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Gantt chart: critical path

The longest chain of dependent tasks in a project. It sets the shortest possible finish time, and any delay to a task on it delays the whole project. Tasks off it have float.

Part of: VCE Software Development - U3O2 - Analysis and Design — Module 19, VCE Software Development - U4O1 - development and evaluation — Module 185, VCE Data Analytics - U3O2 - Analysis and Design — Module 15

Understanding Gantt chart: critical path in VCE Software Development U3O2

What it does: The longer path (9 days) controls the finish time, so it is the critical path and the project cannot finish sooner than 9 days. Critical tasks have no float, so any delay to one pushes back every task after it and the project end date. The shortest chain would finish early and does not control the end date. It should say longest chain (9 days).

Common mistakes: Build cannot depend on Test, because Test comes after Build and this would create a loop. Build should start after A, so the line is 'B Build 4d after A'. The critical path A,B,D is only valid with correct dependencies. The critical path is the longest chain of dependent tasks, not the shortest. Path 1 takes 8 days, so it is the critical path.

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This module's key terms are also in a printable crossword (Modules 12–24) and word search (Modules 2–24).

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Learning
Duo
Which describes the critical path of a project?
The longest chain of dependent tasks, which sets the earliest possible finish dateThe chain of tasks with the shortest total time, which finishes first
Matches
Critical path = shortest chain of tasks (6 days)
↓
The critical path is the longest chain of dependent tasks, not the shortest, because the longest chain sets the minimum project time.
Applying
Meanings
Term
critical path
Meaning
The longest chain of dependent tasks in a project. It sets the shortest possible finish time, and any delay to a task on it delays the whole project. Tasks off it have float.
Practice
A Plan 3 days
Testing
Gaps
pathLength ← taskA + taskB taskD
Check Answer
Spots
1A Plan 3d start
2B Build 4d after D

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Quick Questions

1. Which describes the critical path of a project?
A. The chain of tasks with the shortest total time, which finishes first
B. The longest chain of dependent tasks, which sets the earliest possible finish date ✓
The critical path is the longest dependent chain. It decides the shortest time in which the whole project can be finished.
2. Task A (3 days) leads to Task B (4 days). Task C (2 days) runs alongside them. All three start together. Which tasks are on the critical path?
A. A and B, because the chain takes 7 days and C takes only 2 ✓
B. C only, because it is the shortest and finishes first
A then B takes 3 + 4 = 7 days, which is longer than C at 2 days. The longest path is the critical path.
3. A task on the critical path is delayed by 2 days. What happens to the project?
A. The finish date moves back by 2 days unless time is made up elsewhere ✓
B. Nothing changes because other tasks will absorb the delay automatically
Critical tasks have no float, so any delay to one pushes back every task after it and the project end date.
4. What does it mean if a task has float (slack)?
A. It can start late or run longer, within limits, without delaying the project ✓
B. It must be finished first because it is the most important task
Float is spare time. Tasks off the critical path have float, so small delays do not move the project finish date.
5. Which statement about float is correct?
A. Tasks on the critical path have the most float
B. Tasks on the critical path have zero float ✓
Critical tasks have no spare time. That is why a delay to them delays the whole project.

Match the Pairs

A(2) -> B(3) -> D(4) = 9 days → Adding the durations along a chain of dependent tasks to find its total length; the longest chain is the critical path
Float = 3 days → A non-critical task can be delayed by up to 3 days without delaying the project finish
The critical path decides the shortest possible project length, because it is the longest chain of dependent tasks → Path 1: 9 days, Path 2: 6 days -> Project = 9 days
If a critical task is delayed, the whole project finish date is delayed by the same amount → Critical task: 4 days -> 6 days, Project: 9 days -> 11 days
Critical path = shortest chain of tasks (6 days) → The critical path is the longest chain of dependent tasks, not the shortest, because the longest chain sets the minimum project time.
Task off the critical path delayed 1 day (float 5) -> Project finishes 1 day late → A task with 5 days of float can slip 1 day without delaying the project, so the finish date does not change.

Key Term

critical path
The longest chain of dependent tasks in a project. It sets the shortest possible finish time, and any delay to a task on it delays the whole project. Tasks off it have float.

Fill in the Blanks

1. pathLength ← taskA + taskB + taskD
Hint: Type the arithmetic operator that adds up task durations along one chain of dependent tasks.
2. pathOne ← 3 + 4 + 2 criticalPath ← MAX(pathOne, pathTwo)
Hint: Type the function name that picks the larger value, because the critical path is the longest path.
3. float ← latestStart - earliestStart
Hint: Type the operator that finds how much a task's start can slide, by taking one value away from another.
4. IF float = 0 THEN SET onCriticalPath ← TRUE END IF
Hint: Type the amount of float that a critical task has, meaning it has no spare time.
5. IF taskDelay > 0 AND onCriticalPath THEN projectEnd ← projectEnd + taskDelay END IF
Hint: Type the variable name that shows the delayed task is on the longest chain, so the whole project finish moves.

Spot the Error

Question 1
A A Plan 3d start
B B Build 4d after D
C C Docs 2d after A
D D Test 1d after B,C
E Critical path: A,B,D = 8d
Line B — Build cannot depend on Test, because Test comes after Build and this would create a loop. Build should start after A, so the line is 'B Build 4d after A'. The critical path A,B,D is only valid with correct dependencies.
Question 2
A Path 1: A-B-D = 3+4+1 = 8d
B Path 2: A-C-D = 3+2+1 = 6d
C Critical path = Path 2, 6d
Line C — The critical path is the longest chain of dependent tasks, not the shortest. Path 1 takes 8 days, so it is the critical path.
Question 3
A A=3d, B=4d, C=2d, D=1d
B A-B-D = 3+4+1 = 7d
C A-C-D = 3+2+1 = 6d
D Float of C = 8 - 6 = 2d
Line B — 3 + 4 + 1 is 8, not 7. A wrong total could make you pick the wrong longest path. The line should be 'A-B-D = 3+4+1 = 8d'.
Question 4
A Critical path = shortest path
B A-B-D = 8d, A-C-D = 6d
C Project needs at least 8d
Line A — The critical path is the longest chain of dependent tasks. It sets the shortest possible project finish time. The line should say 'longest path'.
Question 5
A C is off the critical path
B C has 2d float
C C can slip 2d safely
D C slips 3d: finish +3d
Line D — C has 2 days of float, which absorbs the first 2 days of delay. A 3 day slip only delays the project by 1 day (3 - 2). The line should be 'C slips 3d: finish +1d'.

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