critical path method case study

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Use cases for the critical path method

Learn how the critical path method can be used with our clear set of examples that apply the project management technique to various use cases.

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Jan 12, 2023

The critical path method (CPM) is a complex project management technique that works well in a diverse range of use cases. Used to determine a project’s critical activities, CPM helps project managers efficiently schedule their work timeline in order to meet deadlines with minimum costs . CPM has a varied list of applications:

• Planning and releasing a new product;
• Installing and debugging an IT system;
• Manufacturing and assembling job-lot machines;
• Constructing a building or highway;
• Research and engineering design projects;
• Scheduling ship construction and repairs.

But why is critical path analysis a good fit for such examples? Our blog post will cover the answer to this question and also provide a set of clear, actionable examples that you can start from to analyze and schedule your project plans.

You can download the sample templates as PowerPoint files for free and customize them either manually or automatically, with the Office Timeline add-in.

For what type of projects is the critical path method suitable?

The critical path method proves to be an efficient approach for managing projects that share the following essential characteristics:

• They are repeatable in nature and rely on a well-known activity time period.
• They consist of a well-defined series of tasks ( activities ) which, once completed, indicate the end of the initiative.
• The project’s ancillary tasks may be started or stopped independently of one another. This prerequisite reduces the restrictions of a continuous-flow process, where operations have to occur in a successive order without any slack.
•  The project’s essential tasks are arranged in clear, logical sequences . For instance, in the construction of a house, the foundation must be laid before the walls are erected.

How was the critical path method first used?

Developed in the late 1950s, the critical path method was first used by the American company DuPont to reduce the downtime for maintenance at its Louisville plant, which produced an intermediate product in the neoprene process. CPM allowed DuPont engineers to analyze the maintenance schedule and cut downtime for maintenance from 125 to 93 hours.

The project management technique also highlighted other possible refinements that further reduced total time to 78 hours. As a result, the intermediate was no longer a bottleneck in the overall neoprene production process, and the performance of the plant increased by approximately one million pounds in 1959.

How do you use the critical path method in project management?

There are six key steps to successfully applying the critical path method in project management:

• Identify each task in your project.
• Organize all your tasks in sequences and define dependencies between them.
• Create a network diagram, also known as a critical path analysis chart , to illustrate the activities and dependencies mapped out at the two previous steps.
• Estimate the duration of each task (the time necessary to complete each activity).
• Determine your project’s critical path by looking at the longest activity sequence needed to complete the initiative.
• Create work schedule and show progress by updating the critical path diagram.

Practice the steps above with concrete examples using our guide on how to identify a project’s critical path . To speed up the process, you can choose to use one of the best critical path analysis software we’ve reviewed for you.

Applied examples of the critical path method

To help you understand how various types of projects can lend themselves to analysis by CPM, we have prepared three critical path diagram use scenarios:

1. Critical Path Construction Template

This PowerPoint critical path template for construction projects visually represents the minimum amount of time required to complete the given initiative.

By highlighting the critical tasks in red, the chart clearly indicates the critical path to follow and which activities cannot be delayed without negatively impacting the project.

2. Project Management Critical Path Template

The project management critical path template for PowerPoint provides a visual representation of a project’s work breakdown structure, with project stages and tasks, importance for each activity, and timeline bar.

By showing the critical tasks in red and the durations for each of them based on their start and end dates, the chart helps you create a clear schedule of the work to be done and efficiently manage your project plan.

3. Event Management Critical Path Template

Use this PowerPoint template to identify the critical path for your event planning activities and to make sure you complete work on time.

Reflecting the steps in an event management process along with task predecessors, the chart shows you which activities cannot be delayed and which ones are flexible.

Edit the template to add your time-bound parameters and set how much slack time you can allow for your tasks without exceeding your event deadline.

FAQs about using the critical path method in project management

Let’s find out the answers to some of the most frequently asked questions about the critical path method.

What are the applications of the critical path method?

The critical path method can be used to manage a variety of projects, ranging from construction and manufacturing to software development and event planning. However, any project with dependencies can benefit from this project management technique, especially when multiple project tasks occur simultaneously and it is hard to visualize how their deadlines can impact your project’s duration and chance of completion.

Is the critical path method right for my project?

In some cases, yes. The critical path method can be your go-to approach if the following statements are factual about your project:

• It relies on many interdependent tasks – if the evolution of one task depends on another one’s output, then CPM can help you manage these interrelations and keep your schedule on track.
• Project tasks have tight deadlines – since it focuses on identifying and managing your project’s critical path (the sequence of activities that must be finished on time for the project to be completed at the target date), CPM can help you prioritize tasks, allocate resources accordingly, and quickly detect and address potential disruptions.

When to use CPM and when PERT?

The critical path method (CPM) and Project Evaluation and Review Technique (PERT) were both developed in the 1950s. Both of them analyze a project’s list of required tasks, estimated duration for each task, and task dependencies .

However, the main difference between the two resides in their level of certainty around activity durations , because PERT is used to estimate the time required to complete activities, whereas CPM is used when the activity durations are already estimated. In other words, PERT is generally used to manage uncertain project activities, whereas CPM manages predictable project activities. PERT also focuses on meeting or reducing a project’s duration, while CPM focuses on time-cost trade-offs.

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Critical Path Method in Project Management (Examples & How-To)

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Last updated on 30th June 2023

In this article we’re going to take a look at the Critical Path Method and answer the question: What is a critical path in project management?

Project management is the future. According to Harvard Business Review , by 2027 around 88 million people worldwide are likely to be working in project management, and the value of project-oriented economic activity will have reached $20 trillion. 

Research also shows that the majority of projects – around 65% – are unsuccessful . In other words, most projects fail and a lot of time and money is wasted. 

To avoid this failure, project managers need to manage projects effectively. And that’s where the critical path method comes in. 

So, let’s get into it…

What is the critical path method? A definition

The Critical Path Method (also known as CPM) is a project management technique that helps you manage your project efficiently by calculating the shortest route to entire project completion. 

The idea is that you identify all of the tasks required to complete your whole project, and then map out your tasks so that you can schedule your project in the most productive way and get an accurate project timeline. 

The Critical Path Method is ideal for complex projects that have a lot of moving parts. By breaking a big project into smaller, more manageable tasks project managers can gain a better understanding of how to get from point A – Z in the most efficient way. 

The history of the critical path method

Critical path finds its origins in the 1950s at the DuPont company . DuPont is a multinational chemical company, and has been involved in everything from developing Teflon to even playing a major role in the Manhattan Project.  

Two mathematicians (James Kelley and Morgan Walker) who were working at the DuPont company in 1957 are credited with developing the critical path algorithm. They were looking for ways to avoid the costs of plant shutdowns and restarts caused by inefficient scheduling. Their research found that if they focused their efforts on performing the right tasks at the right times, they could avoid these issues. And so, CPM was born! 

Prior to this, the company was simply flooding every problem they had with more labour in order to try and stay on schedule. By implementing the brand new critical path method instead, DuPont was able to save 25% on shutdowns .

How to implement critical path in project management

1. define the scope of the project .

The first step towards implementing the critical path method is defining the scope of your project. This means understanding all the tasks that need to be completed in order for you to consider your project a success. 

So, for step one, make a list of all your project tasks. Pretty simple! 

2. Divide your tasks 

Step two involves looking at those tasks in more detail and dividing them up so you can better understand the when, who, and how of the tasks for your project. 

This is important because some tasks will be critical tasks, some will be dependent tasks, and some tasks will be fine to work on in tandem. As a quick example, if you’re making a chicken sandwich then you can toast your bread at the same time as preparing your salad and/or sauce, but you can’t do either of those things unless the chicken is already cooked. So, the remaining tasks are dependent on the first task of cooking the chicken. 

Once you get the hang of it, the critical path method can be used for pretty much everything! 

3. Calculate the shortest route to completion  

Step three – the final step – is about finding your project’s critical path. In other words, scheduling your tasks to calculate the shortest route to completion. CPM is all about efficiency, so if you can work on tasks in parallel then you absolutely should in order to complete the project in the shortest amount of time. 

It can help to assign durations to your tasks here so that you can get a better understanding of how long everything will take. Sticking with the very simple chicken sandwich analogy, this would look something like this:

This is a very simple example of a project’s critical path, but hopefully you get the idea! 

Critical Path Method examples

Now let’s take a look at some more concrete examples of the critical path method in action.  

We’re going to give both a personal and professional example to really look at CPM from all sides and gain the best possible understanding of how to apply it when it comes to managing complex projects.

Planning a family holiday

Planning a family holiday involves a lot of different tasks, some of which can be done in tandem, while others are dependent tasks. 

The first thing you need to do is make a list of the tasks for your whole project. For example: 

• Research different locations
• Find accommodation 
• Book flights
• Book airport transfers
• Buy sunglasses
• Pack suitcase

And anything else you might want to add to the above list! 

The next step is to divide your tasks up, so Mum can be in charge of the location research and booking accommodation, Dad can be in charge of booking flights and airport transfers, and so on. 

This is also where it’s important to identify those tasks that are dependent on one another. So, for example, the airport transfers cannot be booked before the flights or accommodation. But you can shop for sunglasses and pack your suitcase at any time! 

The critical path for this project could look something like this: 

Creating an explainer video

Now for a professional example. We know all about managing explainer video projects because that’s actually how Project.co first came to be! More on that here if you’re interested . 

The tasks required for an explainer video project are: 

• Storyboarding
• Voiceover recording

Again, after listing these tasks the next step is to define and allocate them, and also find out which can be done in tandem. For example, the storyboarding process cannot start without the script. But once the script has been finalised, the voiceover can be recorded in tandem with the storyboard being created. 

If we were to calculate the critical path for an explainer video project it might look a little something like this: 

And that’s that! Why not try following these 3 steps for planning different projects in your life? It’s a great way to get used to the critical path method. 

5 Tips for successful critical path management 

1. use a project management tool .

Implementing the critical path method successfully relies on project managers having the best visibility of all tasks (critical tasks, dependent tasks, basically every single task required throughout the entire project!). Project management software can be very useful here. 

The best project management tools – like Project.co ! – allow you to not only view your tasks in a number of different ways, but allocate them to different team members, add files, notes, priority tags, and so much more. 

Project.co allows you to manage as many different projects as you want with an easy-to-use interface that you can customise to match your branding. You can also invite your clients and stakeholders to collaborate. 

2. Delegate responsibilities

Another key component of CPM is understanding who is responsible for what. This is crucially important if you have multiple tasks being completed in tandem, and it’s also necessary for dependent tasks (as team members need to know when it’s their turn to step in so that they can manage their schedule successfully). 

For project managers, this means delegating these responsibilities and overseeing the schedule to make sure everything is moving smoothly along the critical path. 

Again, project management software can help here because it makes it easy to view your entire team’s tasks at a glance. 

Project.co offers a number of ways to visualise your tasks, including kanban, list view, calendar, or the scheduler view (seen above) which allows you to view multiple team members’ tasks all on one screen.

3. Map out your project visually

Visualising your project will help you to understand how to get from point A to point Z in the quickest way possible, which is what CPM is all about. 

When using the critical path method, one of the best ways to map out your project visually is with a Gantt chart. 

A Gantt chart is essentially a bar chart that illustrates your project schedule. You can see when each task is due, which tasks are dependent on one another, and which can be completed in tandem. 

4. Create predictions

As much as we all wish for every project to sail through with no issues, the likelihood is that something unexpected will pop up. The best way to prepare for this is to make some predictions for what could go wrong and make a plan for what would happen if it did. 

We’d recommend creating a list of assumptions and risks for your project before getting started. It’s also helpful to create a list of resources that you will need so that you have a clear understanding of the scope of your project before getting started. 

5. Assign a project leader 

The critical path method is all about efficiency, which means there’s going to be a lot of moving parts at any given time. It’s important for everyone involved to be focused on their own tasks to ensure that there are no bottlenecks and the project moves forward smoothly. But, additionally, it’s also important for one person to oversee the project to ensure everything stays on track. 

In other words, to successfully implement the critical path method in project management you should assign a project leader whose sole responsibility is making sure that everyone else is managing their tasks. 

Most projects see a couple of hiccups along the way, and it’s the job of the project leader to manage these setbacks as and when they occur so that your project can still be completed as quickly and efficiently as possible.

Final thoughts

Project management techniques like the critical path method help you keep your projects on track so you can complete more projects on time and on budget. 

Interested in finding out about some more project management techniques? Take a look at this next: 10 Best Project Management Techniques for PMs in 2023 . 

Written by Samantha Ferguson

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

• Critical path method: getting started in CPM & CPA
• Understand the CPM
• What is the CPM and what is a critical task?
• CPM definition
• The critical path algorithm explained
• Float or slack in project management
• What are the benefits of CPM?
• How to use the CPM
• A step-by-step method for using the CPM
• CPM vs. gantt chart
• CPM vs. pert
• Use critical path for better project management

Browse more blogs

Originally published May 22, 2022. Updated June 5, 2024

Critical Path Method: Getting Started in CPM & CPA

Our CPM guide includes everything you need to get started with the Critical Path Method - step-by-step examples, solutions, and schedules to help you complete your next project 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 formula and apply it to your projects.

Early iterations of the Critical Path Method can be traced 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 several techniques to ensure 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.

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

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

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 size or budget, has some core tasks crucial to completion. A task is defined as critical if it is delayed, slowing 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

To make a good omelet, you need to perform several other tasks. You have to season the eggs with salt and pepper. You could add some vegetables and cheese. You could also 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. You'll still have an omelet even if you don’t perform them. It's not a very good one, but it's an omelet nonetheless.

On the other hand, if you forget to beat the eggs, heat the pan, or cook the eggs, you will have nothing but a cold pan and two eggs.

The three steps in the recipe describe the critical tasks necessary to make the omelet-making project a success.

The sequence of these steps describes the critical path a new cook must take 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 project's duration.”

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 must do it sequentially.

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

In any project, there will be 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 requires different amounts of time and resources. For example, 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 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 the critical path sequence is delayed, your project will also suffer.

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, duration, and finish time to determine 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), 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 lasts 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 shows 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 are called “free float.”
• Any delay in the overall project is called “total float.”

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

However, plenty of other activities in the project 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 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 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 use it. However, 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.

Therefore, the first step of the CPM process 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 all.

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 and 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 10 minutes to paint a 2’ x 2’ board (4 sq ft), you can estimate that it will take 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 confidence.

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

List each activity's duration (t) 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, totaling 90 hours.

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

Hence, B, C, and 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 is 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.

WHY MUST NON-CRITICAL TASKS BE MONITORED?

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 before the project can 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 the 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 to be used as a guide for future projects.

The critical path method example above shows that 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 , which includes critical path method 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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The Ultimate Guide to the Critical Path Method

By Kate Eby | April 30, 2015

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In this article, you’ll learn the meaning of the critical path method, and how this method is used in project management. We’ve interviewed leading experts to help explain the key advantages of the critical path method.

Included on this page, you’ll find the six steps in the critical path method , the easiest way to find the critical path , and the best critical path software to use with step-by-step instructions.

What Is the Critical Path Method (CPM)?

CPM is a step-by-step project management technique to identify activities on the critical path. The approach breaks a project into work tasks, displays them in a flow chart, and then calculates the project duration based on estimated time frames for each. It identifies tasks that are critical, time-wise.

The text, A Guide to the Project Management Body of Knowledge (PMBOK ® Guide), an internationally recognized collection of processes and knowledge areas accepted as best practice for the project management profession, defines the critical path as “the sequence of scheduled activities that determines the duration of the project.” It is the longest sequence of tasks in a project plan that must be completed on time in order for the project to meet its deadline. If there is a delay in any task on the critical path, then your whole project will be delayed. Although many projects have only one critical path, some projects may have multiple critical paths.

