Understanding the Critical Path in Project Management! Complete Explanation with Example

Knowing the tasks of a project is not everything. One can schedule the project tasks using inter-links and duration. However, how long a project is going to take for completion is always a valid question. Thus, project managers use different techniques to calculate the critical path in project management.

The critical path of a project is very useful for multiple reasons. It provides useful information about project activities such as critical and non-critical activities.

Although, there are several other techniques for perfect scheduling of a project. So, we will explain everything about the critical path method and analysis in this article.

This article will answer the following questions:

  1. What is the Critical Path?
  2. What is the Importance of Critical Path in Project Management?
  3. How to find a Project Critical Path?
  4. What is Critical Path Analysis?
  5. Definition of Critical Path Terminologies
  6. How to Perform Critical Path Analysis with Example?
  7. Benefits of Critical Path Analysis

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Critical Path in Project Management

What is the Critical Path?

By definition, a critical path is the longest route to completion of a project. It has the longest distance between the start and finish of the project. It provides the time for completion of all the tasks of a project.

As there are several types of projects. Mostly the project tasks are dependent on each other. There are four types of dependencies. So, the critical path analysis results in a path that is keeping the dependency relationship intact.

There are some tasks in the project schedule that goes on in parallel while some tasks depend on the same predecessor. Thus, such relation results in the creation of more than one path to the completion of the project.

However, each path of the project may require a different duration from start to the finish of the project. Now, the path that requires the longest duration for completion is the critical path.

The critical path joins all the project activities that have zero margins of delay in start or completion. So, all the activities that exist on the critical path are known as critical activities.

Further, if any critical activity gets delay, the whole project will get a delay in the same value of time. Thus, the critical activities are the most crucial activities of a project and key focus points for project managers.

Moreover, the early completion of a critical activity due to any special arrangement of resources and mitigation of vulnerable risks may result in the early completion of a project.

What is the Important of Critical Path in Project Management?

The project management has four major phases. The planning phase is the most extensive and success-oriented. So, the project managers put all the efforts into the earliest or timely completion of a project.

A project is not an entity of a single stakeholder. There are a lot of stakeholders linked with the project such as business owners, project teams, sponsors, customers, and suppliers.

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Importance of Critical Path for Investors

Almost all the projects require funds from investors. Investors have different considerations to invest in a project. One of the most important is the project duration.

They are not concerned with how many tasks the project has and how they are linked. The only point of interest for investors in the project schedule projects a critical path.

The investors just want to know what is the longest path to completion of the project and how many activities exist on that path?

The project tasks that exist on a project critical path are crucial and considered a bottleneck for any improvements.

Thus, the investors’ focus first preference is to choose that project which has minimum tasks as a barrier for improvement in project completion time.

Moreover, the project managers enlist the project activities, their precedence, and durations. Now the task network diagram is made to find out all the possible routes for completion of the project.

Are you an investor and looking forward to investing your money in some project or business startup. Wait! make sure to check out our guide on How to analyze Business Feasibility before investing money into the business or project. It will help you to choose the best option for investment.

Importance of Critical Path for Project Managers

The critical path is important for the project team for many reasons. So, the most important one is to find the critical activities and look for alternatives for the earliest completion of those activities.

However, if some activities are rigid enough for any alternatives and improvements to lower the duration. Then the key focus is the best to plan, execute, track, and control critical tasks.

Now the focus of the project team shifts from emphasizing the timely completion of critical tasks. Thus, a special risk management analysis and mitigation strategy are devised for critical activities.

Critical activities are marked as high priority activities in the project timeline and all types of schedules.

As critical activities are the building block of a critical path. So, all efforts work collectively to lower or maintain the longest duration of a project.

Furthermore, the project managers have to properly plan and track the project activities. So, free project planning and tracking templates are very useful in this regard. Thus, don’t forget to check out our Best Free Project Planning and Tracking Templates.

Related Article: Best Free Project Plan Templates for Excel | A Guide to Project Planning

How to Find a Project Critical Path?

