The critical path is the shortest time duration in which a project may be completed. The critical path also has zero float, which means that a delay in any activity along the critical path will result in an extension of the project schedule duration. Most scheduling software programs like Oracle Primavera P6 and Microsoft Project calculate the critical path automatically after the user inputs the schedule tasks and relationships among the tasks. It is important to understand how the critical path is computed so that the project plan can be understood and clearly communicated to all stakeholders.
There are two competing methods to the calculation of the critical path. One method boasts the adoption by Oracle Primavera P6 while the other is considered the appropriate approach on the Project Management Institutes (PMI) Project Manager Professional certification exam. It is not the intent of this article to decide the correct approach, but to describe the similarities, differences, and, perhaps, logic behind both approaches.
Both approaches use what is termed the forward pass and backward pass. The forward pass calculates the Early Start (ES) and Late Start (LS) dates of each activity. The backward pass determines the Early Finish (EF) and Late Finish (LF) dates for all the activities listed in the project schedule. To clarify, the ES is the earliest that an activity can start given the logic and constraints of the path. EF is the earliest that a task can finish given, again, the logic and constraints of the path. LS is the latest an activity can start provided the respective logic and constraints of the path. LF is the latest an activity can finish with the governing logic and constraints of the path. Activities in both methods are displayed as connected nodes.
The differences and confusion between the approaches has to do with the designation of the first activity. In the apparent PMI method the first node for the first activity is zero, whereas, the other Primavera method designates the first node on the first activity as one. For the PMI method you simply add the activity duration to determine the ending activity node. When you look at the flow diagram that uses the PMI method it is easy to see that you simply add the duration to the ES to find the EF on the forward pass and subtract the duration from the LF to find the LS on the backward pass. The Primavera method at first glance does not look as “nice”. To find the EF you add the duration to the ES and minus one. So on a forward pass an activity with a start day of 1 and a duration of 7 will have and EF of 7. That is 1 plus 7 minus 1.
This makes more sense when you recognize that the 1 designating the first day is in the morning before work has begun. So in your calculation you have to subtract the 1 to bring the equation to a morning start time. On the opposite side of the equation for the Primavera method backward pass you subtract the duration from the LF and add one to find the LS. As an example, if the LF is 21 and the duration is 7 you subtract the duration from the LF and add 1 to find the LS, which will be 15. This, perhaps, make more sense when you realize that the LF ends at the end of the day, so you need to add one to the equation to account for the end of the day finish.
The amount of time that an activity can be moved without affecting the project finish date is the total float. Total float is calculated the same for both critical path methods. The total float is simply the LS minus the ES or the LF minus the EF. It gets complicated again when considering free float. Free float is the amount of time a task can be delayed without affecting it nearest successor. The equation for free float using the PMI method is simply ES of successor minus EF of present. Dissimilarly, the free float for the Primavera method is ES of successor minus EF of present minus one.
The critical path is an important concept for understanding the flexibility that a project has. Both critical path methods, starting at zero and starting at one, can become complicated as the number of tasks becomes significant. It is particularly important for the Primavera method to stringently use the appropriate equation. Understanding the equations and logic behind the equations is important to understanding and communicating a projects flexibility.