what is critical path in operation research

What Is the Meaning of the Critical Path Method in Operations Research?

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Key Milestones in Projects

How to draw a schedule for a large construction project, critical path planning and scheduling.

• Why Scheduling Issues Affect Project Management
• Examples of Time Constraints in Project Planning

The critical path method, a product of operations research, helps you set timetables for complicated projects made up of multiple interdependent tasks. Getting these kinds of projects done in the most efficient manner means determining which tasks to complete in which order -- and identifying which tasks must be done on schedule and which have some wiggle room.

Operations Research

Operations research involves applying mathematical concepts to decision making. When you have a project or proposal you're considering, you set it up much like a math problem: You identify all your variables, such as time requirements and costs, and define your desired outcome. You then "solve the equation" -- or, more likely, you have a computer do it by running simulations until it finds the most efficient solution. Operations research has generated an array of tools now common in business, including the critical path method.

Interlocking Tasks

Some projects are straightforward, with one task leading to the next until the project is done, much like an assembly line. Other projects, though, may be made up of dozens, hundreds, even thousands of separate tasks, many of them interdependent. For example: You must finish Task A before you can start Task B; Task C can start anytime, but you can't start Task D until both C and A are finished; Task E depends on completion of B, and so on. Construction projects are often like this, but smaller-scale projects, such as switching to a new computer system or remodeling a store, can get complicated, too.

On the Critical Path

In the critical path method, you lay out all the tasks involved in the project, determine how long it will take to complete each task and identify how each task is dependent upon other tasks. With that information, you can identify a target date for completing the whole project. For each task within the project, you identify the date by which the task should start and the date by which it should be finished. Some tasks will have "slack" or "float," meaning they can start late or finish late without upsetting the overall timetable. Other tasks, however, must be completed on time or the entire project will fall behind. Those tasks are said to be on the "critical path." A day's delay in a critical path task sets the whole project back a day. Project managers commonly use computers to help them identify the critical path within complicated projects.

When the Path Veers

The critical path in a project can take detours. Say you've got a peripheral task with plenty of slack, something that can take place anytime within a three-month span. That project may not be on the critical path when the project starts, but if it doesn't get done, it may well force its way onto the critical path. Installing the doors in a house under construction, for example, may not be identified as a critical path task. But you can't put the doorknobs and locks on until the doors are up, and you can't install a security system until that's done, and you can't install window treatments until the security system is in. So if the doors just never get put on, the whole project is delayed. Project managers must be focused on the critical path, but it can't be their only focus.

• Stanford University: Critical Path Method

Cam Merritt is a writer and editor specializing in business, personal finance and home design. He has contributed to USA Today, The Des Moines Register and Better Homes and Gardens"publications. Merritt has a journalism degree from Drake University and is pursuing an MBA from the University of Iowa.

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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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*The Project Management Professional (PMP) and PMBOK Guide are registered marks of the Project Management Institute, Inc. ​

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• Critical Path Analysis: A Comprehensive Guide

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What is Critical Path Analysis?

CPA can help to determine the minimum amount of time needed to complete a project or process, and can be used to plan and manage projects more efficiently. In short, CPA is a technique that helps to identify the tasks that must be completed in order to reach a desired outcome, while also helping to identify tasks that can be delayed or omitted with minimal impact. At its core, CPA involves the identification of all tasks within a given project, and then determining the order in which they must be completed in order to reach the desired outcome. This is done by examining the individual tasks and their dependencies on one another. Once this is done, the CPA will identify the “critical path”, which is the sequence of tasks that must be completed in order for the entire project to be completed on time.

How Does Critical Path Analysis Work?

What are the benefits of using critical path analysis, what are the limitations of critical path analysis, how to use critical path analysis as a problem solving tool, how to use critical path analysis as a planning tool.

Additionally, it can help project managers identify tasks that can be completed simultaneously or out of sequence without delaying other tasks. By using CPA as a problem solving and planning tool, project managers can ensure that their projects are completed on time and within budget. In conclusion, critical path analysis is an invaluable tool for problem solving and project planning. It allows users to identify the most important activities in a process and the order in which they must be completed. It also allows users to determine the minimum amount of time needed to complete a project or process.

By using CPA, users can plan and manage projects more efficiently.

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Lesson 20. CRITICAL PATH METHOD (CPM)

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• Project management

critical path method (CPM)

• Paul Kirvan

What is critical path method?

The critical path method (CPM) is a step-by-step project management technique for process planning that defines critical and non-critical tasks with the goal of preventing project schedule problems and process bottlenecks . CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.

In applying CPM, the following five steps are often followed:

• Define the required tasks and arrange them in an ordered, sequenced list.
• Create a flowchart or other critical path diagram showing each task in relation to the others.
• Identify the critical and non-critical relationships or paths among the tasks.
• Determine the expected end date or execution or completion time for each task.
• Locate or devise alternatives or backups for the most critical paths.

What is the critical path method?

When developing an overall project management plan it is essential to identify the project scope , which is all the activities and tasks that must be performed. In addition, those tasks must be assembled in the correct sequence and estimated time frames to complete provided for each. This helps project managers track the following:

• where the project is at any time;
• whether activities are ahead of or behind the critical path schedule;
• which steps need additional resources;
• which steps need to be rescheduled; and
• whether the project is on budget.

The critical path method is the piece of the project management plan that identifies the steps that must be completed -- the critical path. CPM also provides insight into ancillary activities that support the outputs and deliverables needed for other critical path activities and parallel critical paths that are linked to the primary critical path. These are all important to keeping a project on schedule and budget and reaching its goals .

In Figure 2, the critical path is highlighted. It includes the activities that must be completed for the project to reach its conclusion and is usually the longest path in the diagram. The diagram also depicts other elements of project planning : the sequence of tasks and the ancillary activities that are initiated from other parts of the plan and the activities they impact. The arrows identify the sequence of events.

Each activity box could be filled in with specific details related to each activity, such as a project timeline that includes the earliest start time and earliest finish time for each task, required resources and options to launch if the activity is not completed on time. Depending on the complexity of the project, more information may be embedded in each activity box.

Steps in the CPM process

CPM encompasses the following six steps:

• Identify each activity to be completed in the project; start with the high-level ones and then identify ancillary activities.
• Define the activity sequence. This also requires identifying dependencies among activities, such as which ones occur before or after others and which should occur concurrently.
• Build a flow diagram , also called a network diagram, similar to the one in Figure 2, that positions all activities for the entire project.
• Estimate the amount of time for completion of each activity and map that to the whole project plan, including the estimated completion date.
• Perform a critical path analysis to define the activities that must be completed to ensure project completion and success.
• Update the plan as the project progresses, accounting for delays, resource allocation, staffing issues and other factors. For this step, project management software with CPM capabilities is essential. These tools use a critical path algorithm that automatically adjusts the plan based on specific inputs, such as changes in scope or time frame .

Pros and cons of using CPM

Some of the advantages of using the critical path method include the following:

• identifies the sequence of activities and work breakdown structure;
• defines the activity duration for all elements of the plan;
• specifies cross-functional relationships among project activities;
• identifies dependent tasks for each activity;
• cites risks to the project, such as failure to complete a specific activity on time ;
• identifies ways to shorten time frames;
• compares the plan with performance to quickly identify issues;
• helps optimize project resources;
• identifies opportunities to change time frames, adjust team members and their duties, and modify the overall plan to achieve the desired outcome.

