Critical path method in Software Engineering - Step-by-Step Execution

Concept Flow - Critical path method

List all tasks with durations

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Identify dependencies between tasks

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Draw network diagram

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Calculate earliest start and finish times

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Calculate latest start and finish times

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Find tasks with zero slack (critical path)

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Determine total project duration

The critical path method finds the longest sequence of dependent tasks to determine the shortest project duration.

Execution Sample

Software Engineering

Tasks: A(3), B(2), C(4), D(2)
Dependencies: B after A, C after A, D after B and C
Calculate earliest and latest times
Find critical path

This example shows tasks with durations and dependencies, then calculates the critical path.

Analysis Table

Step	Task	Earliest Start (ES)	Earliest Finish (EF)	Latest Start (LS)	Latest Finish (LF)	Slack	Critical?
1	A	0	3	0	3	0	Yes
2	B	3	5	3	5	0	Yes
3	C	3	7	3	7	0	Yes
4	D	7	9	7	9	0	Yes
5	End	9	9	9	9	0	Yes

💡 All tasks processed; critical path is A -> B -> C -> D with total duration 9

State Tracker

Variable	Start	After Task A	After Task B	After Task C	After Task D	Final
Earliest Start (ES)	N/A	0	3	3	7	N/A
Earliest Finish (EF)	N/A	3	5	7	9	N/A
Latest Start (LS)	N/A	0	3	3	7	N/A
Latest Finish (LF)	N/A	3	5	7	9	N/A
Slack	N/A	0	0	0	0	N/A

Key Insights - 3 Insights

Why does task B have slack while tasks A, C, and D do not?

Task B has slack because its latest start (5) is later than its earliest start (3), giving it 2 units of slack. This means it can be delayed without affecting the total project duration, unlike tasks on the critical path (A, C, D) which have zero slack.

How do we know which tasks form the critical path?

Tasks with zero slack form the critical path. In the execution table rows 1, 3, and 4, slack is zero and critical is 'Yes', indicating these tasks are on the critical path.

What does the earliest finish time represent for each task?

Earliest finish time is the soonest a task can be completed considering dependencies and durations. For example, task B starts at 3 and finishes at 5, meaning it cannot finish before time 5.

Visual Quiz - 3 Questions

Look at the execution table, what is the slack for task D?

A 2

B 0

C 1

D 3

💡 Hint

Check the 'Slack' column for task D in the execution table (row 4).

At which step does the earliest finish time for task C occur?

A Step 3

B Step 2

C Step 4

D Step 1

💡 Hint

Look at the 'Earliest Finish (EF)' column for task C in the execution table.

If task B took 3 units instead of 2, how would the total project duration change?

A It would decrease

B It would increase to 8

C It would stay 9

D It would become 9

💡 Hint

Consider how increasing task B's duration affects the critical path length in the execution table.

Concept Snapshot

Critical Path Method (CPM):
- List tasks with durations and dependencies.
- Calculate earliest start/finish and latest start/finish times.
- Slack = LS - ES; zero slack means critical task.
- Critical path is longest path with zero slack.
- Project duration = sum of durations on critical path.

Full Transcript

The Critical Path Method helps find the longest sequence of dependent tasks in a project. First, list all tasks with their durations and dependencies. Then, draw a network diagram showing task order. Calculate earliest start and finish times by moving forward through the tasks. Next, calculate latest start and finish times by moving backward. Slack is the difference between latest and earliest start times. Tasks with zero slack form the critical path, which determines the shortest time to complete the project. For example, tasks A, B, C, and D have zero slack and form the critical path with total duration 9 units.