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How to use critical path method for complete beginners (with examples).

• What is critical path in project management?
• Understand the critical path method
• The critical path algorithm explained
• Float or slack in project management
• Dealing with contingencies and constraints
• What are the benefits of the critical path method?
• How to use the critical path method

Why must non-critical tasks be monitored?

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Originally published May 22, 2022. Updated with new information on September 21, 2022

 How to use the critical path method for complete beginners

Critical path method: getti ng started in cpm & cpa.

Our CPM guide includes everything you need to get started in the Critical Path Method - with step-by-step examples, solutions, as well as schedules to help get your next project done faster and easier.

The Critical Path Method (CPM) is a simple but powerful technique for analyzing, planning, and scheduling large, complex projects. It is used to determine a project’s critical path—the longest sequence of tasks that must be finished for the entire project to be complete. 

 CPM, also known as Critical Path Analysis (CPA), identifies dependencies between tasks, and shows which tasks are critical to a project. 

The Critical Path Method (CPM) is one of the most important concepts in project management, and certainly among the most enduring. But what is the Critical Path Method, exactly? This beginner-friendly guide will help you understand the Critical Path Method and apply it in your projects.

Early iterations of the Critical Path Method can be traced all the way back to the Manhattan Project in the early 1940s. Given the ambition, scale, and importance of this world-altering project, scientists - and the managers behind them - developed a number of techniques to make sure that the project delivered results on time. For a project management technique , the Critical Path Method has quite an illustrious history.

One of these techniques was to map out the most important tasks in any project and use that to estimate the project completion date.

Today, we know this technique as the Critical Path Method.

The Critical Path Method in project management is a cornerstone of project planning even to this day. How long a project takes often depends on the most important tasks that constitute it.

If you can map out these tasks and their duration, you can get a reasonable estimate of the project’s timeline and budget.

Don’t worry if all this sounds too much like jargon to you. In this beginner-friendly guide, I’ll teach you everything you should know about the Critical Path Method (CPM) and how it applies to project management.

Understand the Critical Path Method

Have you ever heard of the Theory of Constraints (TOC) ?

First described by Eliyahu Goldratt in his 1984 book, The Goal, this theory states that your ability to complete any activity hinges on a few critical resources or constraints.

For example, if you’re making a sandwich, you might have all the butter, ham, and cheese you need, but if you don’t have bread, you can’t make a sandwich.

The bread, in this case, would be the constraint your sandwich-making project depends on.

The Critical Path Method is similar to this theory, but broader in focus. According to this method, the success of any project depends on tasks along a critical path being completed on time.

Let’s look at this method in more detail.

What is the Critical Path Method and what is a Critical Task?

Every project, regardless of its size or budget, has some core tasks that are crucial to its completion. A task is defined as critical if delaying it will slow down the completion of the entire project.

Take something as simple as making an omelet.

If you had to create a short recipe for making an omelet, it would look something like this:

• Beat 2 eggs
• Heat a pan, add butter/oil when hot
• Pour in the beaten eggs and cook for 5 minutes

There are several other tasks you need to perform to make a good omelet. You have to season the eggs with salt and pepper. Maybe add some vegetables and some cheese. Perhaps you could flip it on the other side so the eggs are fully cooked through.

However, these activities are in addition to the three core steps in the recipe. Even if you don’t perform them, you’ll still have an omelet. Not a very good one, but an omelet nonetheless.

On the other hand, if you forget to beat the eggs, or heat the pan, or cook the eggs, you won’t have anything but a cold pan and two eggs.

This is to say, the three steps in the recipe describe the critical tasks necessary to make the omelet-making project a success.

And the sequence of these steps describes the critical path a new cook must take if he wants to make an omelet.

This is the Critical Path Method in a nutshell.

Critical Path Method Definition

The Critical Path Method is defined in the Project Management Body of Knowledge (PMBOK) as follows:

“The Critical Path Method is the sequence of scheduled activities that determines the duration of the project.”

These scheduled activities must be performed if the project is to be considered a success. Moreover, they must be completed in a specific order. If you’re building a house, you can’t construct the walls and then dig the foundation; you have to do it in a sequence.

The important bit to understand is that the CPM describes the longest sequence of tasks in the project.

That is, in any project, you’ll have multiple task sequences. The CPM would describe the sequence that takes the most time.

For example, if you’re building a house, you would have several task sequences as follows:

Each task takes a different amount of time and resources. It takes more time to build walls and lay the roof than to install faucets and fixtures.

If you had to figure out the project’s ‘Critical Path’, you would look at the sequence that takes the most amount of time, like this:

The total time taken to complete the sequence along this critical path would give you an idea of the project’s minimum duration.

You might undertake several task sequences simultaneously, but if there are any delays in the critical path sequence, your project will suffer delays as well.

The Critical Path Algorithm Explained

At its heart, the Critical Path Method is essentially an algorithm for decision-making. This algorithm takes a task's start time, its duration, and finish time to figure out which activities deserve the most attention (i.e. are "critical" for the project).

Let's consider an example to understand the critical path algorithm better.

Suppose you have a list of tasks as shown below. Columns C and D list the tasks that must be accomplished for the activity to begin, and the duration of the activity, respectively.

Since the project manager's goal is to complete the project as quickly as possible (without compromising on quality, of course), we'll try to find the earliest finish time for each activity.

To do this, organize all tasks into a flowchart and note their durations next to the task ID. The arrows indicate the sequence of activities. We'll mark the Earliest Start (ES) time to the left of the activity, and the Earliest Finish (EF) time to the right.:

Mark the Start Time (S) to the left and right of the first activity. Usually, this would be 0.

Now mark the Earliest Start (ES) time of each activity. This is given by the largest number to the right of the activity's immediate predecessor (i.e. its Earliest Finish time, or EF).

If the activity has two predecessors, the one with the later EF time would give you the ES of the activity.

The EF of an activity is given by its Earliest Start time (ES) and its duration (t), i.e. ES + t.

Thus, if an activity's ES is 20 and will last for 10 days, its EF will be 30.

Mark all these figures in the flowchart.

The longest path will be the “critical path”.

The final figure to the right of the last task in the sequence will give you the minimum time the project will take to finish.

Float or Slack in Project Management

A concept related to, and crucial for using the Critical Path Method is float or slack.

In project management, “float” defines the amount of time a task can be delayed without causing a delay in:

• Any subsequent, dependent tasks - called “free float”
• Any delay in the overall project - called “total float”

Any activity or task on the critical path has zero float. That is, you can’t delay it at all without causing a delay in the project or dependent tasks.

However, there are plenty of other activities in the project that can be delayed. The quantification of this delay is called the “float”.

For example, when you’re making an omelet, “Heating the pan” has zero float since it is on the critical path.

Seasoning the eggs, however, has a lot of float. You can add salt to the raw egg mixture, while the eggs are cooking, and even after they’ve cooked.

The importance of slack should not be understated. Calculating the float or slack of all activities in the project is crucial for better distribution of resources.

If an activity has a high float, you can divert its resources to a higher-priority task.

Generally speaking, high float activities will be lower down the priority list, while those on the critical path (aka ‘zero float’ activities) will get prime attention.

Dealing with Contingencies and Constraints

Rare is the project that goes according to plan. You will invariably have delays, scope changes, and client demands that will force you to hasten some activities and delay others.

The Critical Path Method includes several measures to deal with such contingencies:

1. Fast Tracking

Fast-tracking is the process of running multiple activities on the critical path in parallel in order to reduce overall project time.

Fast-tracking is only possible for activities that don't have "hard" dependencies, i.e. they don't depend completely on their predecessors to start.

For example, you need to dig the foundation before you can build the walls of a house. But while you're doing the digging, you can also buy bricks and mix the cement.

Thus, while "build walls" is dependent on "dig foundation", you can run "buy bricks" and "mix cement" in parallel to digging the foundation.

Obviously, fast-tracking requires additional resources. It can also impact overall quality since you're distributing resources to multiple tasks. Good resource management will come in particularly handy in situations where you need to run activities in parallel.

2. Crashing

What if you need to rush an activity because of an early deadline?

In such a situation, you can allocate additional resources to the activity to bring it to completion faster.

This process is called 'crashing'.

Having a crash duration is useful in activities that:

• Benefit from having additional resources, i.e. follow a linear relationship between resources and time to completion.
• Can utilize resources from activities with high floats. Since there is significant "slack" in these activities, you can delay them without jeopardizing the project

Crashing is generally not recommended barring emergencies since it can impact activities on and outside the critical path. If you have to do it, however, divert resources from high-float tasks, not those on the critical path.

What Are the Benefits of the Critical Path Method?

In its September 1963 issue , Harvard Business Review had this to say about the Critical Path Method:

“Recently added to the growing assortment of quantitative tools for business decision making is the Critical Path Method—a powerful but basically simple technique for analyzing, planning, and scheduling large, complex projects.”

Since then, this method has established itself firmly in the theory and practice of project management. And for good reason - using the Critical Path Method offers countless benefits:

• Reduce delays: The Critical Path Method helps identify the most important sequence of tasks in a project. Managers can use this information to reduce delays by optimizing the work along the critical path, proactively preventing delays before they occur.
• Visualize dependencies: The CPM depends on listing all tasks associated with a project and their dependencies. The chart thus created can help you visualize all dependencies and prioritize tasks accordingly. Visualizing a Critical Path Method schedule can also simply give all stakeholders and resources a general roadmap of what to expect in any given CPM-driven process.
• Improve organization: In complex projects, the CPM helps break down deliverables into sequences, and sequences into tasks. This, along with the focus on visualizing dependencies, mapping constraints, and defining the critical path of tasks drastically improves project organization, ultimately making projects more manageable.
• Optimize efficiency: By mapping the critical path, project managers get a better idea of important tasks in the project. They can use this information to allocate resources more efficiently, adding/removing resources depending on the task's importance.
• Float calculation: Float, as we'll learn below, defines how much a task can be delayed without impacting the project schedule. This is an important part of the Critical Path Method. Calculating the float can help you distribute resources more effectively while being better prepared for any unforeseen issues that may arise at any point throughout the project.

If you’re a project manager - or aspiring to be one - there is another reason to understand the Critical Path Method: it is a core part of the PMP exam. You can’t really hope to be a certified project management professional without a deep understanding of this method.

In the next section, I’ll do a deep dive into CPM and show you how to use it in your projects.

How to Use the Critical Path Method

Project managers (PMs) use CPM to find the best way to schedule all the tasks in a project so that they can be completed as quickly and cheaply as possible. It helps them to prioritize tasks, anticipate bottlenecks, and identify task dependencies, resource constraints, and project risks . 

The Critical Path Method can seem overly complicated until you actually put it to use. If you have a good understanding of core project management concepts such as the Work Breakdown Structure (WBS), you’ll find that CPM is delightfully simple.

I’ll walk you through a step-by-step process for using the Critical Path Method below.

A Step-by-Step Process for Using Critical Path Method

Recall our article on work breakdown structures (WBS)?

This WBS is the first ingredient in using the Critical Path Method. If you don’t understand the role of the WBS or how to create one, I encourage you to read our beginner-friendly article first.

Once you have a WBS, jump straight to the first step.

Step #1: Identify activities based on WBS

If you know your WBS, you would know that it describes deliverables, not activities. This is why all its components are described using nouns or adjectives, not verbs.

The CPM, however, focuses on activities described using verbs.

The first step of the CPM process, therefore, is to list all the activities required to create deliverables at each level of the WBS.

For example, if you’re making a sandwich, you might have the following activities associated with it:

This list of activities will form the foundation of the CPM, so make sure it is thorough.

Step #2: Identify all dependencies

Any project has two types of tasks:

• Tasks that depend on other tasks for their completion, i.e. dependent tasks
• Tasks that are independent of others and can be done in parallel to others, i.e. concurrent tasks

For example, if you’re making a sandwich, you can buy bread, vegetables, cheese, and chicken for it simultaneously. You can also chop vegetables while the chicken is cooking. Thus, these would be concurrent tasks.

However, buying bread and toasting bread are dependent tasks. You can’t toast bread if you don’t buy it, after a ll.

The next step in the CPM process is to establish which of the tasks are dependent and which are concurrent.

Go through your list of activities and identify which tasks each depends on, and in what order, like this:

A list of dependent tasks is called an activity sequence. You’ll use these sequences to figure out the critical path.

Step #3: Create a network diagram

Once you’ve identified all tasks and their dependencies, it’s time to create a network diagram, also known as a critical path analysis chart.

This chart visualizes separate activity sequences and enables you to map dependencies easily. To create it, make a list of all activity sequences. Create separate boxes for each task in the sequence.

Next, use arrows to identify dependencies between tasks in each sequence, like this:

This network diagram will form the basis of the final critical path.

Step #4: Estimate the duration of each activity

Recall that the critical path method describes the longest sequence of activities necessary to deliver the project successfully.

Thus, to figure out the critical path, we first need to estimate the duration of each activity. The activity sequence that takes the longest time would then be our critical path.

There are several tactics you can adopt to estimate the duration of an activity:

• Guesswork based on experience and knowledge
• Estimate based on past project data
• Estimate based on industry benchmarks
• Estimates based on extrapolated data

For example, if you know that it takes you 10 minutes to paint a 2’ x 2’ board (4 sq ft), you can estimate that it will take you 250 minutes to paint a 10’ x 10’ wall (100 sq ft).

However, even the best estimates can be inaccurate. Some tasks might be delayed because of unproductivity, delayed dependent tasks, or errors. Others might be completed earlier than expected because of an efficient worker.

To account for such contingencies, it is common to use three estimates for each activity:

• Best-case scenario, i.e. shortest duration (A)
• Normal scenario, i.e. expected duration (B)
• Worst-case scenario, i.e. longest duration (C)

The average of these three cases would give you a reasonable estimate of each activity’s duration.

Activity Duration = (A + B + C) / 3

If you’re dealing with activities you’ve performed several times in the past, you’ll likely have a better idea of its duration. In such a case, you can use a weighted average, giving additional preference to the “normal” scenario (B) according to your own confidence.

Weighted Activity Duration = (A + 2B + C)/4

List the duration (t) of each activity next to its name in the network diagram.

Step #5: Calculate the Critical Path

In your network diagram, write down the start and end time of each activity next to its box.

The first activity in the sequence would have a start time of ‘0’. Its end-time would be its duration.

The second activity’s start time would be the end time of the first activity. Its end-time would be the start time + the duration.

Do this for all the activities in every sequence, like this:

Now, look at the last activity in each sequence. The figure to its right would tell you the duration of the entire sequence.

The activity sequence with the longest duration would be your critical path.

Step #6 (Optional): Determine Floats

Float, as I mentioned earlier, is the amount of time an activity can be delayed without causing a delay in the project.

Calculating the float for all activities can help in resource planning. If an activity has a high float, you can divert resources from it to a higher priority task.

To determine float, follow this process:

• Find the second longest sequence of activities in the network diagram.
• Subtract its total duration from the duration of the critical path sequence
• The difference between the two durations will give you the float for each activity in the second sequence.
• If there are any common activities in both sequences, it will have a float of 0 since it is also on the critical path

You can do this for all other sequences to determine floats for every activity.

For example, in the diagram below, activities E, F, G, H, and I make up the critical path. Their total duration is 100 hours.

Activities B, C, D and E make up the second longest sequence with a total duration of 90 hours.

The difference between their total duration is 10 hours. However, since activities E is common and in the critical path, it would have zero float.

Hence, B, C, D - which are the non-common activities in the second sequence - would have a float of 10.

That’s it! You just used the Critical Path Method in a hypothetical project.