CPM provides many benefits, but it may not always be the most appropriate method for managing a project. For example, smaller, less complicated projects may not need the complexity of CPM. Various project management applications provide simpler tools and templates that might be more applicable to a less complicated project.

For complex projects, a project management team with CPM experience is essential. That, however, requires factoring in the overhead and related costs of using CPM.

What was the origin of CPM?

DuPont developed CPM in the 1950s. The chemical company first used the methodology in developing neoprene, a type of synthetic rubber. CPM streamlined production and maintenance in that development process.

Around the same time, the U.S. Navy developed a similar project management method -- Program Evaluation Review Technique (PERT) -- to address the development and production of submarine-based Polaris missiles . The two methods have similar objectives. PERT and Gantt charts are often used as part of project planning methodologies.

As a project planning tool, CPM has been adapted to other fields, including hardware and software product research and development. Various computer programs are available to help project managers use CPM.

CPM is part of overall project management and business process management (BPM) practices. Learn more about BPM best practices and how they affect project success .

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

Approx reading time:

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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A beginner’s guide to the critical path method in project management

Last updated

21 December 2023

Reviewed by

Mary Mikhail

Large and complex projects require the use of many materials and working parts. Without a clear plan for undertaking such a job, it’s easy to become overwhelmed and skip important tasks. When this happens, your project is less likely to meet critical deadlines. Or it could fail completely.

CPM is used to identify the vital aspects of any project and its dependent factors to define tasks and ensure the project is completed accurately and on time.

Read on to find out exactly what CPM is and how to use it. You’ll also find some examples of successful use cases.

• What is the critical path method?

The critical path method is a project management method used for calculating, planning, and scheduling large or complex projects. It enables project planners and teams to create a clear roadmap of the jobs or activities that are critical to completing a project on time. By identifying and scheduling fundamental tasks, project managers can assign a specific job’s start time, expected duration, and finish time.

Every project contains vital tasks that determine whether it’s completed on time. If any of these tasks fall behind schedule, so does the whole project.

CPM is a step-by-step plan for identifying critical tasks and creating a clear timeline (or path) in which these tasks will be completed. The schedule of these core project steps is the critical path. Once these tasks are scheduled, you can add other (less crucial) activities to the timeline.

What is a critical task?

A critical task is a job or activity central to a project’s timeline. Other activities will also be delayed if these central tasks are not completed on time.

Every project includes core tasks that must be finished before dependent tasks can begin. For example, you can’t put a roof on a home if the frame hasn’t been erected. In essence, critical tasks are the activities that must be carried out as planned to avoid disrupting the project timeline.

Why must non-critical tasks be monitored?

Critical tasks aren’t the only tasks you’ll need to take care of to complete an entire project. You’ll need to carry out other jobs, too. However, these can be executed less urgently. Since they aren’t core steps, you can choose to delay them until they fit into the schedule better.

By monitoring non-critical tasks alongside the undertaking of critical tasks, you can make informed decisions about when each task should be completed. This approach enables teams to complete several tasks simultaneously without critical delays.

Where was CPM first used?

While the US Navy’s Fleet Ballistic Missile (Polaris) Program was running behind schedule, the chemical company DuPont faced delays in plant turnarounds. Those running these projects needed a technique to get them back on track and deliver them as planned.

The developers of the Polaris Program created a solution called the project evaluation and review technique (PERT). DuPont developed the critical path method.

The PERT method calculates three different time estimations to determine the most accurate duration of each task. DuPont’s CPM plan uses a single time duration for the entire task to measure extra costs that would accumulate if the project duration is decreased.

Why is CPM important in project management?

CPM creates a project roadmap that establishes the longest sequence of tasks that must be executed to complete an entire project. By defining core tasks and the tasks that depend on them, project managers can outline the timeframe in which the project can be successfully executed. This helps reduce noise and align priorities, enabling multiple teams to complete tasks simultaneously without delays.

When should you use critical path analysis?

Critical path analysis is a way to refer to the early stages of CPM. CPM typically aims to develop an accurate project schedule, so the process occurs before the project’s start date—perhaps during the project’s planning phase or even during the process of developing a bid or project proposal.

Understanding a project’s critical path can help project managers estimate costs and resources and develop a predictable schedule.

• How to calculate the critical path

Virtually every project is planned based on completing the job as quickly and cost-effectively as possible without compromising quality. This approach offers the best return on investment (ROI) and ensures minimal resource waste. You can use CPM to make informed decisions about the best way to achieve this goal.

To calculate the critical path, start by identifying all tasks in the project. Once you have a clear idea of everything that needs to be done, you can assign levels of urgency based on dependencies and the estimated time needed for each task.

Take these steps to calculate your project’s critical path:

Define all the tasks required to complete the project.

Define the time requirements for each step based on existing knowledge or industry standards.

Establish dependencies (tasks that must be completed before another specific step can begin) for each task.

Identify which activities must be completed on time to avoid delays due to dependencies. These are your critical tasks.

Align critical paths in a sequential timeline with assigned start and finish times.

The significance of float or slack in CPM

Projects are rarely executed exactly as planned. Delays, resource constraints, unexpected incidents, and scope creep create conditions that cause any task to take longer than planned. To prepare for such issues, project managers should consider the consequences of delays.

The time a task can be delayed for without affecting dependent tasks or delaying the overall project is referred to as float or slack .

Activities on the critical path have zero float. If a critical task is delayed, it will immediately affect dependent tasks and the completion of the project. However, many other tasks can have varying levels of float.

High-float tasks can be delayed with minimal consequences. They simply need to be completed before the project deadline or before they affect another non-critical task. Label high-float tasks as low priority so that you focus on assigning resources to critical tasks. When team members become available, they can take care of high-float tasks while other tasks progress simultaneously.

Identifying slack for each task lets you assign start times and juggle tasks without affecting the project’s timespan.

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• Planning for unexpected contingencies and constraints

Large and complex projects can take weeks, months, or even years to complete. Long time frames combined with project intricacies may create unexpected changes that force you to expedite some tasks and postpone others.

To take these contingencies in your stride, you’ll need methods in place to address how such issues impact the overall project timeline.

The two most common methods of dealing with contingencies and constraints when using CPM are fast-tracking and crashing.

Fast-tracking

Fast-tracking is easy to understand if you’re used to multi-tasking to stay on schedule. When deadlines are looming, fast-tracking is the process of executing multiple jobs on the critical path simultaneously. This approach requires you to dilute resources to complete multiple jobs at once and can only be used for activities without dependencies.

When you need to meet updated or emergency deadlines, crashing is the process of allocating more resources to speed up activities. You might bring in more professionals or use resources from tasks with high floats.

Crashing is typically used in emergencies because it can impact critical tasks and project scope . When the project scope is affected, you’ll need to inform all project stakeholders .

• Comparing CPM to other methods

CPM isn’t the only project management method for scheduling and prioritizing project tasks. Comparable methods are used to evaluate the duration and dependencies of specific tasks. While these methods have similarities, their overarching goals differ.

Critical path method vs Gantt charts

Gantt charts map out projected activities and track them against a set timeline. Like CPM, they show dependencies between tasks, and you can use them to create a timeline. However, there are distinct differences between the goals of CPM and Gantt charts and how they are displayed.

