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Module 6 · L7 of 12 ~25 min MST-12-S2-07 ⚡ +50 XP available

Introduction to Critical Path Analysis

Sydney Metro project managers use critical path analysis to identify which construction tasks cannot be delayed without pushing back the entire line opening date. This lesson introduces the activity network, the diagram that makes those decisions visible and mathematical.

Today's hook, Building a house: foundations (3 days), framing after foundations (5 days), roofing after framing (2 days), electrical during framing (4 days). What is the minimum build time? Can electrical and framing really run together?
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Orient and prepare

Connect project timing to activity networks, precedence and the critical-path idea.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Build Foundations & guided practice Apply Application practice Master Mastery challenge Build custom Build your own from any module question
01
Recall, your gut answer first
+5 XP warm-up

Building a house: foundations (3 days), framing after foundations (5 days), roofing after framing (2 days), electrical runs during framing (4 days). What is the minimum number of days to complete the build?

Before reading on estimate the minimum time and explain your reasoning.

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The big idea, longest path = minimum time
reference

Critical Path Analysis (CPA) models a project as a network of activities. The critical path is the longest path through the network, it determines the minimum time to complete the project. Activities on this path cannot be delayed.

Activity: a task with a specified duration. Shown as an arrow in the network.

Precedence: activity A is an immediate predecessor of B if B cannot start until A finishes.

Activity network: a directed graph where arrows = activities, nodes = events (start/end points).

Minimum project time: the length of the longest path through the network (the critical path).

The critical path is the longest path and sets the minimum project duration.
House build: foundations(3) + framing(5) + roofing(2) = 10 days. Electrical(4) runs during framing, parallel, so it does NOT add to total. Minimum = 10 days.
Precedence table first
Always convert the verbal description to a precedence table (Activity | Duration | Immediate predecessors) before drawing the network.
Longest path = critical path
The critical path is the LONGEST route from start to end. It equals the minimum project duration. Shorter paths have "spare time" (float).
Parallel = max, not sum
When activities run in parallel, the total time is the MAXIMUM duration, not the sum. Both must finish before the next activity starts.
03
What you will master
Know

Key facts

  • Activity, duration, precedence definitions
  • Minimum project time = longest path
  • Critical path cannot be delayed
Understand

Concepts

  • How parallel vs sequential tasks differ
  • Why longest path = minimum time
  • How to read a precedence table
Can do

Skills

  • Build a precedence table from a description
  • Draw an activity network from a table
  • Find the minimum project time
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Key terms
ActivityA task that takes time to complete, shown as an arrow in the activity network.
DurationThe time required to complete an activity.
Immediate predecessorThe activity that must finish directly before another can begin.
Activity networkA directed graph showing activities (arrows) and events (nodes) with dependencies.
Critical pathThe longest path through the activity network, determines the minimum project duration.
Minimum project timeThe shortest possible time to complete the project, the length of the critical path.
2

Read a precedence table

Translate activity, duration and predecessor information into a project structure.

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Reading a precedence table
core concept

A precedence table has three columns: Activity, Duration, Immediate predecessors. It completely defines the project network.

Rules for reading:

  • Activities with ", " as predecessors can start immediately (at time 0).
  • Only list immediate predecessors, the network captures indirect dependencies automatically.
  • Multiple predecessors in one row means ALL must finish before this activity starts.

Example, office fit-out:

ActivityDuration (days)Immediate predecessors
A, Strip out2
B, Electrical4A
C, Plumbing3A
D, Fit-out5B, C
Analysis: A must finish before B or C can start. B and C can run in parallel (both need only A). D needs both B and C finished. Paths: A–B–D = 2+4+5=11. A–C–D = 2+3+5=10. Minimum = max(11,10) = 11 days.
Quick check: Activities B and C both require A as their only immediate predecessor. This means B and C:

A precedence table lists each activity, its duration, and which activities must finish before it can start (its predecessors). It captures all project constraints and is the starting point for drawing an activity network.

Pause, copy the three columns of a precedence table: activity name, duration (days/weeks), and predecessors (activities that must finish before this one starts) into your book.

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Draw an activity network

Represent each activity and dependency in a directed network.

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Drawing an activity network from a precedence table
core concept

A precedence table lists every activity with its duration and predecessors, the activities that must be completed before it can start. Converting that table to a network diagram maps each activity to a directed arrow, with nodes representing start/finish events; predecessor arrows must all arrive at a node before any successor arrow can leave it.

