Program evaluation and review technique: Difference between revisions

Revision as of 19:04, 5 May 2022

Latest revision as of 09:18, 20 July 2025

(43 intermediate revisions by 26 users not shown)

Line 1:

{{Short description|Statistical tool used in project management}}

{{Use dmy dates|date=May 2014}}

{{Redirect|PERT}}

{{Use dmy dates|date=May 2014}}

[[File:Pert chart colored.svg|thumb|309px|PERT network chart for a seven-month project with five [[Milestone (project management)|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 [[task (project management)|tasks]] involved in completing a given [[project]].

FirstPERT was originally developed by Charles E. Clark for the [[United States Navy]] in 1958,; it is commonly used in conjunction with the [[criticalCritical pathPath methodMethod]] (CPM), thatwhich was also introduced in 19571958.<ref name="origins">{{cite journal |last1=Kelley |first1=James E. |last2=Walker |first2=Morgan R. |last3=Sayer |first3=John S. |title=The Origins of CPM: a personal history |journal=Project Management |date=February 1989 |volume=3 |issue=2 |page=18 |url=https://www.pmi.org/learning/library/origins-cpm-personal-history-3762 |access-date=20 March 2024 |publisher=Project Management Institute }}</ref>

== Overview ==

PERT is a method of analyzing the tasks involved 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. It incorporates uncertainty by making it possible to schedule a project while not knowing precisely the details and [[Duration (project management)|durations]] of all the activities. It is more of an event-oriented technique rather than start- and completion-oriented, and is used more in thosefor projects where time is the major factorconstraint rather than cost. It is applied onto very large-scale, one-time, complex, non-routine infrastructure andprojects, onas Researchwell andas Development[[R&D]] projects.

PERT offers a management tool,{{sfn|Kerzner|2009}}{{rp|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."<ref name="MB 1968" />

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."<ref name="MB 1968" />

==History==

"PERT" was developed primarily to simplify the planning and scheduling of large and complex projects. It was developed forby the [[United States Navy Special Projects Office|U.S.]], Navy[[Lockheed Special Projects OfficeAircraft]], inand 1957[[Booz Allen Hamilton]] to support the U.S. Navy's [[Polaris nuclear submarinemissile]] project.<ref name="MRCW 1959">Malcolm, D.Donald G.; Roseboom, J.John H.; RoseboomClark, C.Charles E. Clark,; [[Willard Fazar|W.Fazar, FazarWillard]].; "Application of a Technique for Research and Development Program Evaluation,", ''OPERATIONSOperations RESEARCH,Research'', Volvol. 7, Nono. 5, September–October 1959, pp. 646–669</ref><ref name="byte198205">{{Cite magazine |last1=Zimmerman |first1=Steve |last2=Conrad |first2=Leo M. |date=May 1982 |title=Programming PERT in BASIC |url=https://archive.org/details/eu_BYTE-1982-05_OCR/page/n466/mode/1up?view=theater |access-date=2024-12-29 |magazine=BYTE |pages=465–478}}</ref> It found applications all overthroughout industry. An early example is when it was used for the [[1968 Winter Olympics]] in [[Grenoble]] which appliedused PERT from 1965 until the opening of the 1968 Games.<ref>[http://www.la84foundation.org/6oic/OfficialReports/1968/or1968.pdf 1968 Winter Olympics official report.], p. 49. Accessed 1 November 2010. {{in lang|en|fr}}</ref> This project model was the first of its kind, a revival for the [[scientific management]], founded byof Frederick Taylor ([[Taylorism]]) and later refined by Henry Ford ([[Fordism]]). [[DuPont]]'s [[critical path method]]CPM was invented at roughly the same time as PERT.

[[File:PERT Summary Report Phase 2, 1958.jpg|thumb|upright|''PERT Summary Report Phase 2'', 1958]]

Initially PERT stood for ''Program Evaluation Research Task,'' but by 1959 was renamed.<ref name="MRCW 1959" /> 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.''<ref>U.S. Dept.Department of the Navy., ''[https://web.archive.org/web/20151112203807/http://www.dtic.mil/dtic/tr/fulltext/u2/735902.pdf ''Program Evaluation Research Task, Summary Report, Phase 1].'' Washington, D.C.], Government Printing Office, Washington (DC), 1958.</ref> and ''Phase 2.''<ref>U.S. Dept.Department of the Navy., ''[https://catalog.hathitrust.org/Record/100954569 ''Program Evaluation Research Task, Summary Report, Phase 2].'' Washington, D.C.], Government Printing Office, Washington (DC), 1958.</ref> both primarily written by Charles F. Clark.<ref name="origins" /> In a 1959 article in ''[[The American Statistician]]'' the main, [[Willard Fazar]], Head of the Program Evaluation Branch, Special Projects Office, U.S. Navy, gave a detailed description of the main concepts of the PERT. He explained:

