Program evaluation and review technique

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PERT network chart for a seven-month project with five milestones (10 through 50) and six activities (A through F). Pert chart colored.svg
PERT network chart for a seven-month project with five milestones (10 through 50) and six activities (A through F).

The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project.

Contents

PERT was originally developed by Charles F. Clark for the United States Navy in 1958; it is commonly used in conjunction with the Critical Path Method (CPM) which was also introduced in 1958. [1]

Overview

PERT is a method of analyzing the tasks involved in completing a project, especially the time needed to complete each task, and to identify the minimum time needed to complete the total project. It incorporates uncertainty by making it possible to schedule a project while not knowing precisely the details and durations of all the activities. It is more event-oriented than start- and completion-oriented, and is used more for projects where time is the major constraint rather than cost. It is applied to very large-scale, one-time, complex, non-routine infrastructure projects, as well as R&D projects.

PERT offers a management tool, [2] :497 which relies "on arrow and node diagrams of activities and events: arrows represent the activities or work necessary to reach the events or nodes that indicate each completed phase of the total project." [3]

PERT and CPM are complementary tools, because "CPM employs one time estimation and one cost estimation for each activity; PERT may utilize three time estimates (optimistic, expected, and pessimistic) and no costs for each activity. Although these are distinct differences, the term PERT is applied increasingly to all critical path scheduling." [3]

History

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 to support the U.S. Navy's Polaris nuclear submarine project. [4] It found applications throughout industry. An early example is the 1968 Winter Olympics in Grenoble which used PERT from 1965 until the opening of the 1968 Games. [5] This project model was the first of its kind, a revival for the scientific management of Frederick Taylor and later refined by Henry Ford (Fordism). DuPont's CPM was invented at roughly the same time as PERT.

PERT Summary Report Phase 2, 1958 PERT Summary Report Phase 2, 1958.jpg
PERT Summary Report Phase 2, 1958

Initially PERT stood for Program Evaluation Research Task, but by 1959 was renamed. [4] It had been made public in 1958 in two publications of the U.S. Department of the Navy, entitled Program Evaluation Research Task, Summary Report, Phase 1. [6] and Phase 2. [7] both primarily written by Charles F. Clark. [1] In a 1959 article in The American Statistician , Willard Fazar, Head of the Program Evaluation Branch, Special Projects Office, U.S. Navy, gave a detailed description of the main concepts of PERT. He explained:

Through an electronic computer, the PERT technique processes data representing the major, finite accomplishments (events) essential to achieve end-objectives; the inter-dependence of those events; and estimates of time and range of time necessary to complete each activity between two successive events. Such time expectations include estimates of "most likely time", "optimistic time", and "pessimistic time" for each activity. The technique is a management control tool that sizes up the outlook for meeting objectives on time; highlights danger signals requiring management decisions; reveals and defines both methodicalness and slack in the flow plan or the network of sequential activities that must be performed to meet objectives; compares current expectations with scheduled completion dates and computes the probability for meeting scheduled dates; and simulates the effects of options for decision— before decision. [8]

PERT Guide for Management Use, June 1963 PERT Guide for management use, June 1963.jpg
PERT Guide for Management Use, June 1963

Ten years after the introduction of PERT, the American librarian Maribeth Brennan compiled a selected bibliography with about 150 publications on PERT and CPM, all published between 1958 and 1968. [3]

For the subdivision of work units in PERT [9] another tool was developed: the Work Breakdown Structure. The Work Breakdown Structure provides "a framework for complete networking, the Work Breakdown Structure was formally introduced as the first item of analysis in carrying out basic PERT/CPM." [10]

Terminology

Events and activities

In a PERT diagram, the main building block is the event, with connections to its known predecessor events and successor events.

Besides events, PERT also tracks activities and sub-activities:

Time

PERT defines four types of time required to accomplish an activity:

Management tools

PERT supplies a number of tools for management with determination of concepts, such as:

Implementation

The first step for 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.

Example

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 (te) is computed using the formula (o + 4m + p) ÷ 6. [2] :512–513

ActivityPredecessorTime estimatesExpected time
Opt. (o)Normal (m)Pess. (p)
A2464.00
B3595.33
CA4575.17
DA46106.33
EB, C4575.17
FD3484.50
GE3585.17

Once this step is complete, one can draw a Gantt chart or a network diagram.

