Program Evaluation and Review Technique

The Program Evaluation and Review Technique, commonly abbreviated PERT, is a statistical tool, used in 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...

, that is designed to analyze and represent the tasks involved in completing a given 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...

. First developed by the United States Navy

United States Navy

The United States Navy is the naval warfare service branch of the United States Armed Forces and one of the seven uniformed services of the United States. The U.S. Navy is the largest in the world; its battle fleet tonnage is greater than that of the next 13 largest navies combined. The U.S...

in the 1950s, it is commonly used in conjunction with the critical path method

Critical path method

The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

or CPM.

History

Overview

PERT is a method to analyze the involved tasks in completing a given project, especially the time needed to complete each task, and to identify the minimum time needed to complete the total project.

PERT was developed primarily to simplify the planning and scheduling of large and complex projects. It was developed for the U.S. Navy Special Projects Office in 1957 to support the U.S. Navy's Polaris nuclear submarine project. It was able to incorporate uncertainty by making it possible to schedule a project while not knowing precisely the details and durations of all the activities. It is more of an event-oriented technique rather than start- and completion-oriented, and is used more in projects where time, rather than cost, is the major factor. It is applied to very large-scale, one-time, complex, non-routine infrastructure and Research and Development projects. An example of this was for the 1968 Winter Olympics

1968 Winter Olympics

The 1968 Winter Olympics, officially known as the X Olympic Winter Games, were a winter multi-sport event which was celebrated in 1968 in Grenoble, France and opened on 6 February. Thirty-seven countries participated...

in Grenoble

Grenoble

Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...

which applied PERT from 1965 until the opening of the 1968 Games.

This project model was the first of its kind, a revival for scientific management

Scientific management

Scientific management, also called Taylorism, was a theory of management that analyzed and synthesized workflows. Its main objective was improving economic efficiency, especially labor productivity. It was one of the earliest attempts to apply science to the engineering of processes and to management...

, founded by Frederick Taylor (Taylorism) and later refined by Henry Ford (Fordism

Fordism

Fordism, named after Henry Ford, is a modern economic and social system based on industrial mass production. The concept is used in various social theories about production and related socio-economic phenomena. It has varying but related meanings in different fields, as well as for Marxist and...

). 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...

's critical path method

Critical path method

The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

was invented at roughly the same time as PERT.

Conventions

A PERT chart is a tool that facilitates decision making. The first draft of a PERT chart will number its events sequentially in 10s (10, 20, 30, etc.) to allow the later insertion of additional events.
Two consecutive events in a PERT chart are linked by activities, which are conventionally represented as arrows (see the diagram above).
The events are presented in a logical sequence and no activity can commence until its immediately preceding event is completed.
The planner decides which milestones should be PERT events and also decides their “proper” sequence.
A PERT chart may have multiple pages with many sub-tasks.

PERT is valuable to manage where multiple tasks are occurring simultaneously to reduce redundancy

Terminology

PERT event: a point that marks the start or completion of one or more activities. It consumes no time and uses no resources. When it marks the completion of one or more tasks, it is not “reached” (does not occur) until all of the activities leading to that event have been completed.
predecessor event: an event that immediately precedes some other event without any other events intervening. An event can have multiple predecessor events and can be the predecessor of multiple events.
successor event: an event that immediately follows some other event without any other intervening events. An event can have multiple successor events and can be the successor of multiple events.
PERT activity: the actual performance of a task which consumes time and requires resources (such as labor, materials, space, machinery). It can be understood as representing the time, effort, and resources required to move from one event to another. A PERT activity cannot be performed until the predecessor event has occurred.
optimistic time (O): the minimum possible time required to accomplish a task, assuming everything proceeds better than is normally expected
pessimistic time (P): the maximum possible time required to accomplish a task, assuming everything goes wrong (but excluding major catastrophes).
most likely time (M): the best estimate of the time required to accomplish a task, assuming everything proceeds as normal.
expected time (T_E): the best estimate of the time required to accomplish a task, accounting for the fact that things don't always proceed as normal (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time).

