I think the critical path method is both one of the simplest and most complicated concepts in project management.
I remember hearing about it in college and I always thought, “Okay. Find the critical activities and you will be able to estimate your project’s duration. Change your logistics or find a way to do some of them concurrently and you can reduce your project duration.” Easy peasy, right?
It wasn’t until I had to do it myself that I realized that it is more complicated than it initially seemed. While what I understood it to be did not change drastically—it remains essentially the same—the practice of it required that you have a full handle on all your activities and an understanding of how these activities are linked. That is the complicated part.
Can you imagine having to understand the dependencies and successions of hundreds of interrelated activities? How about visualizing the way a simple change in the start date of one activity will affect the schedule of another activity, the timeline of the project, or even the viability of an entire program?
This is why you need project scheduling software when dealing with complex projects.
But we’re here to talk and learn about the critical path method, so discuss it we must and shall. I will provide a firm grasp of what it is, how to calculate it, and how you can use it on your project.
It is likely that you will be using a project management software to create project schedules. Even so, it will still help to understand how to do it yourself.
Think of it this way. While you probably would not manually compute 3,785,345 divided by 7,689, you still understand what steps you need to go through to do it — if you must.
I’ll cover:
- What Is The Critical Path Method?
- A Critical Path Method Example
- How To Use The Critical Path Method In Your Projects
- How To Calculate The Critical Path
What Is The Critical Path Method?
First, the short and the sweet. The critical path method is one of the methods you can use to come up with a viable schedule for your project.
Of course, it’s a tad more complicated than that. So, for the not-so-short (but still sweet) version, let’s begin by talking about schedule network analysis.
Schedule Network Analysis
To create a project schedule, project managers perform schedule network analysis, which is the detailed and systematic process of developing a project schedule. This involves taking an initial or a tentative schedule, maybe even just a known target start or target end date, and applying a combination of different techniques to come up with the project’s final schedule.
During schedule network analysis, you develop a schedule using various inputs. Some of these inputs include specific activities that make up the project, estimated activity durations, target milestones, required resources, resource availability, tools and equipment availability, and many more.
Schedule network analysis has various outputs. One of the most significant is the project schedule, often represented in graphical form like a Gantt chart or a project schedule network diagram.
So, how does all this relate to the critical path method?
The Critical Path Method
The critical path method is one of the techniques you can use in schedule network analysis. Other methods include resource optimization techniques like resource leveling and resource smoothing, and data modeling techniques like simulation and what-if scenario analysis.
At its core, the critical path method is a scheduling framework.
Do you want to know how long your project will take? Do you need to determine when your project will finish? You can use critical path analysis (this is another word for the critical path method).
Essentially, this is what the critical path framework is saying.
- Find the project’s critical path.
- How long your project will take and how soon it can finish will depend on that critical path.
What Is the Critical Path?
According to A Guide to the Project Management Body of Knowledge (Project Management Institute, 2017), the critical path is “the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration.”
In other words, the critical path is the longest path between project start and project end.
Look at the illustration below. Can you guess which is the critical path based on the PMBOK’s definition above?
Clue: The critical path is the longest path through a project.
Notes: A and P represent the project start and end, respectively. Each of the boxes, represented by a unique letter, represents an activity that must be completed to accomplish the project. Finally, the number beside each letter represents that activity’s duration in days.
An analysis of the above diagram should tell you that there are multiple paths from A to P. They are:
- A-B-H-K-O-P
- A-B-H-K-L-P
- A-C-E-F-G-O-P
- A-C-E-F-G-K-O-P
- A-C-E-F-G-K-L-P
- A-D-I-M-N-P
- A-D-J-N-P
Which of these is the critical path? To find your answer, you need to compute the total duration of every path by adding the individual activity durations.
- A-B-H-K-O-P = 37 days
- A-B-H-K-L-P = 48 days
- A-C-E-F-G-O-P = 41 days
- A-C-E-F-G-K-O-P = 46 days
- A-C-E-F-G-K-L-P = 52 days
- A-D-I-M-N-P = 30 days
- A-D-J-N-P = 23 days
The above calculations will tell you that path “A-C-E-F-G-K-L-P,” which has a duration of 52 days, is “the longest path through a project” to use PMBOK’s definition and is, thus, the critical path.
The path “A-C-E-F-G-K-L-P” is also the “shortest possible project duration.” In other words, according to the critical path method, your project will take a minimum of 52 days.
