Consider the Following Program Evaluation Review Technique (Pert) Network

Statistical tool used in projection management

PERT network chart for a seven-month project with v 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 clarify and represent the tasks involved in completing a given project.

Starting time developed past the United states Navy in 1958, it is normally used in conjunction with the critical path method (CPM) that was introduced in 1957.

Overview [edit]

PERT is a method of analyzing the tasks involved in completing a given project, especially the time needed to consummate each chore, and to place 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 of an event-oriented technique rather than start- and completion-oriented, and is used more in those projects where fourth dimension is the major cistron rather than cost. It is practical on very big-calibration, one-time, complex, not-routine infrastructure and on Research and Evolution projects.

PERT offers a direction tool, 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 betoken each completed phase of the total project."^[1]

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

History [edit]

"PERT" was developed primarily to simplify the planning and scheduling of big and complex projects. It was adult for the U.S. Navy Special Projects Office in 1957 to support the U.S. Navy's Polaris nuclear submarine projection.^[2] Information technology constitute applications all over industry. An early on example is when it was used for the 1968 Winter Olympics in Grenoble which practical PERT from 1965 until the opening of the 1968 Games.^[iii] This project model was the beginning of its kind, a revival for scientific management, founded past Frederick Taylor (Taylorism) and later refined by Henry Ford (Fordism). DuPont'southward critical path method was invented at roughly the aforementioned time as PERT.

PERT Summary Report Phase two, 1958

Initially PERT stood for Plan Evaluation Research Task, merely by 1959 was already renamed.^[2] It had been made public in 1958 in two publications of the U.Due south. Section of the Navy, entitled Program Evaluation Enquiry Chore, Summary Report, Phase i. ^[4] and Stage 2. ^[5] 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 primary concepts of the PERT. He explained:

Through an electronic computer, the PERT technique processes information representing the major, finite accomplishments (events) essential to achieve cease-objectives; the inter-dependence of those events; and estimates of time and range of time necessary to consummate each activeness between two successive events. Such time expectations include estimates of "well-nigh likely time", "optimistic time", and "pessimistic fourth dimension" for each activity. The technique is a management command tool that sizes upwardly the outlook for meeting objectives on time; highlights danger signals requiring management decisions; reveals and defines both methodicalness and slack in the menses 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 determination — before decision.
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 Function of the Lockheed Missile Systems Division; and the Programme Evaluation Branch, Special Projects Office, of the Department of the Navy.^[6]

PERT Guide for management apply, June 1963

X years after the introduction of PERT in 1958 the American librarian Maribeth Brennan published a selected bibliography with almost 150 publications on PERT and CPM, which had been published between 1958 and 1968. The origin and development was summarized as follows:

PERT originated in 1958 with the ... Polaris missile design and construction scheduling. Since that fourth dimension, 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 inside a scheduled fourth dimension and cost expenditure; it came into popularity when the algorithm for computing a maximum value path was conceived. PERT and CPM may be calculated manually or with a figurer, merely usually they require major figurer back up for detailed projects. A number of colleges and universities now offer instructional courses in both.^[i]

For the subdivision of piece of work units in PERT^[7] some other tool was developed: the Work Breakup Construction. The Work Breakdown Structure provides "a framework for consummate networking, the Work Breakdown Construction was formally introduced as the first item of analysis in carrying out basic PERT/Price."^[8]

Terminology [edit]

Events and activities [edit]

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

PERT effect: a indicate that marks the get-go or completion of one or more activities. It consumes no time and uses no resources. When it marks the completion of 1 or more than activities, it is not "reached" (does non occur) until all of the activities leading to that event have been completed.
predecessor event: an event that immediately precedes another event without any other events intervening. An event can take multiple predecessor events and can be the predecessor of multiple events.
successor event: an event that immediately follows another event without any other intervening events. An event can have multiple successor events and tin can be the successor of multiple events.

Also events, PERT also knows activities and sub-activities:

PERT activity: the actual functioning of a task which consumes time and requires resources (such as labor, materials, space, mechanism). It can be understood every bit representing the fourth dimension, effort, and resources required to move from 1 issue to another. A PERT activity cannot exist performed until the predecessor event has occurred.
PERT sub-activeness: a PERT activity can exist further decomposed into a set up of sub-activities. For example, activity A1 tin can exist decomposed into A1.ane, A1.2 and A1.3. Sub-activities have all the properties of activities; in detail, a sub-activity has predecessor or successor events just like an activeness. A sub-activity can be decomposed again into finer-grained sub-activities.