T_E = (O + 4M + P) ÷ 6

float
Float (project management)
In project management, float or slack is the amount of time that a task in a project network can be delayed without causing a delay to:* subsequent tasks * project completion date...

or slack
Float (project management)
In project management, float or slack is the amount of time that a task in a project network can be delayed without causing a delay to:* subsequent tasks * project completion date...

is a measure of the excess time and resources available to complete a task. It is the amount of time that a project task can be delayed without causing a delay in any subsequent tasks (free float) or the whole project (total float). Positive slack would indicate ahead of schedule; negative slack would indicate behind schedule; and zero slack would indicate on schedule.
critical path
Critical path method
The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

: the longest possible continuous pathway taken from the initial event to the terminal event. It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.
critical activity: An activity that has total float equal to zero. An activity with zero float is not necessarily on the critical path since its path may not be the longest.
Lead time: the time by which a predecessor event must be completed in order to allow sufficient time for the activities that must elapse before a specific PERT event reaches completion.
lag time: the earliest time by which a successor event can follow a specific PERT event.
fast tracking
Critical path method
The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

: performing more critical activities in parallel
crashing critical path
Critical path method
The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

: Shortening duration of critical activities

Implementation

The first step to scheduling the project is to determine the tasks that the project requires and the order in which they must be completed. The order may be easy to record for some tasks (e.g. When building a house, the land must be graded before the foundation can be laid) while difficult for others (There are two areas that need to be graded, but there are only enough bulldozers to do one). Additionally, the time estimates usually reflect the normal, non-rushed time. Many times, the time required to execute the task can be reduced for an additional cost or a reduction in the quality.

In the following example there are seven tasks, labeled A through G. Some tasks can be done concurrently (A and B) while others cannot be done until their predecessor task is complete (C cannot begin until A is complete). Additionally, each task has three time estimates: the optimistic time estimate (O), the most likely or normal time estimate (M), and the pessimistic time estimate (P). The expected time (T_E) is computed using the formula (O + 4M + P) ÷ 6.

Activity	Predecessor	Time estimates			Expected time
Activity	Predecessor	Opt. (O)	Normal (M)	Pess. (P)	Expected time
A	—	2	4	6	4.00
B	—	3	5	9	5.33
C	A	4	5	7	5.17
D	A	4	6	10	6.33
E	B, C	4	5	7	5.17
F	D	3	4	8	4.50
G	E	3	5	8	5.17

Once this step is complete, one can draw a 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...

or a network diagram.

A network diagram can be created by hand or by using diagram software. There are two types of network diagrams, activity on arrow (AOA

Arrow Diagramming Method

An arrow diagramming method is a network diagramming technique in which activities are represented by arrows.It is used for scheduling activities in a project plan....

) and activity on node (AON

Precedence Diagram Method

The precedence diagram method is a tool for scheduling activities in a project plan. It is a method of constructing a project schedule network diagram that uses boxes, referred to as nodes, to represent activities and connects them with arrows that show the dependencies.* Critical tasks,...

). Activity on node diagrams are generally easier to create and interpret. To create an AON diagram, it is recommended (but not required) to start with a node named start. This "activity" has a duration of zero (0). Then you draw each activity that does not have a predecessor activity (a and b in this example) and connect them with an arrow from start to each node. Next, since both c and d list a as a predecessor activity, their nodes are drawn with arrows coming from a. Activity e is listed with b and c as predecessor activities, so node e is drawn with arrows coming from both b and c, signifying that e cannot begin until both b and c have been completed. Activity f has d as a predecessor activity, so an arrow is drawn connecting the activities. Likewise, an arrow is drawn from e to g. Since there are no activities that come after f or g, it is recommended (but again not required) to connect them to a node labeled finish.

