Understand the idea.
A dependency without work
A dummy activity is a zero-duration logical link, usually drawn as a dashed arrow. It adds no work or resource use, but it carries a completion requirement from one event to another. Removing it can therefore change which activities may start.
In the displayed network, C needs A only, while E needs B and D. Keeping separate events lets C begin after A; the dummy carries B into E's start event without making C wait for B.
Check both sides of the rule
Before adding a dummy, identify both the activities that must inherit the dependency and those that must remain independent. Afterwards, trace their start requirements again. A misplaced dummy can add an unwanted dependency or create a directed cycle.
Zero duration does not make the start event occur earlier. If a dummy comes from a late event, the event at its head must still wait for that completion. Include the dummy in forward and backward scans with duration zero.
See the method in action.
A zero duration can still matter
A finishes at day 4. B finishes at day 7. A dummy from the end of B enters the event where C starts after A. C lasts 3 days. Find C's earliest finish.
Worked solution
- 1
Carry B's finish through the dummy.
The dummy takes no additional time but cannot finish before B does.
- 2
Find the earliest start of C.
C's start event requires completion of A and the incoming dummy.
- 3
Add C's own duration.
C needs three days after all its predecessors are ready.
C finishes earliest at day 10.
Keep one branch independent
A and B start together. C follows A only; D follows both A and B. Explain why making C and D leave one merged A/B finish event is incorrect.
Worked solution
- 1
Interpret a merged A/B event.
Every activity leaving that event must wait until both A and B have finished.
- 2
Identify the unwanted condition on C.
C is supposed to follow A only, so requiring completion of B changes the stated project.
- 3
Separate C's start from D's start.
Let C leave A's finish event. Connect that event and B's finish to D's start, using a zero-duration dummy where needed, so D alone waits for both.
The merged event adds an unwanted B→C dependency. A dummy can record B→D without adding B→C.
Try it yourself.
Check your understanding
In the displayed network, what would be lost if the dummy 3→4 were removed?
Show answer & reasoning
E would no longer be required to wait for B.
E would lose its requirement to wait for B. B finishes at event 3, and the dummy from event 3 to event 4 is the link carrying that completion to E's start event.
Keep practising
6 worksheet questions · 13 marks
Read the questions online
- For the displayed network, state the duration and purpose of the dashed arrow.2 marks
- A dummy joins an event reached at time 9 to an event otherwise ready at time 6. What is the earliest time of the receiving event?2 marks
- P and Q start together. R follows P only, S follows Q only, and T follows both P and Q. Explain why one joint event for the ends of P and Q can be unsuitable.3 marks
- A student gives a dummy a duration of 2 hours to represent administrative waiting. Is that still a dummy?2 marks
- Can a dummy have a direct financial cost in this scheduling model? Explain.2 marks
- A finishes at 5, B at 8, and C at 6. Task D requires all three and takes 4 days. Dummies are used to join the requirements. Find D's earliest finish.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- For the displayed network, state the duration and purpose of the dashed arrow.2 marks
The arrow 3→4 is a logical connection.
It records B's completion without adding a real task.
Duration 0 days; it makes E wait for B as well as D. - A dummy joins an event reached at time 9 to an event otherwise ready at time 6. What is the earliest time of the receiving event?2 marks
The zero-duration dummy arrives at .
Take .
9. - P and Q start together. R follows P only, S follows Q only, and T follows both P and Q. Explain why one joint event for the ends of P and Q can be unsuitable.3 marks
R and S have different predecessor sets.
Use separate finish events and logical dummy links to create T's joint requirement.
It would force R to wait for Q and S to wait for P. - A student gives a dummy a duration of 2 hours to represent administrative waiting. Is that still a dummy?2 marks
A dummy has exactly zero duration.
A genuine two-hour wait must be modelled as a real timed activity or lag.
No. - Can a dummy have a direct financial cost in this scheduling model? Explain.2 marks
It represents a dependency only, not real work.
Costs caused by the resulting schedule must be modelled separately.
No direct task cost is assigned to a dummy. - A finishes at 5, B at 8, and C at 6. Task D requires all three and takes 4 days. Dummies are used to join the requirements. Find D's earliest finish.2 marks
Its starting event is .
Finish time is .
12 days.
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 ↗