In the real world, you’ll rarely use network diagrams to chart the critical path. Instead, you’ll use Gantt charts to visualize tasks and their dependencies.

However, creating network diagrams and mapping critical paths manually can help you understand the concept better. It will also help you when you’re preparing for the PMP exam or actually managing projects.

Critical path method vs. Gantt chart

The Gantt Chart is a graphical tool that is used to display task dependencies and timing information. It can be used to track actual progress against planned progress and can help identify any potential problems with completing a project on time - and are often used in conjunction with Critical Path Method analysis to provide a more complete picture of the project. That said, there are some differences between the two.

If you need to track complex task dependencies and want a more detailed view of the project timeline then the Critical Path Method is the better choice. If you just need a simple way to track progress and don't need every detail, then Gantt Chart may be a preferred option.

In addition, the Critical Path Method should be used when you need to accurately predict the length of a project and when there are multiple dependencies between tasks. Gantt charts are best suited for projects where changes occur frequently and you need to be able to quickly adapt to those changes.

Non-critical tasks are not dependent upon the completion of other tasks so they can be executed before or after a certain project stage has been completed. However, as these tasks still need to be done for the project to be finished, forgetting one will push back the completion date of the whole project.

Critical Path Method vs. PERT

PERT is a project management technique that uses a probabilistic model to schedule and control uncertain activities, while CPM is a statistical technique that uses a deterministic model to schedule and control well-defined activities. The two techniques are quite different in their underlying assumptions and methodology. 

PERT assumes that all tasks in a project are uncertain, and uses a probability distribution to calculate the expected completion time for each task. This allows for the estimation of the project's overall duration - given uncertainty in the individual tasks. CPM, on the other hand, assumes that all tasks are well-defined and can be scheduled with certainty. It uses a mathematical algorithm to calculate the shortest path through a network of tasks, known as the critical path. This allows for the determination of the earliest possible completion date for a project and its latest allowable completion date.

The PERT technique is the best choice when there is significant uncertainty surrounding the individual activities in a project. This uncertainty can be due to the nature of the activities themselves, or because the required resources for those activities are not yet known. The critical path method, on the other hand, is better suited for projects where all of the activities and their dependencies are well-defined and relatively stable.

Recent Updates and Developments in CPM

It's important to note that although CPM continues to play a major role in project management, new theories, and workflows seek to improve processes even further.

That said, the critical path method is still a popular way to schedule projects, despite some newer theories that have arisen in recent years. One such theory is the elasticity theory, which suggests that projects should be scheduled according to the flexibility of the deadlines. This takes into account the fact that unexpected delays can always occur and that it's better to have a project that's finished a little late than one that's rushed or never finished at all. 

Other theories focus on using predictive analytics to calculate the best possible sequence of tasks in order to achieve the desired outcome. For example, some researchers are exploring how artificial intelligence can be used to help identify and optimize critical paths. This could help reduce the amount of time needed to complete a project and improve its overall efficiency.

Earned Value Management (EVM) is another project management technique that integrates cost, schedule, and scope information into a single performance measurement system. EVM can also be put into practice in conjunction with CPM, as EVM contractors often use it to assess project performance and determine whether a project is on schedule and on-budget.

Interestingly, most new updates or theoretical approaches draw inspiration from CPM itself.

Use Critical Path for Better Project Management

While there are no perfect solutions to project management, the critical path method is still one of the most popular ways to get the job done. Put plainly, CPM is used to compress and make schedules more efficient, quickly resolve resource shortages or resignations , and compile data for future use. Compressing a schedule means finding ways to complete the project in less time. This can be done by eliminating unnecessary tasks, shortening task durations, or overlapping tasks. Resolving resource shortages means making sure that all the resources needed to complete the project are available when needed and proactively knowing when additional resources may be needed. This can be done by reallocating resources, negotiating for more resources, or postponing tasks that can be done later. Compiling data for future use means gathering information about how the project was completed so it can be used as a guide for future projects.

As shown in the critical path method example above, CPM is a powerful project management tool. By having a foundational understanding of how CPM works and how it can be applied to your projects - rather than searching for a quick-fix Critical Path Method calculator - you can use it to improve your project management skills and increase your project's chances of success.

For CPM to work effectively, your schedule must be continually updated throughout the project to reflect any changes. Using project management software such as Workamajig will make it quicker and easier to plot and monitor your critical pathway and adjust your schedule when necessary. 

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Critical Path Method (CPM) in Project Management

Presented by projectmanager, the project management software that automatically calculates your project’s critical path..

What Is the Critical Path In Project Management?

What is the critical path method (cpm), cpm vs. pert, when should you use critical path analysis, what is the importance of cpm in project management, critical path diagram, critical path method (cpm) formula, critical path method example, critical path method steps.

• Benefits of Using CPM In Project Management

CPM Training Video

Cpm & project management software, must-have features of critical path software.

• How to Find the Critical Path with ProjectManager

In project management, the critical path is the longest sequence of tasks that must be completed to execute a project. The tasks on the critical path are called critical activities because if they’re delayed, the whole project completion will be delayed. To find the critical path, project managers use the critical path method (CPM).

The critical path method (CPM) is a project management technique that’s used by project managers to create an accurate project schedule . The CPM method, also known as critical path analysis (CPA), consists in using the CPM formula and a network diagram to visually represent the task sequences of a project. Once these task sequences or paths are defined, their duration is calculated to identify the critical path.

Related: 12 Free Project Scheduling Templates for Excel

Finding the critical path is very helpful for project managers because it allows them to:

• Accurately estimate the total project duration.
• Estimate the time that’s necessary to complete each project task.
• Identify critical activities which must be completed on time and require close supervision.
• Find out which project tasks can be delayed without affecting the project schedule by calculating slack for each task.
• Identify task dependencies, resource constraints and project risks.
• Prioritize tasks and create realistic project schedules.

Once done by hand, the critical path can now be calculated automatically with project scheduling software equipped with Gantt charts , which makes the CPM method much easier. ProjectManager is project management software that helps you quickly implement the critical path method. Build a project schedule on our award-winning Gantt chart, then simply filter for the critical path. When it’s time to execute, your team can collaborate with a task list, kanban board or calendar. And you can track everything with dashboards and reports to ensure you stay on track. Get started today absolutely free.

ProjectManager can calculate the critical path for you on our award-winning Gantt charts— learn more .

The critical path method was developed in the late 1950s by Morgan R. Walker and James E. Kelley. The origins of the critical path method are closely related to the Program Evaluation and Review Technique (PERT), a similar method that is commonly used in conjunction with CPM in project management .

The critical path method (CPM) and program evaluation and review technique (PERT) are both project scheduling techniques. But they aren’t interchangeable. We’ve been talking about CPM, but before we compare it to PERT let’s define the term.

PERT is used to get accurate time estimates for complicated projects. It uses an algorithm to calculate the estimated duration for unpredictable activities. It focuses on events and milestones on a PERT chart with nodes in the wireframe when developing projects.

However, while these are two different techniques, PERT and CPM can be used together for project planning and scheduling. The difference between them lies in that PERT is about time planning and time management, while CPM is about time and budgeting. PERT delivers a project quickly and CPM gets the project done on budget and on time.

Now that we know what’s the critical path of a project, we can learn about the critical path method (CPM), an important project management technique that’s based on this concept.

Critical path analysis is another way of referring to the critical path method. As noted, it’s used by industries with complex projects, such as aerospace, defense, construction and product development.

Therefore, critical path analysis is a crucial first step in developing a project schedule. It’s done early in the life cycle of a project, usually in the planning phase , but it’s not unheard of to have CPM as part of a project proposal before the project has been approved.

By understanding which are the critical tasks in a project you can focus on getting those done if time, resources and costs are an issue. Knowing this in advance of executing a project will help you deliver that project successfully.

Related: Free Project Plan Template

Projects are made up of tasks that have to adhere to a schedule in order to meet a timeline. It sounds simple, but without mapping the work, your project scope can quickly get out of hand and you’ll find your project off track.

Using the critical path method is important when managing a project because it identifies all the tasks needed to complete the project. It then determines the tasks that must be done on time, those that can be delayed if needed and how much float or slack you have.

When done properly, critical path analysis can help you:

• Identify task dependencies, resource constraints and project risks
• Accurately estimate the duration of each task
• Prioritize tasks based on their float or slack time, which helps with project scheduling and resource allocation
• Identify critical tasks that have no slack and ensure those are completed on time
• Monitor your project progress and measure schedule variance
• Use schedule compression techniques like crash duration or fast tracking

As you can see in this critical path diagram, project activities are represented by letters and the critical path is highlighted in green. Tasks F, G and H are non-critical activities with float or slack. We can also identify task dependencies between the critical path activities, and also between activities (A, F and G) or (A, H and E), which are parallel tasks.

Before we learn how to use the CPM formula, we need to understand some key CPM concepts.

• Earliest start time (ES): This is simply the earliest time that a task can be started in your project. You cannot determine this without first knowing if there are any task dependencies
• Latest start time (LS): This is the very last minute in which you can start a task before it threatens to delay your project timeline
• Earliest finish time (EF): The earliest an activity can be completed, based on its duration and its earliest start time
• Latest finish time (LF): The latest an activity can be completed, based on its duration and its latest start time
• Float: Also known as slack, float is a term that describes how long you can delay a task before it impacts its task sequence and the project schedule. The tasks on the critical path have zero float because they can’t be delayed

The critical path method formula has two parts; a forward pass and a backward pass.

Forward Pass in CPM

Use the CPM diagram and the estimated duration of each activity to determine their earliest start (ES) and earliest finish (EF). The ES of an activity is equal to the EF of its predecessor, and its EF is determined by the CPM formula EF = ES + t (t is the activity duration). The EF of the last activity identifies the expected time required to complete the entire project.

Backward Pass in CPM

Begins by assigning the last activity’s earliest finish as its latest finish. Then the CPM formula to find the LS is LS = LF – t (t is the activity duration). For the previous activities, the LF is the smallest of the start times for the activity that immediately follows.

Let’s take a look at a critical path example to better understand how the critical path method is used in project management. Although it’s high-level, it can help you visualize the meaning of a CPM schedule .

We’ll use this critical path diagram to explain the elements that make up the critical path analysis process. To keep things simple, we’ve already done the calculations for this example using the CPM formula.

The above critical path method example shows the critical path for getting a website online. All the tasks that are scheduled to build and launch the website are shown in the rectangular nodes.

Some of the tasks are being done at the same time as others. For example, the work on defining a target market is being done as the design is being done and the content for the site is being drafted.

However, not all these tasks are equally important. Some aren’t critical to getting the site live by the deadline. That’s where the critical path comes in. It has identified by the colored arrows all the tasks that must be done in order to complete the project plan on time.

Now that you know the key concepts of the critical path method, here’s how to calculate the critical path in 8 steps.

1. Collect Project Activities

Use a work breakdown structure to collect all the project activities that lead to the final deliverable.

2. Identify Task Dependencies

Determine which tasks are dependent on other tasks before they can begin. Use your judgment and your team members’ feedback. Failing to define task dependencies correctly makes the critical path method useless.

3. Create a Critical Path Diagram

A CPM diagram or network diagram , depicts the order of activities.

4. Estimate the Timeline

To use the critical path method, you’ll need to estimate the duration of each task. Use data from past projects and other sources of information such as subject matter experts.

5. Use the Critical Path Formula

The critical path uses an algorithm, also referred to as the CPM formula. That algorithm has two parts, the forward pass and the backward pass. The forward pass is determined by using the earliest start for each activity (ES) and the earliest finish (EF). The ES of an activity equals the EF of the one before it. The EF is calculated by EF = ES + t (the duration of an activity).

The backward pass assigns the last activity’s EF as its latest finish. Then use the CPM formula to find the LS, which is LF – t. For the activities before that, LF is the smallest of the start times for the next activity.

6. Identify the Critical Path

The activities with 0 float make up the critical path. All of these critical path activities are dependent tasks except for the first task in your CPM schedule. All project tasks with positive slack are parallel tasks to the critical path activities.

7. Revise During Execution

Continue to update the critical path diagram as you go through the project execution phase. These critical path analysis steps determine what tasks are critical and which can float, meaning they can be delayed without negatively impacting the project schedule. Now you have the information you need to plan the critical path schedule more accurately and have more of a guarantee you’ll meet your project deadline.

You also need to consider other changes or constraints that might change the project schedule. The more you can account for these unexpected events or risks, the more accurate your critical path schedule will be. If time is added to the project because of these constraints , that’s called a critical path drag, which is how much longer a project will take because of the task and constraint.

Benefits of Using CPM in Project Management

There are many reasons to use the critical path method. It’s a great project management tool to help you deliver your project on time and within budget , but we’ve already discussed that at length. Here are some other benefits of using CPM.

Critical Path Analysis Improves Team Communication

It fosters better communication within the project team . Everyone is involved in providing input and that brings the expertise of various project team members together for the better good of the project as a whole. This includes subcontractors, architects, electricians, construction managers, etc.

CPM Helps Prioritize Tasks

Naturally, having determined the critical path is going to help you prioritize your work. You know the tasks that must be done and that gives you wiggle room if there are issues with time or cost. You might not get every activity done, but you’ll get the ones finished that are critical to the project.

CPM & PERT Help Create Accurate Schedules

The critical path method will help you make a more accurate project schedule , especially when you use it in conjunction with PERT charts. You can estimate better and discover areas of risk and prepare to respond to them to avoid costly delays.

CPM & Gantt Charts Help Map Out Project Plans

Another benefit is the visual nature of CPM, especially when mapped on the timeline of a Gantt chart . Having a visual element to communicate the project schedule is always a plus. Not everyone absorbs information in the same way. Visual tools help teams better understand what’s expected of them and when it’s expected.

Do you still have questions about the critical path method? In this video, Jennifer Bridges PMP, explains how to find the critical path using a CPM diagram.

As stated, the critical path method (CPM) was first invented in the late 1950s. During those times, project scheduling software didn’t exist, and project managers had to calculate the critical path manually.

Fortunately, today there are many project management software alternatives that can help with the critical path process. Most of them use Gantt charts to represent CPM diagrams and calculate the critical path, but their feature sets vary greatly. One of the most commonly used project management software to identify the critical path is Microsoft Project . However, it has major drawbacks that make ProjectManager a better choice.

Here are some of the main features that you’ll need as a project manager to properly use the critical path method for your scheduling process.

Link Tasks and Avoid Bottlenecks

Tasks that are dependent on another need to be a part of your critical path calculation. There are four types: those that are start-start, start-stop, stop-start and stop-stop. By identifying these task dependencies , you can avoid bottlenecks later in the project.

Get a High-Level View of Your Progress

Dashboards are an essential feature for keeping track of critical path activities. They provide a window into the project’s performance and progress by collecting data and displaying it in graphs and charts that show various metrics, such as costs, tasks and more.

Make More Insightful Decisions

Keeping track of a project’s critical path as it’s executed is how you stay on track. But if the information you’re gathering is dated, then you’re always going to be playing catch up. With real-time data from a cloud-based CPM software, you’re always seeing the project as it currently is.

Know Your Project Variance

Schedules are always changing as the project is impacted by internal and external forces. To ensure you’re on target, you need to have project management software that’s collecting data and displaying project variance, so you can compare the actual progress against where you’ve planned to be.

Keep a Record of Your Plan

The critical path helps you plan the project, but once you’ve finalized the schedule, you need to set a baseline. This saves the schedule so you can compare it to your actual progress and know if you’re on time, behind or ahead. Any critical path software should have this feature.

See Deep Data on Performance

Reports serve two purposes. They take you deeper into the project and expose insightful data on project variance, timesheets and more, which helps you stay on track. Filtering the results and sharing the reports is a great communication tool for stakeholder presentations.

