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Critical Path Calculations
Critical Path calculations are the method used to determine the critical path within a project.
When to use
Normally, the critical path will be calculated by project management software once the project network diagram and task duration estimates have been entered into the software. However, you cannot use software when taking the PMP® exam; so you must be able to calculate critical path manually. I believe the method shown below is the easiest manual technique.
- Create a project network diagram with all tasks. I create a box as shown above for each task in the network and draw arrows between boxes to show the relationships.
- Estimate task Duration for all tasks and put the duration in the center portion of the box. I strongly recommend that you use consistent units. If you are given a problem with different units, convert them to the same units before trying to calculate the critical path.
- Starting with the first task in the network, set the Early Start (ES) equal to zero.
- Add the Duration to ES to calculate Early Finish (EF) for the first task in the network.
- The value of EF for the first task is the value of ES for the next task in the network, just follow the relationship arrow(s).
- Continue to the end of the project adding a task duration to each task’s ES to determine that task’s EF. Then follow the arrow to the next task. If a task has multiple input arrows, use the highest value of EF from predecessor tasks to set the ES. You have now completed the “forward pass.” The critical path may be obvious to you at this time, but you need to do the next steps to determine the task total float. Many questions relating to critical path will ask how much float is available for various tasks in the network. So you need to continue on to do the “backward pass” and float calculations which are outlined in steps 7-11.
- For the final task or milestone in the network, set the value for Latest Finish (LF) equal to the value of EF for that task.
- Subtract the Duration from LF to calculate the Latest Start (LS) for that last task or milestone.
- The value of LS for the last task is the value of LF for the next to last task, follow the network diagram arrow backwards.
- Continue subtracting the task duration from the LF for a task to determine the LS for that task until you have reached the beginning of the project. This is referred to as the “backwards pass.” If there are multiple arrows flowing back into a task, use the lowest value of LS from successor task to set the LF for that task. The final value for LS that you calculate (which would be for the first task in the project) should equal zero. If not you have made a mistake.
- Subtract the EF from LF for each task to determine the Task Total Float.
- Tasks with zero Float are on the critical path.
An example is shown below. The examples used in the PMP® exam will likely be more complex than this. Therefore, be sure to do the exercise so that you have practiced quickly calculating critical path and float.
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PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.