Critical Path Method (CPM) is a project management technique used for scheduling. It was developed in the late 1950s by Morgan Walker & E. Kelley Jr. in the USA. It is an effective technique to identify the activities that directly affect the project duration.

A network diagram is the backbone of CPM. It is made up of activities logically & sequentially linked to each other. Any two activities are linked by one of the below-given relationships in a network diagram, therefore it is important to understand these links.

Finish to Start (FS): Anactivitystarts after the preceding activity ends.
Start to Start (SS): Two activities start together.
Finish to Finish (FF): Anactivity ends with another activity at the same time.

Start to Finish (SF): Successor activity ends before the start of preceding activity.

The above-mentioned links rule the project duration calculation and hence are of utmost importance. A network diagram helps in the easy identification of activities that affect the project completion most. What are these activities called? Read the next Q&A.

Q2: What is a critical path & how does it affect the project completion?

A Critical path is the longest chain of activities in a network diagram that is to be done to complete the project. The activities constituting the critical path are called critical activities. The duration of critical activities governs the total duration of the project.

The critical path duration is the minimum time required to complete the project. Hence, the delay in the execution of a critical activity leads to a delay in project completion. Also, the float or slack for a critical activity is zero.

Confused about the float? what does that mean? The next section answers your query with all the related CPM terminology.

Q3: What terms should I know to understand the critical path method?

Earliest Start Time (EST): The time by which an activity can commence without affecting its predecessor. It is equal to the earliest finish of predecessor activity.

Earliest Finish Time (EFT): Thesum total of activity duration and earliest finish time of an activity is the earliest finish time for an activity. EFT represents the time by which an activity can end at earliest.
Latest Start Time (LST): The LST is the time by which the start of an activity can be delayed without affecting the succeeding activity.
Latest Finish Time (LFT): It is the most delayed time by which an activity can end without affecting its successor.

Milestone: It is a task with zero duration and marks the start or end of the project or an important task.
Dummy Activity: Dummy activity also has zero duration but it is different from milestone. It is added in a network to show the relationship between activities when the relationship cannot be shown by arrows. For example, in below network diagram, a dummy activity is added to show the dependence of activity E on activity C.
Forward Pass: It is a process of calculating the project completion by adding the activity durations starting from the first activity to the last in a network diagram. The ESTs and EFTs for each activity are calculated. The longest path (critical path) in the network diagram has the shortest duration to complete the project.

Backward Pass: It is a process of back calculating the duration of a project starting from its end date. The LSTs & LFTs are calculated.
Float: Itis a duration by which an activity can be delayed without affecting the project completion. The activity float is the difference between EST & LST or EFT & LFT of an activity. As said earlier, the critical activities have zero float and hence the EST=LST & EFT=LFT.
Activity Crash: The process ofreducing the activity duration by assigning additional resources is called activity crash. The cost of crashing an activity generally higher than the normal execution of an activity. It is generally used to cover up the delay on critical path.

Q4: How to identify the Critical Path & calculate the project duration?

We will understand the process with the help of an example. The below table contains a list of activities to complete the project.

We will follow the below-given nomenclature and format for the network diagram.

Let us create a network diagram and calculate the EST, EFT, LST & LFT for each activity.

Network Diagram with Activity Duration to determine Critical Path — Network Diagram with Activity Duration

After the network diagram, we will do a forward pass with the following steps.

Forward Pass

The starting activity is assumed to start on zero date and it acts as EST for activity A.
The EFT of activity A is calculated by (EST + duration of A).

The EFT of activity A acts as EST for its’ predecessor activity (i.e., activity B).
Process is repeated for each activity.
For activity H, the EST comes from two different activities i.e., E &G. The higher value of the two is considered.

The EFT of end activity (i.e., activity H) is the project duration (i.e., 19 days for the given example).

Forward Pass for Calculation of EST & EFT for critical Path Determination — Forward Pass for Calculation of EST & EFT

Now, we will perform a backward pass.

Backward Pass

The EFT of end activity H is its’ LFT.

The LST of activity H is calculated by deducting the duration from LFT.
The LST of each activity acts as the LFT for its’ predecessor.
For activities having two successors, the LFTs are two. Take the smaller value as the LFT of that activity.

Backward Pass for Calculation of LST & LFT for critical path determination — Backward Pass for Calculation of LST & LFT

Float Calculation

The difference between early and late time is float for that activity.