Dr. Larry Bennett , a civil engineer, project manager, and author of four books, including a guide on critical path written in 1978 and titled, “ Critical Path Precedence Networks ,” explains that the critical path method helps manage projects in two different ways: “It produces a planned schedule to guide the project team, and it forms the basis for tracking project schedule performance by comparing actual with planned task progress.”

The Critical Path Method According to Two Experts 

We asked two critical path users for the best way to explain it. Here's what they had to say:

"The critical path is just a fancy way of saying 'How long does each task take before you can finish the project? Use this information to figure out the project's end date.' If a task takes longer than anticipated, the end date is pushed back. There are some tasks that don't immediately impact the project's end date that can be pushed back for some time. There are a whole bunch of calculations that go into figuring out what-ifs, forecasting, and scheduling, but that's where project management software comes in and makes everyone's lives easier. "

Rachel Burger , Capterra Construction Twitter:  @CapterraBuilder

"Some of the activities must happen in parallel. For example, if you tried to make a fried breakfast by doing one task at a time, and one after the other, things would go wrong. The plates need to be warming while other activities are going on. The toast needs to be toasting while the sausages are frying, and at the same time the bacon and sausages are under the grill. The eggs need to be fried last. A critical path analysis is a diagrammatical representation of what needs to be done and when. Timescales and costs can be applied to each activity and resource." Terence Jackson , Ph.D and CEO/Managing Partner at WEpiphany LL

“To learn about combining CPM with PERT for more comprehensive scheduling option, see this guide to combining PERT and CPM .”

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Background & History of Critical Path

Dr. Bennett is no stranger to critical path. He has applied critical path scheduling to a wide variety of projects since 1965. He has also spent 29 years on the engineering faculty at the University of Alaska Fairbanks, teaching undergraduate and graduate courses in technical management, including project management and scheduling.

In addition to his books , he has written more than 50 professional papers and articles on topics ranging from construction management to network techniques for project scheduling. 

Dr. Bennett points out that critical path has come a long way. In fact, the original critical path method was done by hand. As Dr. Bennett describes it: 

“The original critical path method used arrows to represent tasks and tied them together by connecting their beginning and end at nodes, so that proper sequencing was developed. This approach persisted for a decade, when a different method, with the same results, became popular. Professor John W. Fondahl, a professor of construction management at Stanford University, proposed in a 1961 paper that each task be represented by a node – square, circle, or oval – and the nodes be tied together with lines or arrows representing the sequence between tasks. This approach, referred to as the activity-on-node (AON) or precedence method, caught on rapidly and has supplanted the earlier activity-on-arrow (AOA) method in nearly all uses.”

How the Critical Path Method Was Created 

Using the critical path method to schedule projects began in the late 1950s, with two simultaneous, unrelated projects. The US Navy’s Fleet Ballistic Missile (Polaris) Program was behind schedule and needed help resolving the problem. The suggested solution was to divide the project into several thousand tasks, represent each task by an arrow, connect the arrows in proper sequence, estimate the duration of each task, and calculate the project duration and the degree of schedule criticality of each task. 

At about the same time, the EI DuPont de Nemours Company, an American chemical company, was experiencing delays in its plant turnarounds, a project to rearrange production facilities for different products. They, too, needed help and the proposed answer was similar to that of the Polaris Program. 

The developers of the Polaris Program’s approach called their solution the Project Evaluation and Review Technique (PERT), while the DuPont method was called Critical Path Method (CPM).  Although these methods are similar, they used different techniques for estimating task duration. 

The PERT method used three different time estimations for each task duration and calculated the probability of project completion by any given time. The DuPont approach used one time duration for each task; it was concerned not only with project completion time, but also with analyzing the extra costs that would accrue if the project duration were decreased.  

Dr. Bennett says that today, “the terms PERT and CPM are used interchangeably, both meaning any network scheduling method and PERT having lost its inclusion of three time estimates and probabilities.”

The Everyday Advantages of Critical Path

Although it originated in the late 1950s, critical path is still incredibly important to project managers today. It provides a visual representation of project activities, clearly presents the time required to complete tasks, and tracks activities so you don’t fall behind. The critical path method also reduces uncertainty because you must calculate the shortest and longest time of completion of each activity. This forces you to consider unexpected factors that may impact your tasks and reduces the likelihood that an unexpected surprise will occur during your project.

According to Dr. Bennett, the critical path method also has three main benefits for project managers:

• Identifies the Most Important Tasks:  First, it clearly identifies the tasks that you will have to closely manage. If any of the tasks on the critical path take more time than their estimated durations, start later than planned, or finish later than planned, then your whole project will be affected. 
• Helps Reduce Timelines: Secondly, “if, after the initial analysis predicts a completion time, there is interest in completing the project in a shorter time frame, it is clear which task or tasks are candidates for duration reduction,” said Dr. Bennett. When the results from a critical path method are displayed as a bar chart, like a Gantt chart, it is easy to see where the tasks fall in the overall timeframe. You can visualize the critical path activities (they are usually highlighted), as well as task durations and their sequences. This provides a new level of insight into your project’s timeline, giving you more understanding about which task durations you can modify, and which must stay the same. 
• Compares Planned with Actual: And lastly, Dr. Bennett says the critical path method can also be used to compare planned progress with actual progress. “As the project proceeds, the baseline schedule developed from the initial critical path analysis can be used to track schedule progress.  Throughout a project, a manager can identify tasks that have already been completed, the predicted remaining durations for in-progress tasks, and any planned changes to future task sequences and durations.  The result will be an updated schedule, which, when displayed against the original baseline, will provide a visual means of comparing planned with actual progress.”

Experts Share the #1 Advantage of Critical Path   

"For me, the biggest advantage of the critical path method is that it makes risk assessment easy. If I’ve got dependencies laid out and plans change, it’s very easy to say, 'Because you missed that deadline, the next deliverable is going to be late by X days, and that puts us beyond our plan by Y days.' Simple. That said, I don’t think you have to fully adopt a method like critical path to do this on projects. It’s best to adopt the parts of any method that work for your project and your team—being adaptable as a PM will help you find true success."

Brett Harned,  digital project management consultant , writer, speaker, and community builder.

Twitter:  @BrettHarned 

"Two issues that continue to plague projects are the competing priorities of cross functional team members and distractions from 'noise' on the project.  With so much activity, the critical path enables a clear, pointed view of what must happen next and 'who is on the clock' for meeting project commitments."

Robert Kelly, co-founder of  @PMChat  and managing partner of  Kelly Solutions , a project management firm. 

Twitter:  @rkelly976

"I especially like the 'unintended benefits' critical path (CP) analysis brings, including discoveries of hidden dependencies and resource conflicts. CP analysis also often leads to better prioritization and redistribution of team-members.  And CP can expose the needs / opportunities for inserting lags / leads to further improve the schedule."

Jeff Furman, PMP, author of  "The Project Management Answer Book"

Twitter:  @PMAnswerBook  

"The critical path method brings an important level of clarity to your project. It is a visual depiction of the fragility of the balance of your constraints: If one of the activities on the path gets delayed, your project gets delayed. It is also a great way to determine where to invest resources if the project has fallen behind schedule."

Cesar Abeid,  host of the Project Management for the Masses Podcast

Key Steps in the Critical Path Method

There are six steps in the critical path method: 

Step 1: Specify Each Activity

Using the work breakdown structure, you need to identify each activity (or task) involved in the project. This activity specification list should only include higher-level activities. When detailed activities are used, the critical path analysis may become too complex to manage and maintain. 

A work breakdown structure breaks down projects into manageable sections. 

The first step is to identify the main deliverables of a project. Then you can start breaking down the high-level activities into smaller chunks of work. 

You can choose how to display your work breakdown structure. Some people use a tree structure, while others use lists or tables. An outline is one of the easiest ways to represent a work breakdown structure.

Step 2: Establish Dependencies (Activity Sequence)

Some activities will depend on the completion of others. Listing the immediate predecessors of each activity will help you identify the correct order. To correctly identify activities and their precedence, ask yourself these three questions for each activity on your list from step one: 

• Which task should take place before this task happens?
• Which tasks should be finished at the same time as this task?
• Which tasks should happen right after this task?

Step 3: Draw the Network Diagram  

Once you have identified the activities and their dependencies, you can draw the critical path analysis chart (CPA), known as the network diagram. The network diagram is a visual representation of the order of your activities based on dependencies.

This critical path diagram used to be drawn by-hand, but there are now software programs that can create this diagram for you. 

Step 4: Estimate Activity Completion Time

Using past experience or the knowledge of an experienced team member, you must now estimate the time required to complete each activity. If you are managing a smaller project, you will most likely estimate time in days. If you are working with a complex project, you may have to measure time in weeks.

If you don’t feel comfortable using your best-guess estimates, you can use the 3-point estimation method, which is designed to put more weight on the most realistic timeframe. 

In three-point estimation, you must come up with three time estimates for every task, based on prior experience or best guesses. The estimation method is presented in formulas in order to calculate the time duration more accurately. 

a = the best-case estimate m = the most likely estimate b = the worst-case estimate 

These three values identify what happens in an optimal state, what is the most likely, and what happens in the worst case scenario. 

Once you’ve identified these values, you can use them in two different formulas. The first is used to find the Weighted Average, which puts more weight on the “Most Likely” value. The formula is as below. E stands for Estimate, and the 4 and 6 represent the standard method to place more weight on the most realistic value. 

E = (a + 4m + b) / 6

The second way of using these values is known as Triangular Distribution. The main difference is that this method doesn’t put more weight on the “Most Likely” value. The formula is as below. E stands for Estimate, and the 3 represents the standard method.

E = (a + m + b)/3

Step 5: Identify the Critical Path   

There are two ways you can now identify the critical path. You can eyeball your network diagram and simply identify the longest path throughout the network -- the longest sequence of activities on the path. Be sure to look for the longest path in terms of longest duration in days, not the path with the most boxes or nodes. 

You can also identify critical activities with the Forward Pass/Backward Pass technique, identifying the earliest start and finish times, and the latest start and finish times for each activity. 

If you have multiple critical paths, you will run into network sensitivity. A project schedule is considered sensitive if the critical path is likely to change once the project begins. The more critical paths in a project, the higher the probability of a change in schedule. 

Step 6: Update the Critical Path Diagram to Show Progress 

As the project progresses, you will learn the actual activity completion times. The network diagram can then be updated to include this information (rather than continuing to use estimations).

By updating the network diagram as new information emerges, you may recalculate a different critical path. You will also have a more realistic view of the project completion due date and will be able to tell if you are on track or falling behind.

Other Scenarios in the Critical Path Method

One of the biggest benefits of the critical path method is identifying the crucial tasks that, if missed, will impact your project’s completion date. It will also provide visibility into your project’s status, allowing you to see if you are on track. 

Shortening Your Schedule

As you’re going through the critical path method, you may find that you want to intentionally shorten the duration of your project or that you need to compress your project schedule in order to meet the deadline. There are two ways to do this: fast tracking or crashing.

Fast Tracking 

In fast tracking, you look at the critical path and decide which activities can be done parallel to each other, to move the project along faster. You only need to review the activities on the critical path because all the other activities have float (if you shorten the duration of those activities, you’re only giving them more float). 

While fast tracking reduces your project timeframe, it also involves risk because you are performing parallel activities that were originally planned to be performed in sequence. 

Crash Duration 

Crash duration, or crashing, refers to the shortest possible time for which an activity can be scheduled. This happens by adding more resources to completing that certain activity. However, crashing the critical path results in lower quality of work because the goal in crash duration is speed.

Managing Resource Constraints 

As you manage your project, you may also run into resource constraint issues that could change the critical path. If you try to schedule certain activities at the same time, you may find that you need more people than are available. As a result, those activities will need to be rescheduled. Resource leveling is the process of resolving these conflicts. 

Resource Leveling and Expansion 

With resource leveling, you can resolve conflicts over allocating resources. A resource-leveled schedule may include delays due from resource bottlenecks (a resource being unavailable at the necessary time). 

Resource leveling may also result in a previously shorter path becoming the longest or most “resource critical” path. This happens when the tasks on the critical path are affected by resource constraints. 

A similar concept is called the critical chain, which protects activity and project durations from unexpected delays due to resource constraints. 

Assessing the Final Project

These scenarios demonstrate all the unexpected changes that can occur when managing a project, and how they can affect the critical path. While things are always subject to change, the good news is that you can measure the variance from your original project schedule and track how it impacted your final project. 

Flexibility and Assessing Delays

A schedule created from the critical path method naturally involves a lot of fluctuation because you have to use best-guess estimates to calculate time. If one mistake is made in activity completion time, your whole critical path schedule could change. Or, you may need to purposefully delay project activities due to resource constraints. 

Sorting out these delays and determining what caused them can help you avoid similar issues in the future. An important part of your post-project plan is the As Built Critical Path, which analyzes the specific causes and impacts of changes between the planned schedule and actual schedule implemented. The As-Built Critical Path is a schedule that shows the dates that the activities actually occurred and allocates time by determining the responsibility for the delays on the critical path. 

Critical Path Software

When the critical path method was first developed, you had to identify the critical path by hand, drawing the network diagram with “nodes” to present the stages of a project and connecting the nodes with arrows or “arcs.” 

However, drawing nodes, tables, and arrows can be a time-consuming, difficult task, especially when things are constantly changing at the beginning of a project.

Rather than relying on hand-draw diagrams, there are a number of project management software programs available today that will do the work for you and identify the critical path with the click of a button.

Here are two different tools with critical path features:

Find the Critical Path with Microsoft Project

You can display the critical path in the Gantt chart view of Microsoft Project.

First, you must enter all your tasks, their start and end dates, the duration of each task, and identify the predecessors. Then, you can adjust the view of your MS Project file to display the critical path.

• Click View > Gantt Chart.
• Click Format and then select the Critical Tasks check box.  

Tasks on the critical path now have red Gantt bars.

Identify Critical Path in Other Views

You can see the critical path in any task view by highlighting it.

• Click the View tab and select a view from the Task Views group.
• Staying within the View tab, click Critical from the Highlight list. The critical path shows up in yellow.
• To see only the tasks on the critical path, click the Filter arrow and select Critical .  

In a network diagram, tasks on the critical path automatically show up in red. No highlighting is needed.

See the Critical Path in a Master Project

Entire subprojects can be on the critical path when you’re managing a master project. To identify subprojects on the critical path, you can adjust Microsoft Project to treat the subprojects like summary tasks.

• Click File > Options .
• Select Schedule and then scroll down to the Calculation options for this project .  

Make sure the Inserted projects are calculated like summary tasks box is selected.

Change the Tasks on the Critical Path

Critical tasks typically have no slack. However, you can tell Microsoft Project to include tasks with one or more days of slack on the critical path, so you can identify any potential problems that may arise.

• Click Advanced , then scroll down to the Calculation options for this project area.
• Add a number to the Tasks are critical if slack is less than or equal to box.  

Identify the Critical Path in Seconds with Smartsheet

Smartsheet, a work management and collaboration tool in a spreadsheet layout, offers a pre-formatted Gantt chart template  to make it even easier to find the critical path.

With this pre-made Gantt chart template, complete with sections, sub-tasks, and sub-sub-tasks already formatted, all you need to do is enter your own project planning information. A Gantt chart will automatically be made for you, and with the click of a button, you can identify the critical path on the Gantt chart.