CPM is displayed as a network diagram, while Gantt charts are displayed as a horizontal bar chart.

Gantt charts show the resources required for each activity.

Gantt charts plot activities on a timescale, while CPM plots them on a network diagram with an estimated time duration for each task.

CPM identifies critical and non-critical paths and calculates project duration. Gantt charts are designed to visualize how project activities are progressing.

Critical path method vs PERT

The project evaluation and review technique was developed around the same time as CPM to solve similar issues, but the techniques are quite different.

CPM and PERT are both used to evaluate project duration. They identify dependencies and provide an estimated duration for each task. However, they have several notable differences in execution.

PERT is used to estimate the time required to complete activities, while CPM is used when task durations are already estimated.

CPM is designed to evaluate time–cost trade-offs and establish priorities, while PERT focuses on meeting deadlines or shortening a project’s duration.

PERT has three estimates for each activity, while CPM only has one.

PERT is often used for projects that have significant uncertainty, while CPM is better suited to projects where tasks are well-defined.

• CPM benefits

The critical path method is an excellent project management tool to help you deliver your project on time and within budget. It can be useful in recognizing potential delays and scope creep while creating a clearly defined schedule for the project.

Below are some of the most common advantages of using CPM for large and complex projects:

Helps prioritize tasks

CPM’s overarching goal is to identify essential tasks and ensure their timely completion.

Identifying the critical path enables you to clarify which tasks depend on one another, establishing the order in which they must be completed.

Once the critical path is defined, you can prioritize the non-critical tasks based on their slack level. The approach eliminates the “noise” in a multi-faceted project and keeps teams on track.

Improves team communication

Large projects typically require the participation of multiple teams with different specialties. These teams work together to establish an accurate critical path. When the resulting CPM diagram is used as a single source of truth, every participant in the project will have similar expectations of how the work schedule will play out.

Optimizes efficiency

CPM is used to identify the earliest possible starting point and the latest acceptable finishing point for each project task.

Mapping out a schedule with accurate timeframes and dependencies can enable project managers to identify areas that could shorten the critical path. You might achieve this by assigning more people to the job or juggling non-critical tasks for optimal efficiency.

Helps create accurate schedules when paired with PERT

PERT and CPM have distinct differences that naturally complement each other. While both techniques are designed to evaluate time, PERT is focused on time management, while CPM addresses how the project timeline affects the budget.

PERT charts contain three estimates for each task, making it easier to discover potential risks and avoid delays.

Helps map out project plans when paired with Gantt

Gantt charts plot project tasks on a time schedule in a horizontal graph, which acts as a visual communication tool. They can be used to track actual progress against planned progress to help maintain an accurate schedule.

When combined with CPM, Gantt charts give you a more detailed view of the product path, including the required resources for each task.

• How to use the critical path method

Now that you have a clear understanding of the CPM’s purpose, you can apply the process to devise an accurate project schedule. Follow the steps below to plan your project using the critical path method:

1. List project activities

Begin by evaluating your complete project and breaking down the necessary work into manageable steps. Create an ordered list of all the tasks required to complete the job.

2. Identify task dependencies

Some tasks can’t begin until others are finished. Examine your list of tasks and define each activity’s immediate predecessor. Some tasks won’t have dependencies, but critical tasks often do.

3. Create a critical path diagram

Identifying dependencies enables you to create a sequence of events. Create a chart that maps out the tasks in the order they should be completed. The network diagram should include arrows or symbols to identify dependencies.

4. Estimate the timeline for each activity

Estimate the time required to complete each task on the diagram using prior experience or industry knowledge.

Use the PERT method to accurately calculate the best-case estimate, the most likely estimate, and the worst-case estimate. These three values can be used to determine slack more accurately and develop a precise timeline.

5. Use the critical path formula

Once you’ve established estimated durations for each task, you can develop a timeline for the entire project using the critical path algorithm. The critical path formula uses a forward pass and a backward pass to establish a timeline.

The forward pass uses a specified start date as the earliest start (ES) for the first task and calculates the earliest finish (EF) by adding the estimated duration. The process proceeds through the schedule by defining the ES as the highest EF of immediate predecessors.

The backward pass calculates late start (LS) and late finish (LF) dates using the lowest LS value from immediate successors to calculate LF. This pass starts with the last scheduled activity and moves backward through the schedule.

Here’s a simple example using a forward pass and backward pass to establish a timeline for a project with three activities: A, B, and C. The numbers represent the duration of each activity in days. Each activity is dependent on the one before it—B is dependent on A, and C is dependent on B.

Here are the activity durations:

Activity A: 3 days

Activity B: 2 days

Activity C: 4 days

Forward pass

Start at the beginning. Set the ES for the first activity to 0.

Activity A:

Duration = 3

EF = ES + Duration = 3

Activity B:

ES = EF of A = 3

Duration = 2

EF = ES + Duration = 5

Activity C:

ES = EF of B = 5

Duration = 4

EF = ES + Duration = 9

The EF of C is the project duration in this case.

Backward pass

Start at the end. The project duration is the LF of the last activity.

LF = EF of C = 9

LS = LF - Duration = 5

LF = LS of C = 5

LS = LF - Duration = 3

LF = LS of B = 3

LS = LF - Duration = 0

You now have the ES, EF, LS, and LF for each activity.

Critical path

The critical path is the path with zero slack (total float). Activities on the critical path have the same ES as LS and the same EF as LF.

In this example, the critical path is A -> B -> C. The project duration is nine days, and any delay in activities on this path will directly affect the project completion date. Activities A and C are “critical” in the sense that they must be completed on time to avoid delaying the project.

6. Identify the critical path

Define critical tasks as those with no slack level (zero float) and align these tasks into a schedule based on immediate dependencies. Assign a time duration to each critical task derived from the formula used in the previous step. The activity sequence with the longest duration is the critical path.

7. Revise during execution

While the critical path is determined during the planning phase, it shouldn’t be set in stone. Update the critical path chart or diagram as you execute the project. As changes occur in the project schedule, you can define ways to address delays. You can develop a more accurate schedule by updating it to account for constraints and contingencies.

• Examples of the critical path method

The critical path method can be used to manage nearly any type of project in which you can estimate the duration time of specific tasks. Observing examples of CPM in practice can help you clearly visualize how the technique is used.

CPM in construction

Building a house is one of the most common examples used to clearly illustrate project planning with dependencies and potential time constraints. Construction is a complex project with many dependencies.

Conduct excavation

Build a foundation

Construct a wooden frame

Lay brickwork

Box in the walls

Build the roof

Wire electricity

Install plumbing

Install heating and ventilation

Lay flooring

Finish wall carpentry

Fasten gutters and downspouts

Install plumbing fixtures

Finish interior carpentry

Put gutters and downspouts in place

Identifying dependencies

Construction involves many dependencies.

The core jobs will outline your project’s critical path. The process of pouring footers and building a foundation is dependent on the starting task—excavation. Similarly, framing is a critical task that must be completed before walls can be constructed and the roof can be built. However, the brickwork and the electricity can be reasonably postponed until a convenient time.

Jobs with float can be executed in parallel to dependent tasks. For example, an available worker can lay brickwork while others are building the roof.

Therefore, jobs on the critical path are most likely to be excavation, foundation, framing, roof, rough wiring, and rough plumbing. The other tasks in the project will have some float and can run parallel to other tasks.