Critical Path Determination

The chain of activities having zero float is the critical path for the project. In the given example, the critical path is A-B-C-F-G-H.

Q5: How to check critical path?

Now, we have determined the critical path it is important to check if it is the correct one before reporting it to stakeholders. For checking the authenticity of critical there are two methods as mentioned in the DCMA 14-point schedule quality metrics. Let us discuss them.

Critical Path Test

It is a simple test involving a critical activity. Perform this as below mentioned steps.

Choose any one of the critical activities.
Increase the duration of this activity by x number of days.

Recalculate the project duration.
Now, the project duration has also increased by x days. If so, the network diagram is said to have passed the critical path test.

A failed critical path test indicates the missing relationship between the activities.

Critical Path Length Index

This test checks the likelihood of achieving the targeted completion date. Follow the below-given steps to check the CPLI.

Calculate the remaining working days on critical path.
Calculate the total float.

Calculate the total remaining days.
Now, add the remaining working days and total float. Divide the obtained sum by the remaining days. This gives the CPLI.

A CPLI of 1 indicates the project will complete on time. Value lesser than 1 indicates the delay and the CPLI of greater than 1 show the early completion of the project than the planned date.

Q6: Does critical path change?

Yes, it does. During the project execution, some tasks may get delayed, expedited or experience their duration change and hence, their ETs & LTs change. The change in ETs and LTs result in a change in float and hence the critical path.

Let us understand with the same example as explained earlier. During the 9^th day of project execution (after completion of activity B) following points were observed-

The activity B took 6 days to complete against the original duration of 5 days.

The activity D will take 6 days to complete against the original planned duration of 1 day due to various reasons.

Due to the above changes, the forward and backward passes are to be re-done. Now, ETs and LTs of the upcoming activities have changed so is their float. Following are the changes-

Change in Critical Path explained due to duration change — Change in Critical Path

The float of activities C, F & G have increase from 0 to 2 thus, are not on critical path anymore.

The activities D & E have become critical activities as their float of 1 day has reduced to zero.

Q7: What affects the critical path?

If you have gone through the entire post, you must have figured out some of the factors affecting the critical path. Here, I have summarised them.

Inter-dependency between the activities.

Duration of an activity. The uncertainty of activity duration leads to the risk of critical path change. Also, the incorrect estimation of activity duration may generate misguided metrics. Read these 6 powerful methods to correctly estimate the activity durations.
Work breakdown structure. The incorrect capturing of the project scope or the level of decomposition of scope may affect the sequencing and relationship between the activities thus, affecting the critical path.
Resource assignment to the activity. If the assigned resource is changed or increased/decreased or there is difference in planned and actual productivity, the duration of activity changes.

Updating of the project. Inaccurate measurement of works or tasks missed during the update may lead to change in the critical path.

Free Schedule Excel Template to Calculate the Critical Path for Your Project

Download the free excel schedule template for a residential building project. The template calculates the ETs, LTs and the float for each activity. The critical activities are highlighted in yellow and the separate column also tells the critical activity status. The expected completion dates for upcoming and in-progress summary tasks are projected in the actual finish column.

Snapshot of Project Schedule Template for Critical Activity Determination — Excel Template Snapshot

In the in-built Gantt chart, the critical path is highlighted with red bars.

Download the Excel Template for Critical Path Determination

The purpose of this excel is to reinforce the concepts of ET, FT and float calculation. You can also customise this excel to your needs. However, scheduling software like MS Project and Primavera will give more accurate results and hence they are preferable.

Final Words

The importance of a critical path is undeniable in project management. Hence, the correct implementation of the critical path method is necessary to get the correct picture of the progress. The float consumption of near-critical activities should be well observed and reported in advance.

The critical path should also be built with uncertainty to accommodate the minor fluctuations in activity duration. However, the decision for the same should be made in line with the stakeholder’s expectations.

Due to the vast concepts of the critical path method and multiple implications, only the basic information has been covered in this article to introduce the concepts to beginners. Also, the experts can brush up on their basics and provide feedback and expert opinions in the comments below.

Read more about the project schedule in this beginner’s guide for the project schedule.

Get this another project schedule Gantt template for planned and actual cost, delay analysis and dashboard.

Correctly estimate the construction labour requirement with this labour planning template.

Critical Path Explained with 7 Q&As & a Free Excel Template

Q1: What is a Critical Path Method?