Even though an individual not connected to project activities knows a project management term “Critical Path” or “Critical Activities”. In fact, there is no project review meeting that concludes without referring to this vital project scheduling tool.

Due to the excessive use of scheduling software, we pay little attention to the fundamentals of the project schedule network analysis process. Moreover, we rarely analyze the critical path generated by the scheduling software.

Further, as the project progresses, we needlessly expand the list of critical tasks and concentrate our efforts on completing them. As a matter of fact, many of us consider any important or difficult to complete an activity as a critical task. However, this is not true under all circumstances.

Thus, this post describes essential Critical Path Method (CPM) schedule analysis terminology and calculation steps.

Critical Path Method in Project Management

Morgan R. Walker of DuPont and James E. Kelley Jr. of Remington Rand developed Critical Path Method (CPM) in 1958.

The critical path method in project management is a project schedule network analysis technique. CPM analysis helps to identify a sequence of activities that require close monitoring. It is the most important outcome of the critical path method (CPM) network analysis process. Moreover, critical path method schedule analysis ensures that there are no schedule slippages and cost overruns.

Unlike PERT, the critical path method controls both time and cost aspects of a project.

The critical path method also specifies the extent of schedule flexibility permissible in a given logical relationship. CPM analysis further allows the project team to work out various scenarios of schedule delays. The critical path method also helps to establish a probabilistic estimate of project completion targets. Further, critical path analysis in project management also facilitates the accurate assessment of schedule risk.

What is Critical Path

The critical path of a logically structured project schedule network diagram specifies a sequence of activities that need the utmost attention of the project team. Thus, this sequence of activities is the critical path.

The overall project duration is the sum total of the duration of all activities in the critical path. Delay in any activity on the critical path will delay the project completion date.

Critical path signifies that all activities on the path must start and finish as per the schedule dates. Monitoring of activities on a critical path ensures that there are no slippages in the schedule.

Critical Path Characteristics

The following paragraph enumerates various characteristics of the critical path.

• It is the longest path in a project schedule network diagram.
• The critical path establishes the minimum project duration.
• It also indicates the amount of scheduling flexibility in the network diagram.
• Activity on a critical path is called critical path activity.
• A project can have more than one critical path. 
• Critical path changes as the project progresses.
• The total float of activities on the critical path is Zero (0)
• For activities on the critical path, Early Start is equal to Late Start and Early Finish is equal to Late Finish.
• In a project schedule network diagram, a bold line denotes the critical path.

Critical Path Method Definition of Key Terms

Forward Pass

Forward Pass is a technique that calculates early start and early finish dates in the schedule network. In order to conduct a forward pass; move in the forward direction from the project start node to the last node of the network diagram.

Backward Pass

Backward Pass is a technique that calculates late start and late finish dates in the schedule network. In order to perform a backward pass; move in the backward direction from the project end node to the start node of the network diagram.

Early Start (ES)

It is an output of forward pass calculation. Early Start is the earliest possible point in time when an activity in the node can start.

Early Finish (EF)

It is an output of forward pass calculation. Early Finish is the earliest possible point in time when an activity in the node can end.

Late Start (LS)

It is an output of backward pass calculation. Late Start is the latest possible point in time when an activity in the node can start.

Late Finish (LF)

It is an output of backward pass calculation. Late Finish is the latest possible point in time when an activity in the node can start.

Total Float

The amount of time that a schedule activity can be delayed from its early start without delaying the project finish date.

Free Float

The amount of time that a schedule activity's earliest finish time can be delayed without delaying the earliest start time of successor activity.

Critical Path Method Schedule Analysis Steps

The critical path method schedule network analysis technique chiefly uses two conventions. According to the first convention, the project starts on day zero (0). As per the second convention, the project starts on day one (1). Here, we will use the convention that the project starts on day 1.

Use the following steps to conduct a critical path method analysis.

1. Draw the project schedule network diagram.
2. Calculate all paths in the schedule network diagram.
3. Calculate the critical path.
4. Perform Forward & Backward Pass Calculations on Critical Path.
5. Perform Forward & Backward Pass Calculations on Non-Critical Path.
6. Calculate Total Float.
7. Calculate Free Float.

Critical Path Method Schedule Network Diagram

The first step of critical path method analysis is to draw the project schedule network diagram.