A Gantt chart created using Microsoft Project (MSP). Note (1) the critical path is in red, (2) the slack is the black lines connected to non-critical activities, (3) since Saturday and Sunday are not work days and are thus excluded from the schedule, some bars on the Gantt chart are longer if they cut through a weekend. Pert example gantt chart.gif
A Gantt chart created using Microsoft Project (MSP). Note (1) the critical path is in red, (2) the slack is the black lines connected to non-critical activities, (3) since Saturday and Sunday are not work days and are thus excluded from the schedule, some bars on the Gantt chart are longer if they cut through a weekend.
A Gantt chart created using OmniPlan. Note (1) the critical path is highlighted, (2) the slack is not specifically indicated on task 5 (d), though it can be observed on tasks 3 and 7 (b and f), (3) since weekends are indicated by a thin vertical line, and take up no additional space on the work calendar, bars on the Gantt chart are not longer or shorter when they do or don't carry over a weekend. Pert example gantt chart.png
A Gantt chart created using OmniPlan. Note (1) the critical path is highlighted, (2) the slack is not specifically indicated on task 5 (d), though it can be observed on tasks 3 and 7 (b and f), (3) since weekends are indicated by a thin vertical line, and take up no additional space on the work calendar, bars on the Gantt chart are not longer or shorter when they do or don't carry over a weekend.

Next step, creating network diagram by hand or by using diagram software

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

A network diagram created using Microsoft Project (MSP). Note the critical path is in red. Pert example network diagram.gif
A network diagram created using Microsoft Project (MSP). Note the critical path is in red.
Early
Start
DurationEarly
finish
Task Name
Late
Start
SlackLate
finish
A node like this one can be used to display the activity name, duration, ES, EF, LS, LF, and slack.

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:

  1. The activity name
  2. The expected duration time
  3. The early start time (ES)
  4. The early finish time (EF)
  5. The late start time (LS)
  6. The late finish time (LF)
  7. The slack

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).

Barring any unforeseen events, 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. 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).

Next step, determination of critical path and possible slack

The next step is to determine the critical path and if any activities have slack. 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 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 (TE) 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.

Therefore, activity b can be delayed almost 4 work days without delaying the project. Likewise, activity dor 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).

A completed network diagram created using Microsoft Visio. Note the critical path is in red. Pert example network diagram visio.gif
A completed network diagram created using Microsoft Visio. Note the critical path is in red.

Avoiding loops

Depending upon the capabilities of the data input phase of the critical path algorithm, it may be possible to create a loop, such as A -> B -> C -> A. This can cause simple algorithms to loop indefinitely. Although it is possible to "mark" nodes that have been visited, then clear the "marks" upon completion of the process, a far simpler mechanism involves computing the total of all activity durations. If an EF of more than the total is found, the computation should be terminated. It is worth saving the identities of the most recently visited dozen or so nodes to help identify the problem link.

As project scheduling tool

Advantages

Disadvantages

Uncertainty in project scheduling

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

One possible method to maximize solution robustness is to include safety in the baseline schedule in order to absorb disruptions. This is called proactive scheduling, however, allowing for every possible disruption would be very slow and couldn't be accommodated by the baseline schedule. A second approach, termed reactive scheduling, defines a procedure to react to disruptions that cannot be absorbed by the baseline schedule.

See also

Related Research Articles

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<span class="mw-page-title-main">Critical path method</span> Method of scheduling activities

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<span class="mw-page-title-main">Project network</span> Diagram showing the order of activities

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<span class="mw-page-title-main">Precedence diagram method</span>

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Willard R. Fazar was an American economist, Head of the Program Evaluation Branch at Special Projects Office, U.S. Navy, and author. He is known as one of co-inventors, and key-developers of PERT."

References

  1. 1 2 Kelley, J.E.; Walker, M.R.; Sayer, J.S. (February 1989). "The origins of CPM: a personal history". Project Management. 3 (2). Project Management Institute: 18. Retrieved 20 March 2024.
  2. 1 2 3 4 5 6 Kerzner 2009.
  3. 1 2 3 Brennan, Maribeth, PERT and CPM: a selected bibliography, Monticello, Ill., Council of Planning Librarians, 1968. p. 1.
  4. 1 2 Malcolm, D. G., J. H. Roseboom, C. E. Clark, W. Fazar. "Application of a Technique for Research and Development Program Evaluation," Operations Research, Vol. 7, No. 5, September–October 1959, pp. 646–669
  5. 1968 Winter Olympics official report, p. 49. Accessed 1 November 2010. (in English and French)
  6. U.S. Dept. of the Navy. Program Evaluation Research Task, Summary Report, Phase 1. Washington, D.C., Government Printing Office, 1958.
  7. U.S. Dept. of the Navy. Program Evaluation Research Task, Summary Report, Phase 2. Washington, D.C., Government Printing Office, 1958.
  8. Willard Fazar cited in: B. Ralph Stauber, H. M. Douty, Willard Fazar, Richard H. Jordan, William Weinfeld and Allen D. Manvel. "Federal Statistical Activities." The American Statistician 13(2): 9–12 (Apr., 1959), pp. 9–12
  9. Desmond L. Cook (1966), Program Evaluation and Review Technique. p. 12
  10. Harold Bright Maynard (1967), Handbook of Business Administration. p. 17

Further reading