Dummy Activities
Master dummy activities for NSW Year 12 Mathematics Standard 2. A dummy is a dashed, zero-duration arrow added to an activity-on-edge network only to show a dependency — it represents no real work and adds no time to the project.
This topic shows you when a dummy is required — to keep two activities uniquely defined, or to carry a shared predecessor forward — where to place it, how many a network needs, and how to read the immediate predecessors of an activity through a dummy, a core Standard 2 skill in critical path analysis for planning festivals, builds, media production and logistics.
Theory
A dummy activity is a dashed, zero-duration arrow used in an activity-on-edge network to show a dependency. This Year 12 Standard 2 (NSW) guide shows when a dummy is needed — to keep two activities distinct or to carry a shared dependency — where to place it, how many a network needs, and how to read the immediate predecessors of an activity through a dummy.
In the activity-on-edge convention, each real activity is a solid arrow from one numbered event to another, and its length in the plan is written as a duration. A dummy activity is different: it is a dashed arrow that represents no real work.
A dummy has zero duration, uses no resources and carries no duration label. It is drawn only to make the network legal and to show how activities depend on one another. Adding a dummy never changes how long the project takes.
Two situations need a dummy. The first is uniqueness: when two activities would otherwise be drawn as two arrows between the same pair of events, a dummy separates them. The second is a shared dependency: when one activity must be carried forward as a predecessor of a later activity without forcing it onto another branch. This Year 12 Standard 2 (NSW) skill is recognising when, where and why a dummy is required, and reading immediate predecessors from a network that contains one.
A dummy activity is defined entirely by its two fixed properties:
Because its duration is zero, a dummy adds nothing to the length of any path through the network:
How to place and read a dummy activity
- Check for uniqueness. If two activities share the same start event and the same end event, insert a dummy so they become two distinct arrows.
- Check dependencies. If an activity must be a predecessor of a later activity without being forced onto another branch, use a dummy to carry the dependency forward.
- Draw it dashed. A dummy is a broken arrow with no duration label; it has zero duration.
- Read predecessors. For any activity, collect every real activity that finishes at its start event, following dashed dummies backwards to pick up the ones they carry.
- Interpret: remember a dummy adds no time, so the minimum completion time is unchanged.
Read the dashed arrow, then trace what must finish before \(D\) starts.
| \(\text{dummy}\) | \(:\) | \(3 \to 4\) |
| \(D \text{ starts at event}\) | \(\) | \(4\) |
| \(C \text{ ends at } 4,\ \text{dummy carries } B\) | \(\) | \(\) |
| \(\therefore\ \text{preds of } D\) | \(=\) | \(B, C\) |
The dummy keeps \(B\) and \(C\) distinct; \(D\) follows \(B\) and \(C\).
The dummy carries \(A\) forward into the event where \(D\) starts.
| \(D \text{ starts at event}\) | \(\) | \(3\) |
| \(B \text{ ends at } 3\) | \(\) | \(\) |
| \(\text{dummy } 2\to3 \text{ carries } A\) | \(\) | \(\) |
| \(\therefore\ \text{preds of } D\) | \(=\) | \(A, B\) |
The dummy passes \(A\) to \(D\) without merging events, so \(C\) still depends on \(A\) only. \(D\) follows \(A\) and \(B\).
Count the dashed arrows and read each one's start and end event.
| \(\text{dashed arrows}\) | \(=\) | \(2\) |
| \(\text{dummy 1}\) | \(:\) | \(2 \to 3\) |
| \(\text{dummy 2}\) | \(:\) | \(2 \to 4\) |
The network has 2 dummy activities, running \(2\to3\) and \(2\to4\).
Check for shared event-pairs or unclear dependencies; then recall a dummy's duration.
| \(B, C \text{ follow } A \to \text{ different events}\) | \(\) | \(\) |
| \(D \text{ follows } B;\ E \text{ follows } C\) | \(\) | \(\) |
| \(\text{no shared event-pair}\) | \(\Rightarrow\) | \(\text{no dummy}\) |
| \(\text{dummy duration}\) | \(=\) | \(0\) |
No dummy is needed — every activity is already uniquely defined. A dummy always has duration \(0\).
Common pitfalls
Frequently asked questions
What is a dummy activity in a network diagram?
A dummy activity is a dashed arrow added to an activity-on-edge network that represents no real work. It has zero duration and uses no resources; it is drawn only to show a dependency between activities or to keep two activities uniquely defined by their start and end events.
Why are dummy activities used?
There are two reasons. The first is uniqueness: if two activities would otherwise be drawn as two arrows between the same pair of events, a dummy separates them. The second is a shared dependency: a dummy carries one activity forward as a predecessor of a later activity without forcing it onto a different branch of the network.
How is a dummy activity shown on a diagram?
It is drawn as a dashed or broken arrow, unlike the solid arrows used for real activities. Because it is not a real task, it has no duration label written on it, and its duration is always zero.
Does a dummy activity add time to a project?
No. A dummy has zero duration, so it adds no time to any path through the network. Inserting a dummy only fixes which activities must come before which; it never changes the minimum completion time.
How do I work out how many dummy activities a network needs?
Count the dashed arrows if the network is already drawn. If you are building it from a precedence table, you need one dummy for each pair of activities that would share the same start and end events, and one for each shared or partial dependency that cannot be shown with solid arrows alone.
How do dummy activities affect immediate predecessors?
The immediate predecessors of an activity are every real activity that finishes at its start event, plus every real activity carried into that event along a dashed dummy. To read them correctly, follow the dummy arrows backwards from the activity's start event.