Dummy activities

Sometimes an activity network cannot show the precedence table correctly with ordinary arcs. Dummy activities fix this.

What a dummy is

A dummy is drawn as a dashed arrow. It has zero duration and no cost; it only carries a dependency. Its direction matters: a dummy from node X to node Y means everything into X must finish before anything leaving Y starts.

Dummies for dependence

Classic case: C depends on A only, but D depends on A and B. Draw A and B to separate nodes; C leaves A's end node; add a dummy from the end of A to the end of B; D leaves B's end node. Now D waits for both A and B, and C waits only for A.

Dummies for uniqueness

Each activity must be uniquely described by its start and end events. If two activities would both run from node 3 to node 4, end one of them at a new node and add a dummy from there to node 4.

Use as few as needed

Exams often ask for the network using the minimum number of dummies. Extra dummies are not wrong in logic but cost marks. In calculations, a dummy behaves like an activity of duration 0.

Worked example

A and B have no predecessors. C depends on A only. D depends on A and B. Draw the network.

A runs from node 0 to node 1; B runs from node 0 to node 2.
C needs only A, so C leaves node 1.
D needs A and B. B ends at node 2, so add a dummy from node 1 to node 2: now everything leaving node 2 waits for A as well as B.
D leaves node 2. C does not wait for B, because nothing joins node 2 back to node 1.

Answer: One dummy, from the end of A (node 1) to the end of B (node 2); C leaves node 1 and D leaves node 2

Key idea: Dummies have zero duration, are dashed, and carry dependence. Use them when activities share some but not all predecessors, or to keep each activity uniquely named.

Check yourself

What is the duration of a dummy activity?
- 1
- 0
- The duration of the activity before it
- The duration of the activity after it
Show answer
0. Dummies only show dependence; they take no time.
C depends on A only; D depends on A and B. Why is a dummy needed?
- The two activities with no predecessors have different durations
- C is critical
- There are four activities
- D needs A as well as B, but C must not wait for B
Show answer
D needs A as well as B, but C must not wait for B. Ordinary arcs alone would either make C wait for B or let D start without B.
A dummy goes from the end of A to the end of B. What does it mean?
- Activities leaving A's end node must wait for B
- Activities leaving B's end node must wait for A
- A must wait for B
- B and A must run at the same time
Show answer
Activities leaving B's end node must wait for A. Everything leaving the head of the dummy depends on everything entering its tail.
Two activities P and Q both start at event 4 and end at event 5. What should you do?
- Merge P and Q into one activity
- Delete event 5
- End one at a new node and add a dummy from that node to event 5
- Draw P and Q as one curved arc
Show answer
End one at a new node and add a dummy from that node to event 5. Each activity must be uniquely defined by its pair of events; the dummy keeps the dependence the same.
In a forward pass, event 3 has earliest time 9 and a dummy runs from event 3 to event 5. Arc K (duration 4) runs from event 2 (earliest time 7) to event 5. Find the earliest event time of event 5.
Show answer
11. Into event 5: dummy gives 9 + 0 = 9; K gives 7 + 4 = 11. Take the larger: 11.
How is a dummy drawn?
- As a double line
- As a dotted node
- As a dashed arrow
- As an arc labelled D
Show answer
As a dashed arrow. Dummies are dashed arrows so they are not mistaken for real activities.

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Last updated 7 November 2026. Spotted a mistake? Tell us.