How to Find the Critical Path With ProjectManager

Figuring out the critical path by hand takes time, and it must be done throughout the project, which is why using project management software streamlines the process. ProjectManager is award-winning software that automates the critical path method process for you.

Our online Gantt chart filters for critical path, links dependent tasks and is integrated into a full project management software. Sign up for a free 30-day trial of our software and follow along to build a dynamic Gantt chart and automatically calculate your critical path in a few easy steps.

1. Start a Project With a Gantt Chart

Managing a project on Gantt charts allows you to both plan and schedule in one place. Add your tasks and their durations, and they’ll automatically appear on a project timeline, allowing you to see your whole project at once.

In the software, upload your tasks manually or upload a pre-existing spreadsheet. Add task descriptions, deadlines, priority, tabs and assign them to one or more team members. We also provide templates to help you get started.

2. Add Task Dependencies

In the software, connect your dependent tasks on the Gantt chart by dragging one onto the other. You’ll see a dotted line indicating that the tasks are linked, and you can then define the type of dependency it is.

3. Set the Project Baseline

Setting the baseline is possible when you’ve finished making your project schedule, complete with deadlines and costs. The baseline captures your data and uses it to compare against your actual progress.

On the Gantt chart, create your baseline for the project by adding the start date to the task and when it’s due to be completed. These planned start and end dates will be compared to your actual project data and show you whether you’re on target.

4. See the Critical Path

Easily find the critical path of your project by using our critical path filter. This helps you know what must be done to complete the project and shows if you’re experiencing any slippage.

5. See Your Overview With a Dashboard

Now that you’ve got your project planned out, viewing it from a dashboard is the best way to get a high-level view of your progress.

From the dashboard view, track if your project is proceeding as planned. Our dashboard monitors several project metrics, such as variance, tasks and more, automatically calculating your data to display it in easy-to-read charts and graphs.

6. Report on Progress

Reporting is crucial to pull data from your project and get and share insights into how it’s doing. Reports come in many varieties, which together provide a snapshot of the whole project’s performance.

Easily generate reports on the critical path, task progress, project status , costs and more in the software. We do the calculations for you, and you can filter the results to show just what you want to see. Our reporting feature is done automatically with one click.

ProjectManager is an online tool that gets real-time data to determine how accurate your planned schedule is to the actual one, so you can adjust immediately if necessary. See how it can help your project by taking this free 30-day trial.

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Critical Path Method Resources

• Critical Path Software
• Project Scheduling Software
• Gantt Chart Software
• Project Management Software
• Work Breakdown Structure (WBS) Template
• Gantt Chart Template
• Work Schedule Template
• Project Scope Template
• Top 10 Project Management Methodologies: An Overview
• 3 Free Tools for Making Network Diagrams
• Project Scheduling Guide
• The Ultimate Guide to Gantt Charts
• What Is a Work Breakdown Structure?
• PERT and CPM: Their Differences and How to Use Them Together

External Articles

• The ABCs of the Critical Path Method – Harvard Business Review
• Understanding the Basics of CPM Calculations – PMI
• What Is the Critical Path in Project Management? – Elmhurst University

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Mastering the critical path: a guide to cpm in construction.

Last Updated Apr 3, 2024

While every task must be completed to complete a construction project, some tasks are more critical than others. It's crucial to be able to identify which activities must be finished before others can be started — and which can’t be delayed without setting back the whole project.

On a construction project, the critical path is the sequence of tasks with no float time and must be completed on time to avoid delays to the master schedule. 

The Critical Path Method (CPM) is a systematic approach to scheduling that compares activities, especially those that happen concurrently, and prioritizes them in order of their impact to the schedule. This process is used to find the critical path. CPM is one of the most common planning techniques in construction. 

In this article, we explore the importance of finding the critical path, how to use CPM in scheduling, and how it is used alongside other planning methods.

Table of contents

What is the critical path?

On most jobsites, numerous tasks are happening at the same time: Contractors may be working on HVAC, plumbing, electrical and landscaping concurrently. While all those activities need to be completed, not all of them are critical to keeping the project on schedule . 

Critical activities are those in which a delay results in a delay to the master schedule. The rest of the activities (i.e., non-critical tasks) have some flexibility — they can start earlier or finish later without impacting the overall schedule.

The critical path is the longest sequence of consecutive tasks with zero float or flexibility between them. Identifying this sequence can help contractors prioritize the allocation of resources, including equipment, materials, and labor. 

Identifying the Critical Path

Project managers use the Critical Path Method to calculate the float time for each task by defining its earliest and latest start and finish dates. The scheduler uses CPM to organize this information and sequences the tasks in a chart, clearly showing the relationship and dependencies between tasks. Initially, figuring out which tasks need to be done often happens by making a work breakdown structure (WBS) , a common organizational system for complex projects.

CPM depends on accurate task durations, so it is most often used for projects where most of the tasks are familiar . Often, durations are easy to estimate, simply because construction companies and contractors have personal experience with or historical data on most activities. 

The Critical Path Method doesn’t help determine a task’s duration in the case of rare or uncertain activities. However, CPM can be used in conjunction with other scheduling methods – such as PERT – to develop probabilistic time estimates.

The Critical Path Method: Steps to Find the Critical Path

Construction scheduling software can simplify the documentation of organizing, visualizing and sharing schedules in ways that clearly identify the critical path. However, anyone can use the critical path method without scheduling software to identify the critical path in a sequence of concurrent activities. 

To illustrate these steps, we will use a simple commercial office project as an example and create a CPM schedule for the “Core and Shell” stage of the project. 

Preparing the Grid Key

When creating a visual organization chart, each activity will be represented by a grid, ultimately displaying the relevant schedule information about each activity. 

The placement of each item in the grid can vary based on the scheduler’s preference. For this article, we are using a 9-box grid with the center row merged to display the activity name. However, to save space many schedulers will assign each activity a letter (e.g. A, B, C) and provide a key that lists all activities with their corresponding letter. What is most important is that everyone who uses the schedule can easily identify the element represented by each number in the grid.

Here is the grid key we will use for this article: 

• Top Center: Task Duration
• Top Right: Earliest Finish Time (EF)
• Center (Merged): Activity Name
• Bottom Left: Latest Start Time (LS)
• Bottom Center: Float
• Bottom Right: Latest Finish Time (LF)

1. Identify all tasks.

Tasks can be listed or pulled directly from the project’s work breakdown structure (WBS). Tasks should be definable and measurable. 

For example, a contractor could use CPM to plan a segment of work, such as completing the interior of an office building . They would start by finding all the tasks between the preceding milestone (completing the foundation) and the subsequent milestone. They might list the following tasks:

• Frame exterior walls
• Frame the roof
• Install windows and doors
• Install the roof membrane
• Install rough electric
• Install insulation 
• Install drywall

2. Organize tasks in sequential order.

Identify the first task needed to start the project or segment. Then, put the rest of the tasks in order by asking the same questions about each of them: 

• What needs to happen before this task? 
• What can be started after this task?
• What tasks can be done at the same time?

Sequence the grids from left to right and connect with arrows in the order they need to be completed. Vertically align tasks that can be done at the same time. 

3. Add the duration for each task.

Durations should be based on past experience, historical data, and the availability or known lead times of materials and labor. For tasks with a lot of uncertainty, the PERT formula can be used to find a probabilistic time estimate. The unit of time should be the same across all activities – typically expressed in days or weeks. 

Put the duration in the top middle square.

4. The Forward Pass: Determine earliest start & finish times.

Determine a task’s earliest start date by considering when its preceding tasks can be completed. Determine the earliest finish time by factoring in the task’s duration from its earliest start date. Move forward in the schedule from left to right and repeat for each task. 

The earliest start date is written in the upper left square and the earliest finish date goes in the upper right square. 

Framing the exterior walls can start on day 10 and will take five days (including day 10). The earliest it is expected to end is day 15. 

That means framing the roof can’t be started until day 15, at the earliest. It takes two days, so its earliest finish date will be day 16.

Framing the roof must be completed before work can begin on three other tasks: the roof membrane, windows and doors, and rough electric. The earliest start date for each of these tasks would be day 17. Since they can be worked on concurrently, they are stacked vertically and the earliest each task can be finished is found based on its respective duration. 

Once rough electric is done, insulation can begin. The earliest this can happen is day 21. Since insulation takes three days, it won’t be done until day 23. 

Drywall is started after completing all of the insulation, windows, doors and the roof membrane.  Even though the roof membrane and windows and doors could be done earlier, insulation isn’t finished until day 23. The earliest the drywall can be started is day 24.

This means the earliest this segment of work can be completed is day 29. 

5. The Backward Pass: Determine latest start & finish times.

So far, the process has moved left to right in what is called a forward pass. Now, the process reverses for a backwards pass. Start on the right and move backwards through the schedule. 

A task’s latest finish time is determined by the latest start time for its successive task. This is written in the bottom right square.

A task’s latest start time is found by subtracting its duration from its latest finish date . This is written in the bottom left square.

Installing the drywall needs to be done on day 29 at the latest. It takes six days (including day 29), which means its latest start time is day 24. 

In order for work on the drywall to begin on day 24, the latest finish days for the roof membrane, windows and doors, and insulation will all be day 23. Each task's respective latest start date is found by subtracting its duration from day 23.

For insulation to begin on day 21, rough electric must be done on day 20. Rough electric’s latest start and finish date are filled in as follows: 

The latest framing the roof can be finished is day 16, so that rough electric can begin on day 17. The earliest start date for framing the roof would be day 15. Repeat for framing the exterior walls.

6. Calculate float time.

Determine the float time for each task by subtracting the earliest start date from the latest. 

According to our grid key, the float time will go in the bottom middle square.

A float of zero indicates that the task is critical. 

For example, rough electric has zero float, so it must be started on day 17 and finished on day 20, or the next task will be delayed.

Other tasks have float time, which makes them non-critical. Windows and doors has a float time of four days (21-17). That means windows and doors can be started any time between day 17 and 21 and still be done in time for the drywall to be started without delay.

7. Identify the critical path.

Find the longest possible sequence of tasks with zero float days. This is the critical path, meaning all these actions can’t be delayed without changing the schedule. If you’ve followed the process correctly, the critical path will reveal itself. Two concurrent tasks cannot both have zero float . 

The Benefits of CPM

Even beyond effectively finding the critical path, CPM is helpful in many ways.

• Visualization: The diagram is easy to understand and illustrates the relationships between tasks, which can increase communication and urgency. 
• Anticipate delays: By highlighting the critical path, schedulers can choose to build in time for delays in order to keep potential delays with the critical tasks from impacting the project’s completion date.
• Respond to delays : When issues arise that affect the timeline, CPM’s visualizations quickly and effectively help contractors understand the severity of the issue and whether to ask for more time or compensation, if allowed by their contract.

CPM: A Key Piece of the Planning Puzzle

CPM is one of the most common planning techniques in construction. Even when it isn’t a project manager’s personal go-to method, it’s important to be familiar with it as they will almost certainly encounter it when working on other people’s projects. 

There are many types of planning methods. CPM is a type of “push” planning, which starts by looking at the beginning of a project, moves forward, and can allow a project manager to quickly and effectively create schedules for projects that are familiar and easy to anticipate. In contrast, pull planning starts with an end goal and moves backwards. 

A successful pull planning session can increase team buy-in and the quality of planning. Effective project managers use both push and pull planning to refine the schedule and confirm that the sequence and durations are accurate and up-to-date.

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Ben Ashburn

Ben Ashburn is a Senior Construction Education Trainer at Procore. After a successful career as a construction estimator — working his way up from estimating manager to senior estimator — Ben has spent the most recent part of his career in construction sharing his skills with other as a construction educator. Ben has an extensive background in construction education: He has been an assistant professor in the Department of Construction Science at Texas A&M, and lectured about estimating, scheduling, management, and other related construction topics at Murray State University. He has been a construction training and learning development partner with Procore since 2019.

James Hamilton

29 articles

James Hamilton is a writer based in Brooklyn, New York with experience in television, documentaries, journalism, comedy, and podcasts. His work has been featured on VICE TV and on The Moth. James was a writer and narrator for the show, VICE News Tonight, where he won an Emmy Award and was nominated for a Peabody Award.

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Prioritizing tasks can be tricky. While some activities may look heavier than others, it doesn’t always mean those tasks require the most attention. An important thing to consider is dependencies, or tasks with outputs that are required to start other tasks. Taking dependencies into consideration can make estimating a project’s duration and prioritizing tasks more complex. One useful technique to manage this is the critical path method.

Read more: Best Project Planning Software & Tools

What Is the Critical Path Method?

The critical path method is the process of identifying the string of tasks and dependencies that take the longest time to complete in a project. This group of to-dos is called the critical path, while the tasks inside it are called critical activities.

The total duration of the critical path is the minimum time you’ll need to complete a whole project. Any delay for critical activities will result in extending the total project duration.

Read More: What is Project Management? Definition, Types & Examples

How to Identify a Project’s Critical Path

You can find your project’s critical path by using project management tools that use algorithms to find it for you. However, you can also calculate critical path by doing a forward and backward pass.

Step 1: List All Project Tasks

Start by breaking your project down into milestones, deliverables, and actionable tasks. This helps you visualize the day-to-day activities you and your team have to accomplish to progress.

Here’s an example of all the tasks associated with planning an online press conference:

Step 2: Identify Dependencies and Estimates

Once you have all project tasks laid out, identify dependencies, or the tasks that can’t proceed without another’s output. List them out in a table, along with an estimate of how long each task would take.

Returning to the example above:

Step 3: Use a Network Diagram That Traces Dependencies

A network diagram is a series of boxes and arrows that help visualize the connections of specific variables. In this case, it’s used to represent tasks and their relationships.

Dependencies point to the tasks that can proceed once they’re finished. For example, “Collect contacts to publications” (Task 1) points to “Send out invites” (Task 3) because Task 3 can only proceed once Task 1 is finished.

Step 4: Do a Forward Pass

There are two variables to consider when doing a forward pass:

• Early Start Time (ES): The earliest time a task can start
• Early Finish Time (EF): The earliest time a task can finish

In the diagram, put each task’s ES at the upper-left corner and its EF at the upper-right.

To get the EF, simply add the duration of the time to the ES. So, if Task 1 can start at day 0 and take 0.5 days to finish, then ES = 0 and EF is 0.5.

As for Task 3, the earliest time it can start is when Task 1 is completed. So, Task 3’s ES is 0.5. With a 0.5 day duration, its EF is 1.

If there are conflicts where three tasks are pointing to it, as is the case with Task 11, pick the highest EF as its ES.

In the above example, Task 3’s EF is 1, Task 5’s is 1.5, and Task 10’s is 6. Because 6 is the highest EF, this will be Task 11’s ES.

Step 5: Do a Backward Pass

Once you’re done with the forward pass, you may now do the backward pass; however, there are two new variables to consider:

• Latest start time (LS): The latest time that a task can be started without delaying the whole project
• Latest finish time (LF): The latest time a task can be finished without delaying the project

In the network diagram, the LS is at the lower-left side of the task, while the LF is at the lower-right side of the task.

To start computing for each task’s LS and LF, begin by copying the last task’s EF as its LF. In our case, copy Task 11’s EF (6.5) at its upper-right side, and write it on the lower-right side as well.

Find the LS by subtracting the duration from the LF. In Task 11’s case, LS is 6.

Use task 11’s LS as the LF of all the tasks pointing to it: Task 3, Task 5, and Task 10. Subtract their durations to find their LS, respectively.

For tasks that point to more than one task, use the lower LS as its LF.