Time [edit]

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

optimistic time: the minimum possible time required to achieve an activity (o) or a path (O), bold everything proceeds improve than is usually expected
pessimistic time: the maximum possible time required to reach an action (p) or a path (P), assuming everything goes wrong (just excluding major catastrophes).
most likely time: the best estimate of the fourth dimension required to attain an activity (m) or a path (K), bold everything proceeds as normal.
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 equally normal (the implication being that the expected time is the average fourth dimension the task would require if the task were repeated on a number of occasions over an extended period of time).

te={\frac {o+4m+p}{vi}}

TE=\sum _{i=1}^{due north}te_{i}

standard deviation of time : the variability of the time for accomplishing an activity (σ_te) or a path (σ_TE)

{\brainstorm{aligned}&\sigma _{te}={\frac {p-o}{6}}\\[8pt]&\sigma _{TE}={\sqrt {\sum _{i=1}^{n}{\sigma _{te_{i}}}^{ii}}}\cease{aligned}}

Direction tools [edit]

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

float or slack is a mensurate of the excess time and resources available to complete a task. It is the amount of time that a project job can be delayed without causing a delay in whatever subsequent tasks (free float) or the whole project (total bladder). Positive slack would bespeak ahead of schedule; negative slack would indicate behind schedule; and nada slack would indicate on schedule.
disquisitional path: the longest possible continuous pathway taken from the initial effect to the concluding issue. Information technology determines the full calendar time required for the projection; and, therefore, any fourth dimension delays along the critical path volition delay the reaching of the last event by at to the lowest degree the same amount.
critical activity: An activeness that has total float equal to naught. An activity with zero free float is non necessarily on the disquisitional path since its path may non be the longest.
lead time: the time by which a predecessor effect must be completed in order to allow sufficient time for the activities that must elapse earlier a specific PERT event reaches completion.
lag fourth dimension: the earliest time by which a successor result can follow a specific PERT consequence.
fast tracking: performing more critical activities in parallel
crashing critical path: Shortening duration of critical activities

Implementation [edit]

The get-go step for scheduling the projection is to decide the tasks that the project requires and the social club in which they must exist completed. The order may be easy to record for some tasks (due east.1000., when building a business firm, the land must exist graded before the foundation can exist laid) while difficult for others (there are two areas that demand to be graded, just there are simply plenty bulldozers to do one). Additionally, the time estimates usually reflect the normal, non-rushed time. Many times, the time required to execute the job can be reduced for an boosted price or a reduction in the quality.

Example [edit]

In the following example there are 7 tasks, labeled A through Thou. Some tasks tin exist done concurrently (A and B) while others cannot exist done until their predecessor task is complete (C cannot brainstorm until A is consummate). Additionally, each task has 3 time estimates: the optimistic time estimate (o), the most probable or normal fourth dimension gauge (chiliad), and the pessimistic time judge (p). The expected fourth dimension (te) 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	four	6	4.00
B	—	three	5	9	5.33
C	A	four	5	7	five.17
D	A	4	6	10	vi.33
E	B, C	4	5	7	5.17
F	D	three	four	8	four.fifty
G	East	3	v	8	v.17

Once this pace is complete, one can describe a Gantt chart or a network diagram.

A Gantt chart created using Microsoft Project (MSP). Note (1) the disquisitional path is in red, (2) the slack is the black lines connected to not-critical activities, (3) since Sabbatum and Sunday are not work days and are thus excluded from the schedule, some bars on the Gantt chart are longer if they cutting through a weekend.

A Gantt chart created using OmniPlan. Annotation (one) the critical path is highlighted, (two) the slack is not specifically indicated on task five (d), though information technology can exist observed on tasks 3 and 7 (b and f), (3) since weekends are indicated past a sparse vertical line, and take up no boosted space on the work calendar, confined on the Gantt nautical chart are not longer or shorter when they do or don't carry over a weekend.

