What is an immediate predecessor?

An activity that must be finished directly before the given activity can start.

In an activity-on-arc network, what do arcs and nodes represent?

Arcs are activities; nodes are events (start or finish of activities).

When can an activity start?

When every activity arriving at its start event has finished.

What is a dummy activity?

A zero-duration dotted arrow, used to show dependence or to give unique event numbers.

Give the two uses of a dummy.

To show dependence correctly, and to ensure no two activities share both start and finish events.

C depends on A only; D depends on A and B. How is this drawn?

A and B end at different events; D starts at B's end event with a dummy from the end of A; C starts at A's end event.

A precedes C and C precedes F. What is F's entry in the table?

C only; A is not an immediate predecessor of F.

What is a redundant dummy?

One that can be removed without changing any dependence.

Activity networks and precedence tablesEdexcel International A Level Maths: Flashcards

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What is a precedence table?

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What is a precedence table?: A list of activities with their immediate predecessors (and durations).
What is an immediate predecessor?: An activity that must be finished directly before the given activity can start.
In an activity-on-arc network, what do arcs and nodes represent?: Arcs are activities; nodes are events (start or finish of activities).
How many start and finish events may a network have?: Exactly one of each.
When can an activity start?: When every activity arriving at its start event has finished.
What is a dummy activity?: A zero-duration dotted arrow, used to show dependence or to give unique event numbers.
Give the two uses of a dummy.: To show dependence correctly, and to ensure no two activities share both start and finish events.
What duration does a dummy have?: Zero.
Where do activities with no predecessors start?: At the start event.
Where do activities which nothing depends on finish?: At the single finish event.
C depends on A only; D depends on A and B. How is this drawn?: A and B end at different events; D starts at B's end event with a dummy from the end of A; C starts at A's end event.
A precedes C and C precedes F. What is F's entry in the table?: C only; A is not an immediate predecessor of F.
What is a redundant dummy?: One that can be removed without changing any dependence.

Exam questions on Activity networks and precedence tables

A project has five activities, A to E. Activities A and B have no predecessors. C has immediate predecessor A only. D has immediate predecessors A and B. E has immediate predecessors C and D. The project is modelled by an activity network with activities on arcs.
Explain why the correct network needs a dummy activity, and state where the dummy is drawn.2 marks
A project has six activities, P to U. P and Q have no predecessors. R has immediate predecessor P only. S has immediate predecessors P and Q. T has immediate predecessor Q only. U has immediate predecessors R, S and T. The project is modelled by an activity-on-arc network.
Explain why S needs dummy activities but R and T do not.2 marks
An activity network has start event 1 and finish event 6. Its arcs are: A from event 1 to event 2; B from 1 to 3; C from 2 to 4; a dummy from 2 to 3; D from 3 to 4; E from 3 to 5; F from 4 to 6; G from 5 to 6.
Write down the immediate predecessors of each of the activities A, B, C, D, E, F and G.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).