Critical path vs. critical chain

Developed by Sophia Lykke Andersen

Abstract

The purpose of this article is to clarify the difference between two well-established terms in project scheduling, which are often confused: critical path and critical chain.

In project management, keeping track of critical project activities is key to managing a schedule. The critical path and critical chain are relevant to project management as these enable the project manager to properly manage the project schedule via e.g. accurate estimation of the project duration, and identification of task dependencies and resource constraints.

When activities have to finish before others can start, start before others can finish, or other relationships, paths of activity-dependencies form. The longest path of activities related to one another from start to finish of a project will be the most critical, as delays within this path will cause the whole project to be delayed. From this phenomenon, the definition of the critical path rises. The critical path is the longest path of dependent activities in a project schedule. In real life, the critical path will only be the most critical considering all resources (people, materials, space, etc.) available at all times. As soon as resources are limited, new dependencies can form, as seemingly unrelated activities cannot necessarily run simultaneously.
Allocating resources, considering additional constraints, and viewing the project schedule holistically allows the manager to see the most critical chain of tasks within the project. The critical chain will be the longest path of activities considering activity independence and resource constraints as well.
The article will take the reader through a historical perspective, review the methods of the two phenomena, and provide an example in order to get a more hands-on understanding. In the end, a discussion of the limitations and principle differences between the two phenomena will be made. Furthermore, the article also provides the reader with a useful glossary explaining the different terms associated with the two phenomena and project scheduling in general, as well as a list of useful programs/software for project scheduling.

Core difference

The terms critical path and critical chain differ in the sense that the critical path solely considers activity dependencies within scheduling, compared to the critical chain, which also considers external factors such as resource constraints, which may ultimately impact the actual duration of the project.

• A critical path identifies the longest sequence of activities to be finished in order to end the project
  
• A critical chain identifies the longest sequence of activities to be finished in order to end the project also considering resource constraints .

History

The critical path method, also known as CPM, was developed by James E. Kelley from Remington Rand and Morgan R. Walker from DuPont at the end of the 1950s, as a tool against ineffective project planning. They figured that costs could be lowered by making sure that the right project activities were carried out at the right time. Around the same time, the American Navy and Booz Allen Hamilton developed a similar method; the Program Evaluation and Review Technique, also known as PERT. Kelley and Walker published their work in 1959, but back in the 1940s, parts of the technique were already used and contributed to the success of the Manhattan Project.
In the 1960s, larger companies such as Mauchly Associates and Catalytic Construction started to make use of the critical path method, but it was not until the technical revolution of computers that the method could be used without large costs for companies.

The critical chain method, also known as CCPM, was later developed by Dr. Eliyahu M. Goldratt in 1997, building on his theory of constraints. He was very focused on limiting factors such as bottlenecks in order to get a project done on time, which led him to develop this method which does not only consider dependencies between activities of a project but also the resource constraints such as people, equipment, and space.

Glossary

Term	Definition
Activity	A task or part of a project, which consumes resources and has a definable beginning and end.
Backward pass	Definition of the latest start and finish dates for all activities in a network, made by considering activity durations starting from the last of the project going backward.
Buffer	Extra time or resources added to the schedule to account for unforeseen changes.
Dependency	A relationship between two activities with regard to start or completion relative to each other.
Early finish	The earliest day an activity can finish considering the activities prior in the schedule and the activity duration.
Early start	The earliest day an activity can start considering the activities prior in the schedule.
Feeding chain/activity	A feeding chain or a feeding activity is a chain of activities or an activity resp., which leads up to the critical chain but is not in fact on the critical chain.
Finish-finish	A relationship where the predecessor has to finish before the successor can finish.
Finish-start	A relationship where the predecessor has to finish before the successor can start.
Forward pass	Definition of the earliest start and finish dates for all activities in a network, made by considering activity durations starting from day 1 of the project going forward.
Late finish	The latest day an activity can finish in order for the project to finish on time, considering the activities coming after in the schedule and the activity duration.
Late start	The latest day an activity can start in order for the project to finish on time, considering the activities coming after in the schedule.
Lag	Lag is a part of a project schedule consuming time but no resources.
Network	A graphical description of a project plan/schedule, showing the activities and their dependencies.
Predecessor	An activity placed prior to the considered activity, defined by the dependency.
Start-finish	A relationship where the predecessor has to start before the successor can be finished.
Start-start	A relationship where the predecessor has to start before the successor can start.
Successor	An activity placed after the considered activity, defined by the dependency.
Total float	The difference between the early start and the late start, or the early finish and the late finish, of an activity.

