The idea, step by step
A dependency without work
A dummy arrow is a logical link with duration zero. It may be drawn dashed to distinguish it from real work. It consumes no scheduled time and is not an extra task, worker or material cost. It exists because an activity-on-arrow drawing sometimes needs an additional connection to record the correct start rules.
For example, E may need both B and D while C needs A only. Joining all earlier activities at a single event can accidentally force C to wait for B. A carefully placed dummy carries B's dependency to E without changing C's start rule.
Check both sides of the rule
When deciding whether to use a dummy, ask which activities should depend on the incoming task and which should remain independent. After adding it, trace every activity's predecessors again. A dummy that points the wrong way can introduce an impossible cycle or reverse a requirement.
A dummy can affect a forward scan even though its duration is zero: the event at its head must still wait for the tail event to occur. Its own duration does not add time, but the dependency it records may control the start of later work.
A common trap
Deleting a dummy because it has duration zero.
Instead: Zero duration means no extra work, not no dependency. Removing it may let a later activity start before a required predecessor is complete.
See the thinking
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.
- The start event for C waits for both A and the dummy carrying completion of B.
- The event occurs at max(4,7)=7.
- C then needs 3 days.
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.
- A merged event is reached only after A and B both finish.
- C would then be forced to wait for B, which is not required.
- Keep C at A's finish and use a dummy connection to make D depend on both.
Check your understanding
In the displayed network, what would be lost if the dummy 3→4 were removed?
Show answer
E would no longer be required to wait for B.
E starts at event 4. The dummy is the only connection carrying B's completion from event 3 to event 4.
Your turn
6 questions · 13 marks · Work at your own pace.
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 9+0=9.
Take max(6,9)=9.
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 max(5,8,6)=8.
Finish time is 8+4=12.
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 ↗