How important it is to find a critical path and tasks of a project is well explained earlier. Now, the question is how to find a critical path for a project?

There are various techniques and tools to calculate the critical path of a project in project management. Although, each technique has its pros and cons.

However, all these techniques are highly accepted and used in major projects worldwide.

  1. Project Gantt Chart
  2. Project Network Diagram
  3. Critical Path Method (CPM) or Critical Path Analysis
  4. Project Evaluation and Review Technique (PERT)

Project Gantt Chart

The project Gantt Chart is a very simple and basic tool for figuring out the critical path of a project. Although, it’s a project scheduling tool. However, it is equally useful to find the critical path of a project.

Anyhow, it can’t provide details such as the list of critical and non-critical activities, float, and slack of each activity.

However, project Gantt chart has several other benefits and project managers must create Gantt chart for their projects.

Are you managing a project and looking for a step by step guide to making a Gantt chart or Timeline in Excel. Check out our guide on How to Create a Gantt Chart in Excel and How to Create a Timeline in Excel.

Related Article: Steps on How to Make Gantt Chart in Excel | Free Template

Project Network Diagram

Further, the project network diagram is the base of the other 3 methods. It can directly help to find out the critical route to project completion or useful in CPM and PERT methods.

The project network diagram provides a critical path and a list of critical activities. However, float or slack of each activity is still missing in the information.

This method is a simple and direct approach. It is usually useful in a project with a smaller number of activities and has only a few routes.

So, the project team can calculate the duration of each path to complete the project. Hence, the path with the longest duration is the critical path, and activities that exist on the critical path are critical tasks.

Critical Path Method (CPM)

Similarly, a network diagram of project tasks is created in the critical path method. Now, the forward and backward pass analyses are performed to find the earliest start, earliest finish, latest start, and latest finish times for each activity.

So, all the activities having the same earliest and latest start time or earliest and latest finish time are critical activities. Hence, joining all the critical activities results in a critical path formation. This technique also helps to provide the float for each activity.

Project Evaluation and Review Technique (PERT)

Finally, the PERT analysis is very similar to CPM. It also makes use of activities network diagrams. However, the PERT analysis is an events-oriented technique while CPM focuses on activities.

Further, PERT includes the allowances for the uncertainties in the completion time of activities. Because it manages unpredictable activities.

While the counterpart CPM uses a predictable estimate of activities duration. The whole technique is the same in implementation with a little difference in the calculation of initial input information.

In the CPM the duration is the natural time to completion of the activity. While PERT analysis uses a duration that is calculated from three-time estimates. Optimistic Time (O), Most Likely Time (ML), and Pessimistic Time (P). The mean time (E) is calculated as: E = (O + 4 * ML + P) / 6

What is Critical Path Analysis?

Critical path analysis is a technique to map out every critical task to complete the project.

It uses the activities duration for completion and their dependencies on other activities to find out the critical path, critical activities, and non-critical activities of the project.

Critical path analysis is commonly known as the critical path method. It uses the activities network diagram to find the longest route to completion of the project.

Further, it has vital importance to find a critical path in project management. Also, other findings of the tools are equally helpful to pinpoint the critical tasks of a project.

Moreover, the concept of critical path emphasizes the task dependencies. This indicates the risk of bottlenecks in the process of project duration improvement.

As there can be many types of dependencies between the project tasks. It is important to understand how a start or finish of a project activity can affect the start or completion of any other dependent activity.

Types of Task Dependencies in Project Management

The project tasks are dependent on each other in different ways. The start or completion of a start can be dependent on the start or completion of any other task or tasks.

So, dependencies are relationships to define the sequence in which the activities are required to be performed. Firstly, the predecessor and successor are the two important terms to understand.

The predecessor is a task whose start or completion control the start or completion of another task.

While the successor is a task whose start or completion is controlled by the start or completion of another task (predecessor). So, there are four types of task dependencies in project management.