An example of this is Task 1. It points to both Task 3 and Task 10. When doing the backward pass, you’ll see that Task 3’s LS is 5.5 and Task 10’s LS is 5. Because of this, Task 1’s LF is 5.

Step 6: Find the Critical Path

To know your project’s critical path, look for the tasks with the same EF and LF. This means that the earliest time it can finish is also the latest time it can finish; therefore, it can’t be delayed.

In this case, the critical path is the creation of the press release:

• Press release outline (Task 6)
• Draft press release (Task 8)
• Finalize press release (Task 9)
• Send out press kit (Task 10)
• Implement press conference (Task 11)

For non-critical activities such as Task 4 (confirming speakers and panelists), failing to finish on day 1 (EF) wouldn’t extend the duration of the project as a whole — as long as it’s finished on or before day 5.5 (LF). But for a critical activity such as Task 9, failing to finish on time will result in the press conference as a whole being delayed.

Read more: Top 5 Steps for Creating a Successful Project Schedule

Benefits of the Critical Path Method

• Prioritizing tasks: Knowing your critical activities will help you identify those tasks you’ll need to pay close attention to and avoid delaying.
• Anticipate and avoid bottlenecks: Laying out tasks and their dependencies can help you anticipate possible bottlenecks you can avoid when you’re scheduling or resource planning.
• Identify slack: Slack, also known as float, is the number of days a task can be delayed before it affects the project’s entire timeline, which can be found by subtracting the EF from the LF.

Read More : Project Management Terms & Concepts to Know

Limitations of the Critical Path Method

Resource dependencies.

The network diagram used to identify the critical path visualizes process dependencies. What it doesn’t illustrate, however, is resource dependencies.

An example of resource dependency is if there’s only one person assigned to do two tasks. Because of this, one task can’t be started until the person finishes the other. These types of dependencies need to be considered when estimating a project’s duration, as well.

Schedule Interruptions

Another dependency the network diagram doesn’t illustrate is time dependencies, such as seasonal interruptions like software maintenance, office closure, holidays, and others. In short, work can’t resume until they’re finished, so these should also be considered when estimating a project’s duration.

Read more: Significance of Keeping Documentation in Project Management

A Great Method for Planning a Project Timeline

The critical path method is a good way to identify the minimum time you need to finish a project. It also points out your critical activities, or tasks that can’t be delayed without compromising your project’s deadline.

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What is the critical path method? Complete guide with examples

“It depends” is a phrase sometimes referred to as the classic product management answer — and it is! While we all would love a simple answer to many of life’s questions, there are often many factors at play which means, well, it depends!

One factor product managers have to consider in their answers is dependencies. These activities might not be in the direct control of the product team but are required as part of the product development effort for success. No matter how best companies structure themselves to minimize dependencies, often they still exist. Finding out which ones matter and which impact timelines the most can be challenging. That is where the critical path method (CPM) can help.

What is the critical path method (CPM)?

The critical path method (CPM) is a widely-used project management technique that helps plan and schedule complex projects. It is used to identify the critical path of a project, aka the sequence of activities that determines the minimum completion time of the project.

What does “critical path” mean?

A critical path is a sequence of “critical” activities in a project that must be completed on time for the project to be completed on schedule. These “critical” activities will also help you to determine the minimum completion time for the project.

For example, if you’re building a house, the critical path might include activities like laying the foundations, building the walls, and installing the roof. All of these are needed to build a house and if any of these activities fall behind schedule, the entire project will be delayed.

What is the critical path method in project management?

The critical path method (CPM) is a tool used to plan and schedule complicated projects. It is based on identifying the critical path of a project and analyzing it to find the minimum completion time for the project.

The method considers the dependencies between different activities and the amount of time required to complete each activity. By understanding the critical path and the amount of “float” or “slack” time available in the schedule, project managers can better plan and control their projects.

A brief history of the critical path method

The Critical Path Method was first developed by Morgan R. Walker of DuPont and James E. Kelley Jr. of Remington Rand in the late 1950s . They were looking for a way to manage the complicated construction projects they were undertaking, so developed the CPM as a tool to help with this.

The method quickly gained popularity and was soon adopted by many companies and industries. Today, the CPM is widely used in project management and is considered an essential tool for planning and scheduling complicated projects.

Key terms associated with the critical path method

• Earliest start time (EST) : the earliest time an activity can start, taking into account the preceding activities and their durations
• Latest start time (LST) : the latest time an activity can start without delaying the project
• Earliest finish time (EFT) : the earliest time an activity can be completed, taking into account the preceding activities and their durations
• Latest finish time (LFT) : the latest time an activity can be completed without delaying the project
• Float or slack : the amount of time that an activity can be delayed without delaying the project
• Critical path : the sequence of activities that determines the minimum completion time for the project

How to find the critical path of a project

You can find the critical path of a project by following these steps:

• List all of the activities in the project, including their durations and dependencies
• Draw a network diagram to represent the dependencies between the activities
• Determine the earliest start time (EST) and earliest finish time (EFT) for each activity by working forwards through the network diagram
• Determine the latest start time (LST) and latest finish time (LFT) for each activity by working backward through the network diagram
• Identify the activities that have zero float (LST = EST) or negative float (LST < EST). These activities are on the critical path

When to use the critical path method

The critical path method (CPM) is an effective tool for planning and scheduling complicated projects. It is best for when the project has a large number of activities, many of which are interdependent. It’s useful when there are a lot of dependencies between different tasks and activities that must be taken into account to schedule the project effectively.

The method can also be useful when there is a desire to accurately predict the completion date for the project, or if resources need to be allocated optimally.

The CPM is generally less effective for simple projects with only a few activities, or projects where the activities are not closely dependent on each other. The method is also not a good fit for projects that have low predictability and require flexibility since the critical path is based on predetermined dependencies and durations.

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The critical path method for product managers

So, if your product development is operating in a project set up and has a high number of dependencies, this tool could be useful for you and your team to better understand your dependencies and the relationship between them.

Also, while many plans are incorrect the moment you finish them, the act of planning can be useful — more useful than the plan itself. Planning gives you space to think about all the factors that will go into your successful product feature or launch and fosters communication between interested parties.

However, CPM is not suitable where there is low predictability or if flexibility is necessary. I have yet to come across a team developing software that can accurately predict how long even the smallest task takes, or that doesn’t have to deal with changing requirements. I believe most product teams operate in a complex environment, over a complicated environment where the CPM is most effective.

The Cynefin framework gives us a way of identifying the structures we operate in and identifies five domains. It covers two of the domains I reference above — the complicated and the complex.

In the complicated domain, things are more predictable and known. You can rely on best practices. Perhaps, if you are developing a product at the later end of the product lifecycle your team is in a complicated domain. However, the complex domain is novel and experimentation is necessary to work out what will be successful. If you are developing anything new you are more likely to fit into this domain and find CPM ineffective.

The critical path method (CPM) is a tool to plan and schedule complicated projects. It is based on identifying the critical path of a project and analyzing it to find the minimum completion time for the project.

For product managers, the analysis of what makes the critical path and consequential planning can be very helpful to foster communication and bring about a shared understanding of the activities needed for success.

However, as many teams operate in a complex, uncertain environment that requires flexibility, the CPM is unlikely to provide the answer you are probably looking for — when will it be done.

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The beginner's guide to Critical Path Method

A critical path is the common method   project managers   use to map out all the ins and outs of a project. It is a powerful, but simple technique for analyzing, plotting, and scheduling large, complex projects. Once the critical path is identified, you know the least amount of time possible to complete the project, where to compromise, and what to expect.

If you do not know or understand your critical path, you are not making calculated decisions about your project and managing your schedule as well as you could. Having a critical path is one way you can illustrate the most important tasks in a project. In fact, a well-rounded critical path tells you how every task and resource is dependent on each other, so you can see the   scope of work   you’re dealing with as well as the time frame.

At the same time, there are so many elements that a critical path includes that it can be difficult to lay it all out. We’ve prepared this guide with recommendations, so you could have everything you need in one place.

What is a critical path?

  By definition, the critical path is the longest sequence of tasks which must be completed on time to deliver the project successfully. Based on the critical path, you can determine the total time and   effort   required to complete the project. It also helps you get the overview of tasks and dependencies that cannot be delayed if you want to finish the project on time. So, let’s call the critical path the most important chain of the project. Consequently, t asks that are placed on the critical path can't be moved so there's the need to control them more than others.

There are four factors to consider when understanding the critical path.   Estimations , task dependencies, set milestones to be reached, and any critical deadlines defined to keep the project and deliverables on track. The connections between tasks are determined by the requirements of tasks and the project altogether. 

In the   project timeline , the critical path is often visualized as a sequence of dependent parts. When it is determined by the project manager, a certain hierarchy builds up and the order in which tasks should be completed becomes clear to everyone. 

Additionally, the critical path also includes slack, or float time, known as a temporary interval of free time that appears naturally whenever there’s lack of activity. Slack then leads to the emergence of parallel paths, so tasks can be completed simultaneously.

Having the critical path as part of the project management process ensures that projects can run smoothly.  

A critical path method example

  Consider baking a cake as a simple example of a critical path. You must follow a recipe to make sure you have the right end product. First, you buy the ingredients, prepare the oven, mix the ingredients, fill the pan to bake, and then you let it cool for half an hour. Thereafter you ice and decorate the cake. 

It’s an everyday example, but it illustrates the critical path perfectly. To ensure quality and a successful project, you mix the right amounts of sugar, flour, butter, etc. Of course, you can't ice and decorate without having baked the cake. So you can see that in the cake example, the critical path is made up of a number of steps that are essential to making the right cake. If you have a closer look at these tasks individually, you’ll notice that some of them simply cannot be started before the others get finished. That is, one task is dependent on another and determining the critical path requires a clear understanding of the project objectives and the flow of tasks.

  Who is a critical path method for? 

A critical path method determines the minimum amount of time required to complete a project by identifying those events that can’t be delayed without delaying the whole project.

Because the aim of a critical path is to make sure that no second is wasted, it is more handy and beneficial for projects where task duration is more or less predictable. It can be very well applied to construction projects, event planning, or manufacturing. First time around, it was used to plan and run a major skyscraper project in 1966 to construct the former World Trade Center Twin Towers in New York City. 

But other than that, any project that involves complementary and dependent activities can apply the critical path method. Any project that on closer inspection is turn-based, chock full of dependencies, and is more likely to result in bottlenecks will benefit from the structure critical method brings to light.

Why work with a critical path in project management

The critical path is the connection between project scope, requirements, and time. So, managing critical paths in your projects is crucial for a healthy project portfolio and the overall health of your business.

For that reason, there are many benefits of applying the critical path method to your project. Firstly, it gives you a breakdown of all the tasks required to complete the project and the time required to complete them. This makes it easier for you to determine which tasks can be delayed in order to affect the overall completion date. Secondly, it also highlights any constraints that might affect task completion.

In addition to this, the key reasons to use critical path in project management are the following:

• When   scoping your project , you understand the sequence of the most critical tasks on your project and, therefore, the shortest time possible to complete the project. 
• Following the critical path ensures that tasks are completed in the correct order with attention to the requirements of each task and the final deliverable. 
• Determining the critical path for your scoped out project is where the project manager can give the best guidance for the project. 
• Visualizing the critical path on a project timeline can ensure that the project can be completed with the resources available.
• Analyzing the critical path helps you take the actions needed to keep a project on track before deadlines are missed. When the project falls behind schedule, you can   level resources   accordingly to meet the delivery date.

Using CPM further down the line, you can determine if there are any holes in the schedule for your project. A hole is where you or a member of your team can be slacking off when completing tasks. There are many different ways to set up a schedule for your project so one method does not work on all projects, but the critical path method is generally a good place to start.

All that said, critical path is an important concept to master as it is a valuable tool for scheduling projects, be it a home repair or software development effort. Critical Path Method (CPM) is one way of looking at the project schedule. It uses both the logic and task dependencies to determine which activities are critical to completing the project successfully, and which can be delayed if needed. Applying the critical path method to a project is also laying the foundation to help you navigate ambiguous situations later in the project.

How to determine a critical path

If you don’t know how to find the critical path, this section is for you. Determining the critical path is a matter of understanding the tasks at hand and the end goal of the project. One way to start determining the critical path is by defining a   project scope . This is done by breaking your project down into smaller packages of work, figuring out their sequence, and setting dependencies.

The CPM technique requires modelling the project in a way that includes the following details:

• A detailed list of all activities required to deliver the project. 
• The duration each task will take to complete.
• Dependencies between tasks. 
• Milestones that group multiple activities towards a certain deliverable.

You want to work on the critical path and make sure that you’re not wasting any time on tasks that won’t contribute to the final product. When you know the tasks that should be completed first, you can have more time on non-critical tasks which will increase your overall efficiency.

Here are a few steps to follow to make sure you check all the boxes above. 

1. Create a work breakdown structure

To have a perfect understanding and visibility of how project requirements translate into action, it’s essential to break down the project into smaller chunks. One way to do it is by creating a work breakdown structure that illustrates milestones and divides them into tasks and subtasks. This is necessary to make the project comprehensive and reduce complicated activities to plain tasks.

2. Define the sequence of tasks

Scoping tasks on a granular level with attention to the flow of tasks is highly beneficial to understand the critical path. In some projects, it’s extremely important to know the order in which tasks can be completed. There are two ways to visualize the order: 1) by setting a start and end date for each task, or 2) by creating dependencies between tasks.  

3. Estimate tasks

To figure out the duration of each task, you’ll need to give each task an estimate. This is not the funniest thing to do, but here’s   one estimation hack   that can help automate this process. Remember that all the way through, you have to keep the communication lines open and make the team part of this process.   Project planning   is a team sport, and you’ll need their full participation and expertise to know what it takes to complete each task.

4. Set dependencies

Going through   dependencies   is the best thing you can do in the beginning of the project to avoid being lopsided in the end. Dependencies not only reveal relationships between tasks, but also inform your resource management decisions - you’ll be able to predict at a higher level if there’s a need to hire additional resources to complete the project. With transparency dependencies brought along, you’ll be able to outline the fastest way to deliver the project. 

5. Create the activity network diagram

Now it’s time to make sure that your tasks are organized chronologically. This step involves creating the activity network diagram, sometimes referred to as the critical path analysis chart. It’s made to illustrate project deliverables, dependencies, and the sequence of activities in your project. It’s a solution that will help you avoid lengthy texts describing the project to stakeholders and display it visually (including your critical path).

To conceptualize the activity network diagram, project managers usually turn their eyes to flow charts. However, a flow chart can easily become unwieldy and unnecessarily complex, especially if you’re   managing multiple projects . There are better alternatives to flowcharts when it comes to visualizing a project chronologically, such as a   project timeline , or Gantt chart. 

How to visualize a critical path

  Having a visual presentation of your project schedule across scoping, resources, tasks, and dependencies guarantees a better flow across all project phases. Because the Gantt chart shares the same components and connections between time, tasks, and order, it is thus one of the best and fastest ways to visualize a critical path and see how the time and tasks line up. 

Likewise, visually presenting business KPIs can help everyone stay on the same page, from teams to stakeholders, and increase overall transparency. Yet another benefit, scheduling tasks on an interactive Gantt Chart will help you improve the understanding of the progress on key project milestones.

But there’s one more thing. Let's say you’ve already scoped out the project. What's next? Tasks are defined and planned out, the team knows what to work on, when, and the project's milestones are visually presented with indicators showing the current status. However, we still need to find the resources to execute the tasks. This is where adding   capacity management   to the picture is crucial.