To draw an activity network (node = event, arrow = activity):

  1. Draw a start node. Draw arrows for all activities with no predecessors.
  2. For each activity, draw a node at its end and an arrow for the activity itself, labelled with name and duration.
  3. Activities with shared predecessors must both end before the successor can start, merge their end nodes or use a dummy arrow.
Which does NOT belong in an activity network?

An activity network is a directed graph where nodes represent start/finish events and arrows represent activities with their durations. Arrows point forward in time; the layout must respect all precedence constraints from the table.

Pause, copy the network convention: nodes = events (start/finish), arrows = activities labelled with duration, and the one rule: every predecessor arrow must arrive at a node before any successor arrow can leave it into your book.

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Identify the critical path

Find the longest path and interpret the minimum project duration.

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The critical path, longest path = minimum time
core concept

The activity network shows every dependency as a directed arrow from the start node to the finish node. The minimum project completion time equals the length of the longest path through this network, called the critical path. Any activity on the critical path has zero float: delay it by even one day and the whole project is delayed.

The critical path is the longest directed path from the start node to the end node. Its length equals the minimum project duration. Key properties:

  • Any delay to an activity on the critical path delays the entire project.
  • Activities NOT on the critical path have spare time (float), they can be delayed without affecting the finish date.
  • A project may have more than one critical path (when two paths tie for longest).
Complete: The minimum project duration equals the path through the activity network.

The critical path is the longest path through the network from start to finish. Its total duration equals the minimum project completion time. Activities on the critical path have zero float, any delay delays the whole project.

Pause, copy the critical path definition (longest directed path from start to finish), the duration property (total = minimum project time), and the zero-float rule (any delay on the critical path delays the whole project) into your book.

5

Study worked networks

Follow complete examples with parallel activities, merges and float.

Worked examples · reveal each step

PROBLEM 1 · BUILD TABLE AND FIND MINIMUM TIME

Activities: A(4), B(3,A), C(2,A), D(5,B&C). Find the minimum project time.

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Draw network: start→A→split→B and C→merge→D→end
A has no predecessor; B and C both need A; D needs both B and C
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PROBLEM 2 · 5-ACTIVITY NETWORK

Activities: A(2), B(4,A), C(3,A), D(2,B), E(5,C&D). Find minimum project time and critical path.

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Identify paths: A→B→D→E and A→C→E
E needs both C and D, so both paths merge at E
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PROBLEM 3 · HOUSE BUILD REVISIT

Foundations(A,3), Framing(B,5,A), Roofing(C,2,B), Electrical(D,4,A). What is the minimum build time?

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A has no predecessors. B needs A. C needs B. D needs A (parallel with B).
Read the precedence information carefully
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Apply and revisit

Solve a new project problem, reconsider the opening house-build estimate, then show me what I've learned →

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Practice activity
+10 XP
  1. A project: A(3), B(2), C(4,A), D(3,B), E(2,C&D). Find the minimum project time.
  2. In the project above, which activities are on the critical path?
  3. Activity F(5) is added to the project above, with predecessors C and D. Does this change the minimum project time? By how much?
  4. Explain why delaying an activity that is NOT on the critical path might still cause a problem in practice.
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Revisit your thinking

The house build minimum time is 10 days: foundations(3) + framing(5) + roofing(2). Electrical runs in parallel with framing: both start on day 3, electrical finishes on day 7 and framing on day 8, so electrical never holds anything up. The critical path is foundations → framing → roofing, and electrical has 3 days of float.

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Show me what I've learned →

Complete the fixed drills and short-answer questions, then check each worked answer.

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Multiple choice
+5 XP per correct

Q1. The minimum project duration is determined by:

Q2. Activities B and C both depend only on A. After A finishes, B and C:

Q3. Project: A(3), B(5,A), C(2,A), D(4,B&C). Minimum project time:

Q4. Which activities are on the critical path for Q3 above?

Q5. An activity that is NOT on the critical path:

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Short answer
ApplyBand 43 marks

SA 1. A project has activities: A(2), B(3), C(5,A), D(4,B), E(3,C&D). (a) Construct the precedence table. (b) Find the minimum project time. (c) State the critical path. (3 marks)

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AnalyseBand 52 marks

SA 2. Explain why the minimum project time equals the LONGEST path, not the shortest path. Give a real-world analogy. (2 marks)

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Answers (click to reveal)

MC 1–D; MC 2–A; MC 3–C: A–B–D = 3+5+4=12. MC 4–B. MC 5–C.

SA 1: (a) Table correct [1]; (b) Min=10 [1]; (c) Both A–C–E and B–D–E [1].

SA 2: Explanation of "all paths must complete" [1]; valid analogy [1].