Understand the idea.
Events are not activities
In an activity-on-arrow network, arrows are tasks and numbered vertices are events. An event occurs only when every incoming activity has finished; it then permits outgoing activities to begin. The arrow label, rather than its drawn length, supplies the duration.
Follow arrows in their direction from the start towards the finish. A valid project network has no directed cycle. At a merge, all incoming branches are required; a path through just one branch does not represent all the work in the project.
Read dependencies carefully
Read the displayed network at the start of each activity. C and D both leave the end of A. E leaves an event reached by D and the dummy from B, so E needs both. F waits for C and E.
Compare each activity with the precedence table. Check both missing requirements and unwanted extra requirements. Forcing independent work into a chain changes the model and can make the calculated project duration longer than the original rules require.
| Activity | Duration | Immediate predecessors |
|---|---|---|
| A | 4 | None |
| B | 3 | None |
| C | 5 | A |
| D | 4 | A |
| E | 2 | B and D |
| F | 3 | C and E |
See the method in action.
Read a start event
An event has incoming activities P and Q, lasting 4 and 7 days from the project start. Activity R leaves that event. When can R first begin?
Worked solution
- 1
Find when each incoming task finishes.
Both durations are measured from the common project start.
- 2
Wait for the later incoming finish.
The shared event requires P and Q, so reaching it through P alone is insufficient.
- 3
Start R at that event.
R can start as soon as its start event occurs, under the stated dependency model.
R can first begin at day 7.
Check a proposed chain
A and B may start together. C follows A only. A student draws A → B → C as one chain. What dependency errors have been introduced?
Worked solution
- 1
Write the required start rules.
A and B have no predecessors; C requires A only.
- 2
Read the first added dependency.
The proposed chain forces B to wait for A, although B is allowed to start immediately.
- 3
Read the second added dependency.
The chain also forces C to wait for B. The correct model allows C after A independently of B.
The drawing incorrectly makes B depend on A and C depend on B.
Try it yourself.
Check your understanding
At event 5 of the displayed network, C and E enter and F leaves. Must both C and E finish before F starts?
Show answer & reasoning
Yes.
Yes. Event 5 is reached only when both C and E are complete. Since F leaves event 5, either unfinished incoming activity prevents F from starting.
Keep practising
6 worksheet questions · 12 marks
Read the questions online
- In the displayed network, give the start and finish event numbers for D.1 mark
- In the displayed network, which labelled real activities may start directly at event 1?2 marks
- A network has A: 1→2, B: 1→3 and C: 2→4. Does C require B to finish? Explain.2 marks
- A project diagram uses arrow lengths 3 cm and 8 cm for tasks of 9 days and 2 days. Is the drawing necessarily wrong?2 marks
- List the real activity sequences along the displayed start-to-finish paths, ignoring the dummy as a real task.3 marks
- Describe one check that detects an accidental extra dependency in a project network.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- In the displayed network, give the start and finish event numbers for D.1 mark
Read the tail and head of the arrow labelled D: 4.
D runs from event 2 to event 4. - In the displayed network, which labelled real activities may start directly at event 1?2 marks
Their arrows leave the project start.
A dummy is not needed for either starting task.
A and B. - A network has A: 1→2, B: 1→3 and C: 2→4. Does C require B to finish? Explain.2 marks
There is no dependency path from event 3 to event 2.
C requires the incoming work at event 2, which is A.
No. - A project diagram uses arrow lengths 3 cm and 8 cm for tasks of 9 days and 2 days. Is the drawing necessarily wrong?2 marks
Activity durations are read from their numerical labels.
Project networks are dependency diagrams, not scaled time lines.
No; arrow length does not encode duration unless a scale is explicitly stated. - List the real activity sequences along the displayed start-to-finish paths, ignoring the dummy as a real task.3 marks
Trace each directed route from event 1 to event 6.
The B route reaches event 4 through the zero-duration dummy.
A–C–F; A–D–E–F; B–E–F through the dummy connection. - Describe one check that detects an accidental extra dependency in a project network.2 marks
A valid drawing must include every stated requirement.
It must not force an activity to wait for an unrelated branch.
Compare the incoming requirements at each activity's start with its immediate predecessors in the table.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics: discrete models, project scheduling and assignment. Activity-on-arrow conventions are used for project networks; technology may verify calculations but does not replace interpreting the model.
Official curriculum source ↗