CPM for shorter tasks

It sometimes helps to consider how project management works from a simpler perspective. If you’re a practiced cook, you’re accustomed to the process of taking care of multiple tasks while being mindful of dependencies. Yet, an inexperienced cook could forget essential steps.

Imagine preparing breakfast for friends. You plan to cook pancakes, eggs, and bacon. You’ll prepare many of these foods in tandem, but some steps have dependencies.

Purchase eggs, bacon, flour, milk, maple syrup, oil, and butter

Preheat the oven to 200 degrees to keep the food warm until serving time

Measure and mix the flour, eggs, oil, and milk to create pancake batter

Fry the bacon

Cook the pancakes

Season the eggs

Fry the eggs

Keep the pancakes warm in the oven while you cook the other foods

Top the pancakes with maple syrup

Again, your starting step for this project is a critical task that must be completed before any other activities can begin: purchasing the ingredients.

Moving forward, you can’t cook the pancakes before mixing the batter. However, since you plan to keep food warm in your preheated oven, you can fry the bacon while you’re mixing the batter or flipping the pancakes. Ideally, you would prepare the eggs last so they will be at the optimal temperature when the meal is served.

The jobs on the critical path are most likely to include buying ingredients, preheating the oven, mixing the batter, and frying the eggs. Other tasks can be completed in parallel to these essential steps.

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Critical Path Method (CPM) in Project Management

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

What Is the Critical Path In Project Management?

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

• Benefits of Using CPM In Project Management

CPM Training Video

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

• How to Find the Critical Path with ProjectManager

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

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

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Critical Path Template

Use this free Critical Path Template for Excel to manage your projects better.

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

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

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

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

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

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

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

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

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

Related: Free Project Plan Template

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

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

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

Free Critical Path Template for Excel

Need help getting started with a critical path analysis for your project? Download this free critical path template for Excel. All the formulas are embedded, the network diagram is made—all you have to do is input your values.

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

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

When done properly, critical path analysis can help you:

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

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

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

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

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

Forward Pass in CPM

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

Backward Pass in CPM

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

Related: 12 Free Project Scheduling Templates for Excel

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

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

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

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

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

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

1. Collect Project Activities

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

2. Identify Task Dependencies

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

3. Create a Critical Path Diagram

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

4. Estimate the Timeline

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

5. Use the Critical Path Formula

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

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

6. Identify the Critical Path

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

7. Revise During Execution

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

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

Benefits of Using CPM in Project Management

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

Critical Path Analysis Improves Team Communication

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

CPM Helps Prioritize Tasks

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

CPM & PERT Help Create Accurate Schedules

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

CPM & Gantt Charts Help Map Out Project Plans

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

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

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

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

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

Link Tasks and Avoid Bottlenecks

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

Get a High-Level View of Your Progress

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

Make More Insightful Decisions

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

Know Your Project Variance

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

Keep a Record of Your Plan

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

See Deep Data on Performance

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

How to Find the Critical Path With ProjectManager

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

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

1. Start a Project With a Gantt Chart

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

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

2. Add Task Dependencies

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

3. Set the Project Baseline

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

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

4. See the Critical Path

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

5. See Your Overview With a Dashboard

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

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

6. Report on Progress

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

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

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

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Critical Path Method Resources

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

External Articles

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

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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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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

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• 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.

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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.  

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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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With roots dating back to the 1960s, the critical path method (CPM) is a technique used during the initial project analysis, planning, and scheduling phases of project management. The process has changed over the years since its inception, and while the modern critical path method mirrors the original in many ways, there are noticeable differences. But what is critical path in project management? 

Critical path in project management is the sequence of tasks or activities that must be completed during the execution of a project, and the critical path method is a means of mapping out these activities. In this article, we will go into greater detail when answering the question of what critical path is in project management and how to implement CPM in the 21st century.

Why It Is Important to Identify a Project’s Critical Path

Critical path is a project management term that refers to the various project tasks and activities that are the most time-consuming. Once the critical path has been identified, the individual tasks along the critical path—known collectively as critical activities—are easily prioritized and delegated as needed.

The overall project timeline ultimately depends on the critical path. Since the critical path represents the minimum amount of time needed to complete the project, it is vital to identify the critical path during the initial project planning phase.

How to Use the Critical Path Method (+ Example)

To illustrate how to use the critical path method, we’ll be using it to plan an online press conference.

Step 1: List all project tasks

Critical path project management begins with a list of all the tasks and activities, as well as the various milestones and deliverables, associated with the project at hand. For small or short-term projects, these activities can easily be listed with a simple, multi-column chart.

When planning an online press conference, for example, you might split activities into various groups: one for guests, another to cover the format of the press conference itself, yet another for logistics planning, and one more for creating an online press kit for distribution to mainstream media outlets.

Larger projects, which could involve dozens or even hundreds of separate tasks, are best managed by using CPM alongside other tools, such as a Gantt chart, to keep everything running as smoothly as possible.

Step 2: Identify dependencies and estimates

Next, take the time to identify any task dependencies within your project. These are tasks that can’t be finished until another related activity is complete. Once you’ve identified and listed dependencies, it’s useful to provide estimates of how long each individual task is expected to take. It’s okay if you don’t know exactly; a rough estimate will suffice.

If you have a list of guests you hope to see at your upcoming press conference, one of your specific tasks will involve sending out invites, either through email or traditional mail. However, you can’t start sending invitations until you’ve created them. And once created, you still need to compile the contact information for each guest.

As such, the activity of sending out invitations is dependent on the separate tasks of creating invitations and collecting contact information. Some activities, like collecting contact details, aren’t dependent on any other tasks. Other activities might have several different dependencies, so it’s important to complete this process for every activity on your list.

Read more: Understanding Task Dependency Types in Project Management

Step 3: Use a network diagram that traces dependencies

Creating a simple network diagram is a helpful way of visualizing the different project activities and their dependencies. In most cases, a diagram can be created using individual boxes to represent each task or activity. Each dependency should ultimately point to all of the tasks that can be started once it is completed. While some activities will point to several other tasks, others might point to only one.

When diagramming complicated or long-term projects, consider using different colors for each dependency. This makes it easier to track specific tasks—and their critical activities—throughout the entire project lifecycle.

Step 4: Do a forward pass

Once you have your basic diagram created, it’s time to move through your diagram with a forward pass. Not only does this ensure the validity and accuracy of your diagram, but it also makes it easy to determine the duration of the entire project. Although we already made rough estimates of the time-to-completion for each specific activity, that doesn’t really cover the project as a whole.

In order to determine the project duration, we need to introduce to new variables to the diagram:

• Early start time (ES) : This is the earliest possible time that any given task can be started.
• Early finish time (EF) : Conversely, this is the earliest possible time that any given task can be completed or finished.

Calculating the ES of each task is a straightforward process. In our project management critical path example above, the first tasks that can possibly be started are those with no dependencies. As such, they have all an ES of 0, as they can be started on day 0. To determine the EF, add the activity’s estimated duration to the ES. If task 1 takes 0.5 days to complete, for example, then the EF is 0.5.

To add these variables to our diagram, put the ES in the upper-left corner of each task box and put the EF in the upper-right corner. When calculating the EF and ES of tasks that depend on earlier tasks, make sure to add the variables from the task’s dependencies too.

