Critical path method

# Critical path method

Overview
The critical path method (CPM) is an algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

for scheduling a set of project activities. It is an important tool for effective project management
Project management
Project management is the discipline of planning, organizing, securing, and managing resources to achieve specific goals. A project is a temporary endeavor with a defined beginning and end , undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value...

.
Discussion
 Ask a question about 'Critical path method' Start a new discussion about 'Critical path method' Answer questions from other users Full Discussion Forum

Encyclopedia
The critical path method (CPM) is an algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

for scheduling a set of project activities. It is an important tool for effective project management
Project management
Project management is the discipline of planning, organizing, securing, and managing resources to achieve specific goals. A project is a temporary endeavor with a defined beginning and end , undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value...

.

## History

The critical path method (CPM) is a project modeling technique developed in the late 1950s by Morgan R. Walker of DuPont
DuPont
E. I. du Pont de Nemours and Company , commonly referred to as DuPont, is an American chemical company that was founded in July 1802 as a gunpowder mill by Eleuthère Irénée du Pont. DuPont was the world's third largest chemical company based on market capitalization and ninth based on revenue in 2009...

and James E. Kelley, Jr. of Remington Rand
Remington Rand
Remington Rand was an early American business machines manufacturer, best known originally as a typewriter manufacturer and in a later incarnation as the manufacturer of the UNIVAC line of mainframe computers but with antecedents in Remington Arms in the early nineteenth century. For a time, the...

. Kelley and Walker related their memories of the development of CPM in 1989. Kelley attributed the term "critical path" to the developers of the Program Evaluation and Review Technique
Program Evaluation and Review Technique
The Program ' Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze and represent the tasks involved in completing a given project...

which was developed at about the same time by Booz Allen Hamilton
Booz Allen Hamilton
Booz Allen Hamilton Inc. , or more commonly Booz Allen, is an American public consulting firm headquartered in McLean, Fairfax County, Virginia, with 80 other offices throughout the United States. Ralph Shrader is its Chairman and Chief Executive Officer. The firm was founded by Edwin Booz in...

and the US Navy. The precursors of what came to be known as Critical Path were developed and put into practice by DuPont between 1940 and 1943 and contributed to the success of the Manhattan Project
Manhattan Project
The Manhattan Project was a research and development program, led by the United States with participation from the United Kingdom and Canada, that produced the first atomic bomb during World War II. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the US Army...

.

CPM is commonly used with all forms of projects, including construction, aerospace and defense, software development, research projects, product development, engineering, and plant maintenance, among others. Any project with interdependent activities can apply this method of mathematical analysis. Although the original CPM program and approach is no longer used, the term is generally applied to any approach used to analyze a project network logic diagram.

## Basic technique

The essential technique for using CPM is to construct a model of the project that includes the following:
1. A list of all activities required to complete the project (typically categorized within a work breakdown structure
Work breakdown structure
A work breakdown structure , in project management and systems engineering, is a deliverable oriented decomposition of a project into smaller components. It defines and groups a project's discrete work elements in a way that helps organize and define the total work scope of the project.A work...

),
2. The time (duration) that each activity will take to completion, and
3. The dependencies
Dependency (project management)
In a project network, a dependency is a link amongst a project's terminal elements.There are four kinds of dependencies with respect to ordering terminal elements :# Finish to start...

between the activities.

Using these values, CPM calculates the longest path of planned activities to the end of the project, and the earliest and latest that each activity can start and finish without making the project longer. This process determines which activities are "critical" (i.e., on the longest path) and which have "total float" (i.e., can be delayed without making the project longer). In project management, a critical path is the sequence of project network activities which add up to the longest overall duration. This determines the shortest time possible to complete the project. Any delay of an activity on the critical path directly impacts the planned project completion date (i.e. there is no float on the critical path). A project can have several, parallel, near critical paths. An additional parallel path through the network with the total durations shorter than the critical path is called a sub-critical or non-critical path.

Although the activity-on-arrow diagram ("PERT Chart") is still used in a few places, it has generally been superseded by the activity-on-node diagram, where each activity is shown as a box or node and the arrows represent the logical relationships going from predecessor to successor as shown here in the "Activity-on-node diagram".
In this diagram, Activities A, B, C, D, and E comprise the critical or longest path, while Activities F, G, and H are off the critical path with floats of 10 days, 5 days, and 20 days respectively. Whereas activities that are off the critical path have float and are therefore not delaying completion of the project, those on the critical path will usually have critical path drag, i.e., they delay project completion. The drag of a critical path activity can be computed using the following formula:

1. If a critical path activity has nothing in parallel, its drag is equal to its duration. Thus A and E have drags of 10 days and 20 days respectively.
2. If a critical path activity has another activity in parallel, its drag is equal to whichever is less: its duration or the total float of the parallel activity with the least total float. Thus since B and C are both parallel to F (float of 15) and H (float of 20), B has a duration of 20 and drag of 15 (equal to F's float), while C has a duration of only 5 days and thus drag of only 5. Activity D, with a duration of 10 days, is parallel to G (float of 5) and H (float of 20) and therefore its drag is equal to 5, the float of G.