{{QuoteBlockquote|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 [[Estimation (project management)|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 [[Schedule (project management)|scheduled]] completion dates and computes the probability for meeting scheduled dates; and simulates the effects of options for decision&nbsp;—decision— before decision.<br />The concept of PERT was developed by an operations research team staffed with representatives from the Operations Research Department of [[Booz Allen Hamilton]]; the Evaluation Office of the [[Lockheed Martin Space Systems|Lockheed Missile Systems Division]]; and the Program Evaluation Branch, Special Projects Office, of the Department of the Navy.<ref name="SDFJWM 1959">[[Willard Fazar]] cited in: Stauber, B. Ralph; StauberDouty, H.Harry M.; DoutyFazar, Willard; FazarJordan, Richard H.; JordanWeinfeld, William Weinfeld; and Manvel, Allen D.; Manvel. "[https://www.jstor.org/stable/2682310 "Federal Statistical Activities]."], ''The American Statistician'', 13(2): 9-129–12 (Apr.,April 1959) , pp. 9-129–12</ref>}}

[[File:PERT Guide for management use, June 1963.jpg|thumb|upright|''PERT Guide for managementManagement useUse'', June 1963]]

Ten years after the introduction of PERT in 1958, the American [[librarian]] Maribeth Brennan publishedcompiled a selected [[bibliography]] with about 150 publications on PERT and CPM, which had beenall published between 1958 and 1968.<ref Thename="MB origin1968">Brennan, Maribeth; ''PERT and developmentCPM: wasa summarizedselected asbibliography'', follows:Council of Planning Librarians, Monticello (IL), 1968, p. 1</ref>

{{Quote|PERT originated in 1958 with the ... [[UGM-27 Polaris|Polaris missile]] design and construction scheduling. Since that time, it has been used extensively not only by the [[aerospace industry]] but also in many situations where management desires to achieve an objective or complete a task within a scheduled time and cost expenditure; it came into popularity when the algorithm for calculating a maximum value path was conceived. PERT and CPM may be calculated manually or with a computer, but usually they require major computer support for detailed projects. A number of colleges and universities now offer instructional courses in both.<ref name="MB 1968">Brennan, Maribeth, ''PERT and CPM: a selected bibliography,'' Monticello, Ill., Council of Planning Librarians, 1968. p. 1.</ref>}}

For the subdivision of work units in PERT<ref>Cook, Desmond L. Cook (1966),; ''Program Evaluation and Review Technique.'', 1966, p. 12</ref> 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/COSTCPM."<ref>[[Harold Bright Maynard|Maynard, Harold Bright]] (1967), ''Handbook of Business Administration.,'' 1967, p. 17</ref>

==Terminology==

Line 36 ⟶ 35:

* ''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.

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

* ''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.

* ''PERT sub-activity'': a PERT activity can be further decomposed into a set of sub-activities. For example, activity A1 can be decomposed into A1.1, A1.2 and A1.3. Sub-activities have all the properties of activities; in particular, a sub-activity has predecessor or successor events just like an activity. A sub-activity can be decomposed again into finer-grained sub-activities.

=== Time ===

PERT has defineddefines four types of time required to accomplish an activity:

* ''optimistic time'': the minimum possible time required to accomplish an activity (o) or a path (O), assuming everything proceeds better than is normally expected{{sfn|Kerzner|2009}}{{rp|512}}

* ''pessimistic time'': the maximum possible time required to accomplish an activity (p) or a path (P), assuming everything goes wrong (but excluding major catastrophes).{{sfn|Kerzner|2009}}{{rp|512}}

* ''most likely time'': the best estimate of the time required to accomplish an activity (m) or a path (M), assuming everything proceeds as normal.{{sfn|Kerzner|2009}}{{rp|512}}

* ''expected time'': the best estimate of the time required to accomplish an activity (te) or a path (TE), 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).{{sfn|Kerzner|2009}}{{rp|512-513}}

::: <math> te = \frac{o + 4m + p} 6 </math>

:::<math>TE = \sum_{i=1}^n te_i</math>

Line 65 ⟶ 64:

* ''[[Critical path method|crashing critical path]]'': Shortening duration of critical activities

== 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'' + 4''m'' + ''p'') ÷ 6.{{sfn|Kerzner|2009}}{{rp|512-513}}

{| class="wikitable"

Line 140 ⟶ 138:

A network diagram can be created by hand or by using diagram software. There are two types of network diagrams, activity on arrow ([[Arrow Diagramming Method|AOA]]) and activity on node ([[Precedence Diagram Method|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 <nowiki>"activity"</nowiki> 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''.

