All subjects · Mathematics · WDM11 (D1)

Activity networks and precedence tables

Critical path analysis plans a project made of activities that depend on each other. The first job is to turn a precedence table into an activity network.

Precedence tables

A precedence (dependence) table lists each activity, its duration and the activities that must be finished immediately before it starts. Only immediate predecessors are listed: if C depends on A and E depends on C, E's row shows C, not A.

Activity on arc

D1 uses activity on arc networks. Each activity is an arc (a straight arrow labelled with its letter and duration). Nodes are events: the moment when all activities into the node are finished and those out of it can start. There is one source node (labelled 0) and one sink node at the end.

Drawing tips

Draw in pencil and plan first. Activities with no predecessors start at the source. All activities with the same set of predecessors leave from the same node. Make sure every arc has an arrow, and number events so that each arc goes from a lower to a higher number.

Reading a network

To write the precedence table from a network, for each activity list the activities whose arcs end at its start node (following any dummies backwards).

Worked example

Draw the activity network for project J.

  1. A and B start at node 0.
  2. C and D follow A: A goes from 0 to 1; C and D leave node 1.
  3. E and F both follow B and C: B and C both end at node 2; E and F leave node 2.
  4. G follows D and E: D and E end at node 3. H follows F (node 4). I follows G (node 5).
  5. H and I end at the sink, node 6.

Answer: Events 0 to 6 with arcs A(0,1), B(0,2), C(1,2), D(1,3), E(2,3), F(2,4), G(3,5), H(4,6), I(5,6)

Key idea: Activity on arc: arcs are activities, nodes are events; one source, one sink; list only immediate predecessors.

Check yourself

  1. Activity K must follow J, and J must follow H. What goes in K's 'immediately preceded by' column?
    • J
    • H and J
    • H
    • Nothing
    Show answer

    J. Only immediate predecessors are listed; H is implied through J.

  2. In the activity network for project J (one source, one sink, no dummies), how many event nodes are there?
    Show answer

    7. Events 0 to 6: seven nodes.

  3. Which activities in project J leave the source node?
    • A, B
    • A only
    • A, B, C
    • B, E
    Show answer

    A, B. Activities with no predecessors start at the source.

  4. In project J, why do E and F leave from the same node?
    • They have the same duration
    • Each of them is critical
    • Their arcs end at the sink
    • They have exactly the same immediate predecessors, B and C
    Show answer

    They have exactly the same immediate predecessors, B and C. Activities with identical predecessor sets can share a start event.

  5. In an activity on arc network, what does a node represent?
    • An activity
    • An event: the moment some activities finish and others can start
    • A worker
    • The duration of an activity
    Show answer

    An event: the moment some activities finish and others can start. Activities are arcs; nodes are events.

  6. Which of these would make an activity network invalid?
    • An arc labelled with a letter and a duration
    • Event nodes numbered in order
    • Straight arcs with arrows
    • Two separate finishing nodes
    Show answer

    Two separate finishing nodes. A network must have exactly one source and one sink.

  7. In the activity network for project J, activity G leaves event 3, and the arcs D and E end at event 3. What goes in G's 'immediately preceded by' column?
    • A, B, C, D, E
    • D, E
    • E only
    • D only
    Show answer

    D, E. Reading a network: an activity's immediate predecessors are the arcs that end at its start node, here D and E.

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