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.
Practise this lesson
Three printable worksheets that build from foundations to mastery — or build your own from any module’s questions.
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.
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).
Key facts
- Activity, duration, precedence definitions
- Minimum project time = longest path
- Critical path cannot be delayed
Concepts
- How parallel vs sequential tasks differ
- Why longest path = minimum time
- How to read a precedence table
Skills
- Build a precedence table from a description
- Draw an activity network from a table
- Find the minimum project time
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:
| Activity | Duration (days) | Immediate predecessors |
|---|---|---|
| A — Strip out | 2 | — |
| B — Electrical | 4 | A |
| C — Plumbing | 3 | A |
| D — Fit-out | 5 | B, C |
What to write in your book
- Precedence table: Activity | Duration | Immediate predecessors.
- "—" = can start immediately. Multiple predecessors = all must finish first.
- Minimum time = longest path through network.
To draw an activity network (node = event, arrow = activity):
- Draw a start node. Draw arrows for all activities with no predecessors.
- For each activity, draw a node at its end and an arrow for the activity itself, labelled with name and duration.
- Activities with shared predecessors must both end before the successor can start — merge their end nodes or use a dummy arrow.
- Draw a final node where all terminal activities end.
What to write in your book
- Node = event (numbered circle). Arrow = activity (labelled with name and duration).
- Left to right: start → activities → end.
- Merged nodes: when multiple activities feed into the same successor.
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 if two paths share the maximum length.
What to write in your book
- Critical path = longest path. Minimum project time = critical path length.
- Activities on critical path: zero float — cannot be delayed.
- Off critical path: has float — can be delayed by up to float amount.
Worked examples · reveal each step
Activities: A(4,—), B(3,A), C(2,A), D(5,B&C). Find the minimum project time.
Activities: A(2,—), B(4,A), C(3,A), D(2,B), E(5,C&D). Find minimum project time and critical path.
Foundations(A,3), Framing(B,5,A), Roofing(C,2,B), Electrical(D,4,A). What is the minimum build time?
- A project: A(3,—), B(2,—), C(4,A), D(3,B), E(2,C&D). Find the minimum project time.
- In the project above, which activities are on the critical path?
- Activity F(5) is added to the project above, with predecessors C and D. Does this change the minimum project time? By how much?
- Explain why delaying an activity that is NOT on the critical path might still cause a problem in practice.
The house build minimum time is 10 days: foundations(3) + framing(5) + roofing(2). Electrical runs in parallel with framing — it finishes in 7 days while framing takes 5, so it doesn't delay anything. The critical path is A–B–C.
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:
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)
SA 2. Explain why the minimum project time equals the LONGEST path, not the shortest path. Give a real-world analogy. (2 marks)
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].
Timed questions on activity networks and critical paths.
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