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  1. Finish to Start: In this relation, the predecessor activity must finish before starting the successor activity. It is the most common type of relation. For example, you can’t start building a house before acquiring land.
  2. Start to Start: In this relation, the successor task can’t start before the start of the predecessor. However, in this case, the successor doesn’t have to wait for the completion of a predecessor task and can run in parallel. For example, you can start plasterwork on walls and don’t have to wait for the completion of all the walls of the house.
  3. Finish to Finish: In this relation, the predecessor task must be finished before finishing the successor task. For example, you can’t paint the whole wall unless the wall plasterwork is finished.
  4. Start to Finish: In this relation, the predecessor task must start before the successor task can finish. For example, the wall plasterwork must start before wall painting can be completed.

Terminologies of Critical Path Analysis in Project Management

Are you the project manager and planning to use a critical path analysis technique on your project? Wait! It is very important to understand each term of the critical path method to apply it correctly.

So, the following are the major terms associated with the use of critical path technique.

Activity:

The activities are the actions that collectively work to achieve the goals of a project. It’s a task that can be subdivided into further subtasks and may have individual monitoring and resources for completion.

So, generally, it is an amount of work to convert the input into the desired output.

Node:

Node is a point on the arrow network diagram to indicate the start or completion of an activity. However, it doesn’t consume any time or resources. However, in the precedence network diagram, the nodes represent the activity.

Activity Network Diagram:

The tasks network diagram is a graphical representation of project tasks and their relationships. It uses arrows to represent activity. While the nodes are here to represent the start and completion of an activity.

The tail of the arrow indicates the start of activity while the head lies on the node to indicate the end of an activity. Sometimes, the length of the arrowhead is useful to represent the duration of activity on a defined scale.

Precedence Network Diagram:

In this type of network diagram the nodes represent the activity while the arrows are there to show the relationship between activities.

Forward Pass:

The forward pass technique is helpful to find out the earliest start and earliest finish time of activity.

Backward Pass:

The backward pass technique is helpful to find out the latest start and latest finish time of activity.

Critical Path:

A critical path is the longest path to the completion of the project. It joins all the activities with zero margins of delay in start or completion. It shows the minimum time required to complete a project.

Slack:

The slack is the margin in time for an activity to start later than the planned time without hurting the total duration of the project.

Float:

The float is the margin in time for an activity to take longer to complete than the planned duration without hurting the total duration of a project.

Critical Activity:

The critical activity is the one that lies on the critical path and has zero value of float and slack.

So, the earliest and latest start or the earliest or latest finish time of this activity is the same. Thus, any delay in the start or completion of critical activity results in a delay in the project completion.

Non-Critical Activity:

All the activities other than critical activities are non-critical activities. These activities have a margin for delayed start or finish.

So, the float and slack of non-critical activities aren’t zero. Also, any delay in the start or completion of non-critical activity doesn’t affect the completion of the project unless the delay is in the available float and slack range.

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Steps to Use Critical Path Analysis in Project Management with Example

After all the above explanation, it seems like this technique is very useful but complex to implement. However, it is not like that. The critical path analysis is a very simple tool with a lot of precious outputs.

It doesn’t require any project management course to use critical path method on your daily life small projects. However, the following information is required to perform critical path analysis on a project.

  • List of Project Activities
  • Precedence Order of Activities (Sequence)
  • Estimate Duration of Activities

Further, it is a simple 4 steps technique for every type of project. It includes the following steps to perform critical path analysis in project management.

  1. Develop a Precedence or Activities Network Diagram using the precedence order of activities.
  2. Use the analysis box and implement the forward pass a method to find out the earliest start and earliest finish time of each activity.
  3. Use the analysis box to apply the backward pass method to find out the latest start and latest finish time of each activity.
  4. Note the activities having the same earliest and latest start time or earliest and latest finish time. Joining these activities with a line will give the project a critical path. Also, simply add the duration of all these activities to find the longest duration for project completion.

Step 1: Precedence Network Diagram

The first step in the implementation of the critical path method is to make a network diagram of the project. The precedence network diagram is commonly used in project management.