The critical path is also the path that will suffer no delays without negatively affecting your schedule. Any delay in the activities on the critical path will lead to a proportionate delay in project completion.
Put another way, the critical path has zero float (more on float later!). Thus, if task C gets delayed by two days—so task C’s duration changes from 10 days to 12 days—the entire project would also get delayed by two days, the project duration will change form 52 days to 54 days, and the project completion date will move by two days.
Adjusting the Critical Path Method Schedule
Is 52 days your final project duration? Let’s not forget that the critical path method is only one of the techniques you can employ in schedule network analysis. Thus, the critical path method schedule may not be your final schedule.
For instance, if the resources your activities need are unavailable in the schedule indicated by critical path analysis, you may have to apply resource leveling. This can change the project’s critical path and extend the duration of the project.
Let’s plot the above example on a Gantt chart to illustrate.
As you can see from the above chart, the project is set to start on 1 April (A) and end on 13 June (P). 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, A-C-E-F-G-K-L-P.
However, what if Geoffrey, the person assigned to task E, has been assigned to another project and will not be available until 20 April. As you can see from the Gantt chart above, Task E is supposed to start on 15 April.
Let’s suppose no other person can take on Geoffrey’s role on task E. In that case, we apply resource leveling by adjusting the schedule around Geoffrey’s availability. This means pushing task E’s start date from 15 April to 20 April, which is a delay of three work days for Task E, the tasks down the line and, ultimately, the project.
See below how the projected end date has now become 16 June instead of 13 June. Note that the critical path remains A-C-E-F-G-K-L-P, but it has become longer with a total project duration of 55 instead of 52 days.
What if the stakeholders are demanding that the project be completed in less than 55 days? In this case, you may have to apply schedule compression techniques like crashing and fast tracking to complete the project in a shorter period.
Crashing means adding resources to activities to shorten duration. Crashing is performed by adding more people or equipment, and/or increasing people’s hours (i.e., overtime). Fast tracking, meanwhile, is performing some tasks in parallel. A task that will have been started only after its predecessor is completed may be started while the preceding task is still in progress.
In our example, suppose we perform crashing by doubling the number of people assigned to tasks G and L. Consequently, task G’s duration decreases from 12 days to six, while task L’s duration drops from 15 days to 8. This shortens the A-C-E-F-G-K-L-P path duration from 55 days to 42 days.
We also bring forward task O so it will begin immediately after the preceding task, task K. Doing this, however, still means task O ends one day later than task L, which means crashing has actually changed the project’s critical path (the longest path) from A-C-E-F-G-K-L-P to A-C-E-F-G-K-O-P with a duration of 43 days.
Critical Path Method: Major Points
To sum up, the critical path method identifies a project’s critical path, which is the longest path across a project and the shortest possible duration a project can have.
The activities on the critical path are called critical activities because completing them according to schedule will determine whether your project will finish on schedule. The activities on the critical path have the least flexibility among all other activities. Thus, any delays in these critical activities will almost always surely lead to project delays.
In other words, critical activities are not necessarily the most important tasks, but they are crucial to completing a project on time.
Critical path analysis gives you an initial, workable project schedule—the critical path method schedule—which may or may not be final depending on project constraints.
Resource availability, supply delivery schedules, stakeholder’s demands, and changing project scope, among others, can lengthen or shorten your critical path schedule. They may even change your project’s critical path.
Finally, your critical path method diagram will help track project progress. How much progress have you made and are you on track to finish the project according to schedule? Your CPM diagram will show you that.
A Critical Path Method Example
Take for example a hyperlocal ecommerce app. The first iteration was a failure, no two ways about it. The platform is currently working, but we’re in the process of launching our version 2 of a minimum viable product. This is how our CPM diagram (technically a Gantt chart) looks.
The above might look complicated, but you can do this easily yourself. An analysis of the chart would yield the following salient points.
- The project will start on 4 April.
- The target launch date is 20 June.
- The project has a duration of 56 days.
What may not be so obvious, however, is the critical path. Which path corresponds to the project duration, and which path has zero or the least amount of float, i.e., cannot suffer delay without delaying the project?
An analysis of the chart should tell you that the following tasks comprise the critical path.
START
- 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
- MVP Launch
Why are these the critical activities? If you ask me, the application development tasks are more important than the business development tasks identified by the critical path method.
However, don’t be confused by the terminology. The “critical activities” or the tasks on the critical path are not necessarily the most important. They are simply the tasks with the least amount of float, and they are only critical because delaying any of them will delay the entire project.
