Schedule risk analysis uses the same principles as cost risk analysis for modeling general uncertainty and risks and opportunities. However, it must also cope with the added complexity of modeling the inter-relationships between the various tasks of a project. This section looks at the simple building blocks that typically make up a schedule risk analysis and then shows how these elements are combined to produce a realistic model.

A number of software tools allow the user to run Monte Carlo simulations on standard project planning applications like Microsoft Project and Open Plan. However, most of these products do not have the flexibility to model discrete risks and feedback loops, described below, which are common features of a real project. The software program "@RISK for Project" is an exception. However, we use here a spreadsheet format with Crystal Ball to illustrate most clearly the principles you need to understand.

A project plan consists of a number of individual tasks. The start and finish dates of these tasks can be related in a number of ways:

one task cannot start until another has finished (the link is called finish-start or F-S). This is the most common type of linking in project planning models;

one task cannot start until another task has started (start-start or S-S);

one task cannot start until another has been partially completed (start-start+lag or S-S+x);

one task cannot finish until another has finished (Finish-Finish or F-F).

Figure A below shows how these inter-relationships are represented diagramatically.

**Figure A**

In the rest of this section we will use the notation "(a,b,c)' to denote a Triangular(a,b,c) distribution. So: Lag(5,6,7) wks is a lag modeled by a Triangular(5,6,7) distribution in units of weeks; Task1(2,4,6) wks is a task (Task1) with duration Triang(2,4,6) distribution in units of weeks.

It is essential that a schedule risk model is set up to be as clear as possible, because it can easily become rather complex. Figure B below illustrates a useful format, where all of the assumptions are immediately apparent.

**Figure B**

More complex relationships involving several tasks can now be constructed. So far, bold lines have been used to indicate the links between tasks. Dashed lines are now introduced to illustrate links that may or may not occur (i.e. probabilistic events, or "risks'). Risks and opportunities (risks where the impact is a good thing) can be modeled in two ways: by modeling the additional impact on the task's duration should the risk occur, as shown in Figure C below, or by separately modeling the total durations of the task should the risk occur or not occur, as shown in Figure D.

**Figure C**

In the example above, Task 2 is expected to take (6,7,9) weeks but there is a 20% chance of a problem occurring that would extend the task's duration by (4,6,9) weeks. In Figure D below, Task 2 is estimated to take (6,7,9) weeks but there is a 20% chance that a particular risk will increase its duration to (10,12,15): there is also an opportunity, with about a 10% chance of occurring, that would reduce the duration to (5,6,8). The start of Task 3 is equal to a Discrete distribution of the finish dates of Task 2's possible scenarios.

**Figure D**

The most common multiple relationship between tasks in a project schedule is where one task cannot start until several others have finished, which is modeled using the MAX function.