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Statistical tool used in project management From Wikipedia, the free encyclopedia
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.
PERT was originally developed by Charles E. 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]
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]
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.
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]
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]
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:
PERT defines four types of time required to accomplish an activity:
PERT supplies a number of tools for management with determination of concepts, such as:
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.
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
| Activity | Predecessor | Time estimates | Expected time | ||
|---|---|---|---|---|---|
| Opt. (o) | Normal (m) | Pess. (p) | |||
| 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 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) 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.
| Early Start |
Duration | Early finish |
| Task Name | ||
| Late Start |
Slack | Late 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:
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).
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 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).
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.
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.
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