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 which concludes without referring to this vital project scheduling tool.

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

Further, as the project progresses, we needlessly expand the list of critical tasks and concentrate our efforts in completing them. As a matter of fact many of us consider any important or difficult to complete 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.

Critical path method in project management is a project schedule network analysis technique. CPM analysis helps to identify a sequence of activities that requires close monitoring. It is the most important outcome of 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, critical path method controls both time and cost aspect 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. Critical path method also helps to establish a probabilistic estimates of project completion targets. Further, critical path analysis in project management also facilitates accurate assessment of schedule risk.

## What is Critical Path

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

The overall project duration is the sum total of 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 critical path ensures that there are no slippages in schedule.

## Critical Path Characteristics

The following paragraph enumerates various characteristics of critical path.

- It is the
**longest path**in a project schedule network diagram. - Critical path establishes the
**minimum project duration**. - It also indicates the amount of
**scheduling flexibility**in the network diagram. - Activity on critical path is
**critical path activity.** - A project can have
**more than one**critical path. - Critical path
**changes**as the project progresses. - Total float of activities on critical path is
**Zero**(0) - For activities on 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 forward pass; move in forward direction from the project start node to the last node of 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 backward pass; move in it move in backward direction from project end node to the start node of 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 stat 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 project starts on day 1.

Use the following steps to conduct critical path method analysis.

- Draw the project schedule network diagram.
- Calculate all paths in the schedule network diagram.
- Calculate the critical path.
- Perform Forward & Backward Pass Calculations on Critical Path.
- Perform Forward & Backward Pass Calculations on Non-Critical Path.
- Calculate Total Float.
- 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 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 project schedule network diagram using Precedence Diagramming Method (PDM). 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 a logically correct project schedule network diagram.

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

Also read: Sequence Activities Tools and Techniques

## How To Calculate Critical Path

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

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

## Critical Path Method Schedule Analysis Forward Pass Calculation

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

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

- Conduct forward pass for activities on critical path and calculate early start and early finish for each activity (node)
- At first node
- Early Start (ES) of the first activity = 1
- Early Finish (EF) = ES + Activity Duration (D) – 1

- ES of the next node is the earliest finish time of the immediately preceding activity. In this case it is EF of first node plus 1 = EF + 1
- For activities with more than one preceding activity ES is
**latest**of the earliest finish times of the preceding activities. - 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.

- At 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

- For the next node in 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.

- Once you reach the first activity your backward pass is complete.

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

## Critical Path Method Schedule Analysis Total Float Calculation

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

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

## Critical Path Method Schedule Analysis Free Float Calculation

Use the following formula to calculate 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 critical path method (cpm) example with solution please refer to the following post.

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

To know more about PERT please refer to my post.

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

## Conclusion

To sum it up, present day scheduling software do 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.

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