Next footstep, creating network diagram by paw or by using diagram software [edit]

A network diagram tin be created by hand or by using diagram software. There are ii types of network diagrams, activity on arrow (AOA) and activeness 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 first. This "action" has a duration of zippo (0). Then you describe each activity that does non have a predecessor activity (a and b in this example) and connect them with an arrow from outset to each node. Next, since both c and d list a every bit a predecessor activity, their nodes are fatigued with arrows coming from a. Activity e is listed with b and c equally predecessor activities, and then 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. Besides, an arrow is drawn from east to thousand. Since in that location are no activities that come after f or g, information technology is recommended (simply once more not required) to connect them to a node labeled finish.

A node like this one (from Microsoft Visio) can be used to display the activeness proper noun, duration, ES, EF, LS, LF, and slack.

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

The activity name
The expected duration fourth dimension
The early start time (ES)
The early terminate time (EF)
The late start time (LS)
The late finish time (LF)
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 equally the maximum EF of all predecessor activities, unless the activeness in question is the first activeness, for which the ES is zero (0). The EF is the ES plus the task duration (EF = ES + duration).

The ES for commencement is nada since it is the first activeness. Since the duration is zero, the EF is also cipher. 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 go an EF of iv. This EF is used as the ES for c and d.
The ES for b is naught. The elapsing (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 v.33 and c has an EF of 9.17, the ES of eastward is 9.17. The duration (5.17 work days) is added to the ES to get an EF of xiv.34. This EF is used equally the ES for g.
The ES for f is 10.33. The elapsing (iv.5 work days) is added to the ES to get an EF of 14.83.
The ES for grand is 14.34. The duration (v.17 piece of work days) is added to the ES to become an EF of nineteen.51.
The ES for cease is the greatest EF of its predecessor activities (f and one thousand). Since f has an EF of xiv.83 and thousand has an EF of 19.51, the ES of finish is 19.51. Finish is a milestone (and therefore has a duration of naught), and then the EF is also xix.51.

Barring whatsoever unforeseen events, the project should take 19.51 piece of work days to consummate. The next step is to determine the belatedly outset (LS) and tardily terminate (LF) of each activity. This volition eventually bear witness if there are activities that have slack. The LF is defined as the minimum LS of all successor activities, unless the action 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 cease is equal to the EF (19.51 work days) since information technology is the final activity in the project. Since the duration is aught, the LS is also 19.51 work days. This will exist used as the LF for f and grand.
The LF for g is nineteen.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 piece of work days. The duration (four.v work days) is subtracted from the LF to get an LS of 15.01 piece of work days. This will be used equally the LF for d.
The LF for eastward is 14.34 work days. The duration (5.17 work days) is subtracted from the LF to go an LS of 9.17 piece of work days. This will be used as the LF for b and c.
The LF for d is xv.01 work days. The duration (6.33 work days) is subtracted from the LF to get an LS of eight.68 work days.
The LF for c is 9.17 work days. The duration (5.17 piece of work days) is subtracted from the LF to get an LS of iv work days.
The LF for b is 9.17 piece of work days. The duration (five.33 work days) is subtracted from the LF to become an LS of 3.84 piece of work days.
The LF for a is the minimum LS of its successor activities. Since c has an LS of 4 piece of work days and d has an LS of 8.68 work days, the LF for a is 4 work days. The duration (four piece of work days) is subtracted from the LF to go an LS of 0 work days.
The LF for commencement 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 piece of work days, the LS is 0 work days.

Next stride, conclusion of disquisitional path and possible slack [edit]

The next pace is to determine the disquisitional path and if any activities have slack. The disquisitional 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 take slack can be delayed without changing the overall time of the project. Slack is computed in one of 2 ways, slack = LF − EF or slack = LS − ES. Activities that are on the critical path have a slack of zip (0).

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

The disquisitional path is aceg and the critical time is 19.51 work days. It is important to annotation that there can be more than one disquisitional path (in a project more than circuitous than this example) or that the critical path can alter. For example, permit's say that activities d and f take their pessimistic (b) times to complete instead of their expected (T_{Due east}) times. The critical path is at present adf and the critical time is 22 work days. On the other hand, if activity c can be reduced to one work twenty-four hour period, the path fourth dimension for aceg is reduced to xv.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 activeness can now exist determined.