Task 3, for example, has an EF of 0.5; however, it can’t be started until tasks 1 and 2 are finished. Instead of adding the two together, we simply pick the highest EF. In this case, task 3 has an EF of 1 because of its own time (0.5 days to finish) and the EFs of the previous tasks. 

Step 5: Do a backward pass

Next, complete a backward pass. Again, this process introduces two new variables to the diagram:

• Latest start time (LS) : This is the latest possible time that a task can be started without causing delays throughout the entire project.
• Latest finish time (LF) : Likewise, this is the latest possible time that a task can be finished without causing delays throughout the entire project.

To determine the LF, start by copying the final task’s EF and pasting it as the LF. As you can see in the example above, task 11 has 6.5 for both its EF and its LF.

To determine the LS, simply subtract the task’s duration from its LF. Since task 11 has a duration of 0.5 and an LF of 6.5, its LS is 6. For dependencies, use task 11’s LS as the LF of any tasks that lead directly to it. Using our critical path example, this includes tasks 3, 5, and 10. To determine the LS of these earlier tasks, simply subtract their duration from task 11’s LF. If a task points to more than one other task, use the lower LS as that task’s LF.

Step 6: Find the critical path

In order to find the project’s critical path, follow the tasks that have the same EF and LF. In our example, this has us starting on task 6 and proceeding to tasks 8, 9, 10, and 11—this is the critical path.

Remember, only critical activities can extend the project’s duration. While failing to finish task 9 on time would delay the entire project, a slight delay in task 4 or 5 wouldn’t have much effect, as long as they’re all completed by their respective LFs.

Benefits of the Critical Path Method in Project Management

Critical path aids skilled and novice project managers alike in optimizing and streamlining the entire project lifecycle. But how exactly does it help?

Prioritizing tasks

The critical path method makes it easy to prioritize and delegate tasks. Critical activities should be given the highest priority, since the project ultimately depends on those for completion. Non-critical activities can then be scheduled around the completion of these other, more important tasks.

Anticipating and avoiding bottlenecks

The CPM also helps you anticipate and avoid bottlenecks in the workflow, especially when it comes to scheduling and resource planning. Identifying the tasks that take the longest time to complete at the very beginning of your project ultimately helps you plan ahead and make the necessary accommodations before it’s too late.

Identifying slack

Sometimes known as float , slack refers to the total number of days that a task can be delayed before it affects other activities within the project. To identify slack in individual tasks, subtract the task’s EF from the LF.

Limitations of the Critical Path Method in Project Management

As useful as the CPM is, the process isn’t perfect. It has flaws, disadvantages, and limitations project managers should keep in mind.

Resource dependencies

While the critical path method makes it easy to understand individual task dependencies, it doesn’t accommodate resource dependencies. For example, assigning one person to complete two different tasks. Since the second task can’t be started until the first one is finished, there could be unexpected delays in the project duration.

Scheduling interruptions

Holidays, system updates, and PTO could all increase the overall project duration. While you certainly can’t plan for unexpected interruptions, some, like regular holidays and scheduled vacation time, should be taken into account when determining your project’s overall duration.

The CPM is best used when planning and organizing smaller projects. Large or complicated projects with hundreds or even thousands of individual tasks quickly become too bulky to be of any real use.

Manual vs Automated Critical Path Mapping

For most projects, critical path mapping can be completed manually. Our example illustrated above walks you through the steps needed to create a network diagram and critical path map without the use of software automation. For those who want to save even more time, however, there are apps and utilities that can automate much of the process.

While every software solution offers its own combination of features and functionality, some of the common elements of CPM software include:

• Drag-and-drop interface for adding tasks and dependencies
• Customizable templates for individual tasks
• Automated identification of your project’s critical path
• Collaboration amongst teammates and stakeholders
• Milestone tracking and notification
• Automated analysis and updating of start dates, due dates, and task durations

Automated CPM software is ideal for small project teams that are regularly working on large or complicated projects. It can also be used by novice PMs to guide them through the critical path method during their next project.

Critical Path Method: A Great Method for Planning a Project Timeline

The critical path method is one of the easiest and most straightforward ways of planning, analyzing, and disseminating a project timeline for project teammates, clients, and stakeholders. In project management , mapping out critical path can be implemented by novices and PM veterans alike, and it’s a proven way to streamline the typical project lifecycle while making it easier to prioritize activities and track productivity.

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Critical Path Method (CPM) Guide for Project Management

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Timely project completion ensures that projects stay within budget and fulfill the expectations of stakeholders. The critical path method is a project management technique that is integral to achieving these objectives.

CPM was developed in the late 1950s by James E. Kelley of Remington Rand and Morgan R. Walker of DuPont to address the challenges of complex project scheduling. It is beneficial for projects with interdependent activities, where delays in one task can have cascading effects on subsequent tasks and the project’s completion date.

In this guide, I explain the concept of CPM, analyze its benefits, and show you how to implement and calculate critical paths. Whether managing a small project or a large-scale enterprise operation, understanding and implementing CPM can significantly enhance the likelihood of success.

What is the critical path method?

The critical path method is a step-by-step project management technique used to identify the sequence of tasks that must be completed on time for the entire project to be finished by the deadline. These tasks form the “critical path,” which is the longest stretch of dependent activities that determines the shortest possible project duration.

CPM focuses on the most crucial tasks that cannot be delayed without affecting the project timeline. By calculating the critical path, project managers can determine the minimum project duration and identify which tasks have flexibility (float) and which do not. This method also highlights potential bottlenecks and helps project managers prioritize tasks essential for on-time project completion.

This knowledge allows for better resource allocation, risk management, and scheduling, ensuring the project stays on track.

Benefits of CPM

CPM allows project managers to focus on critical tasks, better manage their time to avoid delays, and ensure that the project stays on track. Aside from timely project completion, CPM also offers the following benefits.

Manages budget

CPM enables project managers to optimize resource allocation by providing a precise sequence of critical tasks, therefore reducing unnecessary expenses. For instance, when you identify float time in non-critical tasks, you can reassign resources like employees to critical functions that are behind schedule, thus avoiding unnecessary overtime costs.

This proactive approach ensures that every dollar is spent where it has the most impact. CPM’s structured timeline also makes it easier to plan for material deliveries just in time, which minimizes storage costs and reduces the likelihood of tying up capital in excess inventory.

Identifies critical tasks

CPM offers a clear view of the tasks that are critical to the project’s success, which helps project managers set priorities and allows for the proactive management of potential delays. This focus ensures that the project stays on track and reduces the risk of missing deadlines. It also helps identify potential risks early on so that proactive measures can be taken to mitigate them.

Visualizes the project timeline

Typically depicted through a network diagram or flowchart, CPM highlights the sequence and duration of each task within a project. This visual representation allows project managers to easily see how tasks are interrelated and which ones are critical to the project’s overall timeline. This clarity simplifies the planning process, making allocating resources and anticipating potential delays easier.

Improves team communication

By clearly defining the critical path and task dependencies, CPM enhances communication within the project team. Each person knows which tasks are critical, who is responsible for them, and the impact of delays. This shared understanding fosters collaboration, reduces misunderstandings, and ensures the team is aligned toward the project’s goals.