Precedence Diagram Method (PDM)

The critical path method analysis uses Precedence Diagram Method (PDM) technique to represent the schedule network logic. Precedence Diagramming Method is a technique that uses a logical relationship among schedule activities to construct the network diagram. Activity-On-Node (AON) is one example that uses PDM to construct the schedule network logic.

Activity on Node Network Diagram

Activity-on-Node (AON) is a technique to create a project schedule network diagram using Precedence Diagramming Method (PDM). The activity-on-Node network diagramming technique indicates schedule activities on nodes. Further, it uses arrows to graphically link the activity nodes. Thus, these links indicate logical relationships among activity nodes. Therefore, this relationship in activity nodes indicates the correct sequence to perform project work. Hence, this helps to construct a well-structured and logically correct project schedule network diagram.

The figure below is an example of a typical schedule network diagram using the activity on node technique.

Also read: Sequence Activities Tools and Techniques

How To Calculate Critical Path

The following list enumerates steps in identifying the critical path of a project schedule network diagram using the critical path method.

1. Identify the total number of paths in the project schedule network diagram.
2. Add duration of each activity on the path.
3. Calculate the total duration of each path.
4. The path with the longest duration is the critical path.
5. Indicate the critical path with a bold line.

Critical Path Method Schedule Analysis Forward Pass Calculation

In the critical path method, forward pass and backward pass calculations indicate the amount of scheduling flexibility. This calculates important parameters like an early start, early finish, late start, and late finish of each activity node.

First, perform forward and backward pass calculations on the critical path, then repeat the calculations for non-critical path activities. The following paragraphs enumerate the steps in forward and backward pass calculations.

1. Conduct forward pass for activities on the critical path and calculate early start and early finish for each activity (node)
2. At first node
   • Early Start (ES) of the first activity = 1
   • Early Finish (EF) = ES + Activity Duration (D) – 1
3. ES of the next node is the earliest finish time of the immediately preceding activity. In this case, it is EF of the first node plus 1 = EF + 1
4. For activities with more than one preceding activity, ES is latest of the earliest finish times of the preceding activities.
5. Repeat the calculation till you reach the last node.

Critical Path Method Schedule Analysis Backward Pass Calculation

Upon completing the forward pass now move in backward direction to complete backward pass calculation.

1. At the last node commence backward pass
   • LF of the last activity is equal to the EF of that activity
   • Late Start (LS) = LF – Activity Duration (D) + 1
2. For the next node in the backward pass
   • LF = The latest start time of the previous node minus 1 = LS -1
   • For activities with more than one previous node, LF is the earliest of the latest start times of those activities.
3. Once you reach the first activity your backward pass is complete.

The figure below illustrates formulas used in the critical path method schedule analysis process.

Critical Path Method Schedule Analysis Total Float Calculation

Total float is the amount of time that a schedule activity can be delayed or extended from its early start date without delaying the project finish date or violating a schedule constraint.

Now Calculate the total float of an activity using the following steps.

• for activities on a critical path total float is equal to zero (0)
• LS – ES or LF – EF represents the total float of activities not on the critical path

Critical Path Method Schedule Analysis Free Float Calculation

Free float is the amount of time that a scheduled activity can be delayed without delaying the early start date of any successor or violating a schedule constraint.

Use the following formula to calculate the Free float of an activity.

• Free Float of current activity = (ES)_S – (EF)_C – 1 Where S = Successor Activity and C = Current Activity

The schedule network analysis is complete once you have established the critical path, estimated the total float and free float.

CPM Schedule Analysis Example With Solution

For a critical path method (CPM) example with a solution please refer to the following post.

• Critical Path Analysis – Solved Example.

Also, read the following post for a comprehensive list of project management formulas for pmp examination.

• Project Management Formulas

To know more about PERT please refer to my post.

• Program Evaluation And Review Technique

In order to know the differences between CPM and PERT please read

• Difference Between CPM and PERT

Take the Critical Path Method Quiz

• Critical Path Method PMP Exam Questions

Conclusion

To sum it up, present-day scheduling software does all the critical path method calculations. Therefore, the project manager or the project team never performs these calculations. However, it is necessary to understand these calculations in order to use scheduling tools more effectively. Solving a critical path method example problem will assist in understanding the steps in CPM analysis.