By itself, the network diagram pictured above does not give much more information than a Gantt chart; however, it can be expanded to display more information. The most common information shown is:

The activity name
The normal duration time
The early start time (ES)
The early finish time (EF)
The late start time (LS)
The late finish time (LF)
The slack
Float (project management)
In project management, float or slack is the amount of time that a task in a project network can be delayed without causing a delay to:* subsequent tasks * project completion date...

In order to determine this information it is assumed that the activities and normal duration times are given. The first step is to determine the ES and EF. The ES is defined as the maximum EF of all predecessor activities, unless the activity in question is the first activity, for which the ES is zero (0). The EF is the ES plus the task duration (EF = ES + duration).

The ES for start is zero since it is the first activity. Since the duration is zero, the EF is also zero. This EF is used as the ES for a and b.
The ES for a is zero. The duration (4 work days) is added to the ES to get an EF of four. This EF is used as the ES for c and d.
The ES for b is zero. The duration (5.33 work days) is added to the ES to get an EF of 5.33.
The ES for c is four. The duration (5.17 work days) is added to the ES to get an EF of 9.17.
The ES for d is four. The duration (6.33 work days) is added to the ES to get an EF of 10.33. This EF is used as the ES for f.
The ES for e is the greatest EF of its predecessor activities (b and c). Since b has an EF of 5.33 and c has an EF of 9.17, the ES of e is 9.17. The duration (5.17 work days) is added to the ES to get an EF of 14.34. This EF is used as the ES for g.
The ES for f is 10.33. The duration (4.5 work days) is added to the ES to get an EF of 14.83.
The ES for g is 14.34. The duration (5.17 work days) is added to the ES to get an EF of 19.51.
The ES for finish is the greatest EF of its predecessor activities (f and g). Since f has an EF of 14.83 and g has an EF of 19.51, the ES of finish is 19.51. Finish is a milestone (and therefore has a duration of zero), so the EF is also 19.51.

Barring any unforeseen events

Theory of Constraints

The theory of constraints adopts the common idiom "A chain is no stronger than its weakest link" as a new management paradigm. This means that processes, organizations, etc., are vulnerable because the weakest person or part can always damage or break them or at least adversely affect the...

, the project should take 19.51 work days to complete. The next step is to determine the late start (LS) and late finish (LF) of each activity. This will eventually show if there are activities that have slack

Float (project management)

In project management, float or slack is the amount of time that a task in a project network can be delayed without causing a delay to:* subsequent tasks * project completion date...

. The LF is defined as the minimum LS of all successor activities, unless the activity is the last activity, for which the LF equals the EF. The LS is the LF minus the task duration (LS = LF - duration).

The LF for finish is equal to the EF (19.51 work days) since it is the last activity in the project. Since the duration is zero, the LS is also 19.51 work days. This will be used as the LF for f and g.
The LF for g is 19.51 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 14.34 work days. This will be used as the LF for e.
The LF for f is 19.51 work days. The duration (4.5 work days) is subtracted from the LF to get an LS of 15.01 work days. This will be used as the LF for d.
The LF for e is 14.34 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 9.17 work days. This will be used as the LF for b and c.
The LF for d is 15.01 work days. The duration (6.33 work days) is subtracted from the LF to get an LS of 8.68 work days.
The LF for c is 9.17 work days. The duration (5.17 work days) is subtracted from the LF to get an LS of 4 work days.
The LF for b is 9.17 work days. The duration (5.33 work days) is subtracted from the LF to get an LS of 3.84 work days.
The LF for a is the minimum LS of its successor activities. Since c has an LS of 4 work days and d has an LS of 8.68 work days, the LF for a is 4 work days. The duration (4 work days) is subtracted from the LF to get an LS of 0 work days.
The LF for start is the minimum LS of its successor activities. Since a has an LS of 0 work days and b has an LS of 3.84 work days, the LS is 0 work days.