While you might have an understanding of who will be assigned to the project, it’s still important to check if your project schedule doesn’t contradict the person’s workload and schedule on other projects. Heatmaps that showcase the entire resource pool turn out to be great for figuring out what’s everyone’s availability for the next months:

Capacity management ensures that you have the resources needed to perform the tasks you’ve set up to complete. Connecting scoping and resources is primarily based on factors such as the time estimations of tasks and the total available working hours of each role on your team. So if resources are connected in the scoping process, there is extra attention to the capacity limits in the schedule.  

Critical path analysis

  Critical Path Analysis is an important part of your project management plan where each activity is given a timetable for its execution and delivery. These activities have dependencies, risks, and resources associated with them which are outlined in the activity list. Once all of these factors are considered, you can then determine the "critical path" of activities – that is, the total duration required to deliver the project. Critical Path Analysis can help project managers reduce bottlenecks and delays caused by dependent activities and even re-allocate resources to improve the completion date or outcome.

In short, analyzing the critical path can help you understand the project, potential delays, and the expected delivery. A project can have several critical path sequences, and have a direct impact on whether deadlines are able to be met. Any delays happening in the critical path can have significant consequences for the further progress.

Using data and visual insights can greatly improve your chances of avoiding delays in projects and along the critical path. Combining project and resource data from your company with a visual schedule and live insights can give you the perspective you need to make the right business decisions. To ensure profitability and swift decisions the critical path must show when the project needs to be completed.  

Insights such as a burn up chart, sprint burndown, or the cumulative flow can give you this overview of your projects’ progress. These insights help project managers detect the health of a project and give stakeholders the information they need to make the best decisions for the future of the company.

Although not a widely used technique, the critical path method (CPM) remains an important tool for project managers to successfully deliver projects on time and within budget. It is a one important tool that will help you control the risk involved in any activity.

Defining the critical path begins with understanding the scope, the requirements, and the natural development of the project. Combining project and resource data to form a better perspective gives you the overview to make the right decisions for your projects.

Visualization is known to be one of the key elements in understanding and gaining insight. Using visual components such as Gantt charts, burn-up charts, total utilization levels, and a schedule that connects projects, people, and scoping, gives you a better foundation for making the right business decisions. 

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• 1. Introduction to CPM Guided: Ruchita shah Presented By: Kajal Vasar(115371) Khushi Makwana(115372) Mahesh Parmar(114352) Dushyant Nasit(114339)
• 2. Project Management  Managers have been planning, scheduling, monitoring, and controlling large scale projects for hundred years, but it has only been in the last 50 years that management science techniques have been applied to major projects.  They are two types: 1. Critical Path Method(CPM) 2. Project Evaluation and Review Technique(PERT)
• 3. Introduction- CPM  Defination:- Critical path is a sequence of activity between a project’s start and finish that takes the longest time to complete.  Critical path method is based on mathematical calculations and it is used for scheduling project activities.  In 1950, Critical path method(CPM) was developed by Kelly and Walker to assist in building and maintains of chemical plants.  The initial critical path method was used for managing plant maintenance projects.
• 4.  Critical path is the sequential activities from start to the end of a project. Although many projects have only one critical path, some projects may have more than one critical paths depending on the flow logic used in the project  The essential technique for using CPM is to construct a model of the project that includes the following:  A list of all activities required to complete the project (typically categorized within a work breakdown structure  The time (duration) that each activity will take to completion,  The dependencies between the activities .
• 5. Terminologies used in CPM In order to explain the purpose, structure and operation of CPM, it is helpful to define the following terms: Activity:An activity carries the arrow symbol.This represent a task or subproject that uses time or resources Event:- A node (an event), denoted by a circle , marks the start and completion of an activity, which contain a number that helps to identify its location. For example activity A can be drawn as: Dummy Activity: An activity, which is used to maintain the pre-defined precedence relationship only during the construction of the project network, is called a dummy activity. Dummy activity is represented by a dotted arrow and does not consume any time and resource 21 A
• 6.  Parallel activity: There are two activity which being at same event and end at same event.this activities are called parallel activity. Not allowed…..  Path: A path is a series of adjacent activities leading from one event to another.  Critical path: A critical path is the sequence of critical activities that forms a continuous path between the start of a project and its completion. 1 2
• 7. Situations in network diagram A B C A must finish before either B or C can start, it called burst event. A B C both A and B must finish before C can start, it called merge event. Dangling events is not allow. A C B D Dummy A must finish before B can start both A and C must finish before D can start, it’s called dummy activity. A B C
• 8. Forward pass:  The Early Start and Early Finish Time Calculated by moving Forward Through the Network.  Consider Maximum.
• 9. Backward pass:  The Latest Start and Latest Finish Time Calculated by moving Backward Through the Network.  Consider Minimum
• 10. Float activity:  Float activity For an Activity is The Difference between its Earliest and Latest Start Time or Earliest and Latest Finish Time .
• 11. Steps in Critical Path Method  Step 1: Make a forward pass through the network as follows: For each activity i beginning at the Start node, compute: Earliest Start Time (ES) = the maximum of the earliest finish times of all activities immediately preceding activity i. (This is 0 for an activity with no predecessors.). This is the earliest time an activity can begin without violation of immediate predecessor requirements. Earliest Finish Time (Ef) = (Earliest Start Time) + (Time to complete activity i. This represent the earliest time at which an activity can end. The project completion time is the maximum of the Earliest Finish Times at the Finish node.
• 12. Continue..........  Step 2: Make a backwards pass through the network as follows: Move sequentially backwards from the Finish node to the Start node. At a given node, j, consider all activities ending at node j. For each of these activities, (i,j), compute: Latest Finish Time (LF) = the minimum of the latest start times beginning at node j. (For node N, this is the project completion time.). This is the latest time an activity can end without delaying the entire project. Latest Start Time (LS) = (Latest Finish Time) - (Time to complete activity (i,j)). This is the latest time an activity can begin without delaying the entire project.
• 13. Continue..........  Step 3: Calculate the float time for each activity by: float = (Latest Start) - (Earliest Start), or = (Latest Finish)-(EarliesFinish). A critical path is a path of activities, from the Start node to the Finish node, with 0 float times.
• 14. Example 1. Construct the CPM Network using the details below and determine the critical path Activity Immediate Completion predecessors Time (week) A - 2 B A 3 C A 3 D C 4 E D 8 F B,E 6 G F 2 Total …… 28
• 15. 1 2 765 43 0 0 25 25 23 23 9 9 17 17 5 5 2 2 A(2) B(3) D(4) C(3) E(8 ) F(6) G(2)
• 16. Activity Tme Earliest Start (ES) Earliest Finish (EF) Latest Start (LS) Latest finish (LF) Slack (LS-ES) Critical path A 2 0 2 0 2 0 Yes B 3 2 5 14 17 12 No C 3 2 5 2 5 0 Yes D 4 5 9 5 9 0 Yes E 8 9 17 9 17 0 Yes F 6 17 23 17 23 0 Yes G 2 23 25 23 25 0 Yes
• 17. 1 2 765 43 0 0 25 25 23 23 9 9 17 17 5 5 2 2 A(2) B(3) D(4) C(3) E(8 ) F(6) G(2)
• 18. Critical Path:- Cp = 1 - 2 – 3 - 4 – 5 – 6 – 7 = A – C -D - E - F - G = 2 + 3 + 4 + 8 + 6 + 2 = 25
• 19. Benefits of CPM  Useful at many stages of project management  Mathematically simple  Give critical path and float time  Provide project documentation  Useful in monitoring costs  Visual representation
• 20. Limitations to CPM  Specified precedence relationship  Activity time estimates are subjective and depend on judgment  Can be more difficult understand ten grant charts  The time needed for tasks is not as clear as with grant charts

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Top 10 Critical Path Template With Samples and Examples

Nawsheen Muzamil

There are no shortcuts to success in business, or in life. For there’ll be no character development, no great lessons learned, and no sense of achievement if success was delivered to all of us on a platter.  In fact, the very flavor of life emerges with difficulties and challenges in it. So, if you savor business challenges step by step, failure just melts always and you will have a deeper sense of accomplishment. This is the real purpose of a critical path too.

In business terms, a critical path refers to the roadmap, tracing which tasks can be successfully executed. Each step involved in a critical path is, thus, a lesson that must be obeyed. Once a critical roadmap is defined, teams can allot time to each task and, in this way, forecast the total time taken and the resources that will be expended. Thus using the skill and knowledge of critical path analysis, tasks will be completed efficiently and on schedule. 

Critical Path in Project Management

In project management , critical paths define the time constraints by which each task can start and finish without delaying the project schedule. Since a critical path is the longest path through the project network diagram, it points out the minimum time needed to complete the project. 

A critical path template in project management is, thus, the most searched tool for managers and team players. It typically includes a list of all tasks in the project, the dependencies between tasks, the duration , and the earliest and latest start and finish dates for each task. A critical path template benefits project managers and project team members equally. It helps them:

• Understand the interdependencies between tasks, 
• Identify potential bottlenecks and areas of risk, and 
• Make informed decisions on resource allocation and task prioritization 

It helps project managers in:

• Communicating project plan to stakeholders and 
• Tracking progress towards completion

With that, we present our most downloaded collection of critical path diagram templates and critical path chart templates for you to trace this journey.

Template 1: Critical Path Analysis for New Product Launch PPT Template

A product launch must be strategized before committing wealth and resources to it. Here is a PPT Layout to carve out the critical path to achieve this. Identify the core steps of launch, such as kick-off meets, notifying suppliers, commencing production, conducting launch. Along with the necessary steps, highlight other necessary steps like customer research, designing concept, testing prototype, etc to garner better results from this campaign. Get ahead of your competition with a download now!

Download this template

Template 2: Strategic 100-Day Plan Critical Path

Of the many uses of devising a critical path, estimation and scheduling of project activities is the favorite of project managers.. With this 100-day plan strategic layout, identify the major activities to be covered and distribute them within this time. Then, share this plan with your teammates to help them better focus on sticking to the critical path. Grab this PPT Layout now!

Template 3: Critical Path Structure in Project Control Techniques

The smooth induction of the project is only possible when enough control is exercised on the factors impacting it. With this critical path layout, identify control techniques that need to be practiced throughout the project. Use this PPT Design to allot control mechanisms at each of the critical steps. Determine the time allotted for each core activity and let your project operate within it. Grab this PPT Design now.

Template 4: Critical Path Analysis Involving PERT Technique With Eleven Milestones

The PERT(Program Evaluation Review Technique) technique approach comes in handy when charting out a project pathway. If you have done the PERT analysis, lay down its critical path with this dedicated PPT Design. Cite the primary path i.e. the critical path and the accessory events that can add more value to this undertaking. Impress the importance of coordinated execution of tasks using numbering of steps as shown in this PPT Design. Get your team on the same page by using this PPT Template. Download now.

Template 5: Critical Path Method Project Strategy Process Scope and Schedule PPT SlideShow

Guide your team in differentiating between the critical path and the non-necessary parts to help them direct their efforts. Use this characteristic template to distinguish between the primary pathway and the complimentary steps to help the team focus better and in the interest of overall effectiveness of the project. Use this color-coded PPT Diagram and use alphabetical assortment to align steps. Get it now.

Template 6: Critical Path Analysis Showing Three Paths to Complete Project

It’s possible in critical path analysis to identify more than one defined path in achieving a satisfactory end-result. If you are at a crossroads of this situation and perceive multiple pathways to achieve your objective, then it’s time you chart out the individual roadmaps on a single sheet for comparison purposes. Once the paths are defined, you can look for the most feasible and time-saving course of action for you or experiment with any of them to reach your end goal. Deploy the convenience of its alpha-numeric coding and get this PPT Slide now.

Template 7: Critical Path Project Management PPT Design

 To devise the most feasible, all-encompassing critical path, it’s important to look at the key players of your project and identify resources involved. Assemble the components of your project with this infographic PPT Template. These could be the supply-chain, stakeholders, emergency services and other activities that represent the essence of the project. Identify your variables with this PPT Diagram and get started on carving out your most ideal critical path.

Template 8: Critical Path Analysis Showing Task Completion by Months

Having a critical path defined grants project managers the convenience to create a timeline for their project. Here is one ready-made design that combines the supremacy of Gantt Chart and editability that will help you monitor and schedule tasks. Identify tasks and define their duration and overall result expected with this wonderful PPT Layout. It’s a timeless PPT Template that you will definitely need for your business. The link is shared below.

Template 9: Critical Path Analysis Showing Time in Days and Weeks

Chop-chop! Is your project schedule so precisely planned that you do not even have a second to lose? For you hours count, let alone months? Then use this daily and weekly timeline template to keep track of your critical path activities. Set their duration and monitor progress with its embedded Gantt Chart  representation. Grab this editable PPT Design from the link below.

Template 10: Critical Path Analysis Shown Using Multiple Tasks

Here is another PPT Design to convey the framework of your critical path in a simple manner. Identify tasks by their unique title and number them in the order these to be implemented as shown in this PowerPoint Layout. Edit this ready-made design now to direct your project activities. Locate the download link below.

Deploy your PPT Template of choice to help your team conform to a plan.

PS:  All-hands are meetings to inform about major company updates, policy changes, or to extend felicitations. If one is coming up in your organization, you need to check this guide comprising 5 all-hands meeting templates to frame the correct approach of invite and conduction of these all-members-on-board meetings.

FAQs on Critical Path

What is critical path with example.

In project management, the critical path is the sequence of project tasks that determines its minimum duration. This is the longest path through the project, which includes the most time-consuming tasks. Every task on the critical path must be completed on time for the project to be completed on schedule. This means that tasks that are not on the critical path can have some flexibility in their start and end dates.

For example, consider building a house . The critical path might include obtaining building permits, pouring the foundation, framing the house, and installing the plumbing and electrical systems. These tasks must be completed in a specific order and within a certain time frame, because each task builds upon the previous one’s completion. Any delays in these tasks will elongate the project duration. On the other hand, tasks such as painting and installing finishes are not on the critical path and may have some flexibility in their schedules.

What is the purpose of a critical path?

 By focusing on the critical path, project managers can identify potential bottlenecks and take steps to prevent delays. This can help minimize duration of the project and increase the likelihood of meeting the project deadline. 

The critical path is also useful for identifying the minimum amount of time required to complete a project. This can be useful for setting deadlines, determining resource requirements, and developing contingency plans. 

Overall, a critical path helps project managers prioritize tasks, allocate resources efficiently. 

How do you identify a critical path?

There are a few steps you can follow to identify the critical path of a project:

• Identify all tasks that make up the project. 
• Determine dependencies between the tasks. 
• Estimate the duration of each task. 
• Draw a network diagram to represent the sequences and dependencies.
• Identify the critical path by finding the longest path through the network diagram. 

 The critical path can change as the project progresses. As tasks are completed and new information becomes available, the duration of tasks may change and the critical path may shift. It is a good idea to regularly review and update. 

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8 Steps to Project Planning With the Critical Path Method

September 21, 2022

The critical path method is a way to organize projects and sort out your priorities. I’ve found critical paths to be a very useful tool for project planning, which can scale to support all organizational levels: individuals, pods, teams, and the org writ large. They’re useful when working on one-off projects, and can improve recurring processes and optimize concurrent software.

Project graphs are a visual representation of the work required for your project. Each node on the graph is a discrete task. Arrows indicate dependencies, where a task is dependent on work from another task. Numbers display time, rather than cost, and assume no resource bottlenecks.

Critical paths provide project managers and teams with important insights, and an ability to evaluate a project as a process. After talking through these insights and why teams might adopt this method, I’ll explain how to build a project graph and identify your own critical path in eight steps. I’ll also provide two ways to mutate your graph to adjust as needs change.