Here’s how to find the critical path in Smartsheet, using a Gantt chart template:

1. Choose a Gantt Chart Template

• Go to Smartsheet.com and login to your account (or start a free 30 day trial ).
• From the Home screen, click Create New and choose Browse Templates .
• Type “dependencies” in the Search Templates box and click the magnifying glass icon.
• Select the Basic Project with Gantt & Dependencies and click on the blue Use Template in the upper-right corner.
• Name your template, choose where to save it, and click the OK button.  

2. List Your Task Information

A pre-made, formatted template will open with sample content filled in for reference. This section is where you add your activities, or tasks, from your work breakdown structure. This is also where you can show the hierarchy, or relationship, between tasks.

The yellow cells at the top are there simply for instructional reference. To delete them, right-click on each yellow box and select Delete Row .

• Add your tasks under the Task Name column.
• Use the cells named Section 1, Section 2, and Section 3 to establish hierarchy (for more information on hierarchies, click here ).
• If you need to delete a row, right-click on the cell in the row you’d like to delete and select Delete Row .  

On the left side of each row, you can attach files directly to a task or start comments with a colleague about a task, adding more context to your project.

3. Provide Start and End Dates

Add start and end dates for each task. If you click and drag either end of a green task bar on the right in the Gantt view, Smartsheet will automatically change the matching dates in the task table.

• Select a cell in the Start Date or End Date column.
• Click on the calendar icon and choose a date.  

You can also manually enter a date in the cell. Smartsheet will automatically calculate the duration of each task for you.

4. Add % Complete and Assigned To Information

The % Complete and Assigned To columns provide more context around your project. In the Gantt view on the right side, you can quickly see how much of a task has been completed by the length of the thin grey bars inside the task bars.

The Assigned To column allows you to assign the task to a particular team member, providing visibility into who is doing what.

• In the % Complete column, enter the percentage of work complete for that task. Enter a whole number and Smartsheet will auto-fill the percentage sign.
• In the Assigned To column, choose a name from the drop-down menu or manually enter a new name.

5. Establish Predecessors

Predecessors are used to create dependencies between tasks (identifying which tasks need to happen before or after another task).

• On the far-left of the sheet, each row is assigned a number. In the Predecessor column, enter the row number that represents the row of the preceding task. This will create a link from the current row (the dependent task) to the specified row (the predecessor task).
• Enter the row numbers of all other predecessors in the Predecessor column.  

You can also create predecessor dependencies from the Gantt chart on the right. Drag the bottom, right-corner of a Gantt bar down to the Gantt bar of the task that should follow it. The Predecessor column will be automatically updated.

6. Identify the Critical Path

Now that you have created a Gantt chart in Smartsheet, you can identify the critical path on the Gantt chart with the click of a button.

• On the right side of the screen, where your Gantt chart is displayed, click the far-right button that depicts a critical path (the two red Gantt bars).
• On the Gantt chart, the tasks that are on the critical path will be outlined in red.  

How to Import a Microsoft Project File (.MPP) into Smartsheet

Smartsheet works with Microsoft Project, so if you already have your project planning information stored in Microsoft Project, you can easily import that directly to Smartsheet.

• Click the Home tab and click the grey Import button.
• Choose the Import MS Project File .  

• Click Select, choose the file you would like to import, and click Open .
• Click Continue and an Import Settings form appears. Select the row in the form that contains your column headers (it will probably be the first row) and click Import .
• The imported file will appear as a new sheet within Smartsheet. Click on the sheet name to open it.

Studying for the PMP® Exam? Here’s What You Need to Know about the Critical Path Method

To earn your Project Management Professional (PMP) ® credential, you need to pass the PMP exam, a 200-question, multiple choice test offered by the Project Management Institute (PMI).

Critical path is an important part of the PMP Exam and there will certainly be questions about it on the test. You’ll need to be able to draw a network diagram, identify the critical path, use the Forward Pass/Backward Pass technique, and calculate slack.

Here is an overview of the most important things to know about the critical path method to help you pass the PMP exam:

How to Draw a Network Diagram

On the PMP Exam, you will be asked to draw a network diagram. The exam will list all the activities in a project and will tell you when the activities can start. With that information, you’ll be asked to identify the critical path and its duration.

To explain how to draw a network diagram, Bennett has created a sample eight-task project:

• Design Tank Project (10 days) can start right away.
• Construct Tank Foundation (25 days) and Select Tank Supplier (8 days) can start as soon as Design Tank Project is finished.
• Manufacture Tank Components (10 days) can start as soon as Select Tank Supplier is finished.
• Deliver Tank to Jobsite (4 days) can start as soon as Manufacture Tank Components is finished.
• Prepare Installation Drawings (3 days) can start as soon as Select Tank Supplier is finished.
• Assemble Tank (15 days) can start as soon as Deliver Tank to Jobsite, Prepare Installation Drawings and Construct Tank Foundation are all finished.
• Test & Commission Tank (4 days) can start as soon as Assemble Tank is finished.
• After Test & Commission Tank is finished, the project is complete.  

To answer the question, you’ll need to draw a network diagram.

Here’s how:

• Draw a box and label it as your first activity (Design Tank Project). In the box, make sure to write the duration in days (in this case, it is 10 days).
• Begin your diagram by drawing the relationship between Design Tank Project, and Construct Tank Foundation and Select Tank Supplier. You can do this by drawing a box for the other activities, and drawing arrows to these boxes from Design Tank Project.
• Continue drawing boxes to represent activities, and arrows to represent when an activity can begin.  

After you have drawn the network diagram, you will be able to find the critical path. Remember: the critical path is the longest duration path throughout the network in days, not the path with the most boxes.

In this example, the critical path is Design Tank Project, Construct Tank Foundation, Assemble Tank, and Test & Commission Tank, with a total duration of 54 days.

You can identify the critical path by eyeballing the diagram to find the longest duration in days, or you could use the Forward Pass/Backward Pass Technique outlined in the next section.

How to Use the Forward Pass/Backward Pass Technique

The Forward Pass/Backward Pass technique is another way to find the critical path. It is best used when you have multiple branches, or multiple entry points, for an activity. 

You may also need to use the Forward Pass/Backward Pass technique if you are asked to identify the earliest start or finish times, or latest start or finish times, for an activity. Or, to find the slack (or float) for each activity.

Before you start using the Forward Pass/Backward Pass technique, here are some terms that you first need to understand:

• Earliest start time (ES): The earliest time an activity can start once the previous dependent activities are completed.
• Earliest finish time (EF): The earliest start time for the activity plus the time required to complete the activity (the earliest an activity can be completed).
• Latest finish time (LF): The latest time an activity can be completed without delaying the entire project.
• Latest start time (LS): The latest finish time minus the time required to complete the activity.

As you run the Forward Pass/Backward Pass technique through your network diagram, arrange each value according to the following legend (SL stands for slack, which we’ll cover in the next section).

How to Do the Forward Pass: Finding the Earliest Start Time and Finish Time

There are two formulas in the Forward Pass/Backward Pass technique. The first is the Forward Pass formula for you to use as you move from beginning to end in your network diagram (from your first activity to your last). This formula will find the earliest start time (ES) and the earliest finish time (EF) for each activity.

To start the Forward Pass, make the ES of the first task zero. For all other tasks, the ES is the same as its immediate predecessor’s EF.

Use this formula to calculate EF:

EF = ES + Duration

So, for Design Tank Project, the ES is zero and, the EF is 10 (10+ duration of 0). We also know that the ES for Select Tank Supplier is 10 and the EF is 18 (10 + duration of 8). Continue like this throughout the network diagram.

How to Do the Backward Pass: Finding the Latest Start Time and Finish Time

The second formula is for Backward Pass, when you are moving from the last activity to the first activity (you are moving backwards). This formula will find the latest start time (LS) and latest finish time (LF) for each activity.

To start the Backward Pass, make the last activities LF the same as its EF. For all other tasks, the LF is the same as its immediate predecessor’s LS.

Use this formula to calculate LS:

LS = LF - Duration

For the Test & Commission Tank, the LF is 54 and, the LS is 50 (54 - duration of 4). For Assemble Tank, the LF is also 50 and, the LS is 35 (50 - duration of 15 days). Continue this formula throughout the network diagram.

To check that you’ve done Backward Pass correctly, the first activity (Activity A) should have an LS (latest start time) of 0.

Here’s the completed Forward Pass/Backward Pass technique:

Two Rules to Remember for Forward Pass/Backward Pass

During the Forward Pass, if you find activities that join (multiple activities that flow into one activity), you must run the Forward Pass formula for each entry point and use the highest value from the formulas.

During the Backward Pass, if you have activities that join, you must run the formula for each entry point and use the lowest value.

How to Calculate Float or Slack on the PMP Exam

Now that you have calculated ES and LS for each activity, you can find the float (or slack).

The slack time, also known as float time, for an activity is the time between the earliest and latest start time. Critical activities, activities on the critical path, will always have zero slack.

There are two formulas to calculate slack based on the values you identified in the Forward Pass/Backward Pass technique.

Slack = LF - EF

Slack = LS - ES

You will have to use this process if you are asked to identify an activity’s slack on the PMP exam. Or, if you’re not sure which activities are on the critical path, you could find the slack of each activity, knowing that activities on the critical path always have zero slack.

The final figure below shows the slack values for each task. You can see that the four tasks on the critical path have zero slack -- Design Tank Project, Construct Tank Foundation, Assemble Tank, and Test & Commission Tank.

Key Critical Path Terms for the PMP Exam

Here are the most important terms related to the critical path method that you should understand before taking the PMP exam.

• Critical path method (CPM): The critical path method is a step-by-step project management technique for process planning that identifies critical and noncritical tasks, preventing timeframe problems and process bottlenecks.
• Critical Path DRAG (Devaux’s Removed Activity Gauge): The amount of time that an activity on the critical path is adding to the project’s duration. Or, alternatively, the amount of time the project completion date would be reduced by decreasing a critical path activity’s duration to zero.
• Criticality Index: Used in risk analysis, the Criticality Index shows how often a particular task was on the critical path during analysis. Tasks with a high Criticality Index are more likely to cause delay to the project since they’re more likely to be on the critical path.
• Earliest start time: The earliest time an activity can start once the previous dependent activities are completed.
• Earliest finish time: The earliest start time for the activity plus the time required to complete the activity.
• Latest finish time: The latest time an activity can be completed without delaying the entire project.
• Latest start time: The latest finish time minus the time required to complete the activity.
• Total float: The amount of time an activity can be delayed from its early start date without delaying the entire project.
• Free float: The amount of time an activity can be delayed without delaying the early start date of a successor activity.
• Forward pass: The process to determine the early start or early finish times for activities in the critical path method.
• Backward pass: The process to determine the late start or late finish times for activities in the critical path method.
• Network diagram: A schematic display of the relationships between project activities, always drawn from left to right to reflect the order of the project.
• Network analysis: The process of breaking down a complex project into components (activities, durations, etc) and plotting them to show their interdependencies and interrelationships.

The Easiest Way to Find the Critical Path

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Critical Path Method (CPM): The Ultimate Guide

Updated: Jun 18, 2024, 9:01am

Table of Contents

What is the critical path method, 7 benefits of the critical path method, example of critical path method process, how to find the critical path in 6 steps, bottom line, frequently asked questions (faqs).

Project managers must juggle resources, talent, budgets and expectations to ensure a project’s execution is successful and completed on time. The critical path method (CPM), when done correctly, serves as a guide to help project managers juggle it all like pros. In this guide, learn what the CPM is and how it benefits businesses, then view an example of the project management technique and access a beginner-friendly step-by-step guide on how to use it.

The critical path method identifies the longest sequence of dependent tasks within a project. If those tasks are completed on time, the project can be completed at the earliest date possible. It also identifies the tasks that can be completed in parallel to critical tasks with more buffer time around them. By prioritizing tasks that have no buffer time and completing other tasks around them, project managers can efficiently keep projects progressing to an on-time completion.

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The critical path method offers project managers the ability to stay on budget more easily, schedule talent and resources efficiently, monitor progress, not get overwhelmed with project management demands, monitor and report on project progress and keep scope creep in check.

Here is a deeper look into each of these benefits of the critical path method.

1. Easy Budget Control

With a clear path to ensure the project finishes on time, you reduce wasted time that adds to your human and other resources budget. For example, if there is float time around one task, you can relocate employees to critical path activities, thereby reducing costly busy work or idle time. A clear breakdown of your project also makes it easier to allocate other resources to the right place at the right time, thereby cutting inventory storage costs.

2. Effective Scheduling

In addition to pulling employees off tasks with lots of float time as needed, project managers can also allocate employees strategically to tasks that have float time. For example, they may assign employees who are still going through a learning curve to tasks with float time so these employees may take their time learning new skills. Alternatively, more experienced employees can be assigned to critical path tasks that don’t come with buffer time.

3. Simplified Project Management

Instead of looking at a large, complex project as a whole, the critical path method breaks down a project into the baby steps needed to complete it. In this way, project managers can focus on managing a project on a task-by-task basis as the project progresses, making it easier to manage resources, budgets and talent.

4. Efficient Resource Allocation

The critical path method helps project managers know exactly when every activity must be completed and, by extension, when resources are needed to complete them. As such, when resources come in, it is easy to know where their allocation should be prioritized at any given point in the project. More importantly, it is easy to know when resources can be redirected away from activities that can wait so they can be used to complete more pressing tasks.

5. Effortless Project Monitoring

The critical path method requires project managers to break down the project into progress chunks using clear charts, often within project management systems . As such, it creates a progress checklist that can be followed easily. It also breaks down the project schedule so that project managers can quickly see if they are at the right point in the project on any given day and, if so, they are scheduled to complete the project on time.

6. Straightforward Reporting

First, charts within project management software help project managers identify a project’s critical path. Then, after project initiation, those same charts are used to assess in real-time whether the project is on time for completion, on schedule in the moment and fully resourced. As such, reports are updated in real-time and downloadable at a moment’s notice for instant and clear reporting.

7. Enhanced Scope Creep Management

As project managers go through the critical path, they can easily see if a given task along the path is taking more time or more resources than was originally allocated to it. As such, any deviation from the planned critical path alerts project managers that scope creep may be occurring, giving project managers the cue to enact their change management plans before scope creep gets out of control.

Let’s look at a real-world example by walking through the process of baking a cake. To figure out the critical path, first identify all the activities within the project’s execution. Then, identify activity dependencies—or activities that must be completed one after another. Next, decide which ones are part of the critical path—or the longest sequence of dependent tasks. Also, decide which activities can be completed in parallel to critical path activities. Finally, map the project’s critical path and parallel activities.

Listing Project Tasks Example

As a very basic example, when baking a cake, the general steps are as follows:

• Combine wet and dry ingredients and mix them well.
• Preheat the oven to 350 degrees Fahrenheit.
• Pour the ingredients into a greased baking pan.
• Bake the cake for 30 to 35 minutes.
• Take the cake out of the oven and let it cool for one hour.
• Make the frosting.
• Frost the cake.

Identifying a Project’s Critical Path Example

Some of these tasks need to be completed one after another (sequentially) while other tasks are completed in parallel (concurrently). For example, a baker must wait until the oven is preheated to bake the cake. After 35 minutes, they must remove the cake from the oven or it will burn. The cake must only be frosted after it has had time to cool or the frosting will melt and look awful. Because none of these tasks should be initiated until the previous one has ended, they are dependent on one another.

Other tasks, however, can be completed in parallel to these dependent tasks. The baker can, for example, make the frosting while the oven is warming or wait until the cake is baking. There is more flexibility regarding when to make the frosting without delaying the completion of the entire project. This scheduling flexibility is called float time.

