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Critical Path Method (CPM)

Identifying the longest path and earliest completion time in a schedule.

5 minutes 5 Questions

Critical Path Method (CPM) is a mathematical algorithm used for project scheduling that analyzes and represents the project network to identify the longest path through the network diagram, determining the shortest possible project duration. The critical path consists of activities that must be com…

Concepts covered
Schedule Network Diagram ConstructionFloat CalculationTotal Float and Free FloatResource Leveling and Its Impact on the Critical PathForward and Backward PassSchedule Compression Techniques: Crashing and Fast-TrackingLeads and Lags in Critical Path MethodDependency Determination and Types in CPMLead and Lag Times and Their Effect on the Critical PathSchedule Risk Analysis and Contingency Planning in CPMLeads and Lags in Project SchedulingPERT Analysis within CPMForward Pass and Backward Pass CalculationsCritical Path IdentificationWorking Calendars and Their Impact on CPM SchedulingDependency Determination and Types in CPM SchedulingCritical PathActivity Sequencing and Dependencies in CPM
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PMI-SP - Critical Path Method (CPM) Example Questions

Test your knowledge of Critical Path Method (CPM)

Question 1

When performing both Forward Pass and Backward Pass calculations in a PDM network, what is the correct relationship between Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) for any activity on the critical path?

Correct Answer: ES = LS and EF = LF for all activities on the critical path

On the critical path, there is zero total float, which means that the early and late dates must be equal to each other.

For any activity on the critical path:
ES (Early Start) must equal LS (Late Start)
AND
EF (Early Finish) must equal LF (Late Finish)

This is a fundamental principle in network diagrams and critical path calculations. When these values are equal, it indicates that the activity has no flexibility in its schedule timing and must be completed exactly as scheduled to maintain the project timeline.

The other answers are incorrect because:
- Equating ES to LF and EF to LS is mathematically impossible in a network diagram
- Having ES less than LS would indicate float, which does not exist on the critical path
- The sum relationship suggested in the last option is not a valid network scheduling principle

Question 2

In a forward pass calculation, Activity A has an ES of 8 days and duration of 6 days, while Activity B has an ES of 12 days and duration of 4 days. If these activities merge into Activity C, which scheduling principle best describes how to determine Activity C's Early Start (ES)?

Correct Answer: Activity C's ES equals the highest EF value from its predecessor activities

Let's solve this step by step:

  1. For Activity A:
  2. ES = 8 days
  3. Duration = 6 days

  4. Therefore, EF = ES + Duration = 14 days

  5. For Activity B:

  6. ES = 12 days
  7. Duration = 4 days

  8. Therefore, EF = ES + Duration = 16 days

  9. When activities merge into a successor activity, the Early Start (ES) of the successor activity equals the highest Early Finish (EF) of all predecessor activities.

  10. In this case:

  11. Activity A's EF = 14 days
  12. Activity B's EF = 16 days
  13. Therefore, Activity C's ES = 16 days (the highest EF)

This is a fundamental principle in network diagramming and critical path analysis. The highest EF ensures that all predecessor activities are completed before the successor activity begins.

The other options suggesting using lowest EF values, averages, or sums are incorrect as they would result in starting Activity C before all predecessor activities are complete, which violates basic scheduling principles.

Question 3

During network calculations, if Activity P's Early Finish (EF) is 30, Late Start (LS) is 25, and Total Float (TF) is 8 days, which formula would correctly determine its Free Float (FF)?

Correct Answer: FF = ES of successor - EF of Activity P

Free Float (FF) is calculated by taking the Early Start (ES) of the successor activity and subtracting the Early Finish (EF) of the current activity.

The formula FF = ES(successor) - EF(current) is the standard formula used in network calculations.

This calculation represents the amount of time an activity can be delayed before affecting the Early Start of its successor activity.

While Total Float considers the entire project end date, Free Float focuses only on the relationship between an activity and its successor.

The other formulas are incorrect as they:
- Mix Late Start with Early Finish, which doesn't provide the correct buffer time between activities
- Include unnecessary duration calculations
- Attempt to use Total Float in ways that don't align with Free Float's definition

The correct formula maintains the focus on the early dates between sequential activities, which is essential for Free Float calculations.

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