How to calculate the critical path

Calculating the critical path involves several steps that require a detailed understanding of the project’s tasks and dependencies. Here’s a step-by-step guide:

Step 1: List all tasks (activities) required for the project

Identify and list all the tasks required to complete the project. Each task function or activity should be clearly defined and its expected duration should be included.

Step 2: Determine dependencies (sequence of activities)

Identify the dependencies between tasks to understand which tasks must precede others. Mapping these dependencies is vital for comprehending the sequence of activities.

Step 3: Estimate task durations

Assign a duration to each task. This can be done using historical data, expert judgment, or estimation techniques like the Program Evaluation and Review Technique (PERT).

Project managers can also use the Forward Pass and Backward Pass techniques to calculate tasks’ earliest and latest start and finish times. These techniques are integral to identifying the critical path and ensuring the project stays on schedule.

• Forward Pass technique: Determine each task’s earliest possible start and finish times. This process helps schedule tasks as early as possible, minimizing project duration.
• Backward Pass technique: Define each task’s latest start and finish times, ensuring that the project is completed by its deadline. This process enables PMs to identify the flexibility in the schedule and the latest possible start times without delaying the project.

Step 4: Draw a network diagram of the critical path

Using the information from the previous steps, create a network diagram (also known as a project schedule network diagram). In this diagram, tasks are represented as nodes and dependencies are shown as arrows connecting the nodes. This visual tool helps to illustrate the sequence of tasks and their interrelationships clearly.

Step 5: Identify the critical path

The critical path is the longest sequence of activities in the network diagram that must be completed in order to finish the project, and it represents the shortest possible time for completion.

To identify the critical path, calculate the earliest start (ES) and earliest finish (EF) times for each task, followed by the latest start (LS) and latest finish (LF) times.

• Calculate ES and EF: Begin at the start of the network diagram and calculate the earliest time each task can start and finish. The earliest start time is the earliest time a task can begin, considering the completion of preceding tasks. The earliest finish time is calculated by adding the task duration to its earliest start time (EF = ES + task duration).
• Calculate LS and LF: Work backward from the project completion date to determine the latest time each task can start and finish without delaying the project. The latest start time is calculated by subtracting the task duration from its latest finish time (LS = LF – task duration).
• Calculate Float (Slack) for each task: Float, or Slack, is the amount of time a task can be delayed without affecting the project’s completion date. It is calculated by subtracting the earliest start time from the latest start time (Float = LS – ES). Tasks with zero float are on the critical path, meaning any delay in these tasks will delay the project.

Step 6: Analyze and adjust

Review the critical path and identify any potential issues or bottlenecks. Adjust the schedule as needed to optimize the project timeline. If critical tasks are at risk of delay, consider reassigning resources or adjusting the project plan to keep the project on track.

Examples of critical path method

To better understand how CPM works, here are two real-world examples where it could be implemented to support a project.

Developing a website

In this instance, you are managing the project to create a corporate website. The project includes planning, designing, developing, testing, and launching the website.

Tasks and durations

• A. Project Planning (2 days)
• B. Requirements Gathering (3 days): Starts after A
• C. Design Mockup Creation (5 days): Starts after B
• D. Design Approval (2 days): Starts after C
• E. Website Development (10 days): Starts after D
• F. Content Creation (7 days): Starts after B
• G. Content Integration (3 days): Starts after E and F
• H. Testing (4 days): Starts after G
• I. Final Approval (2 days): Starts after H
• J. Website Launch (1 day): Starts after I

Critical path calculation

Step 1: Identify all possible paths.

• Path 1: A → B → C → D → E → G → H → I → J
• Path 2: A → B → F → G → H → I → J

Step 2: Calculate the duration of each path.

• Path 1: A (2 days) + B (3 days) + C (5 days) + D (2 days) + E (10 days) + G (3 days) + H (4 days) + I (2 days) + J (1 day) = 32 days
• Path 2: A (2 days) + B (3 days) + F (7 days) + G (3 days) + H (4 days) + I (2 days) + J (1 day) = 22 days

Step 3: Determine the critical path.

• Critical path: Path 1
• Duration: 32 days

The critical path for developing this website is Path 1, with a total project duration of 32 days. Tasks on Path 2, such as Content Creation (F), do not influence the overall project duration as they can be completed in parallel without delaying the project, as long as they are done before the Content Integration (G) task, which is also part of the critical path.

Building a house

For this example, you’re managing a project to build a single-family home. All of the blueprints have already been approved, so your focus here is on the physical actions of construction. The project includes laying the foundation, framing, roofing, plumbing, electrical work, and interior finishing.

• A. Site Preparation (3 days)
• B. Laying Foundation (5 days): Starts after A
• C. Framing (7 days): Starts after B
• D. Roofing (4 days): Starts after C
• E. Plumbing (6 days): Starts after C
• F. Electrical Work (5 days): Starts after C
• G. Interior Finishing (8 days): Starts after E and F
• H. Final Inspection (2 days): Starts after G
• I. Handover to Client (1 day): Starts after H
• Path 1: A → B → C → D → G → H → I
• Path 2: A → B → C → E → G → H → I
• Path 3: A → B → C → F → G → H → I
• Path 1: A (3 days) + B (5 days) + C (7 days) + D (4 days) + G (8 days) + H (2 days) + I (1 day) = 3 + 5 + 7 + 4 + 8 + 2 + 1 = 30 days
• Path 2: A (3 days) + B (5 days) + C (7 days) + E (6 days) + G (8 days) + H (2 days) + I (1 day) = 3 + 5 + 7 + 6 + 8 + 2 + 1 = 32 days
• Path 3: A (3 days) + B (5 days) + C (7 days) + F (5 days) + G (8 days) + H (2 days) + I (1 day) = 3 + 5 + 7 + 5 + 8 + 2 + 1 = 31 days
• Critical path: Path 2

In this case, Path 2 is critical because it includes the longest sequence of dependent tasks. Any delay in these tasks will push back the entire project timeline.

CPM vs PERT

CPM and PERT are both project management tools used for planning and scheduling. They have distinct differences and are not interchangeable. However, they can complement each other when used together.

CPM is deterministic, providing a fixed timeline based on known task durations. It is used when precision is required. It focuses on identifying the longest sequence of dependent tasks (the critical path) to determine the project’s completion date. CPM is ideal for projects with well-defined tasks and stable timelines.

Conversely, PERT is probabilistic, allowing for flexibility in planning by considering different outcomes. It is useful for projects with high uncertainty, allowing project managers to plan for different scenarios. PERT is determined using three points:

• Optimistic (O): The minimum time needed if everything goes perfectly.
• Most Likely (M): The duration if the activity takes place under normal circumstances.
• Pessimistic (P): The maximum time needed if major problems occur.

How do you calculate the critical path?

The critical path is calculated by identifying all tasks, determining their dependencies, estimating their durations, and then calculating the earliest and latest start and finish times. Tasks with zero float make up the critical path, and any delay in these tasks will delay the entire project.

What are the four key elements of the critical path method?

• Critical path analysis.
• Float determination.
• Early start and early finish calculation.
• Late start and late finish calculation.

Why is the critical path method used?

CPM is used to identify the longest sequence of tasks in a project. This allows project managers to focus on the most time-sensitive activities to ensure on-time project completion. It also helps with practical project scheduling, resource management, and the identification of potential delays.