Tasks that do not have float time are part of the critical path. They must be completed one after another. They are also the longest string of dependent tasks in the project. So, you cannot wait to complete critical path activities. Any delays in these activities will delay the completion of the entire project. Other strings of dependent tasks can float around them in that they can be scheduled when it is most convenient in the trajectory of the project.

For example, if you wait to preheat the oven until after you mix your ingredients, your entire project must stop until your oven is preheated. For this reason, heating your oven is part of the critical path. However, while you bake your cake, you can gather the ingredients for your frosting, put them in a bowl and mix them well. These parallel dependent tasks are completed in addition to the critical path.

Critical Path Diagram Example

To demonstrate which activities are part of the critical path and which are not, project managers create a diagram. The diagram uses boxes to show which tasks are part of the critical path (have no float time) and which can be completed in parallel to those tasks (have flexibility in when they can be completed). The below graph is a basic example of a critical path diagram. Note that the critical path is highlighted in red and parallel tasks in yellow.

To find the critical path method, first list all project activities, then identify which activity initiations depend on the completion of others. Next, create a critical path diagram and calculate the duration and float times of all tasks. Finally, identify the critical path and those activities that can be completed in parallel to it.

Here are six steps to find the critical path.

1. List Project Activities

For the purposes of eliminating redundancy, if you have created a project management plan for your project, you likely created a work breakdown structure . Use this structure to source a list of all the activities you must complete for each milestone of your project.

If you have not created a work breakdown structure for your project, you should list all the activities you must complete to create your project’s final deliverable. For example, if your project aims to plan a wedding, the tasks that must be complete to produce a planned wedding may include meeting with the couple, writing a guest list, booking vendors and coordinating with the venue. List out everything you expect to do in order to prepare for the big day.

Now, estimate how much time it will take to complete each task. For example, it may take two days to gather the couple’s preferences, budget and wedding date and a week to select and book a venue. Continue adding a duration time to each task. Then, compile it all into a table with a row for a task ID―you can assign a letter of the alphabet to each one―the name of the task and a task duration in whatever time interval most appropriately fits your project.

2. Identify Activity Dependencies

A dependency refers to an activity within a project that cannot be initiated until another activity has been completed. In our wedding planning project, for example, the planner must first book the venue, then write the guest list, given that the venue selection determines how many guests can attend the wedding comfortably. So, writing the guest list is dependent on first booking the venue.

To record dependencies, use the list from step one, then add an “immediate predecessors” column to the right side of the table. Next, for each activity, determine “which task needs to be completed before beginning this task?” Then, in the “immediate predecessors” column for each activity, list the Task ID of all activities that must be completed before the activity you are addressing can begin.

For example, in the table below, “writing the guest list” is dependent on booking the venue. So, we wrote C (the task ID for “book a venue”) in the “immediate predecessor” column for “write a guest list.” It is also important to know the couple’s preferences before writing the guest list in order to avoid uncomfortable confrontations during dinner. Therefore, we write the task ID for “gathering the couple’s preferences”—or B—in the immediate predecessor’s column for “write a guest list.”

Here’s an example of a dependencies table to serve as a guide for completing this step.

3. Create a Critical Path Diagram

To create a critical path diagram, draw a box to represent each task on the dependencies table you created in step two. Then, show dependencies by drawing arrows that connect each predecessor task to its dependent task(s). (You can see an example of this in the example section of this article.)

For example, since booking the venue (Task ID C) is dependent on gathering the couple’s preferences (Task ID B), create a box titled “gather the couple’s preferences – B” and a box labeled “book a venue – C.” Next, draw a line from the “gather the couple’s preferences” box to the “book a venue” box. Continue until all your tasks and their dependencies are recorded on your chart.

Pro tip: You can easily create a free critical diagram chart using Google Draw . Follow the prompts to choose a flowchart template, then adjust the template to your needs and add text to label each box. Finally, select the arrow tool to drag an arrow from one box to the next, thereby adding dependency arrows. Your diagram can then be saved to your Google Drive account.

4. Calculate the Duration of Each Activity

You have already figured out how long each activity will take. Now, it’s time to figure out the earliest start and end dates of each activity. This will help you to know when you must schedule each activity to ensure the entire project is finished on time with all tasks completed. Use the forward pass and backward pass techniques to calculate the earliest start and earliest finish dates of each activity.

Forward Pass

The forward pass helps you determine the earliest start time and earliest finish time you can employ for each activity. To do so, determine the early start time of each activity by recording the finish date of the previous activity. Put simply, the early start time is equal to the finish time of the previous activity. Then, add the duration of the activity to this recorded time.

Continue calculating the earliest start and finish day of each activity until you get to the last activity. The number you arrive at for the earliest finish day of last activity in the project is the earliest finish day of the project or the target completion day of the project.

Backward Pass

Your next calculation—the backward pass—will tell you the latest start date and latest finish date of each activity. Begin with the last activity and work backward in your project timeline to the very first activity. Use the following calculation to do so:

Late start (LS) = Late finish (LF) – activity duration

* Use the lowest late start (LS) value of the previous activity as the late finish value (LF) for this formula.

5. Estimate Float Time

In project management, figuring the float time helps you determine if an activity can take longer than expected without risking finishing the next task late or the overall project late. It can also tell you if you can start it late or early while still finishing all tasks in the project on time. Simply put, it tells you how much flexibility you have when scheduling and completing each task. Use the following formula to determine the float time for each activity:

Slack time = Late start (LS) – Early Start (ES)

6. Calculate the Critical Path

The critical path is the longest sequence of dependent activities. Some activities may run parallel to this path but they can be completed simultaneously around critical path activities without delaying the project’s finish date. To calculate the critical path, isolate the activities with a zero float time and put them in order. Alternatively, start with the first activity, add all dependent activities to it and then calculate the duration of the longest dependent sequence of activities.

The float times from each activity will now help you calculate the critical path. Isolate all activities with a float time of zero. Together, these make up your critical path. These activities cannot be started or ended early or late or the whole project may risk either not finishing on time or finishing with a lower quality. Other activities that have a float time of more than zero are activities that must be completed in parallel to the activities that make up your critical path.

Another way to calculate your critical path is by assigning a zero start time to the first activity. Add to that zero the duration of the first activity. From there, add subsequent activities that must be finished after your first activity and their duration times. Continue adding on dependent activities and their durations until you reach the last activity in the dependency sequence. The sequence of activities with the longest total duration makes up the critical path.

The critical path method breaks down a project, revealing exactly what to focus on during any given moment of project execution. Thus, it shows you how to allocate funding, scheduling, talent and other resources properly to complete the project on time and with an as- or better-than-expected final deliverable. To get used to this method, use this guide to practice on a small project, then apply your learnings to larger and more complex projects.

Why is the critical path method used?

The critical path method is used to first determine the earliest possible completion date of a project, then schedule all activities within a project’s execution to finish by that date. In doing so, it ensures that a project does not take any more time than necessary to complete and, by extension, does not take more money and resources than necessary.

How is the critical path method calculated?

First identify all the tasks that must be completed for the project to finish. Then, identify the longest sequence of tasks that must be completed one after another (are dependent) and their durations. Add those durations together to determine the earliest projected project completion date. Finally, schedule other tasks to complete in parallel to those included in the critical path so they may be completed before the end date of the critical path.

Where is the critical path method used?

The critical path method is used in project management. It can be applied to any project in which project managers need to closely monitor to ensure all project resources are allocated efficiently and the project finishes on time.

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Critical path method: How to use CPM for project management

The critical path method is a technique that allows you to identify tasks that are necessary for project completion. The critical path in project management is the longest sequence of activities that must be finished on time to complete the entire project. Below, we break down the steps of how you can find the critical path for your next project.

Building out a project roadmap can help you visualize what needs to be done to reach your end goal. The critical path method helps you do exactly that. It’s a project management technique that involves mapping out key tasks or critical tasks necessary to complete a project. 

Leveraging this technique allows you to manage task dependencies and set realistic timeframes. Read on to find out how the critical path method works and how you can use it with your team to optimize project timelines . 

What is the critical path method (CPM)?

Also called critical path analysis (CPA), the critical path method (CPM) is a technique where you identify tasks that are necessary for project completion and determine scheduling flexibilities. A critical path in project management is the longest sequence of activities that must be finished on time in order for the entire project to be complete. Any delays in critical tasks will delay the whole project.

CPM revolves around discovering the most important tasks in the project timeline, identifying task dependencies, and calculating task durations.

CPM was developed in the late 1950s as a methodology to resolve the issue of increased costs due to inefficient scheduling. Since then, CPM has become popular for planning projects and prioritizing tasks. It helps you break down complex projects into individual tasks and gain a better understanding of the overall project flexibility.  

Why use critical path analysis?

CPA can provide valuable insight on how to plan projects, allocate resources, pace towards milestones, and schedule tasks. 

Here are some reasons why you should use the critical path method: 

Improves future planning: CPM can be used to compare expectations with actual progress. The data used from current projects can inform future project plans. 

Facilitates more effective resource management : CPM helps project managers prioritize tasks, giving them a better idea of how to avoid resource constraints. 

Helps avoid bottlenecks: Bottlenecks in projects can result in lost valuable time. Plotting out project dependencies using a network diagram will give you a better idea of which activities can and can’t run in parallel, allowing you to schedule work accordingly.   

How to find a project's critical path

Finding the critical path involves identifying the longest path between the start and end of the project by comparing the duration of critical and non-critical tasks. Below is a breakdown of the steps, with examples. 

1. List activities

Use a work breakdown structure to list all the project activities or tasks required to produce the deliverables. The list of activities in the work breakdown structure serves as the foundation for the rest of the CPM.

For example, let’s say the marketing team is producing a new interactive blog post. Here are some tasks that might be in the work breakdown structure:

Once you have a high-level idea of everything that needs to be done, you can start identifying task dependencies for the whole project.

2. Identify dependencies

Based on your work breakdown structure, determine the tasks that are dependent on one another. This will also help you identify any work that can be done in parallel with other tasks.

Here are the task dependencies based on the example above:

Task B is dependent on A

Task C is dependent on B 

Tasks C and D can run in parallel

Task E is dependent on D

Task F is dependent on C, D, and E

The list of dependent tasks is referred to as an activity sequence, which will be used to determine the critical path. 

3. Create a network diagram

The next step is to turn the work breakdown structure into a network diagram, which is a flowchart displaying the chronology of critical path activities. Create a box for each task and use arrows to depict task dependencies. 

You’ll add other time-bound components to the network diagram until you have the general project schedule figured out. 

4. Estimate task duration

To calculate the critical path, the longest sequence of tasks, you first need to estimate the duration of each activity. 

To estimate the duration, try: 

Making educated guesses based on experience and knowledge

Estimating based on previous project data

Estimating based on industry standards

Alternatively, try using the forward pass and backward pass technique:

Forward pass: This is used to calculate earliest start time (ES) and earliest finish time (EF) by using a previously specified start date. ES is the highest EF value from immediate predecessors, whereas EF is ES + duration. The calculation starts with 0 at the ES of the first activity and proceeds through the schedule. Determining ES and EF dates allows for early allocation of resources to the project. 

Backward pass: This is used to calculate the latest start (LS) and latest finish (LF) dates. LS is LF - duration, whereas LF is the lowest LS value from immediate successors. The calculation starts with the last scheduled critical path activity and proceeds backward through the entire schedule.    

The early and late start and end dates can then be used to calculate float, or scheduling flexibility of each task. 

5. Calculate the critical path

Calculating the critical path can be done manually, but you can save time by using a critical path algorithm instead. 

Here are the steps to calculate the critical path manually:

Step 1: Write down the start and end time next to each sequence of activities to calculate the sequence's "duration."

Find the start time of the first activity in the sequence

Find the end time of the last activity in the sequence

The duration is the end time of the last activity minus the start time of the first activity

Step 2: Determine the number of dependencies along each sequence.

Step 3: The sequence of activities with the longest duration (end of sequence date - beginning of sequence date) is the critical path. If multiple sequences of activities have the same duration, the sequence with the greater number of dependencies is the critical path.

Using the same example above, here’s what the critical path diagram might look like:

Once you have the critical path figured out, you can build the actual project schedule around it.

6. Calculate the float

Float, or slack, refers to the amount of flexibility of a given task. It indicates how much the task can be delayed without impacting subsequent tasks or the project end date. 

Finding the float is useful in gauging how much flexibility the project has. Float is a resource that should be used to cover project risks or unexpected issues that come up. 

Critical tasks have zero float, which means their dates are set. Tasks with positive float numbers belong in the non-critical path, meaning they may be delayed without affecting the project completion date. If you’re short on time or resources, non-critical tasks may be skipped. 

Calculating the float can be done with an algorithm or manually. Use the calculations from the section below to determine the total float and free float. 

Total float vs. free float

Here’s a breakdown of the two types of float:

Total float: This is the amount of time that an activity can be delayed from the early start date without delaying the project finish date or violating a schedule constraint. Total float = LS - ES or LF - EF 

Free float: This refers to how long an activity can be delayed without impacting the following activity. There can only be free float when two or more activities share a common successor. On a network diagram, this is where activities converge. Free float = ES (next task) - EF (current task)

There are a few good reasons why project managers benefit from having a good understanding of float:

It keeps projects running on time: Monitoring a project’s total float allows you to determine whether a project is on track. The bigger the float, the more likely you’ll be able to finish early or on time.  

It allows you to prioritize : By identifying activities with free float, you’ll have a better idea of which tasks should be prioritized and which ones have more flexibility to be postponed. 

It’s a useful resource: Float is extra time that can be used to cover project risks or unexpected issues that come up. Knowing how much float you have allows you to choose the most effective way to use it.

How to use the critical path method

Critical path methodology provides visibility into your project’s progress, allowing you to monitor tasks and their completion times. Below are some additional applications of CPM.

Compress schedules

Though not ideal, there are times when project deadlines may be pushed up. In those situations, there are two schedule compression techniques you can use: fast tracking and crashing.

Fast tracking: Look at the critical path to determine activities that can be performed simultaneously. Running parallel processes will speed up the overall duration. 

Crashing: This process involves allocating more resources to speed up activities. Before obtaining more resources, make sure that they are still within the project scope and let the stakeholders know of any changes.

Having the critical path plotted out can help you choose the appropriate strategy to meet updated deadlines.

Resolve resource shortages

Keep in mind that CPM doesn’t take resource availability into account. When there is a resource shortage, like an overbooked team member or a lack of equipment, you can use resource leveling techniques to solve the issue. 

These techniques aim to resolve resource overallocation issues and ensure that a project can be completed with the resources that are currently available. 

Resource leveling works by adjusting project start and end dates, so you may have to readjust the critical path or apply this technique to activities with float.

Compile data for future use

The schedule created from CPM is subject to change since you’re working with educated estimates for activity durations. You can compare the original critical path to the actual critical path as the project runs.

This data can be used as a reference to get more accurate task duration estimates for future projects. 

Critical path method vs. PERT

CPM and Program Evaluation and Review Technique (PERT) were both developed in the 1950s. PERT is used to estimate uncertainty around project activities by applying a weighted average of optimistic and pessimistic factors. It evaluates the amount of time needed to complete an activity. 

PERT uses three time estimates to find a range for the duration of an activity:

Most likely estimate (M)

Optimistic (O)

Pessimistic (P) 

The calculation for PERT is: Estimated time = (O + 4M + P) / 6

The main difference between PERT and CPM is their level of certainty around activity durations—PERT is used to estimate the time required to complete activities, whereas CPM is used when the activity durations are already estimated. 

Let’s see how the two techniques compare:

PERT manages uncertain project activities; CPM manages predictable project activities.