Critical path

The method of the critical path, also called the critical path method (CPM), strives to plan out the project in the most optimal way possible, according to the activity dependencies. Buffers and considerations about unforeseen changes are not used, but the actual project performance is tracked and the schedule can be updated accordingly. The health of the project is mostly tied to how well the project follows the schedule. The following section will take the reader through the method of identifying the critical path. The critical path is the longest sequence of dependent activities and it defines the duration of the whole project. It can be found by mapping out the project activities in an activity network diagram. An example is made, making use of an example of an activity-on-node network diagram. Firstly, a list of the activities with resp. durations and dependencies is required. An example of such a list can be found below.

List of activities and their dependencies and durations

Activity	Predecessor	Successor	Duration
A	---	C	2
B	C	G	2
C	A	B, D	4
D	C	E, F	4
E	D	G	3
F	D	G	1
G	B, E, F	---	2

Activities with no predecessors mark the beginning of the project (written as "---" in the table above). The dependencies are defined and mapped out by identifying the predecessor of each activity. From the start node, all the activities with no predecessors are drawn as arrows to each their resp. end node. In this example, the only activity with no predecessor is A. The activities are drawn as boxes with thei activity name (letter) and duration inside. The activity boxes are connected with arrows representing the dependencies between the activities. The below image shows the drawn network according to the example:

Figure made by Sophia Lykke Andersen

A check can be made by going back through the drawn network, making use of each activity's successors. An activity with no successor should be pointing towards the end node of the whole network, like the activity G in the example.
When the network is mapped out the forward pass can be carried out considering the duration of each activity. No activity can start before the day after the last day of its predecessor activity. As A in the example takes 2 days to complete, C cannot start before day no. 3 of the project. The earliest start day of each activity as well as the earliest day it can finish (called early start and early finish resp.) is identified and written on top of the boxes and the duration of the whole project can be found. After that, the backward pass can be performed. This is done by going through the network starting at the finish day and considering the duration of each activity going backward. The latest possible start day for each activity in order to finish by the project's end date is identified and written beneath the boxes for each activity. The below image shows the network with added early start, early finish, late start, and late finish days for each activity.

Figure made by Sophia Lykke Andersen

The difference between the forward and backward pass is called the total float, also called slack. At activity B for instance, the total float is 2, as the difference between 10 and 12, or 11 and 13, is 2. Activities that can latest start the same day as they can earliest start will then have a total float of 0. Activities with a total float of zero will be on the critical path, as delays of these activities will delay the whole project. The below image swos the activity float for each activity (green) and marks the path with zero total float, and therefore the critical path, with red:

Figure made by Sophia Lykke Andersen

The duration of the whole project is calculated to be 16 days and activities A, C, D, E, F, and G are on the critical path.

Extending the method

The method of the critical path can be extended to larger networks, the definition of work days and weekends coupled with actual dates and more complicated dependencies between activities.

Relationship:
As for the simplicity of this example, the dependencies have all been kept at what is called a finish-start relationship, where the predecessor has to finish before the successor can start. Other relationships can be start-start, start-finish, and finish-finish relationships.

Lag:
The lag is extra waiting time tied to the relationships between activities, without work or resource impact. In a building project, this could be a waiting time of 28 days for the concrete to dry before the walls can be installed. the relationship would be finish-start, and have a lag of 28 working days.

Critical chain

The critical chain in itself is the longest sequence of dependent activities also considering resources. Compared to the critical path, the critical chain manages the project schedule beyond just focusing on dependencies and durations, as it also considers resource constraints, such as people, equipment, and physical space. The method of the critical chain strives to eliminate delays by efficient use of buffers and resource allocation. The health of the project is mostly tied to how easily the resources are consumed. The critical chain enables the project manager to account for unforeseen obstacles and changes and to utilize the available resources as optimally as possible. . The critical path becomes a very essential part of defining the critical chain, as it is one of the three main parts of the critical chain project management (CCPM): Critical path, Feeding chain, and Resource buffers. Considering other elements than just activity dependencies, activities can be discovered to not truly be independent, and therefore not be able to run simultaneously. Making use of the critical chain method can therefore result in a different calculation of the project duration compared to making use of just the critical path method.

Continuing with the example from the section, 'Critical Path', the below table and figure show the same activities and now also their resources needed. The resources are considered assigned 100% to each activity.

