Even if an individual not connected to project activities knows a project management term “Critical Path” or “Critical Activities”. There is no project review meeting which concludes without referring to this vital project management tool. Due to excessive use of scheduling software we pay little attention to fundamentals of project schedule network analysis process. We rarely analyse the critical path generated by scheduling software. As the project progresses, we needlessly expand the list of critical tasks and concentrate our efforts in completing them. Many of us tend to consider any important or difficult to complete activity as a critical task. However, this is not true under all circumstances. Thus, this post describes Critical Path Method (CPM) terminology and calculation steps.

Contents

- 1 Critical Path Method in Project Management
- 2 What is Critical Path?
- 3 Features of Critical Path
- 4 Critical Path Method Definition
- 5 Critical Path Method Analysis Steps
- 6 How to Draw The Project Schedule Network Diagram?
- 7 How to Calculate Critical Path?
- 8 How to Perform Forward & Backward Pass Calculations?
- 9 How to Calculate Total Float?
- 10 How to Calculate Free Float?
- 11 Conclusion
- 12 Author’s Profile

## Critical Path Method in Project Management

Critical path method technique in project management helps to identify a sequence of activities that requires close monitoring. This sequence of activities is know as critical path. It is the most important outcome of critical path method (cpm) analysis process. Hence, critical path method analysis ensures that there are no schedule slippages and cost overruns. The critical path method 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 method in project management also facilitates accurate assessment of schedule risk.

## What is Critical Path?

Critical path of a logically structured project schedule network diagram that specifies a sequence of activities which need utmost attention of the project project team. The overall project duration is the sum total of duration of all the 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. This also means that no slippages in schedule are acceptable.

## Features of Critical Path

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

**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 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.

## How to Draw The Project Schedule Network Diagram?

The first step of critical path method analysis is to draw the project schedule network diagram. The critical path method analysis uses Precedence Diagram Method (PDM) technique to represent the schedule network logic. Activity-On-Node (AON) is one example that uses PDM to construct the schedule network logic.

## How to Calculate Critical Path?

The following list enumerates steps in identifying critical path using the critical path method (CPM) technique.

- 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.

## How to Perform Forward & Backward Pass Calculations?

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.
- 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 network analysis process.

## How to Calculate Total Float?

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

## How to Calculate Free Float?

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.

For critical path method example with solution refer to my post.

## 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 prudent 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.

View all formulas used for critical path method analysis, please visit the following.

- PMP Formulas on the Resources page.

To understand methods to sequence project activities, please read my post.

To know various steps involved in the project schedule development process, also read my post.

For fundamentals of project planning and scheduling, please visit my post

In case of any query, please visit the contact us page.

## Author’s Profile

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Reblogged this on Atul Gaur.