PERT focuses on meeting or minimizing project duration; CPM focuses on time-cost-trade offs.

PERT is a probabilistic model, and CPM is a deterministic model.

PERT has three time estimates for each activity; CPM has just one.

Differences aside, both PERT and CPM analyze the following components:

List of required tasks

Estimated duration for each task

Task dependencies

These two project management tools can be used in tandem to boost their effectiveness. You can use PERT to get more realistic estimates of task durations before proceeding to calculate the critical path and floats.  

Critical path method vs. Gantt chart

Gantt charts are horizontal bar charts that map out project activities, which can be tracked against a set timeline. Both CPM and Gantt charts show the dependencies between tasks. 

Let’s go over some differences between the two tools:

Visualizes critical and non-critical paths and calculates project duration

Displayed as network diagram with linked boxes

Doesn’t show resources required

Plots critical path activities on a network diagram without timescale

Gantt chart

Visualizes how project activities are progressing

Displayed as horizontal bar chart

Shows resources required for each activity 

Plots critical path activities on a timescale 

Gantt charts can be paired with CPM to track critical paths over time and keep your project running on schedule. 

Use your project’s critical path for better project management

CPM can be a useful asset in project management, particularly for planning tasks and managing resource constraints. With the help of project planning tools, you’ll be able to create schedules and track projects with ease. To further increase your work efficiency, check out these 12 tips to be more productive today.

FAQ: Critical path method

What is the critical path formula.

The critical path formula consists of two parts: the forward pass and the backward pass. The forward pass calculates the earliest start times (ES) and finish times (EF) for each activity, with EF determined by adding the activity's duration (t) to its ES.

EF = ES + t (the duration of an activity)

The backward pass determines the latest start times (LS) and finish times (LF), setting the LF of the final activity equal to its EF and finding the LS by subtracting the activity's duration from its LF.

LF – t (the duration of an activity)

How do you calculate the critical path in a project schedule?

To calculate the critical path in a project schedule, you first identify all possible paths through the project's activity network. Then, for each path, you sum the durations of all activities. The longest path is the critical path. This requires calculating the earliest and latest start and finish times for each activity.

What is a CPM schedule?

A CPM schedule identifies critical and non-critical tasks to prevent delays by focusing on the longest sequence of dependent tasks to calculate the shortest project duration.

When can you use the critical path method?

You can use CPM during the planning phase of a project to identify the longest sequence of dependent tasks and calculate the shortest possible completion time. CPM is particularly useful for optimizing schedules for complex projects with multiple activities, milestones, and task dependencies.

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The critical path method in project management: Your guide

July 10, 2024 - 10 min read

The critical path method (CPM) is a sophisticated project management technique for planning, scheduling, and managing the tasks necessary to complete a project from start to finish. It is also sometimes referred to as critical path analysis (CPA) . 

The critical path method does two main things:

• It helps project managers find the most important tasks in a project that critically affect how long a project will take. 
• It helps project managers make an efficient schedule so they can finish the entire project on time and within budget.

Any team in any industry can use critical path methodology to manage complex projects. What’s more, a good project management software platform will be able to take the CPM data of a project and turn it into a visual representation, displaying the tasks, their dependencies, and the critical path to make it easy to understand and manage the project at a glance. 

In this article, we’ll tell you everything you need to know about the critical path method, and answer questions such as:

• What is the critical path in project management?
• What are the steps for using CPM for project management?
• How do you calculate the length of your project?
• How do you maintain a project schedule that provides flexibility within your critical path?

We’ll also show how Wrike’s project scheduling template and Gantt chart software will help you visualize and manage your project’s critical path. 

What is the critical path method?

The critical path definition.

The critical path method involves identifying all the tasks that are needed to complete a project, determining the sequence in which these tasks must be carried out, and then calculating the most prolonged duration of time it will take to complete the project from start to finish. 

The most prolonged project duration is known as the critical path, and it provides a clear timeline for project completion.

In the CPM, tasks are categorized as critical and non-critical . Critical tasks must be completed on time to ensure the project is finished on schedule. Any delay in a critical task will result in a delay in the project. Non-critical tasks, on the other hand, have some flexibility in their scheduling, so they’re less likely to cause a delay in the project completion.

The CPM is especially valuable for projects with numerous interdependent activities, as it allows project managers to see where potential bottlenecks may occur and where resources can be allocated most effectively. By identifying the critical path, project managers can prioritize tasks, mitigate risks, and better ensure a project progresses and is completed on time.

Benefits of using the critical path method in project management

The CPM offers many benefits that can significantly enhance the effectiveness of project management. 

• CPM provides a clear visualization of the project timeline. It usually looks like a flowchart. By illustrating the sequence and duration of each task, the CPM allows project managers to gain a comprehensive understanding of the project’s flow, making it easier to plan and manage resources effectively.

• CPM clearly identifies critical tasks. This not only helps in prioritizing tasks but also allows for the proactive management of potential delays. By understanding which jobs have the flexibility to be delayed without affecting the overall timeline, project managers can better manage changes or issues that arise during the project life cycle.
• CPM aids in risk identification and mitigation. Highlighting the critical path allows project managers to foresee potential bottlenecks or delays and proactively mitigate these risks. This can lead to a significant reduction in project downtime and associated costs.
• CPM promotes better communication within the project team. With a clear visual representation of the project’s timeline, team members can better understand their roles, responsibilities, and the impact of their tasks on the overall project. This can lead to improved collaboration, efficiency, and overall project success.

In summary, CPM is an indispensable tool in project management. It gives you enhanced planning, risk mitigation, resource management, and team collaboration capabilities.

How to calculate the critical path of a project

Step 1: identify all tasks required to complete the project.

Start by listing all the functions or activities that need to be completed for the project’s successful conclusion, also known as a work breakdown structure . When created thoroughly, the work breakdown structure is a roadmap that guides a team when completing projects — whether simple or complex. Here’s a powerful work breakdown structure example from Wrike.

​​ Step 2: Determine the sequence of tasks

Next, identify the order in which the tasks need to be performed. Some tasks may depend on the completion of others before they can begin, while others may be carried out concurrently. This step is crucial in understanding the dependencies and relationships between tasks.

Step 3: Estimate the duration of each task

Assign a time estimate to each task. This should be the total time required to complete each task from start to finish. Make sure to account for any potential delays or issues that may arise by incorporating buffers or contingency time into your estimates.

Two techniques that can help project managers accurately determine each task’s duration are the forward and backward pass techniques: 

• Forward pass : Starting from the beginning of the project and moving forward through the critical path diagram, calculate the earliest start time and finish time for each activity. This helps determine the earliest possible project completion date for the entire project.
• Backward pass : Work your way backward from the project’s end date through the CPM chart, calculating the latest start time and finish time for each activity. This helps identify the latest possible project completion date for the project and determines the amount of scheduling flexibility or slack time available for each activity.

Step 4: Draw a network diagram of the critical path

Using the information from the previous steps, draw a network diagram . This visual representation should depict all the tasks, their sequence, and their dependencies. Each task is represented as a node on the diagram, and the arrows between nodes represent the task dependencies.

Step 5: Identify the critical path

The critical path is the longest path from the start to the end of the project, passing through all the essential tasks to the project’s completion. In other words, the longest sequence of tasks determines the minimum time needed to complete the project. On your network diagram, this is your critical path, the longest duration from the initial to the final task.

Step 6: Calculate the float

The total float or slack is how long you can delay a task without postponing the project’s completion. Tasks on the critical path will have zero float, meaning they can’t be delayed without impacting the project timeline. However, non-crucial tasks may have some float, allowing for some flexibility in scheduling.

Within the overall float calculation is also free float, which is the amount of time an activity can be delayed without delaying the start of its successor activity. 

Step 7: Monitor the critical path

Once the project is underway, closely monitoring the tasks on the critical path is essential. Any delays in these tasks will directly impact the project timeline. Regularly update and review the critical path to help identify potential issues early and keep the project on track.

Consider using Wrike’s project scheduling template to augment this process further. This prestructured template simplifies identifying your project’s critical path, saving time and enhancing your project planning efficiency.

Example of the critical path method in action

Now we’ll demonstrate with a simple, real-life critical path method schedule and example: planning a killer party. How should someone plan and execute this project?

1. Define the project scope

First, we need to define all of the tasks that must be finished to complete the project. For our party example, it might look like this:

• Choose a date and venue
• Make the ultimate playlist
• Set up the sound system
• Invite your friends
• Buy the food and drinks
• Cook your famous casserole
• Host the party

When we look at these tasks individually, we realize that some of them cannot be started before the others are completed. That is, some tasks are dependent on others. We’ve designated these relationships in the table below:

The actions “Invite your friends,” “Buy the food and drinks,” “Cook your famous casserole,” and “Host the party” form a sequence of tasks that must be performed in a specific order, one right after the other, to ensure a successful result. Such tasks are called sequential activities.

Together with the start of our project (“Choose a date and venue”), these tasks are the most critical steps in completing our project. Thus, these actions will be placed on the critical path.

2. Define different project paths

You can have multiple critical paths in a project so that several paths run concurrently. This can result from multiple dependencies between tasks or separate sequences that run for the same duration.

In planning a party, various project paths will consist of tasks that need to be completed. For example, one path could involve tasks related to booking the venue, such as researching options, visiting potential locations, and finalizing the booking. Another path might focus on the catering, which includes deciding the menu, finding a caterer, and arranging the food and drink delivery. Another path could be about entertainment, involving tasks like hiring a DJ or band and planning games or activities.

While separate, each of these paths is an integral part of the overall project and must be coordinated effectively to ensure a successful party. By clearly defining these different project paths, you can better manage the tasks and timelines associated with each one.

3. Consider the resource constraints

Traditional critical path schedules in project management are based only on causal dependencies. We’ve already marked these dependencies in our plan. (e.g., it’s impossible to cook the casserole without buying the ingredients). However, a project may have limited resources that need to be taken into consideration, such as how to calculate load in resource planning. These limitations will create more dependencies, often referred to as resource constraints .

If you work on a team, you may split the project work between team members. In our example, while you’re choosing a date and venue and inviting people, one of your friends can make a playlist, and another can get the food and drinks. The tasks can be done in parallel, as in our chart above. 

However, if you’re the only person responsible for the project, you have a resource constraint because you can’t be in two places at the same time. In this case, your critical path will look different.

In the table above, we assume you first need to choose the date and venue, and only later can you make a playlist. However, depending on the project conditions, these tasks can be performed in a different order.

4. Calculate the length of your project

Let’s assume you have to do everything by yourself. We estimated the activity duration of each task. Also, we determined the approximate start time for each task on the critical path. Here’s what we came up with:

Now, if we add up all of our critical tasks’ duration, we’ll get the approximate time we need to complete the whole project. In our case, three days and six hours, since “Make the ultimate playlist” and “Set up the sound system” are not on the critical path. If we add the duration to the start time, we can calculate the earliest project completion time. Understanding the CPM allows us to make this calculation quickly and accurately.

5. Leave space for flexibility

The critical path method was developed in the late 1950s for complex but fairly predictable projects. However, in real life, we rarely get to manage such projects. Let’s say you plan to redecorate your living room with a friend.

Your task list may look like this:

• Get rid of the old furniture
• Paint the walls
• Fix the ceiling
• Install the new furniture

Your friend’s responsibilities are to:

• Choose the new curtains
• Hang the new curtains

The curtain tasks form a subproject and can be treated as a non-critical path. Your friend can “choose the new curtains” and “hang the new curtains” any time before the end of your project. The curtain tasks have flexibility in the start date and end date, considered float. These tasks are parallel and will not be placed on the critical path. 

Here’s how  this project would look on a Gantt chart :

If any of the parallel tasks were to be significantly delayed, it would prevent our whole project from being completed on time. Therefore, you should always keep an eye on parallel tasks.

6. Adjust to changes in the critical path

Let’s assume that choosing the curtains took our friend longer than we initially expected. This will delay the end of the project.

Our redecoration is incomplete without the new curtains, so the path that previously was non-critical becomes critical. The initial critical path changes.

To monitor your non-critical tasks, your project schedule must be current. That’s the only way you’ll know exactly where your project is at any given moment and whether it will be delivered as initially planned.

7. Compress the schedule (if necessary)

If a project deadline is moved up, you might have to find a way to expedite tasks. While this is not an optimal scenario, there are two ways to accomplish schedule compression within the CPM framework:

• Fast-tracking: This involves overlapping parallel tasks originally planned to be done sequentially in order to shorten the project duration. Fast-tracking can potentially increase project risk due to dependencies between tasks.
• Crashing: This involves the allocation of additional resources (such as manpower or equipment) to critical activities in order to accelerate their completion. Crashing often results in increased costs, so it’s important to let stakeholders know of any budget changes.

Critical path method vs. PERT

CPM and the program evaluation and review technique (PERT) are valuable project management tools. However, they each have distinct characteristics and are better suited to different types of projects.

CPM is a deterministic approach that assumes a fixed time frame for each task. This makes it ideal for projects with well-known task durations and little variability, like construction or manufacturing projects. The CPM focuses on the critical path, meaning the sequence of activities or tasks that determines the project’s shortest possible duration. Identifying this path allows project managers to prioritize tasks directly impacting the project’s critical path timeline.

PERT is similar to the CPM in that they are both used to visualize the timeline and the work that must be done for a project. However, with PERT, you create three different time estimates for the project:

• The shortest possible amount of time each task will take
• The most probable amount of time
• The most extended amount of time tasks might take if things don’t go as planned

This makes PERT ideal for research and development projects or any other project with uncertain task durations. While both methods help in project planning and scheduling, PERT’s ability to handle uncertainty makes it more flexible in the face of potential changes or delays. The CPM’s focus on the critical path can make managing and controlling tasks critical to the project’s timeline easier.

The choice between CPM and PERT should be based on the nature of your project and the level of certainty or uncertainty in task durations. Both methods offer valuable insights that can help drive project success.

CPM success stories

This case study provides a practical example of the critical path method in action and illustrate its potential in managing large-scale, complex projects.

The Hoover Dam

The Hoover Dam , constructed between 1931 and 1936, is a testament to effective project management’s power. While the critical path method hadn’t been formally defined yet, the principles of its essential algorithm were applied during the dam’s construction. 

The project had many activities, each with dependent tasks and timelines. The project managers had to coordinate these activities in such a way as to ensure the project was completed on time and within budget. They effectively identified the project’s critical path, focusing resources and attention on the tasks that would cause the most significant delays if not completed on time.

The Hoover Dam was completed two years ahead of schedule despite the project’s complexity. This early completion was primarily due to the effective use of what we now know as the critical path method, making it a compelling case study for successfully implementing this technique. 

How Wrike can help you implement the critical path method 

Manually determining the critical path of a project isn’t exactly a quick process. That’s why Wrike has a feature that automatically determines your critical path for you . To use this feature, all you have to do is input these essential elements in your schedule on Wrike:

• Start and end dates of all project tasks
• Duration of each task
• Task relationships or dependencies 

To further facilitate the process, we’ve also designed a prebuilt template for project scheduling that will help you progress through the steps of building out your critical path. Our project scheduling template allows our customers to visualize the critical path on a Gantt chart, assign tasks to team members, and drag and drop project activities to ensure proper resource management.

If an issue comes up, you’ll have a clear view of how to alter your project schedule without causing delays and missing deadlines. 

Ready to use Wrike for your critical path analysis? Start a free trial now .