Why the Critical Path?

The critical path method does more than document progress. Critical paths reveal reliable and actionable insights that empower project managers, specifically in four areas.

Minimum Time to Completion

When can you expect your project to be done? By mapping the discrete tasks and the effort they’ll require, you can easily find the longest path on your project roadmap. The critical path provides a meaningful basis for explaining this timeline, and allows you to look for risk areas and opportunities to shorten the timeline.

Critical Lines of Work

Critical lines of work are those areas where an individual delay would cause a delay for the whole project. These choke points become apparent by tracking dependencies.

When a parent task must be completed in its entirety before a child task is started, the child task is said to have a dependency on the parent task. Graphs can display this information in different formats: - Earliest start - Latest start - Latest finish - Discrete start/stop nodes

Prioritization

The beginning of a project starts with a critical chain of big tasks. By front-loading the big, heavy tasks, you can reduce uncertainty over the course of the project.

Resource Allocation and Scheduling

The critical path can be invaluable for scheduling heterogeneous teams. By thinking of the project as a process, the critical path shows which roles will be needed over time. This enables intelligent scheduling that overlaps across different projects.

8 Steps to Build the Project Graph

Creating a project graph and identifying the critical paths within can seem daunting at first. But the eight steps below become quite intuitive after completing a couple examples.

1. Establish Level of Granularity

The critical path method can work for groups and projects of all sizes, but the way you define different elements will depend on your group size: - Individual - Pod - Team - Organizational/Company

2. Establish a Time Scale

The time scale should correspond to the size of the graph’s level of granularity and discrete tasks. On average, are these things that can be completed in an hour, a day, or a week?

3. Identify Tasks

List out all of the tasks or user stories that need to be completed. The size and scope of these tasks should align with the level of granularity and time scale. When encountering unknown elements of a project, adding a larger, less granular task may be necessary. This task can later be broken down into smaller tasks as they become apparent.

4. Identify Task Dependencies

For each task, identify tasks that must be completed before its work can begin. Draw dependencies between these tasks as directed edges, with arrows pointing from the parent (earlier) task to the child (later) task. Reorganize the task list along these relationships.

5. Refine Tasks and Dependencies

This dependencies diagram might already help frame your project in a different way, and you can adjust tasks at this point to create a smooth process from start to finish. Because projects ultimately need to finish, there cannot be any circular dependencies, and the project graph must be a directed acyclic graph (DAG). There are a few ways to address dependency chains when they do arise: - Break up tasks into smaller subtasks, pulling out the work that can be done ahead of time without waiting on dependencies. - Merge tasks together. - Pick the priority task between mutually exclusive tasks.

6. Estimate Tasks

Each task should be given a time estimate. Note that tasks should be estimated by time, not cost. For example, when estimating the task of pouring a concrete driveway, you should include the time for the concrete to dry even though the curing process requires little work.

When encountering uncertainty, err on the side of caution and give a higher estimate.

7. Compute Longest Paths

Begin computing the longest paths by recording an “earliest finish time” for each task, starting with the tasks that have no dependencies.

Repeat this step in the next row, adding the next task’s estimate to the previous task’s earliest finish time, until the graph is complete with the earliest finish time of all nodes.

8. Identify the Critical Paths

Identifying the critical path is simple enough to be described in two steps: (1) Highlight the tasks with the latest “earliest finish” time, and then (2) highlight that task’s children with the latest “earliest finish” time. Repeat step 2 until a starting task (with no dependencies) has been highlighted. The critical paths are the paths between the highlighted tasks.

Mutating the Project Graph

As projects evolve, requirements become more fleshed out, timelines become clear, and plans change the project graph. The next section describes two common scenarios that result in changes to the project graph and how insights that can be derived from those changes.

Project managers will always get asked how they can speed up a project, and the critical path provides a meaningful basis for explaining where, if anywhere, that’s possible.

Splitting tasks introduces additional labor and overhead. If a software change was going to need one cycle of Q&A and review, it will now need twice those efforts on the split tasks.

The critical path allows us to see whether the extra effort will pay off. If tasks are split up that are not on the critical path, the project duration stays the same. It’s only when tasks are split up on the critical path that project velocity can be influenced.

Adding Scope

It’s also common for stakeholders to want to add scope to a project as it comes to life. The critical path identifies when and where scope can be added, and how those additions affect the project duration.

If there’s slack in the plan and the team and materials are available, capacity can be added that won’t impact the project timeline. However, if the work gets added to the critical path, it will delay the overall timeline.

The project graph also provides a good explanation for why throwing more developers at a project won’t actually help. If those developers aren't working on the critical path, they aren't influencing the overall velocity.

Project Graphs can be helpful and illuminating tools for teams of all sizes, and they can help coordinate diverse needs, unblock workflows, and unlock your team’s potential. They are fairly easy to create, and they can be manipulated and used to provide complex visualizations into your team’s processes.

If you’re interested in learning more, I recommend reading about calculating slack and the PERT estimation method.

The Critical Path Method with Example | PMP Notes

When I was preparing for my PMP exam, it was tough for me to understand this CPM concept. I watched tons of videos and read blogs, but nothing was working for me. Eventually, after a hard practice, I cracked the way out.

Today, I am going to discuss the easiest methods to understand concepts. If you are going for a PMP exam , then make sure to draw the network diagram always, as there may be more than one question relating to that network. But if you got a network diagram already in question, you need to visualize and crack the questions.

You may also like PERT & CPM .

Moreover, in a project management life, critical path understanding is the primary area discussed daily, weekly, and monthly meetings. That’s why understanding every concept is quite remarkable.

Let’s see how to get a network diagram from the given table or conditions.

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What is a Critical Path?

How to find critical path, forward pass in cpm, backward pass in cpm, float calculation in cpm, locating the cpm, zero-day start | method, final words, featured posts.

If you see a path met with the below conditions on any network diagram, it is a Critical Path.

• The longest path in the complete network diagram
• The path with the shortest duration to complete a project .

There are some conditions like every activity that should be connected. See if you find if more are mentioned on the given data.

To find a critical path on any project or given conditions, you need to follow the below steps;

Step – 1: Construct a network diagram.

Step – 2: Determine Project Completion time.

Step – 3: Perform Forward and Backword pass (Not necessary every time!)

Step – 4: Calculate the float .

Step – 5: Mark the Critical path with zero float activities.

How to Draw a Network Diagram?

First of all, we need data in tabular form or any proper format;

Now, please read it and see all the conditions to implement during a draw. If you are doing it on plain paper, make sure to use boxed and right angles. This will prevent you from messing around with things and logic.

•  Early Start – ES
• Early Finish – EF

we will get by using  forward pass, and then

• Late  Start – LS
• Late  Finish – LF

we will get by using a backward pass.

Then we will calculate the float that will help to find a critical path.

First of all, I put all the activities as per the given condition on our table. I have also applied the logic, as you can see.

Now, we will calculate the forward pass. for this, you can start with 0 0r 1. There is no condition, but in PMBOK, they took 1. This is logical as my first day on any project should be 1, not 0 days. Still, some school thoughts agree to start with 0. Like they have zero semesters in a college 🙂

I will explain below how I have calculated the forward pass.

From the start, I put 1 and added 7 and then minus one, and hence the formula is like

• Early Start (ES) = Early Finish of predecessor activity + 1
• Early Finish (EF) = Activity Time + Early Start of Activity – 1

I did the same, keeping in view the logic, as shown as per arrowheads. I hope I am clear now. If you feel any nag, comment below, and I am happy to answer.

The next step is to calculate the Backward pass. it is the same as the forwarding pass, but this time we need to keep in view the below formulas;

• Late Start (LS) = Late Finish of Activity – Activity Time + 1
• Late Finish (LF) = Late Start of Successor Activity – 1

This one the most natural part of CPM but the most important one. It helps to locate the critical path in a particular network.

Below are the simple formulas to calculate float;

• Total float for an Activity  = LS of Activity – ES of Activity
• Total float for an Activity  = LF of Activity – LF of Activity

You can apply any, and the answer will be the same. If not, then you are doing something wrong.

It would help if you found all the activities with zero float, or we also call it slack.

In our network diagram, there are different paths like;

• Start – ACF – Finish
• Start – BDEG – Finish
• Start – AEG – Finish
• Start – AEF – Finish
• Start – BDEF – Finish

But we have to look for a path having all the activities with zero float on. In our diagram, Activities BDEF are with zero floats, and hence this is the critical path. This is the longest path, also with 32 days. Rest is less; you can calculate on your own.

That is how you can calculate a critical path. But as I said earlier, you need not go for forwarding and backward path in most of the PMP  exam. Just calculate the longest path from activities durations and check all the possible paths in glace and hopefully, you will get it right, or else you can calculate this method – Practice it hard and let me know in the comments if I can add more on it.

If you belong to other schools of thought, then you will get a final shape like the below picture;

I have explained this with a bit complex diagram so that if you get a hard question, you can still calculate it easily. I got a question to estimate free float and total float on a particular activity, and I just found out that this activity is on a critical path, so I select the answer as zero.

You will get plain paper and a lead pencil during your PMP exam , and make sure to draw boxes for activities and join them with straight and right-angle lines so that you don’t mess up there.

Good Luck! Any questions or you found any mistakes – comment, please.

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1 thought on “The Critical Path Method with Example | PMP Notes”

In the backward pass CPM example here shouldn’t the LS(Activity G) be 28? LF(G) – t(G) + 1 =32-5+1 = 28

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Table of Contents

CPM or the Critical Path Method is an algorithm used in project management that is used to schedule project activities. The critical path refers to the longest stretch of the activities, and a measure of them from start to finish. 

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What is the Critical Path Method (CPM)?

A strategy for surveying plan adaptability and distinguishing undertakings fundamental for project culmination is the critical path method (CPM). In the project, the executives, the basic way is the longest succession of undertakings that should be done on time for the task to be done. If crucial tasks are postponed, the project will also be delayed.

CPM Key Elements

The elements of CPM in project management are as follows: 

Earliest Start Time (ES)

The initial stage in the project is when an activity can be begun. You cannot make this decision without initially understanding whether you have any task dependencies.

Latest Start Time (LS)

The very last second when a task can be started without affecting the timeline for your project.

Earliest Finish Time (EF)

The earliest a task can be finished is determined by its duration and earliest start time.

Latest Finish Time (LF)

The latest that a task can be finished is calculated using its duration and latest start time.

The concept of "float" refers to how long an activity can be postponed without affecting its task order or the project timeline. The critical path tasks have no float since they cannot be delayed.

Why Use the Critical Path Method?

CPM can advise sage on setting priorities, distributing resources, and scheduling projects.

There are various reasons to use this method, including the ones listed below:

Improves Future Planning

Improves future planning by utilising CPM to compare expectations with actual progress. Future undertaking thoughts can be affected by the information accumulated from progressing projects.

Facilitates More Effective Resource Management

It lets project managers prioritise tasks, giving them a better understanding of how and where to deploy resources.

Helps Avoid Bottlenecks

Project bottlenecks can cost precious time. By outlining project dependencies using a network diagram, you can more accurately decide which tasks can and cannot be finished in parallel. After that, you can adjust your schedule accordingly.

With the help of CPM, we’ll be able to create a model that enables you to determine the following: 

• Tasks required to complete the project
• Dependencies between tasks
• The duration required to complete an activity

Now, before we can get started with CPM or Critical Path Method, we’ll have to understand two major concepts which are Events and Activities. To help understand them better, let’s have a look at the network diagram (which is also the output) of the process. 

This output represents some of the most important parts of the process: Events and Activities.

Events are represented by a circle and will occur at the start and end of an activity. Event 1 is the tail event and Event 2 is the head event. In the case of our example, the events are 1, 2,3,4, 5, and 6. Taking into consideration, nodes 1 and 2, and the connection between them, 1 will be referred to as the tail event, and 2 will be referred to as the head event. 

Similarly, for 2 and 3, 2 is the tail event, and 3 is the head event. 

Activities represent action and consumption of resources like time, money, and energy required to complete the project. In the case of our example, A, B, C, D, E, and F represent the activities taking place between their respective events. 

Dummy Activity

A dummy activity represents a relationship between two events. In the case of the example below us, the dotted line represents a relationship between nodes 4 and 3. The activity between these nodes will not have any value. 

Other rules to consider

• The network should have a unique starting and ending node. In the case of our example, event 1 represents a unique starting point and 6 represents the unique completion node
• No activity can be represented by more than a single arc (the line with an arrow connecting the events) in the network
• No two activities can have the same starting and ending node. 

Now, let’s talk about the process of the Critical Path Method with an example. 

The Critical Path Method

The objective of the question below is to determine the critical path, based on the information available, like activity, immediate predecessor, and duration (which in this case, we’ll take as months)

First, let’s analyze the activities and their immediate predecessors. 

Activities A, B, and C don’t have any immediate predecessors. This means that each of them will have individual arcs connecting to them. First, we’ll draw nodes 1 (which is the starting point) and 2. We’ll add the activity on the arc, along with the duration. 

We’ll have to also keep in mind that A acts as the immediate predecessor for both nodes E and F. Similarly, let’s draw the arcs for nodes B and C. 

Before we can draw the nodes for activity D, a quick look at the table will tell us that it is preceded by activity B and that a combination of activities C and D act as immediate predecessors for activities H and J. This means that both activities C and D have to connect at some point. That’s why we’ll be drawing an arc from events 3 and 4. 

So now, we’ve completed activities A, B, C, and D of the critical path method. Next, let’s take a look at activity E. 

Activity E is preceded by activity A and acts as the immediate predecessor for activity J. Since this is an independent activity, we’ll be able to draw an arc like this.

If we have a look at activity F, it’s preceded by activity A, and a combination of F, G, and H act as immediate predecessors for the activities K and L. So let’s wait before we take it up. Instead, let’s shift our attention to activity G. It’s preceded by B. So, we’ll draw it like so.

Now, let’s take a look at activity H. It is preceded by both C and D and will act as the immediate predecessor for K and L, along with F and G. So, we can connect node 4 to 6. 

Now that we’ve done that, let’s go back to activity F.  Now that we know where activities G and H connect to, we can combine nodes 2 and 6, fulfilling the conditions required for activities K and L.

Following this, we have an activity I. The activity I is preceded by activities C and D. It also acts as an immediate predecessor to activity M. Since it’s an independent activity, we can draw it like so. 

Next, let’s take a look at activity J. Activity J is preceded by activity E. We can also see that a combination of J and K will act as an immediate predecessor for activity N. We can then draw an arc like this. 

Let’s go on to activity K. Here we can see that K is preceded by F, G, and H. It also acts as an immediate predecessor to activity N. So, we’ll connect nodes 6 to 8. 

Next, let’s continue with activity L. The table now shows that L, M, and N don’t act as immediate predecessors for any other activity. Hence it can be assumed that it’ll connect to the final node. 

L is preceded by activities by F, G, and H. The arc can be drawn like so. 

We’ll now go to activity M. This activity is preceded by activity I. Similarly, we can connect an arc from node 8 to 9 for activity N. 

Now, the network is complete! 

Now, to find the critical path. For this, we’ll need to find two values, Earliest Start Time (Es) and Latest Completion Time (Lc).

The process of determining the Es for all events is called a forward pass. 

The process of determining the Lc for all events is called a backward pass.

Let’s get into the forward pass. For this, first, we’ll need to create boxes at all nodes. These are then divided into two. The lower half of the box represents the earliest start time of the node, while the upper half represents the latest completion time. 

Your network diagram should look something like this. 

