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Strategic Cost Management · Network Analysis - PERT, CPM

Network Analysis Basics: Activities, Events and Diagrams

Updated 11 October 2026

Network analysis plans a project as an arrow diagram. Each activity is an arrow, each event is a node, and dummy activities show dependencies that take no time or resource. To draw it, list predecessors, start with activities that have none, join the rest, add dummies where needed, then number the events.

Understand Network Analysis Basics: Activities, Events, Diagrams

A project is a set of jobs that must be done in a set order, such as building a plant or launching a product. Network analysis is a way to plan and control such a project by drawing the jobs and their order as a diagram. PERT and CPM both start from this diagram.

An activity is a job that takes time and resources. You draw it as an arrow. The arrow shows direction of work, not scale, so its length means nothing. An event is a point in time when one or more activities start or finish. It takes no time and is drawn as a circle (node). The tail event is where an activity starts. The head event is where it ends.

The order of work comes from predecessors. An activity's predecessor must finish before it can start. The activity table in the question gives these. Your diagram must show exactly these dependencies, no more and no fewer.

A dummy activity is a dotted arrow with zero time and zero cost. It does not do any work. You use it for two reasons. First, to show a dependency that cannot be shown by joining arrows directly. Second, to stop two activities sharing the same start and end event, so each activity has a unique pair of event numbers.

The first event is the start event and the last is the end event. A normal project network has one start and one end. If several activities have no predecessor, they all leave the start event. If several have no successor, they all join the end event. Events are numbered so that the tail number of every arrow is smaller than its head number (Fulkerson's rule).

Key rules to remember

Rule 1: One start and one end
Single start event and single end event
Activities with no predecessor leave the start event. Activities with no successor go to the end event.
Rule 2: Unique event pair
No two activities share the same tail and head event
If two activities run in parallel between the same events, add a dummy to one of them.
Rule 3: No loops or cycles
No path may return to an earlier event
A project cannot depend on itself. A loop means the activity table has been misread.
Rule 4: Dummy use
Dummy duration = 0; drawn as a dotted arrow
Use it only to show a dependency or to keep event pairs unique.
Rule 5: Event numbering
Tail event number < head event number for every activity
Number from left to right, usually 1, 2, 3 and so on. Gaps such as 10, 20, 30 are also allowed.
Rule 6: No dangling events
Every event except start has an incoming arrow; every event except end has an outgoing arrow
A dangling event means a missing link or a missing dummy.

How to solve Network Analysis Basics: Activities, Events, Diagrams questions

Use this method for any question that gives an activity table and asks you to draw the network.

  1. 1Read the table and write each activity with its immediate predecessors. Mark activities with no predecessor.
  2. 2Draw the start event. Draw all activities with no predecessor from it.
  3. 3Take the remaining activities one by one in order. Join each to the head event of its predecessor.
  4. 4If an activity depends on two or more predecessors, join those predecessors to a common head event. If it depends on only part of what another activity depends on, use a dummy.
  5. 5If two activities would share the same tail and head events, insert a dummy to separate them.
  6. 6Join all activities that have no successor to a single end event.
  7. 7Number the events from left to right so that every arrow goes from a smaller to a larger number.
  8. 8Check each activity against the table. Confirm no loops, no dangling events and no repeated event pairs.

Quickest way: Predecessor-successor scan

When to use it: Use when the table is long and time is short.

  1. Add a successor column. For each activity, list those activities that name it as a predecessor.
  2. Find groups of activities with the same predecessor set. They can share a head event.
  3. Find the activities that appear in some predecessor lists but not others. A dummy is usually needed there.
  4. Draw in pencil on rough paper first, then copy neatly.
  5. Number events last. Redraw only if the numbering breaks the smaller-to-larger rule.

Common mistakes in Network Analysis Basics: Activities, Events, Diagrams

  • Showing a dependency that the table does not give

    Students join activities that look related, or merge two events too early.

    Fix: Draw each arrow only from the predecessor column. After drawing, trace back from every activity and check its predecessors match the table exactly.

  • Leaving out a dummy where two activities share the same start and end events

    Students try to draw parallel arrows between two nodes.

    Fix: Break one of the parallel activities with a dummy so each activity has its own pair of event numbers.

  • Using a dummy that is not needed

    Students add dummies to be safe.

    Fix: Add a dummy only when it is required to show a dependency or to keep event pairs unique. An extra dummy can add a false link.

  • Wrong numbering of events

    Students number events in the order they were drawn, not left to right.