These results, including the drag computations, allow managers to prioritize activities for the effective management of project completion, and to shorten the planned critical path of a project by pruning critical path activities, by "fast tracking" (i.e., performing more activities in parallel), and/or by "crashing the critical path" (i.e., shortening the durations of critical path activities by adding resources).

#### Crash duration

"Crash duration" is a term referring to the shortest possible time for which an activity can be scheduled. It is achieved by shifting more resources towards the completion of that activity, resulting in decreased time spent and often a reduced quality of work, as the premium is set on speed.
Crash duration is typically modeled as a linear relationship between cost and activity duration, however in many cases a convex function or a step function is more applicable.

### Expansion

Originally, the critical path method considered only logical dependencies
Dependency (project management)
In a project network, a dependency is a link amongst a project's terminal elements.There are four kinds of dependencies with respect to ordering terminal elements :# Finish to start...

between terminal elements. Since then, it has been expanded to allow for the inclusion of resources related to each activity, through processes called activity-based resource assignments and resource leveling
Resource Leveling
Resource leveling is a project management technique used to examine unbalanced use of resources over time, and for resolving over-allocations or conflicts....

. A resource-leveled schedule may include delays due to resource bottlenecks (i.e., unavailability of a resource at the required time), and may cause a previously shorter path to become the longest or most "resource critical" path. A related concept is called the critical chain
Critical chain
Critical chain project management is a method of planning and managing projects that puts the main emphasis on the resources required to execute project tasks. It was developed by Eliyahu M. Goldratt. This is in contrast to the more traditional critical path and PERT methods, which emphasize task...

, which attempts to protect activity and project durations from unforeseen delays due to resource constraints.

Since project schedules change on a regular basis, CPM allows continuous monitoring of the schedule, allows the project manager to track the critical activities, and alerts the project manager to the possibility that non-critical activities may be delayed beyond their total float, thus creating a new critical path and delaying project completion. In addition, the method can easily incorporate the concepts of stochastic predictions, using the Program Evaluation and Review Technique
Program Evaluation and Review Technique
The Program ' Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze and represent the tasks involved in completing a given project...

(PERT) and event chain methodology
Event chain methodology
Event chain methodology is an uncertainty modeling and schedule network analysis technique that is focused on identifying and managing events and event chains that affect project schedules...

.

Currently, there are several software solutions available in industry that use the CPM method of scheduling, see list of project management software. The method currently used by most project management software is based on a manual calculation approach developed by Fondahl of Stanford University.

### Flexibility

A schedule generated using critical path techniques often is not realised precisely, as estimations are used to calculate times: if one mistake is made, the results of the analysis may change. This could cause an upset in the implementation of a project if the estimates are blindly believed, and if changes are not addressed promptly. However, the structure of critical path analysis is such that the variance from the original schedule caused by any change can be measured, and its impact either ameliorated or adjusted for. Indeed, an important element of project postmortem analysis is the As Built Critical Path (ABCP), which analyzes the specific causes and impacts of changes between the planned schedule and eventual schedule as actually implemented.

• Gantt chart
Gantt chart
A Gantt chart is a type of bar chart that illustrates a project schedule. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project. Terminal elements and summary elements comprise the work breakdown structure of the project. Some Gantt charts...

• List of project management software
• List of project management topics
• Program Evaluation and Review Technique
Program Evaluation and Review Technique
The Program ' Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in project management, that is designed to analyze and represent the tasks involved in completing a given project...

(PERT)
• Project
Project
A project in business and science is typically defined as a collaborative enterprise, frequently involving research or design, that is carefully planned to achieve a particular aim. Projects can be further defined as temporary rather than permanent social systems that are constituted by teams...

• Project management
Project management
Project management is the discipline of planning, organizing, securing, and managing resources to achieve specific goals. A project is a temporary endeavor with a defined beginning and end , undertaken to meet unique goals and objectives, typically to bring about beneficial change or added value...

• Project planning
Project planning
Project planning is part of project management, which relates to the use of schedules such as Gantt charts to plan and subsequently report progress within the project environment....

• Work breakdown structure
Work breakdown structure
A work breakdown structure , in project management and systems engineering, is a deliverable oriented decomposition of a project into smaller components. It defines and groups a project's discrete work elements in a way that helps organize and define the total work scope of the project.A work...