Further reading on the critical path method

Here are some further resources you can use to brush up on your critical path method knowledge:

• Critical Path Method , U.S. Department of Health and Human Services
• The ABCs of the Critical Path Method , Harvard Business Review
• How To Use a Critical Path Analysis
• When To Use a Project Calendar vs. a Gantt Chart

Occasionally we write blog posts where multiple people contribute. Since our idea of having a gladiator arena where contributors would fight to the death to win total authorship wasn’t approved by HR, this was the compromise.

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Creating a Gantt Chart for Marketing Projects: A Comprehensive Guide

In the fast-paced world of marketing, staying organized and efficient is essential for successfully managing projects. One effective tool for project management is the Gantt chart. If you're unfamiliar with Gantt charts or need a refresher, this comprehensive guide will walk you through the basics, explain why they're particularly useful in marketing projects, and provide step-by-step instructions on how to create one for your own marketing endeavors. Understanding the Basics of a Gantt Chart A Gantt chart is more than just a visual representation of a project's timeline. It is a powerful project management tool that has been widely used across various industries for decades. By breaking down a project into individual tasks and displaying them in a timeline format, a Gantt chart helps project teams plan, schedule, and track their progress efficiently. Each task in a Gantt chart is represented by a horizontal bar, with its length indicating the duration of the task. The bars are positioned along a timeline, allowing team members to see when each task starts and ends. Also, dependencies between tasks are shown through arrows, indicating which tasks need to be completed before others can begin. The History of Gantt Charts Gantt charts are not a new concept. In fact, they were first developed by American mechanical engineer and management consultant Henry Gantt in the early 20th century, as a visual tool to improve project planning and communication. Initially, Gantt charts were hand-drawn on paper, with each task represented by a horizontal bar and the timeline drawn below. Over time, with advancements in technology, Gantt charts have become digital and more sophisticated. Today, there are numerous software applications available that allow project managers to create, update, and share Gantt charts with ease.  Why Use a Gantt Chart for Marketing Projects? The usefulness of Gantt charts quickly spread beyond manufacturing and found applications in various industries, including marketing. Marketing projects often involve multiple tasks, tight deadlines, and interdependencies between different activities. A Gantt chart allows marketing teams to visualize these complexities and plan their projects in a way that minimizes risks and maximizes efficiency. Marketers can manage their resources effectively and address any potential issues, in order to streamline their projects and achieve success. Essential Elements of a Gantt Chart Now that you understand the purpose and benefits of using a Gantt chart, let's explore the key elements that make up a Gantt chart for marketing projects. Tasks Tasks are the building blocks of any project. If you are running a social media campaign, your tasks might include creating content, scheduling posts, engaging with followers, and analyzing campaign performance. Each of these tasks can be represented as a separate bar on the Gantt chart, allowing you to visualize the sequence and duration of each activity. Durations Every task in a Gantt chart has a specific duration, which represents the amount of time it will take to complete. Estimating task durations requires careful consideration of various factors, such as the complexity of the task, available resources, and potential dependencies. By accurately estimating durations, you can ensure that your Gantt chart reflects the actual time required for each task, helping you manage expectations and allocate resources effectively. Dependencies Tasks within a marketing project often have dependencies, meaning the completion of one task is reliant on the completion of another. In a Gantt chart, dependencies are depicted using arrows that connect the bars representing the dependent tasks. For instance, if you are launching a new product, you may need to complete tasks such as product design, manufacturing, and marketing. The manufacturing task cannot begin until the product design is finished, and the marketing task cannot start until the manufacturing is complete. Deadlines Marketing projects are typically time-sensitive, with specific deadlines that must be met. Including deadlines in your Gantt chart makes sure that everyone involved is aware of the project's timeline and can prioritize tasks accordingly. It also becomes easier to identify critical tasks that need immediate attention and allocate resources accordingly. For example, if you have a product launch scheduled for a specific date, you can set the deadline for the marketing campaign to guarantee that all necessary tasks, such as content creation, social media planning, and advertisement production, are completed in a timely manner. Steps to Create a Gantt Chart for Marketing Projects Now that you're familiar with the essential elements of a Gantt chart, let's dive into the step-by-step process of creating one for your marketing project. Define Your Project Goals Setting clear goals helps you identify the tasks required to achieve those goals so that your Gantt chart accurately reflects the project's objectives. For example, if your marketing project is to launch a new product, your goals might include increasing brand awareness, generating leads, and driving sales. By clearly defining these goals, you can align your tasks and timelines accordingly. Additionally, it's important to consider the specific metrics you will use to measure the success of your marketing project. Will you be tracking website traffic, social media engagement, or conversion rates? Defining these metrics will help you determine the tasks needed to achieve your objectives. List Down All the Tasks Once you have a clear understanding of your project goals, make a comprehensive list of all the tasks that need to be completed to accomplish those goals. Continuing with the example of launching a new product, your tasks might include market research, competitor analysis, creating marketing materials, developing a website, running advertising campaigns, and analyzing campaign performance. By listing down all these tasks, nothing will be overlooked during the planning and execution phases. Additionally, try to prioritize your tasks based on their importance and urgency. This will help you allocate resources effectively so that critical tasks are completed on time. Determine Task Relationships In marketing projects, some tasks can only be started once certain other tasks have been completed. Determine the dependencies between tasks and mark them in your Gantt chart using arrows. For example, before you can start running advertising campaigns, you may need to complete the task of creating marketing materials. Also, consider any parallel tasks that can be worked on simultaneously. This can help optimize your project timeline so that tasks are completed efficiently. Assign Resources to Each Task For each task in your Gantt chart, determine the resources that will be required. Resources can include team members, equipment, software, or any other item necessary for completing the task. Assigning resources to tasks helps you allocate resources effectively and ensure that each task has the necessary support to be completed successfully. When assigning resources, take a look at the availability and expertise of your team members. Verify that you have the right people with the right skills assigned to each task. This will help prevent any bottlenecks or delays caused by resource constraints. In addition to human resources, consider any external resources or vendors that may be needed for specific tasks. For example, if you need to create a video for your marketing campaign, you may need to hire a videographer or a production company. Set Your Timeline The final step in creating your Gantt chart is to set the timeline for your marketing project. Use the durations of the tasks, their dependencies, and the available resources to create a realistic timeline that accounts for potential delays and allows for efficient resource allocation. Consider any external factors that may impact your timeline, such as holidays, industry events, or product launch dates. Be flexible and allow for contingencies in case of unforeseen circumstances. What's more, don't forget to regularly monitor and update your Gantt chart as the project progresses to keep your team and stakeholders informed and on track. By following these steps and utilizing the power of a Gantt chart, you can effectively plan, manage, and execute your marketing projects with confidence. The visual representation of tasks, durations, dependencies, and deadlines will keep your team aligned, and the ability to monitor progress at a glance will allow you to make any necessary adjustments along the way. Remember, a well-designed Gantt chart is an essential tool for any marketing professional looking to conquer the challenges of project management. Design an effective Gantt chart for your marketing projects with Wrike's comprehensive guide. Register for a free trial and elevate your marketing workflow to new productivity heights. Note: This article was created with the assistance of an AI engine. It has been reviewed and revised by our team of experts to ensure accuracy and quality.

Leveraging PERT Charts for Effective Project Management

In the fast-paced world of project management, staying organized and on track is essential to success. One valuable tool that can help achieve these goals is a Program Evaluation and Review Technique (PERT) chart. PERT charts provide a visual representation of a project's tasks, their dependencies, and the estimated time needed to complete each task. By effectively leveraging PERT charts, project managers can enhance communication, improve time management, and increase overall efficiency. Understanding PERT Charts A PERT chart, also known as a network diagram, is a visual representation of a project's workflow, consisting of nodes and arrows to depict tasks and their dependencies. It helps project managers analyze the critical path and allocate resources efficiently. PERT charts provide a clear and concise overview of a project's timeline and task dependencies. They allow project managers to identify the most critical tasks that need to be completed on time to avoid delays in the overall project delivery. By visually mapping out the project's workflow, PERT charts enable project managers to make informed decisions and allocate resources effectively. Key Components of a PERT Chart When examining a PERT chart, there are several key components to consider. Nodes (events): Represent individual tasks or milestones within the project. Can have additional information associated with them, such as the person or team responsible for completing the task, the resources required, and any dependencies on other tasks or milestones. Arrows: Indicate the sequence and dependency between tasks and connect nodes to each other. Each arrow on the chart represents a specific task that must be completed before moving on to the next. Estimated time durations for each task: Allow project managers to gauge the overall timeline of the project. Slack (float): Refers to the amount of time a task can be delayed without affecting the overall project timeline. It represents the flexibility within the project schedule.  The Role of PERT Charts in Project Management Pert charts play a valuable role in project management, assisting with both planning and execution. Let's explore two key ways in which PERT charts can enhance project management processes. Planning and Scheduling  When initiating a project, planning and scheduling are crucial steps to determine the necessary resources and timeline. PERT charts provide project managers with a clear visual representation of the project's tasks and their dependencies, enabling them to allocate resources effectively and identify potential delays or bottlenecks. Let's consider a construction project for building a new office space. The project manager can use a PERT chart to identify all the tasks involved, such as obtaining permits, hiring contractors, and purchasing materials. By visualizing the dependencies between these tasks, the project manager can determine the critical path, which represents the sequence of tasks that must be completed on time for the project to stay on schedule. With this information, the project manager can allocate resources accordingly, so that each task is given the necessary attention and resources to meet the project's timeline. In addition to resource allocation, PERT charts help project managers identify potential bottlenecks or areas of concern. By analyzing the dependencies between tasks, project managers can identify tasks that have a high impact on the overall project timeline. For example, if a specific task has multiple dependencies and any delay in its completion would cause a significant delay in the project, the project manager can focus on monitoring and managing that task closely to prevent any potential setbacks. Risk Assessment Risks are inherent in any project, and effectively managing them is essential to minimizing their impact on project success. This is where PERT charts come into play, since they assist project managers in identifying potential risks by highlighting dependencies and critical paths.  Continuing with the example of the construction project, let's say that one of the tasks involves pouring the foundation. This task has a dependency on the weather conditions, as pouring concrete requires dry weather. By analyzing the PERT chart, the project manager can identify this dependency and recognize the potential risk of delays due to unfavorable weather conditions. With this knowledge, the project manager can develop a contingency plan, such as having alternative tasks ready to be worked on during bad weather days or collaborating with meteorologists to get accurate weather forecasts and plan accordingly. What's more, PERT charts also help project managers assess the impact of changes or delays in specific tasks on the overall project timeline. By visualizing the dependencies between tasks, project managers can identify which tasks have a significant influence on the project's critical path. This allows them to prioritize resources and address potential risks promptly. For example, if a task that is critical to the project's timeline experiences a delay, the project manager can allocate additional resources or adjust the schedule to minimize the impact on the overall project completion date. Advantages of Using PERT Charts in Project Management Now that we have explored the role of PERT charts in project management, let's delve into the advantages that come with utilizing this powerful tool. Enhancing Communication and Collaboration Effective communication and collaboration are vital for successful project management. PERT charts serve as a common visual language that facilitates communication between project managers, team members, and stakeholders. Imagine a scenario where a project manager is presenting a complex project plan to a group of stakeholders. Without a visual representation like a PERT chart, it can be challenging for the stakeholders to grasp the project's intricacies. However, with the aid of this tool, the project manager can visually demonstrate the project's scope, timeline, and resource requirements, making it easier for the stakeholders to understand and provide valuable input. Improving Time Management and Efficiency Time management is a critical aspect of successful project execution. PERT charts enable project managers to estimate the time needed to complete each task accurately. Let's consider a construction project where multiple tasks need to be completed, such as excavation, foundation laying, and building erection. By utilizing a PERT chart, project managers can assign realistic time estimates to each task based on historical data or expert opinions. This accurate estimation helps in creating a well-defined project schedule, ensuring that all tasks are completed within the allocated time frame. Furthermore, PERT charts aid in identifying opportunities for parallel task execution. For instance, if the construction project mentioned earlier requires the excavation and foundation laying to be done sequentially, a PERT chart can reveal that these tasks can be executed simultaneously. By leveraging this information, project managers can optimize time allocation, reducing the overall project duration and increasing efficiency. Constructing a PERT Chart Now let's examine the process of constructing a PERT chart, step by step. Identifying Tasks and Milestones The first step in constructing a PERT chart is to identify all the tasks and milestones involved in the project. Tasks should be specific and measurable, representing the necessary actions for project completion. Milestones, on the other hand, are significant achievements that indicate progress in the project. Overall, the goal is to help project managers understand the scope of the project and break it down into manageable components. For example, in a software development project, tasks could include requirements gathering, design, coding, testing, and deployment. Milestones could be the completion of each phase, such as the completion of the design phase or the successful testing of the software. Estimating Time for Each Task Once the tasks and milestones are identified, project managers must estimate the time required to complete each task (e.g., factors such as task complexity, resource availability, and potential risks). The purpose is to be able to allocate resources effectively, set realistic deadlines, and identify potential bottlenecks or areas of concern. For instance, if a task involves developing a complex algorithm, the time estimate should consider the level of difficulty and the expertise of the team members assigned to the task. Similarly, if a task requires the involvement of external stakeholders, the estimate should account for potential delays due to coordination challenges. Determining Task Dependencies The next step is to determine the dependencies between tasks. Dependencies can be categorized as either finish-to-start, start-to-start, finish-to-finish, or start-to-finish. Finish-to-start is the most common dependency type, where a task must be completed before the dependent task can start. For example, in a construction project, pouring the foundation is a finish-to-start dependency for the subsequent task of erecting the walls. The foundation must be completed before the walls can be built. By establishing task dependencies, project managers can identify the critical path and determine the overall project schedule. Task dependencies also enable project managers to identify potential risks and plan for contingencies. If a task on the critical path is at risk of being delayed, project managers can take proactive measures to mitigate the impact on the overall project timeline. Interpreting PERT Charts Once a PERT chart is constructed, it is essential to understand how to interpret the information it provides. Two key aspects of interpreting PERT charts are analyzing the critical path and understanding slack time. Analyzing the Critical Path The critical path is the longest sequence of tasks through the project that determines the minimum time required for project completion. By analyzing the critical path, project managers can identify tasks that must be completed on time to avoid delaying the overall project. By focusing resources and attention on the critical path, they can ensure that the project stays on schedule. Understanding Slack Time Slack time, also known as float or total float, is the amount of time a task can be delayed without affecting the project's overall timeline. Tasks that are not part of the critical path may have slack time available. Understanding slack time is valuable as it allows project managers to allocate resources efficiently and make informed decisions about task priorities and delays. Leverage PERT Charts with Wrike Leveraging PERT charts is key to effective project management. With Wrike, you can easily manage and create your PERT charts. Wrike allows you to create individual folders for each project, serving as a central hub for all relevant information and updates. Beyond just leveraging PERT charts, Wrike offers a comprehensive suite of tools designed to streamline your workflows, foster collaboration, and drive productivity. From real-time communication to intuitive task management features, Wrike provides everything you need to leverage PERT charts for effective project management. Ready to leverage PERT charts and boost your project management effectiveness? There's no better time to start than now. Get started with Wrike for free today. Note: This article was created with the assistance of an AI engine. It has been reviewed and revised by our team of experts to ensure accuracy and quality.

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Application of Critical Path Method for Project Scheduling -A Case Study

Conventional techniques like Critical Path Method (CPM), are being constantly refined to cope up with the changing trends in Project Scheduling. Distributed resource constrained multi-project scheduling problem has been taken up recently. It primarily focusses on handling resource conflicts. A method has been developed to distinguish between resource dependent and logic dependent activities. The following case study concentrates on the time constraint and involves implementation of CPM in the optimization of the manufacturing procedure of an All-Terrain Vehicle (ATV). The analysis is based on the data collected from the club of College of Engineering, Pune, that manufactures ATVs and the aim of the study is to minimize the total project duration using CPM, considering the limited time and resources available at hand.