For instance, if the business development team fails to complete the Bikolana products task in the allotted four days and extends the activity to six days, the project duration would increase by two days and the MVP launch would be delayed by two days.
In other words, any delay on any of the critical activities will delay the project. Therefore, if you want to complete the project on time, it is critical that you finish every one of the critical tasks on time.
How To Use The Critical Path Method In Your Projects
Follow these steps to use critical path analysis in your projects.
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 at which sequence they occur.
If you need help on creating one, you may read our work breakdown structure guide. You may also check out our statement of work template and example.
Suppose you need to get an online magazine launched by the end of September 2022. The following might be your project’s component activities.
THEME
- Theme ideation
- Theme pitching
- Theme selection
- Theme approval
CONTENT
- Content ideation
- Content assignment
- Content writing
- Content submission
- Content editing and revision
- Content approval
- Graphics creation
- Graphics ideation
- Graphics assignment
- Graphics creation
- Graphics submission
- Graphics revision
- Graphics approval
SPONSORSHIP
- Compile list of prospective sponsors
- Domain specific research
- Prepare sponsorship proposal
- Pitch sponsorship proposal
- Create contacts
- Schedule proposal presentation
- Create advertising content
- Close sponsorship deals
LAYOUT
- Magazine layout design
- Individual content layout design
- Content and ads insertion
- Approval and sign-off
GOING LIVE
- Platform
- Platform research
- Platform selection
- Platform procurement
- Magazine upload
- Launch
The following is how the work breakdown structure document might look.
Step 2: Arrange your activities in sequence
After identifying the individual tasks that make up your project, arrange the task 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 dependencies identified.
| TASKS | DEPENDENCIES |
| Theme ideation | - |
| Theme pitching | A |
| Theme selection | B |
| Theme approval | C |
| Content ideation | D |
| Content assignment | E |
| Content writing | F |
| Content submission | G |
| Content editing and revision | H |
| Content approval | I |
| Graphics ideation | F |
| Graphics assignment | K |
| Graphics creation | L |
| Graphics submission | M |
| Graphics revision | N |
| Graphics approval | O |
| Domain specific research | D |
| Compile list of prospective sponsors | Q |
| Prepare sponsorship proposal | R |
| Create contacts | R |
| Schedule proposal presentation | T, S |
| Pitch sponsorship proposal | U |
| Close sponsorship deals | V |
| Create advertising content | W |
| Design magazine layout | D, J, P,X |
| Design individual content layout | J,P,X, Y |
| Content and ads insertion | Y, Z |
| Approval and sign-off | AA |
| Magazine platform research | - |
| Magazine platform selection | CC |
| Magazine platform procurement | DD |
| Magazine upload | BB, EE |
| Online magazine launch | FF |
Step 3: Approximate Activity Duration
Estimate the duration of each individual task. The PMBOK Guide 6th edition discusses several duration estimation techniques you can use. You can use the most appropriate technique given your specific circumstances. You should even be able to combine different techniques as needed.
Expert Judgment
An expert or a team of experts decides on the duration of an activity. For instance, a content writer decides, based on the content writing topic, how long it will take him to create the content assigned to him.
Analogous Estimation
In analogous estimation, you 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.
For instance, if a graphics artist is used to spending three days creating graphics for the online publication, then he might estimate that his new assignment will take him three days to finish.
Parametric Estimation
Parametric estimation combines historical data and current project parameters to estimate durations. For instance, if a past 2,000-word write-up took a content writer five days to write, and the current project involves 6,000 words, the current write-up might be allotted a duration of fifteen days.
Three-Point Estimation
At its simplest, you can estimate the duration as the average of three possible durations: the most likely duration, the optimistic duration, and the pessimistic duration. For instance, the sponsorship proposal has the following estimated durations:
- Most likely duration: 5 days
- Optimistic duration: 3 days
- Pessimistic duration: 10 days
The three duration estimates are averaged to come up with a triangularly distributed duration estimate.
Estimated duration = (3+5+10)/3 = 6 days
Bottom-Up Estimation
This is useful when an individual task may be further broken down into more specific details. In this case, you can estimate an activity’s duration by aggregating the estimated durations of its component activities.
For instance, if content creation may be broken down into research, outline creation, more research, introduction writing, body writing, conclusion writing, content review, editing, and proofreading, estimating the duration of each of these individual components can give you an aggregate estimate for the content creation activity.