    Fix: Renumber after the diagram is complete. For every arrow, the tail number must be smaller than the head number.

  • More than one end event or dangling activity

    Students forget to join the last activities.

    Fix: Find all activities that are not predecessors of anything. Join all of them to one final event.

  • Treating arrow length as duration

    Students read the diagram like a map.

    Fix: Remember that arrow length has no meaning. Duration is written on or beside the arrow, not shown by size.

Worked examples

Example 1

A project has these activities. A: no predecessor. B: no predecessor. C: A. D: A, B. E: C, D. Draw the network logic and number the events.

Show the solution
  1. A and B have no predecessor, so both start from event 1.
  2. C depends only on A. D depends on both A and B. So D cannot start at the head of A alone, because then it would not depend on B. D also cannot start at the head of B alone, because then it would not depend on A.
  3. Let A end at event 2 and B end at event 3. Draw C from event 2 to event 4. C leaves event 2, so C depends on A only.
  4. D needs A and B. Draw a dummy from event 2 to event 3. Then D leaves event 3. Event 3 is reached by B and, through the dummy, by A.
  5. E needs C and D. Let D also end at event 4, so C and D both finish at event 4. Draw D from event 3 to event 4. C (2-4) and D (3-4) have different tail events, so no event pair repeats.
  6. Let E leave event 4 to the end event 5.
  7. Check numbering: 1→2 (A), 1→3 (B), 2→3 (dummy), 2→4 (C), 3→4 (D), 4→5 (E). Every tail number is smaller than its head number.

Answer: Network: A (1-2), B (1-3), dummy (2-3), C (2-4), D (3-4), E (4-5). This needs one dummy, and event 5 is the single end event. This is one valid layout, not the only one. You could also end D at event 5, add a dummy 4-5 and draw E from 5 to 6. That network is also correct but uses two dummies, and the second dummy is not needed.

Example 2

Activities P and Q both start after R and both must finish before S. P: predecessor R. Q: predecessor R. S: predecessors P, Q. R has no predecessor. Draw the network and say why a dummy is needed.

Show the solution
  1. R has no predecessor, so draw R from event 1 to event 2.
  2. P and Q both follow R, so both leave event 2.
  3. S needs both P and Q, so both must reach the same event before S starts.
  4. If P goes from 2 to 3 and Q also goes from 2 to 3, two activities share the same tail and head events. This breaks the unique-pair rule.
  5. Fix: give Q its own head event. Let Q go from 2 to 3 and P go from 2 to 4. Draw a dummy from 3 to 4. Event 4 is the merge event, and it is reached by P directly and by Q through the dummy.
  6. Numbering check: the merge event has the highest number, so every arrow, including the dummy 3-4, goes from a smaller number to a larger one.
  7. S leaves event 4 to the end event 5. Final check: R 1-2, Q 2-3, P 2-4, dummy 3-4, S 4-5. Every tail number is smaller than its head number.

Answer: Network: R (1-2), Q (2-3), P (2-4), dummy (3-4), S (4-5). Without the dummy, P and Q would share events 2 and 3. The dummy 3-4 lets Q reach the merge event 4 without sharing P's event pair. S depends on both P and Q because P (2-4) and Q (2-3, then dummy 3-4) both reach event 4.

Exam tips

  • Draw the network neatly with a pencil and ruler. Marks are given for correct logic and clear presentation.
  • Write the dummy as a dotted arrow and label it. Do not leave unlabelled dotted lines.
  • Always check your diagram against the predecessor column before moving on to the critical path.
  • In MCQs, look for questions on the purpose of a dummy, the meaning of an event, or the numbering rule. These are quick marks.
  • If a question asks for the network only, still show event numbers clearly. Later parts of the question may depend on them.

Practice questions from Network Analysis - PERT, CPM

Network Analysis Basics: Activities, Events, Diagrams: frequently asked questions

What is a dummy activity in network analysis?

A dummy activity is a dotted arrow with zero time and zero cost. It does not represent any work. You use it to show a dependency or to give each activity a unique pair of start and end events.

What is the difference between an activity and an event?

An activity is a job that takes time and resources, and it is shown as an arrow. An event is a point in time when activities start or finish, and it is shown as a node. An event consumes no time.

How do you number events in a network diagram?

Number events so that every arrow goes from a smaller number to a larger number. Start with 1 at the start event and move left to right. Renumber after the diagram is complete if needed.

Is the length of an arrow important in a network diagram?

No. The diagram is a logic diagram, not a scale drawing. The time for each activity is written beside the arrow.