risk impact of each. It is also referred to as the ‘Monte Carlo method’ or ‘probability simulation’ and is used in many diverse applications such as construction, engineering, finance, project management, insurance, research, transportation and so on.

The name is thought to have been devised by scientists working on the atom bomb in reference to the principality of Monaco – well known for its casinos.

A key characteristic of a **Monte Carlo simulation** is that it provides a more realistic picture of likely future outcomes by generating a range of possible values, not just a single estimate. In construction, it can be used to predict how long a particular task will take and its likely effect on the programme schedule.

# [edit] Mathematical modelling

To begin with, a mathematical model is created using a range of estimates for a particular task. So, for example, a project manager may consider the time it may take to complete a set of tasks by:

- Considering worst case scenarios (ie the maximum expected time values for all variables),
- Considering best-case scenarios (ie the minimum expected time values for all variables).
- Considering the most likely result.

So, for a particular set of tasks on a construction project, the project manager may estimate the following:

Task | Best case (minimum) | Most likely | Worst case (maximum) |

Task 1 | 2 weeks | 4 weeks | 7 weeks |

Task 2 | 3 weeks | 6 weeks | 9 weeks |

Task 3 | 8 weeks | 13 weeks | 18 weeks |

Total | 13 weeks | 23 weeks | 34 weeks |

From the table above, it can be seen that the range of outcomes for completing the three tasks ranges from 13 to 34 weeks.

These estimates are inputted into the **Monte Carlo simulation** which may be run 500 times. The likelihood of a particular result can be tested by counting how many times it was returned in the simulation and a percentage created.

So, it may be that the after 500 simulations, the most likely estimate of 23 weeks completion was only returned 20% of the time (a probability of only 1 in 5). Whereas, completion in 30 weeks was returned 80% of the time (4 in 5), which may be a more realistic basis for the project manager’s decision making.

Note: the extremes may be discounted. It should also be noted that the method is only as good as the original estimates used to create the model. Also, the values outputted are only probabilities but they may give planners a better idea of predicting an uncertain future.

Palisade @RISK for Excel from Palisade Corporation is just one of the available software programmes able to undertake **Monte Carlo simulations**.

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## Comments

In undertaking a Monte Carlo risk analysis it should be noted that the variables to which the probabilities are assigned should be independent of each other. As an example the price of reinforced concrete and the price of steel are not necessarily independent of each other.