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Ultimate Guide To The Critical Path Method For Project Managers

Galen is a digital project manager with over 10 years of experience shaping and delivering human-centered digital transformation initiatives in government, healthcare, transit, and retail. He is a digital project management nerd, a cultivator of highly collaborative teams, and an impulsive sharer of knowledge. He's also the co-founder of The Digital Project Manager and host of The DPM Podcast.

Need to calculate your project's critical path? Most project software nowadays will do this for you, but in case you need to do it manually, here's our in-depth guide on calculating CPM and adjusting the critical path, with plenty of examples.

The critical path of a project is the longest path between project start and project end, and the critical path method is the technique used to determine that path.

Finding the critical path requires you to have a handle on all your activities and an understanding of how these activities and deliverables are linked.

What Is The Critical Path Method?

The critical path method is a strategy that allows you to determine the longest path through a project and the shortest possible duration a project can have (i.e. the critical path).

In a nutshell, the critical path framework allows you to:

• Find the project’s critical path. 
• Know how long your project will take and how soon it can finish will depend on that critical path.

The activities on the critical path are called critical activities and have the least flexibility among all other activities. Any delays in these critical activities will almost always surely lead to project delays.

Resource availability, supply delivery schedules, stakeholder’s demands, and changing project scope or other resource constraints can lengthen or shorten your critical path or change it completely.

Can you guess which is the critical path in the below example?

A and P represent the project start and end, respectively. The number beside each letter represents that activity’s duration in days.

As you can see, there are multiple paths from A to P. To find the critical path, you need to compute the total duration of every path by adding the individual task durations. This will tell you that path “A-C-E-F-G-K-L-P,” which has a duration of 52 days, is the critical path.

It is likely that you will be using project management software or project scheduling software to create project timelines and find your critical path, especially for complex projects.

Read about how CPM differs from PERT , a similar technique.

Critical Path Method Examples

What happens if the resources your activities need are unavailable in the schedule indicated by critical path analysis (CPA)? You may have to apply resource leveling , which might change the critical path and extend the duration of the project.

Let’s plot the example from the previous section on a Gantt chart to illustrate.

The project is set to start on April 1 and end on June 13. That’s a total of 52 workdays, which corresponds to the length of time it will take to complete all of the activities on the project’s critical path.

However, what if the person assigned to task E (which is supposed to start on April 15) has been assigned to another project and isn't available until April 20?

If no other person can take on task E, you can apply resource leveling by adjusting the schedule around that team member's availability.

This means pushing task E’s start date from April 15 to April 20, delaying task E and ultimately the project. The projected end date has now become 16 June instead of 13 June. Note that the critical path remains the same, but it has become longer.

If extending the project end date isn't acceptable, you may have to apply schedule compression techniques like resource crashing and fast tracking to complete the project in a shorter period.

Crashing means adding more resources (such as people or equipment) to activities to shorten duration. Fast tracking involves performing some tasks in parallel.

In our example, suppose we double the number of people assigned to tasks G and L, shortening task G’s duration from 12 days to six and task L’s from 15 days to 8. This shortens the path duration from 55 days to 42 days.

We also bring forward task O so it will begin immediately after the preceding task K. This means task O ends one day later than task L, which changes the project’s critical path to A-C-E-F-G-K-O-P with a duration of 43 days.

Here's a concrete example—a hyperlocal ecommerce app. This is how our critical path diagram (technically a Gantt chart) looks.

Which path corresponds to the project duration, and which path has zero float or the least amount of float, i.e., cannot suffer delay without delaying the project?

• Complete all Bikolana products: 4 days
• Complete all Cam Sur coop products: 4 days
• Complete all eKadiwa products: 4 days
• Complete all traditional market products not available in priority retailers: 4 days
• Find retailers offering products not available in priority retailers: 6 days
• Increase price advantage rate: 5 days
• Upload all products and fixed subcategories to database: 8 days
• Display retailer subcategories and product subcategories: 7 days
• Auto mark up prices per subcategory: 7 days
• Launch marketing campaign. 7 days

How To Find The Critical Path Of Your Project

Here are the step-by-step instructions to find the critical path of your project.

Step 1: Identify your project’s component activities

To start, identify the activities that make up your project. It would help greatly if you have previously created a work breakdown structure document. A WBS document will tell you which activities comprise your project and the sequence of activities. 

Suppose you need to get an online magazine launched. The following might be your project’s component activities (there are many more activities that could be included; this has been simplified for our purposes).

• Theme selection
• Theme approval
• Content ideation
• Content writing
• Content approval
• Graphics ideation
• Graphics creation
• Graphics approval

SPONSORSHIP

• Pitch sponsorship proposal
• Create advertising content
• Close sponsorship deals
• Magazine layout design
• Approval and sign-off
• Platform procurement
• Magazine upload

Step 2: Arrange your activities in sequence

After identifying the individual tasks that make up your project, arrange the tasks in sequence. Which activity needs to go first? Which activities depend on others to be completed?

Using our online magazine publication example, the following are the tasks, arranged in sequence and with dependent tasks identified.

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Step 3: Approximate Activity Duration

Estimate the duration of each individual task using one or more of the following techniques.

• Expert judgment . An expert or a team of experts decides on the duration of an activity.
• Analogous estimation . Use a similar past project as a template for estimating the duration of your project or a similar past activity to estimate the duration of a particular activity. 
• Parametric estimation . Combine historical data and current project parameters to estimate durations.
• Three-point estimation . Estimate the duration as the average of three possible durations: the most likely duration, the optimistic duration, and the pessimistic duration.
• Bottom-up estimation . Break the individual task into more specific sub-tasks. Then estimate an activity’s duration by aggregating the estimated durations of its component activities.
• Consensus decision making . Everyone involved in the project can decide, as a team, on individual activity durations. The lead can assign time estimates, perhaps using any or a combination of the techniques described above, and the project members can vote on duration values. 

Step 4: Create a Network Diagram

Knowing your activities, their sequence of tasks, dependencies, and estimated task durations, you can now plot your network diagram.

Step 5: Identify the Critical Path

Based on the simple network diagram, the critical path is A-B-J-K-L-M-O-P. The following are the critical path activities:

A. Theme selection

B. Theme approval

J. Create advertising content

K. Close sponsorship deals

L. Magazine layout design

M. Approval and sign-off

O. Magazine upload

P. Online magazine launch

Step 6. Determine the Minimum Project Duration

Use the critical path to identify the shortest possible project duration. As you can see from the table below, the critical path has a duration of 30 days. That’s also the minimum project duration.

Step 7: Create a Project Schedule

Now that you know the minimum project duration, you can create an initial project schedule. Use the chart from before to create a critical path schedule.

How about the non-critical activities? When must they start and end? That will depend mainly on the project manager’s preferences, resource availability, and activity dependencies.

As a case in point, activity E (content ideation) can only start after 13 June because it depends on activity D (theme approval). However, it doesn’t necessarily have to start on that date.

If the project manager doesn’t want to start then or if the content ideation team is unavailable on the said date, content ideation can begin at a later date.

Likewise, you must note that non-critical activities, when they are dependencies of critical activities, cannot finish later than the day before the dependent critical activity is scheduled to start.

Step 8: Adjust Your Project Schedule as Needed

Armed with your critical path schedule, you can now apply other project management techniques to shorten or optimize your schedule.

Do you need your project to take fewer than 30 days? You can apply schedule compression techniques like crashing and fast tracking.

Are the resources you need for your activities unavailable or over-capacity on the dates specified by the critical path methodology? You can apply resource optimization techniques such as resource leveling and resource smoothing to adjust your schedule.

Step 9: Update Your Schedule According to Project Progress

This is something you need to do while the project is ongoing. If there are any changes in the CPM schedule—perhaps, there have been delays—you will need to update your schedule accordingly.

A Gantt chart is the ideal project management tool for progress updating. Thus, it will be best to plot your project on a Gantt chart after your critical path analysis has given you a viable schedule. Of course, you will need to have start dates and end dates for all activities in your project before you can create a Gantt chart of your project (likely using a Gantt chart maker tool).

How To Calculate The Critical Path

There are two phases to the critical path method calculation: the forward pass and the backward pass.

The Forward Pass

The forward pass identifies the early start and early finish dates of individual activities.

The Early Start Date

The early start date of any activity is the latest of the following:

• The project start date
• The early finish date of its predecessor activities, plus one day
• If the activity has more than one predecessor activity, the latest of all preceding activities’ early finish dates plus one day
• The date of applicable or existing “not earlier than” constraints (for instance, if a required resource for an activity will be available only on 13 June, that activity may start on 13 June or later but not earlier)
• The current date for the activity (the first day of the remaining schedule after the project has been updated)

The Early Finish Date

The early finish date, meanwhile, is the early start date plus the duration of the activity minus one day (to account for the start date being part of the activity duration). Of course, you may have to adjust the dates to account for weekends if work may proceed only during weekdays.

After determining the earliest start times and earliest finish times of all project activities, you need to perform the backward pass.

The Backward Pass

The backward pass will calculate the latest finish and start dates for all activities. 

Visualize it this way. On the one hand, the forward pass helps you find the start and finish dates of activities beginning from the project start date. On the other hand, the backward pass lets you estimate start and finish dates starting from the project end date. In other words, you work backward, thus the term backward pass.

Since you’re working from backward, the first thing you need to calculate is the late finish date.

The Late Finish Date

The late finish date is the latest date an activity can be completed without delaying the project schedule. It is the earliest of the following:

• The project finish date
• The late finish date of its successor activity minus one day; you subtract one day because a predecessor activity ends one day before its successor.
• If the activity has more than one successors, the earliest of all successor activities’ late finish dates minus one day
• The date of applicable or existing “not later than” constraints

The Late Start Date

You calculate the late start dates based on late finish dates. It’s just the late finish date minus the activity duration, plus one day. We must add one day because simply deducting the duration will give you a date one day before the actual start date. Adding one day, therefore, ensures the start date is part of the duration of each activity.

Calculating Float

Now that we have the early start and finish dates and late start and finish dates, we can calculate float. Total float is the number of days an activity may be delayed without delaying the entire project, while free float is how many days we may delay an activity without affecting the start date of its successor activity.

Float analysis will tell you which activities you can freely delay and by how many days. For instance, it will tell you immediately that critical activities (in bold) may not be delayed if you wish to finish on time; the total and free floats for critical activities are zero. You have more liberty to delay non-critical tasks.

CPM Calculators and Formulae

Project management software should be able to help you identify the critical path, find the start and finish dates, and calculate floats. You can also use a critical path method calculator online.

This PERT (Program Evaluation and Review Technique) calculator or this CPM calculator will help you identify the critical path and the estimated project duration. Manually, you can plot your activities on a diagram, then once you see the paths from start to finish, you can just add the durations of the activities on every path. The path with the highest sum is your critical path.

Once you have identified your critical path, you can use Google Sheets to calculate dates, including the start and finish dates for every activity.

If you need to factor in resource allocation, try resource management software .

Formulae for Calculating Dates and Floats

Remember the following formula:

Early Start Date = PS/PEF+1/NET

That’s the earliest of the project start date, the early finish date of the predecessor plus one day, or any of the not-earlier-than date constraints. 

Early Finish Date = (ES + D) - 1

That’s the activity’s early start date plus the duration, diminished by one day.

Late Finish Date = PF/SLF-1/NLT 

This is the earliest of the project finish date, the late finish date of a successor activity minus one day, or a not-later-than date if any.

Late Start Date = (LF - D) + 1

This is the activity’s late finish date diminished by its duration, plus one day.

Total Float = LF - EF or LS - ES

This is an activity’s late finish date minus its early finish date. It can also be the late start date minus the early start date.

Free Float = (SES - EF) - 1

This is the successor activity’s early start date minus the activity’s early finish date then the difference diminished by one day.

Formulae for Calculating Dates and Floats When Considering Workdays Only

If you are calculating only working days, you must use the WORKDAY and NETWORKDAYS functions. WORKDAYS calculates the date given a start date, duration, and any holidays or non-working days, while NETWORKDAYS counts the number of working days between two dates.

The following are the variations of the above formula, modified using WORKDAY or NETWORKDAYS.

Early Start Date = WORKDAY( PEF, 1, [holidays] )

This function calls for the start date (the predecessor’s early finish date), the duration (this should be one because the early start date is one day after the predecessor’s early finish date), and an optional holidays variable pertaining to any dates that you want considered as holidays (in date or serial format).

This should be unnecessary in case the early start date is the project start date or a not-earlier-than date.

Early Finish Date = WORKDAY( (ES-1), D, [holidays] )

Note that I include the one day deduction inside the function to ensure the resulting date will always be a workday.

Late Finish Date =  WORKDAY( SLF, -1, [holidays] )

This function deducts one day from the late finish date of the successor activity and, if the answer is a weekend or a holiday, returns the preceding working day.

Late Start Date = WORKDAY( (LF+1), -D, [holidays] )

This function calls for the activity’s late finish date plus one day, the duration but turned into negative integers, and holidays or any other non-working dates.

I include the one day addition inside the WORKDAY function to ensure the resulting date will always be a workday.

Total Float = NETWORKDAYS( EF, LF ) - 1

This counts the number of working days from the activity’s early finish date to its late finish date. We diminish it by one because the function also counts the late finish date; we only need the difference.

Free Float = NETWORKDAYS( EF, SES ) - 2

This counts the number of working days from the activity’s early finish date to the successor activity’s early start date. We subtract two from the result: one to account for the one day deduction required by the original formula and another to remove the additional day the function introduces because it counts the early finish date, too.

What's Next?

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Table of Contents

Critical Path Method is an algorithm or a tool to ease complex project scheduling. It finds the sequence of critical tasks that determines the minimum completion time of a project, thus enabling the manager to optimize resources, predict delays, and improve efficiency. Though CPM brings some benefits in the form of greater control and visualization, it could very well miss out on some factors of a large-scale project. It applies key CPM terms such as early start, late start, slack, and float. Other features that can be added to enhance CPM include automated scheduling and resource management. Even though it is usually compared to PERT or Gantt, the choice of method to use should be based on the needs of the project. Steps in applying CPM are given to ensure readiness for its application.

CPM, or the Critical Path Method, is an algorithm used in project management to schedule project activities. The critical path refers to the longest stretch of the activities and a measure of them from start to finish. The primary goals of CPM are to determine the critical path, estimate the minimum project duration, and highlight the tasks that cannot be delayed without affecting the overall timeline.

What is the Critical Path Method (CPM)?

The critical path method (CPM) is a strategy for surveying plan adaptability and distinguishing tasks fundamental for project completion. In the project, the critical path is the longest succession of tasks that must be done on time for the project to be completed. For instance, in a construction project, pouring the foundation might be a critical task. If such tasks are delayed, the project will also be delayed.

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Why Use the Critical Path Method?

Critical path method (CPM) empowers project managers to set priorities, distribute resources, and schedule projects with confidence. There are various reasons to use this method, including the ones listed below:

Improves Future Planning

Improves future planning by utilizing critical path method (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 enables project managers to efficiently prioritize tasks, giving them a clear understanding of how and where to deploy resources, thereby enhancing productivity.

Helps Avoid Bottlenecks

Project bottlenecks can be a source of stress and time loss. By outlining project dependencies using a network diagram, you can more accurately decide which tasks can and cannot be finished in parallel, saving time and reducing stress.