However, one can draw the activities network diagram and follow the same steps to apply critical path analysis.

The precedence diagram is a visual representation of project activities to understand the relationship between activities.

Let’s understand the steps to make a precedence network chart with a very basic example.

Example Project Data: Activities, Predecessors, and Duration

A project has 7 activities named A to G. The precedence relation of each activity is defined in the predecessor column. While the duration for each activity is also available. So, let’s make a precedence network for this project.

Precedence Network Diagram
  1. Draw a Node using any shape to show the activity A.
  2. Now see Activity B has predecessor activity A. So, make another node show activity B and point and arrow from node A to node B to show the relationship between these two activities.
  3. So, repeat step 2 to show activity C and D. However, activities D and E have the same predecessor. Which shows that both these activities can start in parallel after activity C. So, make nodes of both these activity at the same distance from activity C and connect both activities with C to show a relationship with activity C.
  4. Further, see activity F has two activities as the predecessor. It means this activity will have two arrows one from each activity D and E to show a relationship with both activities. So, draw node F at distance from node D & E and make arrows to show relation.
  5. Finally, as activity G also has only one predecessor. So, it will also follow step 2.

Step 2: Critical Analysis Matrix

A critical analysis matrix or boss is useful to apply the forward and backward pass techniques. It helps to fill in the required information to find the critical activities and critical path.

So, simply replace the nodes of the precedence network diagram with the critical analysis matrix and fill in the available information before applying the forward pass method.

Do you know? Matrix is a very powerful tool to easily tool to perform different analyses. The projects are always vulnerable to risks. Thus, our Project Risk Analysis Matrix helps to analyze and mitigate the risk probability for the timely completion of the project.

Critical Path Analysis Matrix

The following are the elements of the critical analysis matrix.

Activity Description: It is the name or description of the project activity.

Duration: It is the time required to complete the activity.

Slack: It is the time allowance available to delay the start of a non-critical task without delaying the completion of the project.

Float: It is the time allowance available to delay the completion of a non-critical task without delaying the completion of the project.

Earliest Start Time: It is the earliest time on which the task can start according to the relationship with predecessors.

Earliest Finish Time: It is the earliest time on which the task can finish according to the relationship with predecessors and activity duration. So, it is equal to the task earliest start time plus the duration of the task.

Latest Start Time: It is the latest time on which the task can start for the timely completion of the project. It uses the full slack margin to show the latest start time for the project. So, it is equal to the sum of the task earliest start time and slack.

Latest Finish Time: It is the latest time on which the task can finish according to the available slack or float of the task and will not delay the project completion. So, it is equal to the sum of the task’s latest start time and duration.

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Critical Path Analysis for Project

Step 3: Forward Pass Method

The forward pass method is useful to calculate the earliest start (ES) and the earliest finish (EF) time of activity. It’s a very simple technique to use.

The following are the steps to apply the forward pass method on our under-consideration example project.

Forward Pass Method to Find Critical Path

Steps to Use Forward Pass Technique

  1. It starts from the first activity and the earliest start (ES) time of first activity is zero. Also, the earliest finish (EF) time of each activity is equal to ES + Duration.
  2. If the successor activity have relation with only one predecessor such as Activity B in our example have only one relation arrow pointing toward it in the precedence diagram. In this case, the EF of predecessor activity is the ES of the successor activity. So, for Activity B the ES = Activity A (EF) + Duration of Activity B.
  3. Step 2 applies to all the activities with only one arrow pointing towards the activity. In this example, activity B, C, & G will use step 2.
  4. If two arrows are pointing away from the activity. Like activity C in our case. It shows activity C is the predecessor of two activities. So, the EF of activity C will be ES of both the successor activities towards which the arrow is pointing.
  5. If two arrows are pointing towards an activity. Like activity F in our case. It shows that activity F has two predecessors. So, the ES of activity F will be equal to the EF of that predecessor activity which has larger EF value. In our case, it is activity E with larger EF. So, ES of Activity F = EF of Activity E.
  6. Finally, the EF of the last activity shows the longest duration to complete the project. That is 29 days in our case.