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For this, we’ll be using the formula, Esj = max (Esi + Dij)

Which when simplified, the earliest start time for the second node (head node), is the maximum of the combination of the earliest start time of the tail node and the duration between the two nodes. 

So, for node 1, the earliest start time is always zero. 

For node 2, it would be, Es2 = 0 (earliest start time for node 1) + 3 (duration between 1 and 2) = 3

For node 3, 

it would be, Es3 = 0(Es1) + 4(D1 to 3) = 4

For node 4, we can see that two arcs connect to it. This means that we’ll need to choose among the largest of the two options available to us. 

Es4 = 0(Es0) + 6 = 6 or

Es4 = 4(Es3) + 3 = 7

We’ll choose 7 since it’s larger.

Similarly, we have three options to choose from when it comes to node 6. Since three arcs connect to it. 

Es6 = 3(Es2) + 1(D2-3) = 4

Es6 = 4(Es3) + 4(D3-6) = 8

Es6 = 7(Es4) + 5(D4-6) = 12

Hence we’ll select the last option since it’s the largest among the three. 

Now, for node 5. Since it’s directly connected to node 2, we can directly apply the formula. 

Es5 = 3(Es2) + 9(D2-5) = 12

Let’s take node 8. 

Es8 = 12(Es5) + 3(D5-8) = 15 or

Es8 = 12 (Es6) + 6(D6-8) = 18 

We’ll choose Es8 as 18 since it’s the larger of the two. 

Now for node 7. We can directly apply the formula to these nodes.

Es7 = 7(Es4) + 4(D4-7)  = 11

Finally, we’ve got node 9.

It has 3 nodes connecting towards it. We’ll have to choose the maximum of the three. 

Es9 = 18(Es8) + 9(D8-9) = 27

Es9 = 12(Es6) + 3(D6-9) = 15

Es9 = 11(Es7) + 6(D7-9) = 17

We’ll choose the arc from node 8 since it’s got the highest value.  

And like that, the forward pass is complete. Now, for the second part of the critical path method.  Let’s take up the backward pass. For that’ we will be using the following formula. 

Lci = min(Lcj - Dij)

This, when put simply, means the latest completion time of the tail node is equal to the latest completion time of the head node minus the distance between the two. 

Let’s start from the final node, number 9. 

The Lc for this node will always be equal to its Es. So, Lc9 = 27.

Next, let’s have a look at the latest completion time for the 8th node. Since it’s directly connected only to the 9th node, we can directly apply the formula mentioned earlier. 

Lc8 = 27(Lc9) - 9(D9-8) = 18

Now, let’s have a look at the latest completion time for node 7. Since there’s a direct connection between nodes 9 and 7. 

Lc7 = 27(Lc9) - 6(D9-7) = 21

Let’s move on to node 6. As we can see in the diagram, there are two points extending to nodes 8 and 9 from node 6. So we have two options to choose from. 

Lc6 = 18(Ls8) - 6(D6-8) = 12 or

Lc6 = 27(Ls9) - 3(D6-9) = 24 

We’ll choose the Lc of node 6 as 12.

We’ll now go to node 5. Since it’s directly connected to the 8th node, we can directly apply the equation.  

Lc5 = 18(Lc8) - 3(D5-8) = 15

Next up, let’s find the latest completion time for node 4. 

Since there are two connections extending from the node, to nodes 6 and 7 respectively, we’ll need to select the minimum between the two. 

Lc4 = 21(Lc7) - 4(D4-7) = 17

Lc4 = 12(Lc6) - 5(D4-6) = 7

We’ll choose 7 as the latest completion time for node 4. 

Now for node 3. 

Since there are two nodes connecting from node 3 to nodes 4 and 6. So, we’ll need to choose between the 2. 

Lc3 = 12(Lc6) - 4(D3-6) = 8 or

Lc3 = 7(Lc4) - 3(D3-4)  = 4

We’ll choose 4 as the latest completion time for node 3. 

Let’s now go to node 2. Again, since there are two connections made from 2 to node 5 and 6, we’ll need to choose the minimum among the two. 

Lc2 = 15(Lc5) - 9(D2-5) = 6

Lc2 = 12(Lc6) - 1(D2-6) = 11

We’ll choose the latest completion time of 2, as 6.

And finally, we have node 1. 

Since there are connections to 2, 3, and 4 from 1, we’ll need to choose from the three.

Lc1 = 6(Lc2) - 3(D1-2) = 3

Lc1 = 4(Lc3) - 4(D1-3) = 0

Lc1 = 7(Lc4) - 6(D1-4) = 1

We’ll choose 0 as the latest completion time for the node.

And there we go! The backward pass is complete. 

Now, for the final step of the critical path method. To determine the critical path, there are three major criteria that need to be satisfied. 

Esj - Esi = Lcj - Lci = Dij

From the diagram, we can see that nodes that satisfy the requirements are: 1, 3, 4, 6, 8, and 9. 

Hence the activities on the critical path are B - D - H - K - N.

Hence the critical path is B + D + H + K + N = 4 + 3 + 5 + 6 + 9 = 27. 

And there we go! We’ve found the critical path! 

Pros and Cons of Ssing CPM

The pros and cons of the critical path method (CPM) are as follows:

Pros of Using CPM in Project Management

The pros of using CPM are as follows:

• Effective Communication: All phases of a project's life span must be considered when creating critical path method schedules. The program's structure becomes more achievable and firm when the skills shared by various team members are integrated.
• Easier to Prioritise Tasks: Project managers can more effectively prioritize tasks and estimate the float of each one by determining the critical path. Float indicates the amount of time a task may be put off before it affects when it will be completed. A lower float indicates a greater priority.
• Accurate Scheduling: CPM is a popular and dependable methodology for enhancing the precision of project schedules. Several project managers utilize CPM with the Programme Evaluation and Review Technique (PERT), which supports teams in estimating overall project length. 
• Better Visualisation: Gantt charts and CPM network diagrams, which show critical path timelines, can help project managers understand a project's timeline and progress more quickly. These visual tools allow them to understand a project's direction more intuitively than a less eye-catching alternative.

Cons of Using CPM in Project Management

Some of the cons of using the critical path method are as follows:

• Multiple Complexities: Several moving elements and detailed computations are involved in the CPM. The software may automate the computations, but entering accurate data requires thorough research and leaves room for human error. 
• Limited Applicability: Not every project type is suited to the critical path method. Projects requiring creativity, like product design or research work, that tend to come along in unforeseen forms fail to lend themselves well to CPM.
• Less Understanding of Resources: The critical path method also lacks sufficient understanding of how resource limitations impact project schedules. The accessibility of equipment or labor resources is not considered in the network diagram or CPM schedule.

Step by Step Guide on How to Find the Critical Path With Examples

The time of essential and non-critical tasks can be used to identify the critical path. This is a list of the steps, along with examples.

List Activities

List all the venture exercises or errands essential to create the expectations utilising a work breakdown structure . The rest of the CPM is built on the list of activities provided in the work breakdown structure.

Identify Dependencies

Choose the occupations based on your work breakdown structure that is interconnected. This can identify any task that can be finished alongside other chores.

These task dependencies are based on the example mentioned above:

• Task A is necessary for Task B.
• Task B is necessary for Task C.
• C and D can be carried out concurrently.
• Task D is necessary for Task E.
• Task F depends on Tasks C, D, and E.

Create a Network Diagram

The network diagram, a flowchart that depicts the order of tasks, must then be created from the work breakdown structure. Each task should be represented by a box, with task relationships shown by arrows.

Until the overall project timetable is determined, you will add other time-bound components to the network diagram.

Estimate Task Duration

You must first estimate each activity's length before determining the critical path, which is the longest series of critical tasks.

Try these to get a sense of the time:

• Using knowledge and experience to make educated assumptions
• Estimating using information from past projects
• Estimating using established industry practices

Try the forward pass and backward pass technique instead:

• Forward pass: This method uses a previously stated start date to determine early start (ES) and early end (EF) dates. ES is the direct ancestor with the highest EF value; EF is calculated as ES plus duration. The calculation begins at ES of the first action with 0 and moves forward through the schedule. Establishing ES and EF dates enables early resource allocation for the project.
• A backward pass determines the dates for late starts (LS) and late finishes (LF). LF is the lowest LS value among immediate successors, and LS is LF - duration. The calculation begins with the final action on the timetable and works its way backward.

The scheduling flexibility of each activity can then be determined using the early and late start and end dates.

Calculate the Critical Path

Although the critical path can be determined manually, adopting a critical path algorithm can save time.

Below are the steps:

Step 1: Next to each action, note the start and end times.

The initial activity lasts for the allotted period and starts at 0.

The start time of the next activity is determined by the finish time of the previous one, and the end time is calculated by multiplying the start time by the duration.

Do this for each activity.

Step 2: To discover how long the entire sequence lasted, look at the last activity in the sequence's end time.

Step 3: The critical path is the series of operations that takes the longest time.

You can construct the entire project schedule around the critical path once it has been identified.

Calculate the Float

It illustrates how much extra time could be added to the task without impacting other activities or the project's deadline for completion.

The project's degree of flexibility can be determined by identifying the float. Use the resource known as "float" to cover project risks or unforeseen problems.

The dates of critical tasks are fixed since they have zero floats. Positive float tasks go on the non-critical route, where their delay won't affect the project's completion. Non-critical jobs might be skipped if you need more time or resources.

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Dealing with Contingencies and Constraints

Two ways to deal with contingencies and constraints in CPM are as follows:

Fast Tracking

Fast-tracking is the method of carrying out several tasks on the critical path while simultaneously minimizing the project's duration. Fast-tracking is feasible for tasks that lack "difficult" attachments or don't start completely dependent on previous tasks. Fast-tracking necessitates more resources. 

Crashing is a process of allocating additional resources to your project to complete it in a faster and more efficient way. Crash durations are effective in projects that would benefit from additional resources and can use some resources from tasks with higher floats. 

Critical Path Method Software

Programs or software specifically designed for project management that lets you create critical path schematics for a given project are called critical path software or CPM software. These tools make your daily activities easier by helping you analyze, schedule, and manage project tasks, reliance, and resources.

Here are some of the critical path method software: 

• Office Timeline
• Zoho Projects 
• LiquidPlanner
• ProjectManager

Features of Critical Path Software

The general features of critical path software are as follows:

• Complete process visibility using Gantt charts and Kanban boards
• Set a task, an overview of the task, assignees, and to-do lists
• Interact on discussions or challenges to projects
• Make dependencies between tasks
• Set both the actual and projected dates
• Control spending and produce a financial summary
• Identify challenges and risks, eventually delegate them
• Integrations by third parties
• Track your tasks

Key Critical Path Terms for the PMP Exam

Some of the critical path terms which can be important for the PMP exam, which includes the question of what CPM is, are as follows: 

• Critical Path Method: It is a sequential managing projects approach for process development that distinguishes between essential and minor duties, thereby avoiding delays and workflow constraints.
• Critical Path DRAG: An essential action's total time adds to the project's overall duration. Alternatively, cutting the length of one essential activity to a minimum would shorten the time needed to complete the project.
• Criticality Index: It is employed in risk analysis, displaying how often a specific activity has been on the critical path throughout the study. High Criticality Index activities are more inclined to be placed on the critical path, which increases the likelihood that they will delay the project.
• Total Float: The amount of time that can be added to an activity's early start date yet to prevent the project as a whole from being pushed back.
• Free Float: The duration of a task can be postponed without pushing back the early start time of a succeeding task.
• Forward Pass: The strategy for figuring out the critical path method's early start or finish times for tasks.
• Backward Pass: The strategy to determine when an activity in the critical path method will have a late start or finish.
• Network Diagram: A diagram that shows the connections between project activities. It is typically created from left to right to symbolize the project's sequence.
• Network Analysis: Deconstructing a complex project into its various components (tasks, timelines, etc.) and then graphing those parts to show how they relate.

Total Float vs Free Float

Total float: This is the amount of time an activity can be postponed from the early start date before the project's completion date or a scheduling restriction is violated. Total float is equal to LS-ES or LF-EF.

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How to Use the Critical Path Method

CPM gives you an insight into the status of your project and enables you to keep track of activities and their turnaround times. These are some additional uses for CPM.

Compress Schedules

There are situations when project deadlines may be advanced, but this could be better. In those circumstances, you can use either fast tracking or crashing as a schedule compression strategy.

Fast-tracking : Analyse the critical path to identify tasks that can be completed concurrently. The entire length will be shortened by using parallel processes.

Increasing resources is a step in the process of "crashing" operations. Be sure the additional resources will still fit inside the project's scope before acquiring them, and inform the stakeholders of any modifications.

Resolve Resource Shortages

Remember that the availability of resources is not taken into consideration by CPM. Therefore, you can employ resource-leveling tactics to resolve a resource deficit, such as an overbooked team member or a lack of equipment.

To ensure that a project can be finished with the currently available resources, these strategies work to alleviate resource over-allocation problems.

You should modify the critical route or use this strategy for activities that have floated since resource-leveling works by changing the start and end dates of the project.

Compile Data for Future Use

Since you're working with informed estimations for activity durations, the schedule generated by CPM is liable to alter. Therefore, as the project progresses, you can contrast the original critical path with the current one.

Future studies can use this information to predict work durations more precisely.

Choose the Right Program

Are you looking to take your project management skills to the next level? Look no further than Simplilearn's comprehensive project management courses!

Our courses are designed to help professionals at every level of experience to develop and enhance their project management skills, whether you're just starting out in the field or looking to advance your career. With our courses, you'll gain practical, hands-on experience in managing projects from start to finish, and learn best practices and industry standards that will set you apart from the competition.

Program Name PMP® Certification Training Course PMP Plus Post Graduate Program In Project Management glyph Icons All Geos All Geos All Geos University PMI Simplilearn University of Massachusetts Amherst Course Duration 90 Days of Flexible Access to Online Classes 36 Months 6 Months Coding experience reqd No No No Skills you wll learn 8+ PM skills including Work Breakdown Structure, Gantt Charts, Resource Allocation, Leadership and more. 6 courses including Project Management, Agile Scrum Master, Implementing a PMO, and More 9+ skills including Project Management, Quality Management, Agile Management, Design Thinking and More. Additional Benefits -Experiential learning through case studies -Global Teaching Assistance -35PDUs -Learn by working on real-world problems -24x7 Learning support from mentors -Earn 60+ PDU’s -3 year course access Cost $$ $$$$ $$$$ Explore Program Explore Program Explore Program

Critical Path Method vs PERT

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Critical Path Method vs Gantt Chart

Horizontal bar charts, called Gantt charts , lay out project activities that may be monitored within a predetermined timeframe. The dependencies between tasks are displayed using both CPM and Gantt charts.

Here are some distinctions between the two tools:

• Project duration is calculated, and critical and non-critical pathways are visualised.
• Shown as a network diagram with connected boxes.
• Does not indicate the resources needed
• Plots activity without a time frame on a network diagram

Gantt Diagram

• Visualises the development of project activity
• Presented as a horizontal bar graph.
• Demonstrates the resources needed for each action
• Creates a timetable of activities

Gantt charts and CPM can be used in conjunction to monitor critical pathways over time and keep your project on schedule.

Learn from experts who help you pass the examination post enrolling in Simplilearn's PMP training course. Sign-up today for PMP® Certification Training Course !

What’s Next?

Now that you know the critical path method, you can go into some of the more complex concepts of project management. For that, we recommend signing up for the PMP® Certification Training , which prepares you for your PMP certification exam. When you use effective tools like Microsoft Excel templates, you can raise your career to a whole new level.

If you have any questions for us, please leave them in the comments section, and our team of experts will be happy to answer them for you at the earliest!