:[[File:pert example network diagram.gif|frame|nonecenter|A network diagram created using [[Microsoft Project]] (MSP). Note the [[critical path method|critical path]] is in red.]]

{{Image frame|width=220|innerstyle=text-align:center|content=

:[[File:pert example node legend.GIF|frame|right|A node like this one (from [[Microsoft Visio]]) can be used to display the activity name, duration, ES, EF, LS, LF, and slack.]]

{{wikitable| class="wikitable" style="text-align:center;"

| style{{=}}"width:70px;" | Early<br/>Start

| style{{=}}"width:70px;" | Duration

| style{{=}}"width:70px;" | Early<br/>finish

|-

| colspan{{=}}"3" | Task Name

|-

| Late<br/>Start

| Slack

| Late<br/>finish

}}

:[[File:pert example node legend.GIF|frame|right|caption=A node like this one (from [[Microsoft Visio]]) 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:

# The activity name

Line 200 ⟶ 211:

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).

:[[File:pert example network diagram visio.gif|thumb|800pxframe|leftcenter|A completed network diagram created using [[Microsoft Visio]]. Note the [[critical path method|critical path]] is in red.]]

{{Clear}}

=== 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.

Line 217 ⟶ 227:

=== Disadvantages ===

* There can be potentially hundreds or thousands of activities and individual dependency relationships.

* PERT is not easilyeasy scalableto scale down for smaller projects.

* The network charts tend to be large and unwieldy, requiring several pages to print and requiring specially-sized 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.

=== 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 the anticipated disruptions. This is called ''proactive scheduling''., A pure proactive scheduling is a utopia; incorporating safety in a baseline schedule whichhowever, allowsallowing for every possible disruption would leadbe tovery aslow baselineand schedulecouldn't withbe aaccommodated veryby largethe make-spanbaseline schedule. A second approach, termed ''reactive scheduling'', consists of definingdefines a procedure to react to disruptions that cannot be absorbed by the baseline schedule.

== See also ==

{{div col|colwidth=22em}}

* [[Activity diagram]]

Line 233 ⟶ 242:

* [[PERT distribution]]

* [[Critical chain project management]]

* [[Critical path method]]

* [[Float (project management)]]

* [[Gantt chart]]

Line 249 ⟶ 257:

==Further reading==

{{Refbegin}}

{{div col|colwidth=30em}}

* {{cite book

| author = Project Management Institute

| title = A Guide to the Project Management Body of Knowledge

Line 258 ⟶ 267:

| isbn = 978-1-935589-67-9

}}

* {{cite book

| first = Ted

| last = Klastorin

Line 267 ⟶ 276:

| isbn = 978-0-471-41384-4

}}

* {{cite book

| lastfirst = Harold Kerzner

| author-linklast = Harold Kerzner

| author-link = Harold Kerzner

| year = 20032009

| title = Project Management: A Systems Approach to Planning, Scheduling, and Controlling

| edition = 8th

| publisheredition = Wiley10th

| publisher = Wiley

| isbn = 978-0-471470-2257727870-03

}}

* {{cite book

| first = Dragan Z.

| last = Milosevic

Line 284 ⟶ 294:

| isbn = 978-0-471-20822-8

}}

* {{cite book

| first = Robert W.

| last = Miller

Line 292 ⟶ 302:

| isbn = 9780070419940

}}

* {{cite book

| first = Harvey M.

| last = Sapolsky

Line 302 ⟶ 312:

| url = https://archive.org/details/polarissystemdev0000sapo

}}

{{Div col end}}

{{Refend}}

== External links ==

Line 313 ⟶ 325:

[[Category:Evaluation methods]]

[[Category:Project management techniques]]

[[Category:Schedule (project management)]]

[[Category:Systems engineering]]

[[Category:Booz Allen Hamilton]]

[[Category:Operations research]]

[[Category:Engineering management]]

[[Category:Management science]]