Step 4: Backward Pass Method

The backward pass method is useful to calculate the latest start (LS) and the latest finish (LF) time of activity. It is a very simple technique to use.

The following are the steps to apply a backward pass method on our under-consideration example project.

Backward Pass Method to Find Critical Path

Note: The backward pass method reads the precedence network from right to left. So, the first activity of a backward pass is the last activity of the project.

Also, the backward pass, the successor activity is the predecessor. So, here everything is opposite to reality or forward pass. So, don’t get confused by arrows direction. Just start reading the network from right to left.

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Steps to Use Backward Pass Technique

  1. So, the latest finish (LF) time of most right activity is equal to the earliest finish (EF) of the last activity. That is 29 days in our case. Also, the latest start (LS) time of each activity is equal to LF – Duration.
  2. Now, start analyzing the precedence network diagram from right to left and consider every left activity is the successor of right linked activity. Like in our case consider activity G is the predecessor of activity F. Although, it is opposite in actual. Mean the activity G is successor not the predecessor of F.
  3. So, If the backward pass successor activity have relation with only one predecessor such as Activity F in our example have only one relation arrow pointing toward it in the precedence diagram. In this case, the LS of predecessor activity is the LF of the successor activity. So, for Activity F the LF = Activity G (LS) and Activity F (LS) = Activity F (LF) – Duration of Activity F.
  4. Step 2 applies to all the activities with only one arrow pointing towards the activity. In this example, the activity F, E, D, B & A will use step 2.
  5. If two arrows are pointing away from the activity. Like activity F in our case. It shows activity F is the predecessor of two activities. So, the LS of activity F will be LF of both the successor activities towards which the arrow is pointing.
  6. If two arrows are pointing towards an activity. Like activity C in our case. It shows the activity C has two predecessors. So, the LF of activity C will be equal to the LS of that predecessor activity which has Smaller LS value. In our case, it is activity E with smaller LS. So, LF of Activity C = LS of Activity E.
  7. Finally, the LS of the last activity must be equal to zero. If it is not zero, there must be some mistake in the implementation of the backward pass technique.

Step 5: Calculate the Float or Slack

Theoretically, the slack and float are different terms. However, mostly the value of slack and float is the same.

The float is the time allowance available to delay the completion of activity without delaying the project completion. It has some value for non-critical activities, and it is zero for critical activities.

Activities Float Calculation

The float of activity is calculated using the following formula.

Float = LS –ES or LF – EF

While in actual the float is equal to the Duration + (LF – ES).

Step 6: Highlight the Critical Path

Everything has already been done. Now, it’s time to highlight and mark the critical path on the precedence network diagram.

Note all the activities which have zero floats. These are the critical activities of the project. While all the activities having some value of float are non-critical activities.

Critical Path of a Project

Now simply make a path by joining all the critical activities. It’s the critical path of the project. In our example, the critical path is A-B-C-E-F-G. So, the critical activities are Activity A, B, C, E, F, and G. While there is only one non-critical activity that is activity D.

If I somehow manage to lower the required duration to complete any of the critical activities. The overall duration of the completion of the project will also decrease.

So, that’s the reason for using critical path analysis for any project to pinpoint the bottleneck activities. So, the effort can be put on to improve the duration or at-least maintain it to avoid any delay in the timely completion of a project.

Benefits of Critical Path Analysis in Project Management

The importance and usage of critical path methods are already well explained earlier. However, let’s just recall the key advantages of using critical path analysis for your project or business.