With the help of critical path method (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

Before we can get started with CPM or the Critical Path Method, we’ll have to understand two major concepts: events and Activities. To help us understand them better, let’s look at the process's network diagram (which is also the output). 

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. 

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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 draw 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 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. 

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! 

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Advantages of Using CPM in Project Management

The advantages of using critical path method (CPM) are as follows:

• Effective Communication: When creating critical path method schedules, all phases of a project's life span must be considered. The program's structure becomes more achievable and firm when the skills shared by various team members are integrated. Therefore, effective communication is the key.
• Easier to Prioritize Tasks: Project managers can prioritize tasks effectively and estimate their float by determining the critical path. Float indicates the amount of time a task may be put off before it affects its completion. A lower float indicates a greater priority.
• Accurate Scheduling: Critical path method (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.

Disadvantages of Using CPM in Project Management

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

• Multiple Complexities: The critical path method (CPM) involves several moving elements and detailed computations. Even with the aid of software, the potential for human error in data entry is a significant concern, underscoring the need for caution and attention to detail.
• Limited Applicability: Only some project types are suited to the critical path method. For instance, projects requiring creativity, like product design or research work, tend to come along in unforeseen forms and fail to lend themselves well to CPM. Similarly, projects with high uncertainty or those that involve a high degree of risk may not be suitable for critical path methods (CPM).

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Key Terminologies in CPM

Some of the fundamental terminologies that are important to understand in critical path method (CPM) for the effective management of project schedules are given below:

• Critical Path: A series of activities in a project which, when delayed, will delay the project completion time. In other words, the longest chain of activities must be completed on schedule if the project must be completed by its due date. Any delay in the chain will directly impact the completion time for the entire project.
• Early Start (ES): The earliest time an activity may start if all activities preceding it begin as early as possible.
• Late Start(LS): The latest time at which an activity can start without causing the project's end date to be delayed. 
• EF(EF): Early Finish: The earliest time an activity may finish, calculated from its ES and duration.
• Late Finish (LF): It is the latest date a task can be finished without impacting the overall project timeline.
• Slack (Float): The time, usually measured in days, that an activity can be delayed without impacting the overall completion of a project. Activities on the critical path have zero slack.
• Total Float: The total time an activity may be delayed without impacting the end date of a project. This is referred to as Total float .
• Free Float: The time that an activity can be delayed without delaying the start of any subsequent activities.
• Duration: The total time for an activity from its commencement to completion.

All these terminologies are basic but form the core for computing and understanding the critical path, which assists the project manager in effectively planning, monitoring, and controlling the project's timeline.

How to Calculate the Critical Path of a Project

Calculating the critical path of a project involves identifying the sequence of activities that will determine the minimum completion time for a project. Here's how you can calculate the critical path:

• List all tasks: Identify all the things that need to be done to complete a project and list them. Every task is supposed to have a defined duration.
• Next, determine dependencies: Understanding the tasks that must be completed before others can start is a strategic move. It puts you in control of the project's sequence and ensures a smooth flow of tasks.
• Create Network Diagram: A network diagram or flowchart can be drawn showing each of the tasks and their dependencies. Every task or event gets represented on a node. Arrows depict relationships among these nodes.
• Estimate Task Durations: State a duration for every task, usually measured in days or weeks. Improving time management skills can be beneficial.
• Forward Pass: Compute ES, the earliest start, and EF, the earliest finish times for every task from the project start. The procedure for doing this is called the forward pass. ES will tell when a task can start as soon as possible, and EF will tell when it can finish as quickly as possible, considering its duration.
• Perform Backward Pass: Work the latest start and finish times from the project's end date. This is called the backward pass. LS represents the latest time a task can start without delaying the project, and LF denotes the latest it can finish.
• Identify the Critical Path: This is the set of activities with ES equalling LS. This means zero slack or float for those activities. Simply put, delays in these activities will directly impact the project completion date.

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How to Use the Critical Path Method

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. You can use fast-tracking or crashing as a schedule compression strategy in such circumstances, that would offer you an opportunity to meet your project goals more efficiently.

Fast-tracking : Analyze the critical path to identify tasks that can be completed concurrently. For instance, if Task A and Task B are not dependent on each other, they can be fast-tracked. By using parallel processes like these, the entire length will be shortened.

Increasing resources is a step in the process of 'crashing' operations. It is crucial to ensure the additional resources fit within the project's scope before acquiring them. Equally important is to inform the stakeholders of any modifications, demonstrating your responsibility and consideration for their involvement.

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Resolve Resource Shortages

Remember that the critical path method (CPM) does not account for resource availability. However, resource-leveling tactics can be a game-changer, helping you resolve resource deficits like an overbooked team member or a lack of equipment and ultimately leading to a more successful project.

Resource-leveling strategies play a crucial and reassuring role in managing project schedules. They help alleviate resource over-allocation problems and ensure that a project can be completed with available resources, instilling a sense of confidence in your project management.

Resource-leveling tactics are a tool of control for project managers. They are highly adaptable, allowing you to modify the critical route or apply this strategy to floated activities. This adaptability makes you feel flexible and agile, giving you the power to manage your project resources effectively and ensuring a sense of security in your project management.

Compile Data for Future Use

Since you're working with informed estimations for activity durations, the schedule generated by the critical path method (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.

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 critical path method (CPM) software. These tools make your daily activities more accessible 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 
• Liquid Planner
• Project Manager
• Lucid Chart

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 that can be important for the PMP exam, which includes the question of what critical path method (CPM) is, are as follows:  1. Critical Path Method: This sequential project management approach for process development is not just a theoretical concept but a practical tool that distinguishes between essential and minor duties, thereby avoiding delays and workflow constraints. 2. Critical Path DRAG: The total time of an essential action adds to the project's duration. However, reducing the length of one basic activity to a minimum could significantly shorten the time needed to complete the project, underscoring the impact of your decisions. 3. Criticality Index: It is a crucial tool 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 urgency for you to master this concept to avoid project delays 4. 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. 5. Free Float: A task's duration can only be postponed by advancing the early start time of a succeeding task. 6. Forward Pass: This is the strategy for determining the critical path method's early start or finish times for tasks. 7. Backward Pass: The strategy to determine when an activity in the critical path method will have a late start or finish. 8. Network Diagram: A network diagram shows the connections between project activities. It is typically created from left to right to symbolize the project's sequence. 9. Network Analysis: This involves deconstructing a complex project into its various components (tasks, timelines, etc.) and graphing those parts to show how they relate. This method can help project managers identify the critical path and allocate resources effectively. It also aids in visualizing the project's timeline and dependencies, which is crucial for project planning and execution.

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Example of Critical Path Method in Action

Here is an example of how the Critical Path Method (CPM) is applied in a real-world project: organizing a large corporate conference. This project involves several tasks, such as booking the venue, arranging catering, sending out invitations, setting up the stage, and preparing presentations.

Step 1: List All Tasks

First, we identify and list all the necessary tasks for the conference:

• Task A: Book Venue
• Task B: Arrange Catering
• Task C: Send Invitations
• Task D: Set Up Stage and Audio-Visual Equipment
• Task E: Prepare Presentations

Step 2: Determine Dependencies

Next, we identify which tasks depend on the completion of others:

• Task B (Arrange Catering) can only start after Task A (Book Venue) is completed.
• Task C (Send Invitations) also depends on Task A (Book Venue).
• Task D (Set Up Stage) depends on Task A (Book Venue).
• Task E (Prepare Presentations) is independent and can start at any time.

Step 3: Estimate Durations

We then assign a duration to each task, estimating how long each will take:

• Task A: Book Venue - 5 days
• Task B: Arrange Catering - 3 days
• Task C: Send Invitations - 2 days
• Task D: Set Up Stage - 1 day
• Task E: Prepare Presentations - 4 days

Step 4: Create a Network Diagram

A network diagram is created to visualize the tasks and their dependencies. This helps in seeing the flow of tasks:

• Task A is the starting point.
• Tasks B, C, and D branch off from Task A.
• Task E is independent.

Step 5: Perform a Forward Pass

We calculate the earliest start (ES) and earliest finish (EF) times for each task:

• Task A: ES = 0, EF = 5 (since it’s the first task)
• Task B: ES = 5, EF = 8 (starts after Task A finishes)
• Task C: ES = 5, EF = 7 (starts after Task A finishes)
• Task D: ES = 5, EF = 6 (starts after Task A finishes)
• Task E: ES = 0, EF = 4 (independent, can start at any time)

Step 6: Perform a Backward Pass

Now, we calculate the latest start (LS) and latest finish (LF) times for each task to determine flexibility:

• Task A: LS = 0, LF = 5
• Task B: LS = 5, LF = 8
• Task C: LS = 6, LF = 8
• Task D: LS = 7, LF = 8
• Task E: LS = 0, LF = 4

Step 7: Identify the Critical Path

The critical path is the sequence of tasks with no slack (float), meaning any delay in these tasks will delay the entire project. In this case:

• The critical path is Task A → Task B, with a total duration of 8 days. This path has zero slack, so any delay here directly affects the conference date.

Step 8: Monitor and Adjust

As the project progresses, the project manager will closely monitor Task A (Book Venue) and Task B (Arrange Catering) to ensure they stay on schedule, as these tasks would delay the entire conference. Other tasks, like Task C and Task D, have some flexibility but still need attention to avoid knock-on effects.

This example shows how CPM helps project managers focus on the most critical tasks, optimize resources, and ensure that the project is completed on time.

Critical Path Method vs PERT

While CPM stands for Critical Path Method and PERT for Program Evaluation and Review Technique , the former applies to known and fixed project durations of tasks. In contrast, the latter deals with uncertain or variable task durations. It finds out the critical path that enables one to minimize project time. This method is deterministic and thus quite ideal for repetitive projects like construction work. However, PERT is used on projects which have uncertainty about task time ranges. It uses three time estimates, optimistic, pessimistic, and most likely, to evaluate expected durations. PERT is probabilistic and very useful in research and development projects where time estimation is uncertain.

Critical Path Method vs Gantt Chart

Horizontal bar charts, called Gantt charts, layout project activities that may be monitored within a predetermined time frame. The dependencies between tasks are displayed using both critical path methods (CPM) and Gantt charts.

Here are some distinctions between the two tools:

CPM (Critical Path Method)

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

Gantt Diagram

• Visualizes 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.

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1. What is the critical path formula? 

It's an independent sequence of activities that determines the minimum duration required for the completion of a project. When locating the critical path, it identifies all activities that have zero slack or zero float: the ES equates with LS and EF equals LF. These important steps include a forward pass to determine the earliest start and finish times and a backward pass for the latest start and finish times.

2. What is a CPM schedule? 

A critical path method (CPM) schedule is one of the project management tools used in outlining the sequence of tasks that must be completed to finish a project. It identifies the critical path, thereby enabling efficient scheduling and resource allocation. It also gives the project manager a better view of the whole timeline of the project, which would help monitor the progress of completion of tasks in the project and adjust the plan to focus on the critical activities to meet the deadlines.

3. What are the four main steps involved within the CPM? 

The four main steps involved in the Critical Path Method (CPM) are:

• List All Tasks: Identify and list all tasks required to complete the project, including their durations and dependencies.
• Create a Network Diagram: Develop a visual representation of the tasks and their dependencies, usually in the form of a flowchart.
• Perform Forward and Backward Passes: Calculate the earliest and latest start and finish times for each task to identify the critical path.
• Identify and Monitor the Critical Path: Focus on the tasks in the critical path, ensuring they are completed on time to avoid delays in the overall project.

4. Can the critical path change during the course of a project?

Yes a project's critical path may change in the course of a project execution. It might be changed at any time because of changes to the length of tasks, the introduction of new tasks, or delays in non-critical tasks that actually turn out to be critical. In this, continuous monitoring and updating of the CPM schedule are important to account for changes and assure that the project stays on track.

5. Can CPM be used for all types of projects? 

While the Critical Path Method is amazingly proficient in most project works, especially those with well-defined tasks and dependencies, it does not quite fit some projects. It applies best in projects with well-defined workflows and durations that are fairly predictable. For projects with high uncertainty, artistic/creative processes, or tasks that are extremely interdependent and iterative, more flexible methods of project management, such as Agile, are applied.

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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.

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Optimizing time and cost of the project using critical path method in the making “lintel set point” (case study: Ravana Jaya Co. Ltd.)

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Muhammad Zainuddin Fathoni; Optimizing time and cost of the project using critical path method in the making “lintel set point” (case study: Ravana Jaya Co. Ltd.). AIP Conf. Proc. 29 November 2023; 2702 (1): 030004. https://doi.org/10.1063/5.0155119

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The planning or scheduling process is one important factor in determining the success of a project. If project scheduling is done properly, the probability of success of a project will be even greater because scheduling is an important element in project success. Therefore, it is necessary to optimize the project so that it can be seen how long a project can be completed and look for the possibility of accelerating the project implementation time with the project objectives can be completed on time and at an economical cost. Applying the critical path method (CPM) in the project schedule is expected to produce a time schedule with the right duration of work and a high probability of success. Making a network diagram is needed to determine the interrelationships between activities so that the critical path of the lintel set point project will be identified. The concept of cost slope is applied by considering the existence of normal costs and acceleration costs to determine project optimization. From the data processing results, this project can normally be carried out with a duration of 171 days and requires a cost of IDR 431,185,000. Applying the CPM method gets the optimal solution where the project can be done in 155 days with a project cost of IDR 429,171,000.

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The ABCs of the Critical Path Method

• F. K. Levy,
• G. L. Thompson,
• J. D. Wiest

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. In essence, the tool provides a means of determining (2) which jobs or activities, of the many that comprise a project, are “critical” in […]

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. In essence, the tool provides a means of determining (2) which jobs or activities, of the many that comprise a project, are “critical” in their effect on total project time, and (2) how best to schedule all jobs in the project in order to meet a target date at minimum cost. Widely diverse kinds of projects lend themselves to analysis by CPM, as is suggested in the following list of applications:

• FL Ferdinand K. Levy has just become Assistant Professor at Stanford University.
• GT Gerald L. Thompson is Professor of Applied Mathematics and Industrial Administration, Carnegie Institute of Technology.
• JW Jerome D. Wiest is Assistant Professor, University of California at Los Angeles.

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Realistic solution of fuzzy critical path problems, case study: the airport’s cargo ground operation systems

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• Published: 16 September 2022
• Volume 8 , pages 617–632, ( 2023 )

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• Fazlollah Abbasi   ORCID: orcid.org/0000-0003-4316-151X 1 &
• Tofigh Allahviranloo 2  

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In fact, this research is executed in an environment where uncertainty is the principal feature of it. One of these uncertainties in the project planning process is estimating the duration of activities. This paper presents a methodology for implementing an extended method of critical path based on the application of fuzzy expert systems to manage schedule uncertainties. To represent the uncertainty involved we have considered the generalized quasi-geometric fuzzy numbers to represent the activity times. Moreover, TA-based fuzzy operations are used to have real solutions for the parameters. Meanwhile, a new approach to ranking generalized quasi-geometric fuzzy numbers and their distance is proposed in detail. Finally, the proposed concepts are applied in the field of critical path analysis and a relevant case study of it is also included to justify the notion.

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Abbasi, F., Allahviranloo, T. Realistic solution of fuzzy critical path problems, case study: the airport’s cargo ground operation systems. Granul. Comput. 8 , 617–632 (2023). https://doi.org/10.1007/s41066-022-00347-w

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Received : 01 June 2022

Accepted : 25 August 2022

Published : 16 September 2022

Issue Date : May 2023

DOI : https://doi.org/10.1007/s41066-022-00347-w

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