List of activities and their dependencies, durations, and resource allocation

Activity	Predecessor	Successor	Duration	Resources
A	---	C	2	X, Y
B	C	G	2	X
C	A	B, D	4	X
D	C	E, F	4	X, Y
E	D	G	3	W, X
F	D	G	1	W, X, Y
G	B, E, F	---	2	X, Y

Figure made by Sophia Lykke Andersen

As seen in the above figure, activity F now has become a part of the critical path as resources are limited. The duration of the whole project is then changed from 14 to 15 days. Before, activity F could be performed simultaneously with activity E, but as both activities E and F need the resources X and W, F cannot start before E has finished. This causes the whole project duration to extend, as it is discovered that the seemingly feeding activity F is in fact a critical activity when resource availability are considered.

Feeding chain

A feeding chain is a chain of activities leading up to the critical path. These activities can also be considered somewhat critical, as delays in these activities can end up causing delays on the critical path, and thereby the whole project. An example of this is activity B from the example. In bigger networks than the one from the example, plenty of activities can be a part of the network, but have very low criticality, as they are not on the critical chain nor even the feeding chain.

Buffers

After the critical chain is identified, buffers can be added to the schedule in an attempt to prevent delays. Buffers are extra resources such as time or materials. Three categories of buffers are listed below:

Project Buffer: A project buffer is extra time put at the end of the network, in order to account for possible delays on the critical chain

Feeding buffers: A feeding buffer is buffer time added in between the feeding chain and the critical chain to ensure that delays o the feeding chain are not affecting the critical chain.

Resource buffers: Resource buffers are extra resources such as extra people, space, or equipment set aside in case they are needed on the critical chain, to prevent delays due to resources.

The buffers are placed with respect to the calculated network and the resources available. Possible bottlenecks should be in focus, as well as the resources available.

Software

Larger project networks are complicated to map out manually, and a program is often used in order to perform the required calculation based on activity durations, dependencies, dates, lag, and other requirements. The softwares/programs listed below are just some of the programs used to calculate project schedules.

• Primavera P6: A software to schedule and manage long-term, complex projects typical for major industries like construction, oil and gas, and others. . A well-established tool for defining the critical path.
• monday.com: A no-code building block application to manage project workflow.
• Microsoft Project
• Asana: A platform for managing multiple teams and multiple projects. Creates and enables easy tracking of workflows.
• ProProfs Project: For managing critical chain activities. Enables allocation of resources. Can create and prioritize tasks within and outside the critical chain.
• ProChain: Manages critical resources and resource allocation, and allows updates on ongoing tasks.
• Aurora CCPM: Manages project schedules in real-time and aligns with project requirements. Interfaces with Primavera P6, Microsoft Project, Oracle, etc.

Additional information on various programs and software used in project management scheduling can be found in the article "Critical Chain Project Management" by ProProfs .

Limitations

Proper management of the critical path or the critical chain enables the project manager to make an estimation of the project duration, provides an overview for allocating resources effectively before the project start, and adjust as the project progresses. The tools are therefore key to successful project execution and will save time and resources in the end, if used correctly. The tools are standard in project management methodologies and well established in the project management work field today.

The difference between the critical path and the critical chain lies mostly within the level of elements that are considered. The critical path method relies mostly on the most efficient network of activities, whereas the critical chain method is more focused on resource utilization and the performance of the project. The critical path method can be less flexible, as it relies on rigid scheduling and activity order, whereas the critical chain method focuses more on keeping the resources leveled and keeping flexibility in the start times of the activities.

As the less flexible alternative but more focused on the most optimal schedule, the critical path method is good for specifically defined ventures with few stakeholders . Yet, in the event of unforeseen changes or limitations/relocation of resources, the critical path method does not provide many tools/procedures other than updating the schedule, and delays must be expected.

The critical chain method will with its larger focus on resources be more concerned with having resources available when needed, and not so much with having the at most optimal schedule progression. The critical chain method can work for both smaller or larger projects, but its flexible structure works best for projects with larger possibilities of unforeseen challenges, as a fixed project duration will also then be harder to define. Resource constraints could even be minimized before the project starts, are the right choices made in connection to the critical chain management. Mapping out the resources as well as the activities makes collaboration easier and makes it possible to identify bottlenecks. For smaller projects, however, that require a fast turnaround time, additional buffers at additional stages of the project would be required, and the critical chain method would therefore not be as suitable.

The terms in themselves are commonly used in the project management world, and much literature touches upon the subject of scheduling and how to make a plan most efficient. Even though different official institutes attempt to make guidelines and explanations for different existing project management phenomena, definitions are not always the same. Eliyahu Goldratt, the inventor of the critical chain method, was very concerned with the theory of constraints. In his book, Critical Chain, he elaborates on defining the most critical sequence of events when resources are limited, calling it a critical 'chain' instead of 'path'. The Project Management Institute (PMI) as well as many other institutions teaching about project management uses the term critical chain in the same way as described by Goldratt, but in the British standard; Project Management: Managing Successful Projects with PRINCE2, the term 'critical chain' is not even mentioned once, and instead, they stick to just using the term 'critical path' also when discussing resource constraints in relation to the critical path. As the word 'chain' in itself is not self-explanatory as to why it also considers resources, the similarity in terminology between 'path' and 'chain', as both refer to a sequence of elements, could be argued as a possible explanation for the confusion between the two phenomena, as well as the fact that the term 'critical chain' is not an as well established term as 'critical path'.