  • The critical path of the project demonstrates the graphical illustration of the project activities in the form of a precedence network diagram.
  • It identifies the critical tasks of the project that require the utmost attention and efficient planning to perfectly manage the tasks.
  • It saves the project managers’ time and helps to reduce the duration of the project.
  • The project managers can compare the actual progress of the project with the planned for analysis.
  • The visual representation helps to better understand the dependencies relationship between different activities.
  • It is a useful tool to assist project managers in planning, scheduling, executing, tracking, and controlling the project activities.
  • The critical path analysis helps to reduce the risk and costs of complicated and extensive projects.
  • It identifies the slack or float of non-critical activities. So, the better allocation of resources may help to reduce project completion time.
  • It is planning as well as the decision-making tool for project managers, entrepreneurs, and investors.

Also, check out our free Template to Make a 2 Week Look Ahead Schedule for your project. It provides better control over the project during execution and saves a lot of resources.

Free Download Critical Path Analysis Template for Project Management

Templates Free Download provides free templates to apply critical path analysis on your projects easily. These templates are useful to record the critical path method data.

Further, it can automatically calculate the critical path and critical activities for any project.

Critical Path of a Project
Critical Path Method Excel Template

Steps to Calculate Critical Path of any Project using TORA

TORA is an operations management algorithm developed for the Hamdy A. Taha Operations Research book.

It has very useful algorithms to quickly solve linear equations, linear programming, transportation model, integer programming, and zero-sum games.

Further, it is very useful to solve advanced operations research techniques such as network models, project planning, and queueing analysis.

Project planning includes an algorithm to quickly solve CPM and PERT techniques. So, we will cover the step by step details to use TORA to find the critical path in project management, critical activities, and float for our project.

Step 1: Launch the TORA and Choose CPM Module

The TORA is compatible with 800 x 600 or 1024 x 768 screen resolution only. So, change your system resolution to install and run the TORA after downloading.

Further on the launch, the welcome screen will introduce the algorithm. So, just click on the “Click Here” button to proceed further.

H Taha Operations Research Algorithm

In the main section, you will see a dropdown list of algorithms to choose from. Simply navigate to Project Planning and CPM – Critical Path Method and left click to proceed.

Now, select input mode and input format. If you are not sure about the setting. Just click on the “Go to Input Screen” button.

Once you are in Project Planning – CPM/PERT module. Enter the “Problem Title” and hit the “Enter” button to initialize the input grid.

Critical Path Algorithm of TORA

Step 2: TORA CPM Data Input Grid

So, the input grid will appear to make entries of your project data in terms of nodes, activities symbols, and duration. Now, one thing is important to understand here that the TORA CPM module requires nodes.

So, you have to make an activity network diagram instead of a precedence network diagram. Thus, the activities network diagram of the same example discussed in the above section will look alike below.

Project Activity Network Diagram

We simply need to enter the “From Node” and “To Node” of activity along with activity symbols and duration for all the project activities.

It’s all you need to do. Now, just click on the “Solve Menu” button to go for a solution.

Project Activities, Predecessor, and Duration Entry

Step 3: Problem Solve by TORA CPM Algorithm

We have made entries, now just click on the “Solve Problem” button if no modification in entries requires. Otherwise, click on the “View/Modify Input Data” to make alterations.

On select output format windows, simply click on the “Go to Output Screen” button to proceed further. Now, as TORA provides two types of output for Project Critical Path, CPM calculation, and CPM bar chart. So, click on the “CPM calculation” option to go for critical path findings.

TORA CPM Solve Problem

Further, you can see the step by step solution by pressing the “Next Step” button or simply click on the “All Steps” button to solve the problem at once.

Whoa! That’s it. The problem is solved. You can see the forward pass and backward pass results for your problem. Also, the earliest start, latest completion, total float, and free float values of the project activities.

TORA CPM Calculations

Moreover, the critical activities are marked red to highlight. Simple note the symbols of critical activities and join on your network diagram to see the project critical path.

Project Critical Path TORA

Further, you can also choose to see the CPM bar chart of your project activities along with the earliest start time, latest start time, earliest finish time, and the latest finish time calculation of your project.

TORA CPM Bar Chart

Finally, it was all about the “Critical Path in Project Management”. Please do share your feedback in the comments section and SUBSCRIBE us to learn more about Project Management.

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