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How to calculate the Critical Path with Examples 🥇

The critical path method is one of the most important concepts in project management; however, many students have difficulties in its application. In this post, you will learn how to calculate the critical path of a project step by step by following practical examples.

Before you start we recommend you to review our post how to create a PERT CPM chart step by step with examples ; where we explain how to graphically represent the relationships between the activities of a project. Creating the chart of project is the starting point to calculate our critical path.

You can also check our online critical path method calculator that performs the steps to calculate the critical path automatically.

What is the Critical Path Method?

The Guide for Project Management (better known as PMBOK Guide), defines the critical path as:

“The sequence of scheduled activities that determines the duration of the project”.

To complete a project, we must perform all the activities that compose it. Some activities can be done simultaneously, but others must be done in a certain order. For example, if I am going to build a house, I must first build the walls before painting them. Of all the sequences of activities that make up the project, the sequence that has the longest duration will be the critical path and determines the total project time . As a consequence, the critical path method specifies the algorithm for finding it.

Why is Critical Path Important?

By identifying the critical path, teams recognize the most important tasks to be performed in a project.

Further, any delay in a critical path activity can cause the entire project to be delayed, so managers take extra care to ensure those activities take place as planned.

Important: Projects may have multiple critical paths.

What methods are used to calculate the Critical Path?

The methods used to calculate the critical path are the Project Evaluation and Review Technique (PERT) and the Critical Path Method (CPM).

The PERT and CPM methods began to be developed in the 1950s to assist managers in scheduling, monitoring and controlling large, complex projects. The CPM method (1957) was implemented as a procedure to assist in the construction and maintenance of chemical plants. The PERT technique was developed independently in 1958 for the U.S. Navy's Polaris project.

Although both methods are similar, they used different techniques to estimate task durations. The PERT method used three different time estimates for the duration of each task, plus it calculated the probability of completing the project at a given time. The CPM method used a single duration for each task; however, it also analyzed the additional costs that would be incurred if the project is accelerated.

The differences between the two techniques are now considered to be minimal; therefore, we can refer to both as an overall method called PERT CPM .

How to calculate the critical path?

To calculate the critical path we will follow the following steps:

• Step 1: Obtain the project data. Make a list of all the activities of the project along with their dependencies and their specific times.
• Step 2: Elaborate the network diagram. We have written a post that explains how to elaborate the project network diagram step by step.
• Step 3: Calculate the Early Start and Late Start Times. Determine the Early Start and Late Start Times for each activity.
• Step 4: Calculate the Early Finish and Late Finish Times. Determine the Early Finish and Late Finish Times for each activity.
• Step 5: Calculate the slack time. The critical path must be determined by finding out the slack for each activity of the process. The activities where there is no slack are the ones making up the critical path.

How to Calculate Early Start, Late Start, Early Finish, Late Finish and Slack (Float)

To visualize the calculation of these values, we will use the following graphic representation of the activity:

Duration (t):

Indicates the time it takes to complete the activity.

Early Start Time (ES):

This is the earliest time that an activity can be started assuming all previous activities have been completed beforehand. For activities that have more than one precedent, the ES is the greatest of the late start time of their precedents.

Early finish Time (EF):

This is the earliest time that an activity can finish. It is equal to the early start time plus its estimated duration (t):

EF = ES + t

Late Finish Time (LF):

This is the latest time at which an activity can be completed without delaying the entire project. It is obtained by equaling the late start time of the activity that immediately follows. If activities have more than one task immediately following them, the LF will be the least of the late start time of those activities.

Late Start Time (LS):

It is the latest time an activity can begin without delaying the whole project. It is equal to the Late Finish Time minus the expected duration of that activity (t):

LS = LF – t

Slack – Float (S):

A period of time when an activity can be delayed without causing the entire project to be delayed. All activities contained in the critical path have zero slack.

Here is how it is calculated mathematically:

S = LS – ES = LF – EF

We will illustrate these concepts with an example:

Imagine that your professor asks you to write an essay to be submitted in 15 days.

According to the length of the topic, it will take you approximately 1 week to prepare it. If you are a very responsible person, you will probably start the essay as soon as possible. The earliest start time (ES=0) , represents the first moment when you can start your essay:

If you start your project at point 0; you will have it ready at point 7. That final value represents the early finish time (EF=7) .

Now let's suppose that you like to do your activities at the last minute; most likely you want to finish your essay right on the day of the presentation. That day would be point 15 and represents the late finish time (LF=15) . You cannot exceed that point because you will no longer submit the paper on time.

In order for you to finish your paper on the 15th day, you have to start 7 days earlier (the time it takes to do the rehearsal); therefore you must start on the 8th day. This point represents the late start time (LS=8) . If you start after this date you will not be able to submit your work on time.

The 8 free days you have between the time you start work and the date of submission is the slack (float) in your activity.

Slack = LS – ES = LF – EF

Slack = 8 – 0 = 15 – 7 = 8

If we change the scenario and our teacher gives us only the one-week deadline to submit the essay. We will no longer have any free time (slack) so I must start working on the essay from the very beginning to get it done on time. Since this activity has no chance of being delayed, we call it a critical activity .

In project management, it is required to calculate these values for each activity which is achieved through a two-path process: a forward path to calculate ES and EF; and a backward path to calculate LS, LF and slack (float).

This procedure will be detailed by means of solved examples:

Draw the activity-on-node (AON) project network associated with the following activities for Dave Carhart’s consulting company project.

• How long should it take Dave and his team to complete this project?
• What are the critical path activities?

Solution 1:

The network diagram would look as follows:

The development of this diagram was explained in detail in our article on creating PERT CPM diagrams . The number at each node represents the duration of each activity.

Forward path

We will now perform the forward path to calculate the ES and EF with an analysis of each activity.

Start node:

This dummy node has all values equal to zero.

Activity A:

Since it is the first activity, its ES will be equal to the EF of the starting node (zero); the EF is calculated as follows:

EF = ES + activity time

EF A = 0 + 3 = 3

Activity B:

It has as precedent only activity A; therefore its ES will be equal to the EF of activity A. In the same way as the previous node, the EF of activity B is calculated by adding its ES + the corresponding time:

EF B = 3 + 4 = 7

Activity C:

It has as precedent only activity A; therefore its ES will be equal to the EF of activity A. The EF of activity C is calculated by adding its ES + the corresponding time:

EF C = 3 + 6 = 9

Activity D:

It has as a precedent only activity B; therefore its ES will be equal to the EF of activity B. The EF of activity D is calculated by adding its ES + the corresponding time:

EF D = 7 + 6 = 13

Activity E:

It has as a precedent only activity B; therefore its ES will be equal to the EF of activity B. The EF of activity E is calculated by adding its ES + the corresponding time:

EF E = 7 + 4 = 11

Activity F:

It has as precedent only activity C; therefore its ES will be equal to the EF of activity C. The EF of activity F is calculated by adding its ES + the corresponding time:

EF F = 9 + 4 = 13

Activity G:

It has as precedent only activity D; therefore its ES will be equal to the EF of activity D. The EF of activity G is calculated by adding its ES + the corresponding time:

EF G = 13 + 6 = 19

Activity H:

This activity has two precedents: E and F; therefore its ES will be equal to the highest EF of both activities. In this case, activity F has the highest value with 13. The EF of activity H is calculated by adding its ES + the corresponding time:

EF H = 13 + 8 = 21

The end fictitious node is joined with the last activities G and H; and the highest value of the EF of both activities is placed as ES: 21. This value represents the total duration of the project. As this node has zero duration (because it is fictitious) its EF will be equal to 21 + 0 = 21.