Consensus Decision Making
Everyone involved in the project can decide, as a team, on individual activity durations. The lead can assign duration 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 and dependencies, and their estimated durations, you can now plot your network diagram.
| TASK | DEPENDENCIES | ACTIVITY DURATIONS (in days) |
| START | ||
| Theme ideation | - | 3 |
| Theme pitching | A | 1 |
| Theme selection | B | 1 |
| Theme approval | C | 1 |
| Content ideation | D | 5 |
| Content assignment | E | 1 |
| Content writing | F | 15 |
| Content submission | G | 1 |
| Content editing and revision | H | 5 |
| Content approval | I | 3 |
| Graphics ideation | F | 5 |
| Graphics assignment | K | 1 |
| Graphics creation | L | 10 |
| Graphics submission | M | 1 |
| Graphics revision | N | 5 |
| Graphics approval | O | 3 |
| Domain specific research | D | 5 |
| Compile list of prospective sponsors | Q | 5 |
| Prepare sponsorship proposal | R | 3 |
| Create contacts | R | 5 |
| Schedule proposal presentation | T, S | 5 |
| Pitch sponsorship proposal | U | 10 |
| Close sponsorship deals | V | 10 |
| Create advertising content | W | 10 |
| Design magazine layout | D, J, P,X | 3 |
| Design individual content layout | J,P,X,Y | 5 |
| Content and ads insertion | Y, Z | 2 |
| Approval and sign-off | AA | 3 |
| Magazine platform research | - | 5 |
| Magazine platform selection | CC | 3 |
| Magazine platform procurement | DD | 3 |
| Magazine upload | BB, EE | 1 |
| Online magazine launch | FF | 1 |
| END |
Step 5: Identify the Critical Path
Based on the simple network diagram, the critical path is A-B-C-D-Q-R-T-U-V-W-X-Y-Z-AA-BB-FF-GG. The following are the critical activities:
A. Theme ideation
B. Theme pitching
C. Theme selection
D. Theme approval
Q. Domain specific research
R. Compile list of prospective sponsors
T. Create contacts
U. Schedule proposal presentation
V. Pitch sponsorship proposal
W. Close sponsorship deals
X. Create advertising content
Y. Design magazine layout
Z. Design individual content layout
AA. Content and ads insertion
BB. Approval and sign-off
FF. Magazine upload
GG. 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 71 days. That’s also the minimum project duration.
| TASK | ACTIVITY DURATIONS (in days) |
| Theme ideation | 3 |
| Theme pitching | 1 |
| Theme selection | 1 |
| Theme approval | 1 |
| Domain specific research | 5 |
| Compile list of prospective sponsors | 5 |
| Create contacts | 5 |
| Schedule proposal presentation | 5 |
| Pitch sponsorship proposal | 10 |
| Close sponsorship deals | 10 |
| Create advertising content | 10 |
| Design magazine layout | 3 |
| Design individual content layout | 5 |
| Content and ads insertion | 2 |
| Approval and sign-off | 3 |
| Magazine upload | 1 |
| Online magazine launch | 1 |
| TOTAL | 71 |
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.
| TASK | DEPENDENCIES | ACTIVITY DURATIONS | Early Start Date | Early Finish Date |
| (in days) | MM-DD | MM-DD | ||
| START | ||||
| A. Theme ideation | - | 3 | 6/6 | 6/8 |
| B. Theme pitching | A | 1 | 6/9 | 6/9 |
| C. Theme selection | B | 1 | 6/10 | 6/10 |
| D. Theme approval | C | 1 | 6/13 | 6/13 |
| E. Content ideation | D | 5 | ||
| F. Content assignment | E | 1 | ||
| G. Content writing | F | 15 | ||
| H. Content submission | G | 1 | ||
| I. Content editing and revision | H | 5 | ||
| J. Content approval | I | 3 | ||
| K. Graphics ideation | F | 5 | ||
| L. Graphics assignment | K | 1 | ||
| M. Graphics creation | L | 10 | ||
| N. Graphics submission | M | 1 | ||
| O. Graphics revision | N | 5 | ||
| P. Graphics approval | O | 3 | ||
| Q. Domain specific research | D | 5 | 6/14 | 6/20 |
| R. Compile list of prospective sponsors | Q | 5 | 6/21 | 6/27 |
| S. Prepare sponsorship proposal | R | 3 | ||
| T. Create contacts | R | 5 | 6/28 | 7/4 |
| U. Schedule proposal presentation | S,T | 5 | 7/5 | 7/11 |
| V. Pitch sponsorship proposal | U | 10 | 7/12 | 7/25 |
| W. Close sponsorship deals | V | 10 | 7/26 | 8/8 |
| X. Create advertising content | W | 10 | 8/9 | 8/22 |
| Y. Design magazine layout | D, J, P,X | 3 | 8/23 | 8/25 |
| Z. Design individual content layout | J,P,X,Y | 5 | 8/26 | 9/1 |
| AA. Content and ads insertion | Y, Z | 2 | 9/2 | 9/5 |
| BB. Approval and sign-off | AA | 3 | 9/6 | 9/8 |
| CC. Magazine platform research | - | 5 | ||
| DD. Magazine platform selection | CC | 3 | ||
| EE. Magazine platform procurement | DD | 3 | ||
| FF. Magazine upload | BB, EE | 1 | 9/9 | 9/9 |
| GG. Online magazine launch | FF | 1 | 9/12 | 9/12 |
As you can see, if the start date is 6 June 2022, the end date is 12 September 2022. That is, if you consider only the critical path and exclude Saturdays and Sundays.
