Program evaluation and review technique
The program evaluation and review technique is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project.
First developed by the United States Navy in 1958, it is commonly used in conjunction with the critical path method that was introduced in 1957.
OverviewPERT 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 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 time is the major factor rather than cost. It is applied on very large-scale, one-time, complex, non-routine infrastructure and on Research and Development projects.
PERT offers a management 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 indicate each completed phase of the total project."
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 and no costs for each activity. Although these are distinct differences, the term PERT is applied increasingly to all critical path scheduling."
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 in 1957 to support the U.S. Navy's Polaris nuclear submarine project. It found applications all over industry. An early example was it was used for the 1968 Winter Olympics in Grenoble 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, founded by Frederick Taylor and later refined by Henry Ford. DuPont's critical path method was invented at roughly the same time as PERT.
Initially PERT stood for Program Evaluation Research Task, but by 1959 was already renamed. 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. and Phase 2. 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:
Ten years after the introduction of PERT in 1958 the American librarian Maribeth Brennan published a selected bibliography with about 150 publications on PERT and CPM, which had been published between 1958 and 1968. The origin and development was summarized as follows:
For the subdivision of work units in PERT 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/COST."
Events and activitiesIn a PERT diagram, the main building block is the event, with connections to its known predecessor events and successor events.
- 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 activities, it is not "reached" 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. 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.
- optimistic time: the minimum possible time required to accomplish an activity or a path, assuming everything proceeds better than is normally expected
- pessimistic time: the maximum possible time required to accomplish an activity or a path, assuming everything goes wrong.
- most likely time: the best estimate of the time required to accomplish an activity or a path, assuming everything proceeds as normal.
- expected time: the best estimate of the time required to accomplish an activity or a path, accounting for the fact that things don't always proceed as normal.
- standard deviation of time : the variability of the time for accomplishing an activity or a path
- float or slack 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 or the whole project. Positive slack would indicate ahead of schedule; negative slack would indicate behind schedule; and zero slack would indicate on schedule.
- critical path: 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 free float is not necessarily on the critical path since its path may not be the longest.
- 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: performing more critical activities in parallel
- crashing critical path: Shortening duration of critical activities
ExampleIn the following example there are seven tasks, labeled A through G. Some tasks can be done concurrently while others cannot be done until their predecessor task is complete. Additionally, each task has three time estimates: the optimistic time estimate, the most likely or normal time estimate, and the pessimistic time estimate. The expected time is computed using the formula ÷ 6.
Once this step is complete, one can draw a Gantt chart or a network diagram.
Next step, creating network diagram by hand or by using diagram softwareA network diagram can be created by hand or by using diagram software. There are two types of network diagrams, activity on arrow and activity on node. Activity on node diagrams are generally easier to create and interpret. To create an AON diagram, it is recommended to start with a node named start. This
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 expected duration time
- The early start time
- The early finish time
- The late start time
- The late finish time
- The slack
- 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 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 is added to the ES to get an EF of 5.33.
- The ES for c is four. The duration is added to the ES to get an EF of 9.17.
- The ES for d is four. The duration 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. 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 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 is added to the ES to get an EF of 14.83.
- The ES for g is 14.34. The duration is added to the ES to get an EF of 19.51.
- The ES for finish is the greatest EF of its predecessor activities. 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, so the EF is also 19.51.
- The LF for finish is equal to the EF 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 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 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 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 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 is subtracted from the LF to get an LS of 4 work days.
- The LF for b is 9.17 work days. The duration 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 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.
Next step, determination of critical path and possible slack
- 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.
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.
- 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.
- * LFa – EFa = 4 − 4 = 0
- * LFc – EFc = 9.17 − 9.17 = 0
- * LFe – EFe = 14.34 − 14.34 = 0
- * LFg – EFg = 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.
As project scheduling tool
- PERT chart explicitly defines and makes visible dependencies between the work breakdown structure 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 and presented in diagram for use in decision making.
- PERT can provide a probability of completing before a given time.
- 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 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
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 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.