Backward path

To finalize the critical path calculation we will perform the backward traversal to calculate the LF and LS, starting from the final node; placing the values at the bottom of the node as follows:

For the end node the LF value is equal to the project duration (21). The LS is calculated by subtracting the LF minus the duration (zero).

LS End = 21 – 0 = 21

Since the final node is the only successor to activity H, its LF will be equal to the LS of the final node (21). The LS of activity H is calculated by subtracting its LF minus its duration:

LS H = 21 – 8 = 13

Since the end node is the only successor of activity G, its LF will be equal to the LS of the end node (21). The LS of activity G is calculated by subtracting its LF minus its duration:

LS G = 21 – 6 = 15

Since activity H is the only successor of activity F, its LF will be equal to the LS of activity H (13). The LS of activity F is calculated by subtracting its LF minus its duration:

LS F = 13 – 4 = 9

Since activity H is the only successor of activity E, its LF will be equal to the LS of activity H (13). The LS of activity E is calculated by subtracting its LF minus its duration:

LS E = 13 – 4 = 9

Since activity G is the only successor of activity D, its LF will be equal to the LS of activity G (15). The LS of activity D is calculated by subtracting its LF minus its duration:

LS D = 15 – 6 = 9

Since activity F is the only successor of activity C, its LF will be equal to the LS of activity F (9). The LS of activity C is calculated by subtracting its LF minus its duration:

LS C = 9 – 6 = 3

How activity B has as successors activities D and E, its LF will be equal to the smaller value of the LS of both. In this case, since both have a value of 9; that value will be the LF of activity B. The LS of activity B is calculated by subtracting its LF minus its duration:

LS B = 9 – 4 = 5

How activity A has as successors activities B and C, its LF will be equal to the smaller value of the LS of both. In this case, the lowest value is that of activity C (3); therefore, that value will be the LF of activity A. The LS of activity A is calculated by subtracting its LF minus its duration:

LS A = 3 – 3 = 0

Initial Node:

Using the same analysis as above we complete the values of the initial node with zero.

Finally we calculate the slack for each node with the following formula:

The final graph would look like this:

The activities with zero float (marked in red) are the critical activities. In this example, these activities follow a single path that will be our critical path: A – C – F – H . Total project time is 21 days.

Shirley Hopkins is developing a program in leadership training for middle-level managers. Shirley has listed a number of activities that must be completed before a training program of this nature can be conducted. The activities, immediate predecessors, and times appear in the accompanying table.

Provide the following:

• AON diagram for these precedencies
• What is the critical path?
• What is the total project completion date?
• What is the slack time for each individual activity?

Solution 2:

We will solve this example by showing the results and analysis of our critical path method calculator :

Each activity is broken down by its precedents and descendants:

This table serves as a guide to build our  network diagram . Two dummy activities were added to show the start and end. The activities with  0 (zero) slack  are the ones that make up the  critical path .

CPM Network Diagram

CPM Network Diagram with Calculations of ES, EF, LS, LF and Float

The following table presents the results to determine the critical path:

• Early Start (ES):  It is equal to the Early Finish to the activity's precedent. If it has more than one precedent, the highest value is taken.
• Early Finish (EF):  It is equal to the Early Start of the activity plus its duration (t). EF = ES + t.
• Late Start (LS):  It is equal to the Late Finish minus its duration (t). LS = LF – t.
• Late Finish (LF):  It is equal to the late start of the activity that follows. If it has more than one successor, the lowest value is taken.
• Slack (S):  It can be calculated in two ways. S = LS – ES = LF – EF. Activities with zero clearance make up the critical path.

The critical path is: B → D → E → G

The total project time is: 26 hours

Final Reflection

The critical path shows us the main activities that will determine the total time of the project; that is why Project Managers must be aware of the fulfillment of each one of them. This does not mean that the other activities should be neglected; on the contrary, if they are delayed longer than their slack, the project will have problems to finish on time.

With the help of our entry, we are confident that you will gain more understanding about the CPM technique and how it can be used to calculate critical path.

Finally, we invite you to follow us on our social networks and join our Facebook group where we can exchange more information with the participants.

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What is the critical path method? Complete guide with examples

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

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

What is the critical path method (CPM)?

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

What does “critical path” mean?

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

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

What is the critical path method in project management?

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

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

A brief history of the critical path method

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

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

Key terms associated with the critical path method

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

How to find the critical path of a project

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

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

When to use the critical path method

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

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

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

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The critical path method for product managers

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

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

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

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

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

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

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

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

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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.

PMP Certification Essential for Senior-Level Roles

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.

Recommended Resources

An Introduction to Project Management: A Beginner’s Guide

PERT and CPM: Vital Gears of Contemporary Project Management

Project Management Interview Guide

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The 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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Definition of a Operations Research Analyst

What does a operations research analyst do, key responsibilities of an operations research analyst.

• Collecting and analyzing data from various sources to identify operational inefficiencies and areas for improvement
• Developing and implementing mathematical models, simulations, and optimization algorithms to solve complex business problems
• Conducting statistical analyses and forecasting to support strategic decision-making and resource allocation
• Collaborating with cross-functional teams, such as operations, finance, and supply chain, to understand business requirements and translate them into quantitative models
• Designing and evaluating alternative scenarios and solutions to optimize processes, minimize costs, and maximize productivity
• Presenting analytical findings and recommendations to stakeholders, including senior management, in a clear and concise manner
• Developing and implementing data visualization tools and dashboards to effectively communicate complex data insights
• Staying up-to-date with the latest advancements in operations research techniques, software, and industry best practices
• Mentoring and training team members on analytical methodologies and tools
• Participating in continuous improvement initiatives and identifying opportunities for process optimization
• Ensuring data integrity, security, and compliance with relevant regulations and policies
• Collaborating with IT teams to integrate analytical solutions into existing systems and infrastructure

Day to Day Activities for Operations Research Analyst at Different Levels

Daily responsibilities for entry level operations research analysts.

• Collecting and organizing data from various sources for analysis
• Performing basic statistical analyses and data visualization
• Assisting in the development of mathematical models and simulations
• Supporting the implementation of process improvement initiatives
• Conducting research on industry best practices and emerging techniques
• Documenting project findings and preparing reports for senior analysts

Daily Responsibilities for Mid Level Operations Research Analysts

• Designing and implementing complex analytical models and simulations
• Leading and mentoring junior analysts on project teams
• Analyzing large datasets to identify operational bottlenecks and inefficiencies
• Collaborating with cross-functional teams to implement process improvements
• Evaluating the effectiveness of operational strategies and making recommendations
• Presenting analytical findings and recommendations to senior management

Daily Responsibilities for Senior Operations Research Analysts

• Developing and overseeing the implementation of comprehensive analytical strategies
• Leading and mentoring teams of analysts across various operational areas
• Collaborating with executive leadership to align analytical initiatives with business objectives
• Identifying and evaluating new analytical technologies and methodologies
• Driving the adoption of advanced analytical techniques across the organization
• Presenting strategic recommendations to executive leadership and stakeholders

Types of Operations Research Analysts

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How To Become a Operations Research Analyst in 2024

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