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 14 June 2022. 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 on 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.
For instance, J (content approval) is necessary to Y (design magazine layout). Since Y has a start date of 23 August, J cannot finish later than 22 August. You will learn more about this later when we calculate the critical path using the critical path algorithm.
Step 8: Adjust Your Project Schedule as Needed
At this point, the critical path method has already given you a viable schedule, albeit only for the critical activities. The next section will tell you how to schedule all of the activities in your project.
Armed with your critical path schedule, you can now apply other techniques to shorten or optimize your schedule.
Do you need your project to take fewer than 71 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 method? You can apply resource optimization techniques such as resource leveling and resource smoothing to adjust your schedule.
See the section, Adjusting the Critical Path Method Schedule, for a discussion on these techniques.
Step 9: Update Your Schedule According to Your 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 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.
The next section on calculating the critical path using the critical path algorithm will teach you how to create a full project schedule, not only for critical activities but also non-critical activities.
How To Calculate The Critical Path
The preceding section has already taught you how to identify the critical path and how long the minimum project duration is based on the critical path. In this section, you will learn how to use the critical path algorithm to identify not only the project duration but also to calculate a detailed project schedule.
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 activities, 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)
To illustrate, I’ll use the online magazine launch example in the preceding section. To determine the schedule for activity E, content ideation, let’s look at the following factors:
- The project start date: 6 June
- The early finish date of its predecessor activities plus one: Its predecessor activity is set to end on 13 June. Add one day and you’ll get 14 June.
- The date of the applicable or existing “not earlier than” constraint, if any: Suppose the content lead won’t be available until 16 June. In this case, the “not earlier than” date is 16 June.
The current date is not a factor in our calculation because our hypothetical project is assumed to be in the planning stages—i.e., not in progress.
Among the above specified dates, the latest is 16 June. That, therefore, is the early start date for activity E, content ideation.
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.
Using the example above, if the early start date for activity E, content ideation, is 16 June, and it has a duration of 5 days:
Early finish date = (16 June + 5 days) – 1 day. That is 21 June – 1 day = 20 June.
Adjust for the weekend (18 and 19 June) = 22 June.
The early finish date for activity E, therefore, is 22 June 2022.
Let’s compute the early start dates and early finish dates of all the activities, assuming that the project has no other “Not Earlier Than” constraints except the content lead availability constraint already mentioned earlier. In other words, the only potential early start date limits are the project start date and the predecessor activities’ finish dates.
