This chapter provides an overview of simulation methods, their role in risk quantification and their relationship to sensitivity, scenario, optimisation and other techniques. We aim to introduce the basic principles in an intuitive and non-technical way, leaving the more technical aspects and implementation methods to later in the text.

For the purpose of describing the fundamental principles of simulation methods, we shall consider a simple model in which:

- There are 10 inputs that are added together to form a total (the model's output).
- Each of the 10 inputs can take one of three possible values:
- A “base” value.
- A “low” value (e.g. 10% below the base).
- A “high” value (e.g. 10% above the base).

Of course, despite its simplicity, such a model (with small adaptations) has applications to many other situations, such as:

- Forecasting total revenues based on those of individual products or business units.
- Estimating the total cost of a project that is made up of various items (materials, labour, etc.).
- Forecasting the duration of a project whose completion requires several tasks to be conducted in sequence, so that the total duration is the sum of those of the individual tasks.

With some reflection, it is clear that there are 3^{10} (or 59,049) possible combinations of input values: the first input can ...

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