Conclusion

The two methods critical path and critical chain are both very relevant methods of project management, as they are crucial for effectively managing project schedules, estimating project duration, and identifying task dependencies, and resource constraints. The critical path method is more focused on finding the most optimal schedule, whereas the critical chain method prioritizes resource utilization and project performance. While both methods have their benefits and drawbacks and their implementation depends on the specific project they are both important methods of scheduling projects and are both commonly used in today's project management. The techniques of the methods require skills to master, and programs are often used to manage the schedules of larger projects. The terms in themselves, 'critical path' and 'critical chain' are often confused, which could be due to their similarity in wording, and maybe also the fact that the term 'critical chain' is not as commonly used as 'critical path'.

Annotated bibliography

The following section is for the reader to find additional reading material on the subject.

PMBOK® Guide - A Guide to the Project Management Body of Knowledge. 6th ed.

In the PMBOK® Guide, Sixth edition, chapter 6, the basics of plan schedule management are laid out. It defines the important elements of a project plan and goes into detail on tools and techniques of sequencing of activities. This book is more a reference-book than a textbook, perfect for looking up terms and quickly get an overview of the desired subject. As written:

"This PMBOK® Guide is different from a methodology. A methodology is a system of practices, techniques, procedures, and rules used by those who work in a discipline. This PMBOK® Guide is a foundation upon which organizations can build methodologies, policies, procedures, rules, tools and techniques, and life cycle phases needed to practice project management." - Ch. 1, p. 2

It contains several topics regarding project, program, and portfolio management, is one of the official PMI standards, and the seventh edition is also listed as mandatory reference material for the course, 42433 - Advanced Project, Program, and Portfolio Management.

Project Management in Practice. 6th ed.

This book provides a broad knowledge of project management and also holds a chapter specifically assigned to describing the elements surrounding Critical Chain: chapter 6.6 - Goldratt's Critical Chain. It focuses a lot on the necessity of resources to be accounted for in scheduling, as it is written:

"To schedule work is also to schedule resource usage." - Ch. 6.6, p. 217

It focuses on Goldratt's thinking, where the longest chain of consecutively dependent tasks will define the duration of the project. The chapter also goes into depth with the techniques of resource leveling and crashing of the project, which is very relevant to this topic, as it takes the management of schedules to the next level from this article. This other Wiki article touch on this topic: Resources loading, leveling and crashing.

Critical Chain, by Eliyahu M. Goldratt

In this book, Goldratt introduces his method of the critical path. He builds it on his theory of constraints and presents the tools of Project Buffers, Feeding Buffers, Limit Multitasking, Improved Communications, and Correct Measurements, which he believes are necessary for project work. It is interesting for this subject as to the way it taking takes the standpoint of traditional scheduling, and from that explains the difference to where the critical chain method is different. As the book is written by the inventor of the method himself, it is more of a guide to the techniques than a critical view of the method.

The ABCs of the Critical Path Method - Harvard Business Review

This article dives into the concepts and methods of the critical path. It touches upon the algorithm in itself and explains the concept of slack, cost calculations, and how to deal with errors. It not only provides a good overview of the techniques and why it is a useful tool with examples and figures. it also provides an overview of the history behind the method and references other useful material on the topic. It ends by touching upon new developments within the field and concludes on the method.

Project Management: Managing Successful Projects with PRINCE2, 6th Edition.

This book touches upon various project management subjects and is listed as mandatory reference material for the course, 42433 - Advanced Project, Program, and Portfolio Management. Especially chapter 9 of this book, Chapter 9 - Plans, is related to this topic, as it dives into the planning of projects, defining milestones, and assigning and calculating resource requirements. This in particular with respect to the critical path, as it states:

"When assigning resources, it is important to recheck the critical path because actual resources assignees may be more or less productive than the assumption made when calculating activity effort and duration." - Ch. 9, p. 112

It derives the technique of making an activity network and finding the critical path but does not touch upon the difference between the critical path and critical chain. In fact, the literature does not distinguish between the phenomena, and the name critical chain is not mentioned in the literature.

References

The following list of resources is used to write this article: