Critical path method in Software Engineering - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Critical Path Method (CPM)?

CPM is a project management technique used to identify the longest sequence of dependent tasks that determine the shortest possible project duration.

beginner

Why is the critical path important in project management?

Because any delay in tasks on the critical path directly delays the entire project completion time.

intermediate

What does it mean if a task has 'float' or 'slack' in CPM?

Float or slack is the amount of time a task can be delayed without affecting the overall project completion date.

intermediate

How do you identify the critical path in a project network?

By calculating the earliest and latest start and finish times for tasks and finding the longest path with zero float.

intermediate

What happens if a task on the critical path is shortened?

The overall project duration can be reduced, as the critical path determines the minimum project time.

What does the critical path represent in a project?

A Tasks with the most resources

B The shortest task in the project

C Tasks that can be delayed without impact

D The longest sequence of dependent tasks

The critical path is the longest sequence of dependent tasks that determines the shortest project duration.

What is 'float' or 'slack' in CPM?

A Extra time a task can be delayed without affecting the project

B The total project duration

C The time a task takes to complete

D The time between project start and finish

Float or slack is the extra time a task can be delayed without delaying the project.

If a task on the critical path is delayed, what happens?

A The entire project is delayed

B Only that task is delayed

C The project finishes earlier

D No effect on the project

Delays on the critical path delay the whole project because it has no slack.

How can the critical path be shortened?

A By adding more tasks

B By delaying non-critical tasks

C By reducing the duration of tasks on the critical path

D By increasing float on all tasks

Shortening tasks on the critical path reduces the total project duration.

Which of these is NOT a characteristic of the critical path?

A It has zero float

B Tasks can be delayed without affecting the project

C It is the longest path of dependent tasks

D It determines the project completion time

Tasks on the critical path cannot be delayed without affecting the project.

Explain the concept of the critical path and why it matters in managing a project.

Think about which tasks control the project finish date.

Describe how float or slack works and how it helps in scheduling tasks.

Consider tasks that can be delayed without delaying the project.

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