Early Start Dates and Early Finish Dates of the Online Magazine Publication Project
| TASK | DEPENDENCIES | ACTIVITY DURATIONS | Early Start Date | Early Finish Date |
| (in days) | MM-DD | MM-DD | ||
| START | ||||
| A. Theme ideation | - | 3 | 6/6 | 6/8 |
| B. Theme pitching | A | 1 | 6/9 | 6/9 |
| C. Theme selection | B | 1 | 6/10 | 6/10 |
| D. Theme approval | C | 1 | 6/13 | 6/13 |
| E. Content ideation | D | 5 | 6/16 | 6/22 |
| F. Content assignment | E | 1 | 6/23 | 6/23 |
| G. Content writing | F | 15 | 6/24 | 7/14 |
| H. Content submission | G | 1 | 7/15 | 7/15 |
| I. Content editing and revision | H | 5 | 7/18 | 7/22 |
| J. Content approval | I | 3 | 7/25 | 7/27 |
| K. Graphics ideation | F | 5 | 6/24 | 6/30 |
| L. Graphics assignment | K | 1 | 7/1 | 7/1 |
| M. Graphics creation | L | 10 | 7/4 | 7/15 |
| N. Graphics submission | M | 1 | 7/18 | 7/18 |
| O. Graphics revision | N | 5 | 7/19 | 7/25 |
| P. Graphics approval | O | 3 | 7/26 | 7/28 |
| Q. Domain specific research | D | 5 | 6/14 | 6/20 |
| R. Compile list of prospective sponsors | Q | 5 | 6/21 | 6/27 |
| S. Prepare sponsorship proposal | R | 3 | 6/28 | 6/30 |
| T. Create contacts | R | 5 | 6/28 | 7/4 |
| U. Schedule proposal presentation | S,T | 5 | 7/5 | 7/11 |
| V. Pitch sponsorship proposal | U | 10 | 7/12 | 7/25 |
| W. Close sponsorship deals | V | 10 | 7/26 | 8/8 |
| X. Create advertising content | W | 10 | 8/9 | 8/22 |
| Y. Design magazine layout | D, J, P,X | 3 | 8/23 | 8/25 |
| Z. Design individual content layout | J,P,X,Y | 5 | 8/26 | 9/1 |
| AA. Content and ads insertion | Y, Z | 2 | 9/2 | 9/5 |
| BB. Approval and sign-off | AA | 3 | 9/6 | 9/8 |
| CC. Magazine platform research | - | 5 | 6/6 | 6/10 |
| DD. Magazine platform selection | CC | 3 | 6/13 | 6/15 |
| EE. Magazine platform procurement | DD | 3 | 6/16 | 6/20 |
| FF. Magazine upload | BB, EE | 1 | 9/9 | 9/9 |
| GG. Online magazine launch | FF | 1 | 9/12 | 9/12 |
*The items in bold are critical activities. All work will be done only during weekdays, so weekends are exempted from scheduling. Note, too, that activity E’s start date is 16 June because of its “not earlier than” constraint.
After determining the early start and early finish dates 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
To illustrate, let’s find the late finish date of activity P or graphics approval.
- The project finish date: 12 September
- Since it has more than one successors, the earliest of all successor activities’ late start dates plus one day: 22 August
Explanation: The activities that succeed P are the critical activities Y and Z. Since the early start and late start dates of critical activities are identical—they have no float—we’ll use their early start dates as their late start dates. Between the two, activity Y has an earlier start date, than activity Z. Thus, the early start date of the successor activity is 23 August, and one day before that is 22 August.
- The date of applicable or existing “not later than” constraints
Suppose you rented special equipment to create your graphics and it must be returned by 19 August, any activity that relies on this equipment must finish by 18 August. Therefore, graphics approval or activity P has a not later than constraint of 18 August.
Among all these potential late finish dates, the earliest is 18 August. Thus, this is the late finish date for activity P.
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 activity duration.
Using the example above, if the late finish date for activity P is 18 August and it has a duration of three days:
Late start date = (18 August - 3 days) + 1 day. That is 15 August + 1 day = 16 August.
The early finish date for activity P, therefore, is 16 August 2022.
Now, let’s compute the late finish and late start dates for all activities, assuming that the project has no other not later than constraint except the graphics equipment return date constraint already mentioned earlier. In other words, the only potential late finish date limits are the project completion date and the successor activities’ late start dates.
