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

Concept Flow - Critical path method

List all tasks with durations

↓

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.

Practice

1. What does the Critical Path Method (CPM) primarily help determine in a project?

easy

A. The total cost of the project

B. The longest sequence of dependent tasks that sets the project duration

C. The number of team members required

D. The quality standards for project deliverables

Solution

1. Step 1: Understand the purpose of CPM

   The Critical Path Method is used to find the longest chain of tasks that must be completed on time to avoid delaying the project.

2. Step 2: Identify what CPM does not measure

   CPM does not calculate cost, team size, or quality standards; it focuses on task sequencing and timing.

3. Final Answer:

   The longest sequence of dependent tasks that sets the project duration -> Option B

4. Quick Check:

   CPM = longest task sequence [OK]

Hint: CPM finds the longest chain of tasks to finish on time [OK]

Common Mistakes:

• Confusing CPM with cost estimation
• Thinking CPM calculates resources needed
• Assuming CPM sets quality standards

2. Which of the following is the correct way to represent a task dependency in a project network diagram?

easy

A. Task A finishes before Task B starts, but they are independent

B. Task A and Task B start at the same time regardless of each other

C. Task B starts only after Task A finishes

D. Task B can start before Task A finishes

Solution

1. Step 1: Understand task dependency in CPM

   In CPM, a task dependency means one task must finish before the next can start.

2. Step 2: Evaluate each option

   Only Task B starts only after Task A finishes correctly states that Task B starts after Task A finishes, showing a dependency.

3. Final Answer:

   Task B starts only after Task A finishes -> Option C

4. Quick Check:

   Dependency = task B after task A [OK]

Hint: Dependencies mean one task waits for another to finish [OK]

Common Mistakes:

• Assuming tasks can start simultaneously without dependency
• Thinking tasks are independent when they have dependencies
• Believing a task can start before its predecessor finishes

3. Given tasks with durations and dependencies:
Task A: 3 days (start)
Task B: 4 days (after A)
Task C: 2 days (after A)
Task D: 5 days (after B and C)
What is the total project duration using CPM?

medium

A. 9 days

B. 7 days

C. 14 days

D. 12 days

Solution

1. Step 1: Calculate paths and durations

   Path 1: A (3) -> B (4) -> D (5) = 3 + 4 + 5 = 12 days
   Path 2: A (3) -> C (2) -> D (5) = 3 + 2 + 5 = 10 days

2. Step 2: Identify the critical path

   The longest path is Path 1 with 12 days, so the project duration is 12 days.

3. Final Answer:

   12 days -> Option D

4. Quick Check:

   Longest path duration = 12 days [OK]

Hint: Add durations along longest dependent path [OK]

Common Mistakes:

• Adding all tasks durations regardless of dependencies
• Choosing the shortest path instead of longest
• Ignoring that D depends on both B and C

4. A project has tasks:
A (2 days), B (3 days after A), C (4 days after B), D (1 day after A)
Which task dependency is incorrect if the critical path is A -> B -> C?

medium

A. Task D depends on Task C

B. Task D depends on Task A

C. Task B depends on Task A

D. Task C depends on Task B

Solution

1. Step 1: Analyze given dependencies

   Tasks A, B, and C form the critical path with dependencies A->B->C.
   Task D depends on A, so it starts after A.

2. Step 2: Check if Task D depends on Task C

   Since D depends on A only, not on C, Task D depends on Task C is incorrect because it states D depends on C.

3. Final Answer:

   Task D depends on Task C -> Option A

4. Quick Check:

   Incorrect dependency = D on C [OK]

Hint: Check if dependencies match critical path order [OK]

Common Mistakes:

• Assuming all tasks depend on the last task
• Mixing up which tasks depend on which
• Ignoring the critical path sequence

5. You have tasks:
W: 2 days (start)
X: 3 days (after W)
Y: 4 days (after W)
Z: 1 day (after X and Y)
If task Y is delayed by 2 days, what is the new project duration?

hard

A. 9 days

B. 10 days

C. 8 days

D. 7 days

Solution

1. Step 1: Calculate original paths durations

   Path 1: W (2) -> X (3) -> Z (1) = 6 days
   Path 2: W (2) -> Y (4) -> Z (1) = 7 days

2. Step 2: Add delay to task Y and recalculate

   Y delayed by 2 days: Y duration = 4 + 2 = 6 days
   New Path 2 duration: 2 + 6 + 1 = 9 days

3. Step 3: Determine new project duration

   Longest path is now Path 2 with 9 days, so project duration is 9 days.

4. Final Answer:

   9 days -> Option A

5. Quick Check:

   Delay added to longest path = 9 days [OK]

Hint: Add delay to longest path tasks only [OK]

Common Mistakes:

• Adding delay to shortest path
• Ignoring delay impact on critical path
• Calculating total duration without dependencies