1. What is the critical path method example?

Any project that requires a flow of certain steps to finish can use the critical path method, such as building a house; each task would need some time and resources to complete and step into the next activity. 

2. What is the difference between CPM and PERT?

The differences between CPM and PERT are as follows:

• PERT is a probability model, whereas CPM is a deterministic model.
• PERT is used to manage uncertain project tasks, and CPM is used to manage certain project tasks.
• PERT is a non-repetitive job, whereas CPM is a repetitive job.

3. Where is PERT used?

PERT calculates a realistic amount of time any project will take to complete. 

4. Why is critical path important?

It is crucial because it determines all the activities required to finish the project. It also indicates the tasks that are needed on time and can be delayed.

5. What is slack or float?

It is the amount of time for which any task can be delayed that would not lead to any delay to other activities or the projected completion time of the project.

Find our PMP® Certification Training Online Classroom training classes in top cities:

About the author.

Rahul is a Senior Research Analyst at Simplilearn. Blockchain, Cloud Computing, and Machine Learning are some of his favorite topics of discussion. Rahul can be found listening to music, doodling, and gaming.

Recommended Resources

An Introduction to Project Management: A Beginner’s Guide

PERT and CPM: Vital Gears of Contemporary Project Management

Project Management Interview Guide

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The Critical Path Method

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Chapter 7 Project Management

Project Management Projects are unique, one-time operations designed to accomplish a specific set of objectives in a limited timeframe Project managers.

ES=32 EF=34 LS=33 LF=35 ES=10 EF=16 LS=10 LF=16 ES=4+6=10 EF=10 LS=4

1 1 Slide © 2001 South-Western College Publishing/Thomson Learning Anderson Sweeney Williams Anderson Sweeney Williams Slides Prepared by JOHN LOUCKS QUANTITATIVE.

Operations Management Session 27: Project Management.

Network Diagramming Network Analysis  The common term for network analysis is PERT  PERT stands for Program Evaluation and Review Technique  The word.

Project Management Project  A series of related jobs usually directed toward some major output and requiring a significant time to perform Project management.

1 Topics to cover in 2 nd part ( to p2). 2 Chapter 8 - Project Management Chapter Topics ( to p3)

PROJECT MANAGEMENT. Outline What is a “project”? Project Management Objectives and tradeoffs Planning and Control in Projects Scheduling Methods Constant-Time.

Project Scheduling Basic Approach. projectA project is a collection of tasks that must be completed in minimum time or at minimal cost. activitiesIt is.

Gantt Chart Graph or bar chart with a bar for each project activity that shows passage of time Provides visual display of project schedule Slack amount.

CSSE 372 Week 6 Day 2 Constructing and Analyzing the Project Network Diagram  PERT Chart PERT was invented for the Nautilus submarine project. Ok, maybe.

1 1 Slide © 2000 South-Western College Publishing/ITP Slides Prepared by JOHN LOUCKS.

Tutorial 2 Project Management Activity Charts (PERT Charts)

PREPARED BY : NOR AZAH BINTI AZIZ KOLEJ MATRIKULASI TEKNIKAL KEDAH PROJECT NETWORK DIAGRAM.

1 1 Slide © 2009 South-Western, a part of Cengage Learning Slides by John Loucks St. Edward’s University.

Project Scheduling. SEEM Project Scheduling (PS) To determine the schedules to perform the various activities (tasks) required to complete the project,

Network planning Learning objectives After these lectures you should be able to: - Produce and analyse activities networks - Calculate earliest and latest.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.

About project

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Course info, instructors.

• Prof. Olivier de Weck
• Dr. James Lyneis
• Prof. Dan Braha

Departments

• Engineering Systems Division

As Taught In

• Project Management

Learning Resource Types

System project management, lecture 02: critical path method.

This resource contains information regarding critical path method.

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Free Critical Path Templates

By Kate Eby | July 31, 2020

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Streamline your project management and scheduling with critical path method (CPM) templates. Choose from a variety of options, including spreadsheet and diagram templates, which you can download and customize for free.

Included on this page are a critical path Gantt chart timeline , critical path chart templates in Excel and PowerPoint , and an event planning critical path template .

Critical Path Tracking Template

Determine and highlight the critical path for your project with an Excel Gantt chart template. Enter project tasks into the CPM spreadsheet along with predecessors and duration for each task. Use the template to calculate expected duration based on your optimistic, most likely, and pessimistic time estimates. The Gantt chart provides a critical path timeline with flexible tasks shown in blue, critical tasks in yellow, and slack time shown in green. 

‌   Excel Template   Smartsheet Template   ‌

Critical Path Construction Schedule Template

This simple construction project critical path template provides a visual representation of the minimum time required to complete a project. Once you identify the critical tasks for a project, enter them in the spreadsheet portion of the template to create a Gantt chart showing the critical path. This chart serves as a reminder of which tasks cannot be delayed without impacting your project’s completion date.

For more information on using the critical path method in construction scheduling, see the guide on CPM and construction management .

Project Management Critical Path Template 

Create a critical path calendar to manage projects efficiently. On this template, you’ll find columns for work breakdown structure, project stages and tasks, status for each activity, and timeline dates. Use the CPM portion of this template to identify the critical tasks, which appear in red on the Gantt chart schedule. The duration for each task is shown in days based on the starting and ending dates you select.

Event Management Critical Path Template

Find the critical path for your event planning activities to ensure that you complete everything on time. Edit the template to reflect the steps in your event management process along with predecessors, which are the activities that you must complete before you can start a task. Add time estimates for each task, and the template will show which tasks are critical and cannot be delayed. Other tasks are flexible, and the bar chart shows how much slack time you can allow for those tasks without going past your event deadline.

‌   Excel Template

Critical Path Diagram Template

This critical path analysis template provides a network diagram that includes nodes with the task name, earliest start and finish dates, latest start and finish dates, duration, and total float time. You can also use the template to display critical path DRAG, which is the amount of time that a critical path task adds to the project duration.

‌   Excel Template ‌   PowerPoint Template

Critical Path Chart Template

The PERT chart template provides a simple visual representation of tasks, duration, and the critical path in red arrows. The chart makes it easy to see the different paths in your project, identify predecessors and successors, and highlight the critical path. This template is available in Excel or PowerPoint for CPM reports or presentations.

How to Use the Critical Path in Project Management

Visit our comprehensive guide to the critical path method to learn about its advantages, how to identify and show the critical path in a CPM chart, how to utilize PERT (Program Evaluation and Review Technique ), and tips for finding the critical path with Microsoft Project.

To learn more about how to determine a project's critical path and the difference between a Gantt chart and critical path analysis, visit our article that covers everything you need to know about Gantt charts and the critical path method .

Easily Identify the Critical Path with Smartsheet for Project Management

From simple task management and project planning to complex resource and portfolio management, Smartsheet helps you improve collaboration and increase work velocity -- empowering you to get more done. 

The Smartsheet platform makes it easy to plan, capture, manage, and report on work from anywhere, helping your team be more effective and get more done. Report on key metrics and get real-time visibility into work as it happens with roll-up reports, dashboards, and automated workflows built to keep your team connected and informed.

When teams have clarity into the work getting done, there’s no telling how much more they can accomplish in the same amount of time. Try Smartsheet for free, today.

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Critical path method template

Project delays holding you back? Create a critical path method template to visualize everything that needs to be done in order to reach your end goal, including which tasks have flexible due dates and which ones are mission-critical.

Sign up to create your own template.

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When your project timeline gets complex, a critical path method template can help. This template helps you visualize the longest, most important chain of events you need to complete for a successful project—so you know which tasks to prioritize and how much time you need to finish everything on time. 

What is a critical path method template?

A critical path method template is a reusable guide that helps you determine the critical path for a project. In project management, this path is the longest sequence of tasks you need to finish on time in order to complete your initiative—meaning any delays in critical tasks will delay your whole project. Determining the critical path helps you prioritize and allocate resources to tasks that have the biggest impact on your project timeline , so you can avoid bottlenecks and keep work flowing smoothly. 

A critical path method template simplifies this process by laying out each step you need to take in order to determine a project’s critical path. It outlines all the information you need to collect, plus how to put that information together. Thanks to your template, you don’t have to start this process from scratch for every new initiative. Instead, you can copy the template, fill in the required fields, and start planning. 

The benefits of a digital critical path method template

Things change during a project. Priorities shift, resources fluctuate, and additional requests can alter your project scope . A digital critical path method template doesn’t just help you plan your timeline at the start of a project—it also helps you adjust and visualize your critical path even when circumstances change. 

Instead of relying on static Excel spreadsheets or paper trackers, you can view any updates to your digital critical path method template in real time as your team completes or changes project tasks. That means you always have an up-to-date view of what your team has accomplished, what’s coming up, and what adjustments you need to make to keep your timeline on track.

By creating your critical path method template with a project management tool , you can:

Visualize which tasks have the biggest impact on your project timeline. 

View project deliverables as a list or Gantt chart -style illustration, without doing any extra work. 

Identify and track project dependencies —tasks that rely on the completion of a different task.

See updates in real time as your team completes and adjusts tasks. 

Update your project timeline if circumstances change. 

Give stakeholders visibility into your project timeline and priorities. 

Add contextual information to tasks by attaching documents, images, and videos to each task. 

What to include in your critical path method template

Your critical path method template should outline all the information you need in order to determine a project’s critical path. This includes: 

A list of all deliverables and sub-deliverables: Everything you need to complete for a successful project, similar to a work breakdown structure (WBS). In Asana, you can include these as tasks and sub-tasks. 

Task dependencies: Tasks that either block, or are blocked by, other tasks. 

Task duration: An estimate of how long each deliverable will take based on previous experience, past projects, or industry standards. 

Total float: The amount of time you can delay a task without impacting your project timeline. This is the number of days between the earliest possible start date of a task and its latest possible start date. 

Free float: How long you can delay a task without impacting the next task in your timeline. This is the number of days between the earliest start of the next task and the earliest possible finish date of the current task.

A label to identify critical vs. non-critical tasks: Tasks in the critical path have zero float—meaning you can’t change their due dates without impacting your entire project timeline. Tasks in the non-critical path have more wiggle room and you can delay them without throwing your project off track. To distinguish the critical and non-critical path even further, you create separate sections in your template. 

A date range for each task: The time span you have to accomplish each deliverable, based on dependencies and the duration of the task. When you use your critical path method template, this is one of the last fields to fill out as you plan your project timeline. 

Integrated features

Timeline View . Timeline View is a Gantt-style project view that displays all of your tasks in a horizontal bar chart. Not only can you see each task’s start and end date, but you can also see dependencies between tasks. With Timeline View, you can easily track how the pieces of your plan fit together. Plus, when you can see all of your work in one place, it’s easy to identify and address dependency conflicts before they start, so you can hit all of your goals on schedule.

Dependencies . Mark a task as waiting on another task with task dependencies. Know when your work is blocking someone else’s work, so you can prioritize accordingly. Teams with collaborative workflows can easily see what tasks they’re waiting on from others, and know when to get started on their portion of work. When the first task is completed, the assignee will be notified that they can get started on their dependent task. Or, if the task your work is dependent on is rescheduled, Asana will notify you—letting you know if you need to adjust your dependent due date as well.

Custom fields . Custom fields are the best way to tag, sort, and filter work. Create unique custom fields for any information you need to track—from priority and status to email or phone number. Use custom fields to sort and schedule your to-dos so you know what to work on first. Plus, share custom fields across tasks and projects to ensure consistency across your organization. 

Start dates . Sometimes you don’t just need to track when a to-do is due—you also need to know when you should start working on it. Start times and dates give your team members a clear sense of how long each task should take to complete. Use start dates to set, track, and manage work to align your team's objectives and prevent dependencies from falling through the cracks.

Clockwise . With the Clockwise + Asana integration, you can add Asana tasks as time blocks in your Google Calendar. The Clockwise + Asana integration allows you to specify the duration of tasks, when they happen, and whether Clockwise can automatically reschedule them. Add tasks to your calendar and make time to get work done.

Loom . Loom videos help you add personality, context, and clarity to your Project Overview. You can easily embed Loom videos to explain your project, set expectations, and highlight key milestones. A Loom video message adds nuance and context to get your team up to speed on the project faster. The best part is—your team can watch the videos without leaving Asana.

Salesforce . Remove bottlenecks by enabling sales, customer success, and service teams to communicate directly with their support teams in Asana. Share attachments and create actionable, trackable tasks for pre-sales needs. With Service Cloud, connect your implementation and service teams with supporting teams in Asana to deliver amazing customer experiences.

GitHub . Automatically sync GitHub pull request status updates to Asana tasks. Track progress on pull requests and improve cross-functional collaboration between technical and non-technical teams, all from within Asana.

Who should I share my critical path method template with?

As a manager, you can share your critical path method template with team members to help them prioritize and plan tasks for every project. Once you create and fill out your template, you can also share it with project stakeholders to give them insight into why specific deadlines are important and why you’ve prioritized certain tasks within your project timeline.

What types of projects can benefit most from a critical path method template?

Any project with dependencies can benefit from a critical path method template—especially when multiple project activities are happening simultaneously, and it’s difficult to understand how task deadlines will impact your project duration and project completion.

Where can I find more information about the critical path method?

Check out our critical path method (CPM) article to learn more about this project management technique, including detailed steps on how to conduct a critical path analysis during project planning, how to create a network diagram, and the differences between CPM, PERT charts , and Gantt charts . 

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Critical Path Method (CPM)

Jul 13, 2014

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Critical Path Method (CPM). David S.W. Lai Sept 9, 2013. Example. from Shtub , Bard, Globerson , Project Management, 2 nd Edition, Pearson, 2005. Activity-on-Node Network. 30. 3. 5. 0. 8. A. D. G. END. K. 15. 7. 2. 0. B. E. H. Start. 10. J. 25. 1. 4. C. F. I.

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Critical Path Method (CPM) David S.W. Lai Sept 9, 2013

Example from Shtub, Bard, Globerson, Project Management, 2nd Edition, Pearson, 2005.

Activity-on-Node Network 30 3 5 0 8 A D G END K 15 7 2 0 B E H Start 10 J 25 1 4 C F I Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

Earliest Start and Earliest Finish 30 3 5 0 8 A D G END K 15 7 2 0 B E H Start 10 J 25 1 4 C F I Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

Latest Start and Latest Finish 30 3 5 0 8 A D G END K 15 7 2 0 B E H Start 10 J 25 1 4 C F I Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 30 3 5 0 8 A D G TS = 0 FS = 0 END K 15 7 2 TS = 16 FS = 0 TS = 0 FS = 0 TS = 1 FS = 1 0 B E H Start 10 J 25 1 4 C F I TS = 0 FS = 0 TS = 16 FS = 16 TS = 0 FS = 0 TS = 0 FS = 0 Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

TS = 8 FS = 8 TS = 1 FS = 0 TS = 1 FS = 0 TS = 0 FS = 0 TS = 0 FS = 0 30 3 5 0 8 A D G TS = 0 FS = 0 END K 15 7 2 TS = 16 FS = 0 TS = 0 FS = 0 TS = 1 FS = 1 0 Critical Path B E H Start 10 J 25 1 4 C F I TS = 0 FS = 0 TS = 16 FS = 16 TS = 0 FS = 0 TS = 0 FS = 0 Notations ES: Earliest Start LS: Latest Start TS: Total Slack EF: Earliest Finish LF: Latest Finish FS: Free Slack

Exercise Question: Determine the critical path and the slacks. Interpret their meanings. To check your solution: The critical path is (C, I). The project duration is 14 days. from Shtub, Bard, Globerson, Project Management, 1st Edition, Prentice-Hall, 1994.

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