Late Finish Dates and Late Start Dates of the Online Magazine Publication Project
| TASK | SUCCESSORS | ACTIVITY DURATIONS | Late Start Date MM-DD | Late Finish Date MM-DD |
| (in days) | ||||
| START | ||||
| A. Theme ideation | B | 3 | 6/6 | 6/8 |
| B. Theme pitching | C | 1 | 6/9 | 6/9 |
| C. Theme selection | D | 1 | 6/10 | 6/10 |
| D. Theme approval | E, Q, Y | 1 | 6/13 | 6/13 |
| E. Content ideation | F | 5 | 7/7 | 7/13 |
| F. Content assignment | G, K | 1 | 7/14 | 7/14 |
| G. Content writing | H | 15 | 7/20 | 8/9 |
| H. Content submission | I | 1 | 8/10 | 8/10 |
| I. Content editing and revision | J | 5 | 8/11 | 8/17 |
| J. Content approval | Y, Z | 3 | 8/18 | 8/22 |
| K. Graphics ideation | L | 5 | 7/15 | 7/21 |
| L. Graphics assignment | M | 1 | 7/22 | 7/22 |
| M. Graphics creation | N | 10 | 7/25 | 8/5 |
| N. Graphics submission | O | 1 | 8/8 | 8/8 |
| O. Graphics revision | P | 5 | 8/9 | 8/15 |
| P. Graphics approval | Y, Z | 3 | 8/16 | 8/18 |
| Q. Domain specific research | R | 5 | 6/14 | 6/20 |
| R. Compile list of prospective sponsors | S, T | 5 | 6/21 | 6/27 |
| S. Prepare sponsorship proposal | U | 3 | 6/30 | 7/4 |
| T. Create contacts | U | 5 | 6/28 | 7/4 |
| U. Schedule proposal presentation | V | 5 | 7/5 | 7/11 |
| V. Pitch sponsorship proposal | W | 10 | 7/12 | 7/25 |
| W. Close sponsorship deals | X | 10 | 7/26 | 8/8 |
| X. Create advertising content | Y, Z | 10 | 8/9 | 8/22 |
| Y. Design magazine layout | AA, Z | 3 | 8/23 | 8/25 |
| Z. Design individual content layout | AA | 5 | 8/26 | 9/1 |
| AA. Content and ads insertion | BB | 2 | 9/2 | 9/5 |
| BB. Approval and sign-off | FF | 3 | 9/6 | 9/8 |
| CC. Magazine platform research | DD | 5 | 8/25 | 8/31 |
| DD. Magazine platform selection | EE | 3 | 9/1 | 9/5 |
| EE. Magazine platform procurement | FF | 3 | 9/6 | 9/8 |
| FF. Magazine upload | GG | 1 | 9/9 | 9/9 |
| GG. Online magazine launch | -- | 1 | 9/12 | 9/12 |
| END |
* The late finish date of activity P is 18 August instead of one day before its successor activity because of the not later than date constraint we introduced earlier.
Notice that the activities on the critical path have the same early and late start dates as well as early and late finish dates. That proves that these dates have zero float and, if the project is to be completed by 12 September, they must take place exactly on these dates.
In contrast, you can see that early start and late start dates as well as late start and late finish dates for non-critical activities vary. Non-critical activities have float, so they may start later than their early start date as long as they can finish by their late finish dates.
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.
Below are the calculated floats for all activities in our hypothetical project.
Total Float and Free Float
| TASK | DEPENDENCIES | SUCCESSORS | ACTIVITY DURATION | Early Start Date | Early Finish Date | Late Start Date | Late Finish Date | Total Float | Free Float |
| (in days) | MM-DD | MM-DD | MM-DD | MM-DD | |||||
| START | |||||||||
| A. Theme ideation | - | B | 3 | 6/6 | 6/8 | 6/6 | 6/8 | 0 | 0 |
| B. Theme pitching | A | C | 1 | 6/9 | 6/9 | 6/9 | 6/9 | 0 | 0 |
| C. Theme selection | B | D | 1 | 6/10 | 6/10 | 6/10 | 6/10 | 0 | 0 |
| D. Theme approval | C | E, Q, Y | 1 | 6/13 | 6/13 | 6/13 | 6/13 | 0 | 0 |
| E. Content ideation | D | F | 5 | 6/16 | 6/22 | 7/7 | 7/13 | 15 | 0 |
| F. Content assignment | E | G, K | 1 | 6/23 | 6/23 | 7/14 | 7/14 | 15 | 0 |
| G. Content writing | F | H | 15 | 6/24 | 7/14 | 7/20 | 8/9 | 18 | 0 |
| H. Content submission | G | I | 1 | 7/15 | 7/15 | 8/10 | 8/10 | 18 | 0 |
| I. Content editing and revision | H | J | 5 | 7/18 | 7/22 | 8/11 | 8/17 | 18 | 0 |
| J. Content approval | I | Y, Z | 3 | 7/25 | 7/27 | 8/18 | 8/22 | 18 | 18 |
| K. Graphics ideation | F | L | 5 | 6/24 | 6/30 | 7/15 | 7/21 | 15 | 0 |
| L. Graphics assignment | K | M | 1 | 7/1 | 7/1 | 7/22 | 7/22 | 15 | 0 |
| M. Graphics creation | L | N | 10 | 7/4 | 7/15 | 7/25 | 8/5 | 15 | 0 |
| N. Graphics submission | M | O | 1 | 7/18 | 7/18 | 8/8 | 8/8 | 15 | 0 |
| O. Graphics revision | N | P | 5 | 7/19 | 7/25 | 8/9 | 8/15 | 15 | 0 |