Get-go and stop are milestones and past definition have no duration, therefore they can have no slack (0 work days).
The activities on the critical path by definition take a slack of zero; yet, it is e'er a expert thought to check the math anyway when drawing by hand.
- LF_a – EF_a = 4 − four = 0
- LF_c – EF_c = 9.17 − 9.17 = 0
- LF_e – EF_east = 14.34 − 14.34 = 0
- LF_yard – EF_chiliad = 19.51 − nineteen.51 = 0
Activity b has an LF of 9.17 and an EF of 5.33, and then the slack is 3.84 work days.
Action d has an LF of 15.01 and an EF of 10.33, and then the slack is 4.68 work days.
Activity f has an LF of nineteen.51 and an EF of xiv.83, so the slack is four.68 work days.

Therefore, activeness b can be delayed virtually 4 work days without delaying the project. Likewise, activeness d or activity f tin be delayed 4.68 work days without delaying the project (alternatively, d and f tin exist delayed two.34 work days each).

Fugitive loops [edit]

Depending upon the capabilities of the information input phase of the disquisitional path algorithm, information technology may exist possible to create a loop, such equally A -> B -> C -> A. This tin crusade unproblematic algorithms to loop indefinitely. Although it is possible to "mark" nodes that accept 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 than the total is found, the computation should exist terminated. It is worth saving the identities of the virtually recently visited dozen or so nodes to help identify the problem link.

As project scheduling tool [edit]

Advantages [edit]

PERT chart explicitly defines and makes visible dependencies (precedence relationships) betwixt the work breakup construction (commonly WBS) elements.
PERT facilitates identification of the critical path and makes this visible.
PERT facilitates identification of early start, late start, and slack for each activeness.
PERT provides for potentially reduced projection elapsing due to better understanding of dependencies leading to improved overlapping of activities and tasks where feasible.
The large amount of projection data can be organized and presented in diagram for use in determination making.
PERT can provide a probability of completing before a given time.

Disadvantages [edit]

At that place can exist potentially hundreds or thousands of activities and individual dependency relationships.
PERT is non easily scalable 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 testify status, although colours tin help, eastward.g., specific colour for completed nodes.

Uncertainty in project scheduling [edit]

During project execution, however, a real-life project will never execute exactly as it was planned due to uncertainty. This tin can be due to ambivalence resulting from subjective estimates that are prone to homo errors or tin exist the upshot of variability arising from unexpected events or risks. The main reason that PERT may provide inaccurate information almost the project completion fourth dimension 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 chosen proactive scheduling. A pure proactive scheduling is a utopia; incorporating condom in a baseline schedule which allows for every possible disruption would lead to a baseline schedule with a very large make-span. A second approach, termed reactive scheduling, consists of defining a procedure to react to disruptions that cannot be absorbed by the baseline schedule.

Meet likewise [edit]

Activeness diagram
Arrow diagramming method
PERT distribution
Disquisitional chain project management
Critical path method
Float (projection management)
Gantt nautical chart
GERT
Precedence diagram method
Project network
Project management
Project planning
Triangular distribution
PRINCE2

References [edit]

^ ^a ^b ^c Brennan, Maribeth, PERT and CPM: a selected bibliography, Monticello, Sick., Quango of Planning Librarians, 1968. p. 1.
^ ^a ^b Malcolm, D. K., J. H. Roseboom, C. E. Clark, W. Fazar. "Awarding of a Technique for Enquiry and Development Program Evaluation," OPERATIONS Inquiry, Vol. 7, No. 5, September–October 1959, pp. 646–669
^ 1968 Winter Olympics official report. p. 49. Accessed 1 November 2010. (in English language and French)
^ U.S. Dept. of the Navy. Program Evaluation Research Task, Summary Report, Phase i. Washington, D.C., Government Printing Function, 1958.
^ U.S. Dept. of the Navy. Program Evaluation Inquiry Task, Summary Written report, Stage 2. Washington, D.C., Regime Printing Function, 1958.
^ 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 thirteen(2): ix-12 (Apr., 1959) , pp. 9-12
^ Desmond Fifty. Cook (1966), Plan Evaluation and Review Technique. p. 12
^ Harold Bright Maynard (1967), Handbook of Business Assistants. p. 17

External links [edit]

Media related to PERT charts at Wikimedia Eatables

johnsonroppin.blogspot.com

Source: https://en.wikipedia.org/wiki/Program_Evaluation_and_Review_Technique