The next step is to determine the critical path

Critical path method

The critical path method is an algorithm for scheduling a set of project activities. It is an important tool for effective project management.-History:...

and if any activities have slack

Float (project management)

In project management, float or slack is the amount of time that a task in a project network can be delayed without causing a delay to:* subsequent tasks * project completion date...

. The critical path is the path that takes the longest to complete. To determine the path times, add the task durations for all available paths. Activities that have slack can be delayed without changing the overall time of the project. Slack is computed in one of two ways, slack = LF - EF or slack = LS - ES. Activities that are on the critical path have a slack of zero (0).

The duration of path adf is 14.83 work days.
The duration of path aceg is 19.51 work days.
The duration of path beg is 15.67 work days.

The critical path is aceg and the critical time is 19.51 work days. It is important to note that there can be more than one critical path (in a project more complex than this example) or that the critical path can change. For example, let's say that activities d and f take their pessimistic (b) times to complete instead of their expected (T_E) times. The critical path is now adf and the critical time is 22 work days. On the other hand, if activity c can be reduced to one work day, the path time for aceg is reduced to 15.34 work days, which is slightly less than the time of the new critical path, beg (15.67 work days).

Assuming these scenarios do not happen, the slack for each activity can now be determined.

Start and finish are milestones and by definition have no duration, therefore they can have no slack (0 work days).
The activities on the critical path by definition have a slack of zero; however, it is always a good idea to check the math anyway when drawing by hand.
- LF_a - EF_a = 4 - 4 = 0
- LF_c - EF_c = 9.17 - 9.17 = 0
- LF_e - EF_e = 14.34 - 14.34 = 0
- LF_g - EF_g = 19.51 - 19.51 = 0
Activity b has an LF of 9.17 and an EF of 5.33, so the slack is 3.84 work days.
Activity d has an LF of 15.01 and an EF of 10.33, so the slack is 4.68 work days.
Activity f has an LF of 19.51 and an EF of 14.83, so the slack is 4.68 work days.

Therefore, activity b can be delayed almost 4 work days without delaying the project. Likewise, activity d or activity f can be delayed 4.68 work days without delaying the project (alternatively, d and f can be delayed 2.34 work days each).

Advantages

PERT chart explicitly defines and makes visible dependencies (precedence relationships) between the WBS
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...

elements
PERT facilitates identification of the critical path and makes this visible
PERT facilitates identification of early start, late start, and slack for each activity,
PERT provides for potentially reduced project duration due to better understanding of dependencies leading to improved overlapping of activities and tasks where feasible.
The large amount of project data can be organized & presented in diagram for use in decision making.

Disadvantages

There can be potentially hundreds or thousands of activities and individual dependency relationships
PERT is not easily scalable for smaller projects
The network charts tend to be large and unwieldy requiring several pages to print and requiring special size paper
The lack of a timeframe on most PERT/CPM charts makes it harder to show status although colours can help (e.g., specific colour for completed nodes)
When the PERT/CPM charts become unwieldy, they are no longer used to manage the project.

Uncertainty in project scheduling

During project execution, however, a real-life project will never execute exactly as it was planned due to uncertainty. It can be ambiguity resulting from subjective estimates that are prone to human errors or it can be variability arising from unexpected events or risks. The main reason that the Program Evaluation and Review Technique (PERT) may provide inaccurate information about the project completion time is due to this schedule uncertainty. This inaccuracy is large enough to render such estimates as not helpful.

One possibility to maximize solution robustness is to include safety in the baseline schedule in order to absorb the anticipated disruptions. This is called proactive scheduling. A pure proactive scheduling is a utopia, incorporating safety in a baseline schedule that allows to cope with every possible disruption would lead to a baseline schedule with a very large make-span. A second approach, reactive scheduling, consists of defining a procedure to react to disruptions that cannot be absorbed by the baseline schedule.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

History

Overview

Conventions

Terminology

Implementation

Advantages

Disadvantages

Uncertainty in project scheduling

See also

External links