| P. Graphics approval | O | Y, Z | 3 | 7/26 | 7/28 | 8/16 | 8/18 | 15 | 17 |
| Q. Domain specific research | D | R | 5 | 6/14 | 6/20 | 6/14 | 6/20 | 0 | 0 |
| R. Compile list of prospective sponsors | Q | S, T | 5 | 6/21 | 6/27 | 6/21 | 6/27 | 0 | 0 |
| S. Prepare sponsorship proposal | R | U | 3 | 6/28 | 6/30 | 6/30 | 7/4 | 2 | 2 |
| T. Create contacts | R | U | 5 | 6/28 | 7/4 | 6/28 | 7/4 | 0 | 0 |
| U. Schedule proposal presentation | S,T | V | 5 | 7/5 | 7/11 | 7/5 | 7/11 | 0 | 0 |
| V. Pitch sponsorship proposal | U | W | 10 | 7/12 | 7/25 | 7/12 | 7/25 | 0 | 0 |
| W. Close sponsorship deals | V | X | 10 | 7/26 | 8/8 | 7/26 | 8/8 | 0 | 0 |
| X. Create advertising content | W | Y, Z | 10 | 8/9 | 8/22 | 8/9 | 8/22 | 0 | 0 |
| Y. Design magazine layout | D, J, P,X | AA, Z | 3 | 8/23 | 8/25 | 8/23 | 8/25 | 0 | 0 |
| Z. Design individual content layout | J,P,X,Y | AA | 5 | 8/26 | 9/1 | 8/26 | 9/1 | 0 | 0 |
| AA. Content and ads insertion | Y, Z | BB | 2 | 9/2 | 9/5 | 9/2 | 9/5 | 0 | 0 |
| BB. Approval and sign-off | AA | FF | 3 | 9/6 | 9/8 | 9/6 | 9/8 | 0 | 0 |
| CC. Magazine platform research | - | DD | 5 | 6/6 | 6/10 | 8/25 | 8/31 | 58 | 0 |
| DD. Magazine platform selection | CC | EE | 3 | 6/13 | 6/15 | 9/1 | 9/5 | 58 | 0 |
| EE. Magazine platform procurement | DD | FF | 3 | 6/16 | 6/20 | 9/6 | 9/8 | 58 | 58 |
| FF. Magazine upload | BB, EE | GG | 1 | 9/9 | 9/9 | 9/9 | 9/9 | 0 | 0 |
| GG. Online magazine launch | FF | -- | 1 | 9/12 | 9/12 | 9/12 | 9/12 | 0 | |
| END |
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. You can see from the table that activities E and F have a total float of 15. The table also shows that linear activities (those that occur in succession, like E, F, K, L, M, N, O, P) all share the same total float.
Free float is ordinarily not more than total float. In our project, however, activity P’s free float is greater than its total float. The reason for this is activity P’s not-later-than-date constraint, which pushed its late start and finish dates two days earlier and made its total float two days shorter.
This illustrates the difference between total float and free float. While activity P may be delayed 17 days without affecting the early start date of its earliest-start successor activity (i.e., activity Y), doing that will delay the whole project because its total float indicates the activity may not be postponed by more than 15 days without delaying the project.
Note, too, that there is zero free float when an activity follows immediately after another. As a case in point, activities E and F have zero free float, so you cannot move the start date of E without changing the start date of F.
CPM Calculators and Formula
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 calculator, this CPM calculator, or this critical path method calculator will help you identify the critical path and the estimated project duration. This program evaluation and review technique or PERT calculator will also help you not only identify but also visualize your project’s critical path.
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.
Formula 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.
Formula 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.
You can learn more about the WORKDAY function here and the NETWORKDAYS function here.
Next Step: Practice Using CPM
Whew! That was one deep dive into the critical path method. At this point, you must practice using the critical path method in coming up with your project schedule. Implement the steps indicated above and manually calculate your start and finish dates as well as your floats.
It can be overwhelming, I know. I wrote this guide, and it was no walk in the park having to explain the process step by step.
However, cliched as the saying is, it’s true. Practice still makes perfect. So apply the techniques you learned here if you want to master using the critical path method in schedule network analysis. You should also check out our critical chain method guide.
Let me know how you’re doing in your critical path method practice by leaving a comment below. Of course, don’t forget to subscribe to The Digital Project Manager newsletter!