Program evaluation and review technique

Program Evaluation and Review Technique
Company type	Project management method
Industry	Project management
Founded	1958
Founder	Charles E. Clark
Headquarters	United States

The program evaluation and review technique (PERT) is a quantitative method utilized in project management to examine and depict the various tasks necessary for project completion.

Developed in 1958 by Charles E. Clark for the United States Navy, PERT is frequently employed alongside the Critical Path Method (CPM), which was introduced in the same year.

Overview

PERT focuses on analyzing project tasks to estimate the shortest possible duration required to finish a project, accommodating uncertainty by enabling scheduling without exact activity timeframes. It is event-driven, prioritizing time constraints over cost considerations, and is particularly suited for large, complex, non-repetitive infrastructure and R&D initiatives.

As a managerial instrument, PERT utilizes diagrams composed of arrows and nodes, where arrows symbolize activities and nodes indicate completed stages.

While CPM relies on single estimates for activity duration and cost, PERT incorporates three time estimates—optimistic, most likely, and pessimistic—and does not factor in costs. Despite these distinctions, the term "PERT" has increasingly become synonymous with all critical path scheduling methods.

History

The origin of PERT traces back to efforts by the United States Navy Special Projects Office, Lockheed Aircraft, and Booz Allen Hamilton to streamline planning and scheduling for the Navy's Polaris missile program. Since its inception, PERT has found widespread application across industries, including its use during the 1968 Winter Olympics in Grenoble.

Originally called Program Evaluation Research Task, the technique was renamed PERT by 1959. Foundational reports published by the U.S. Navy in 1958 were chiefly authored by Charles F. Clark.

In 1959, Willard Fazar elaborated on PERT’s fundamental principles: leveraging electronic computers to process data on key events and activities with three time estimates (optimistic, most likely, pessimistic). PERT functions as a management control system that evaluates schedule viability, identifies risks, determines slack times, contrasts expectations with actual schedules, calculates probabilities of on-time completion, and enables simulation of alternative decisions.

By 1968, librarian Maribeth Brennan had compiled approximately 150 publications related to PERT and CPM.

To facilitate detailed task breakdowns within PERT, the Work Breakdown Structure was developed as an organizational framework for comprehensive network analysis and became an essential component of PERT/CPM methodologies.

Events and activities

Within a PERT chart, the primary unit is the event, which connects predecessor and successor events.

PERT event: signifies the initiation or conclusion of one or more activities; it requires no time or resources. An event denoting completion only occurs after all preceding activities have concluded.
predecessor event: directly precedes another event without any intervening events; may have several predecessors and successors.
successor event: directly follows another event without intermediate events; can have multiple successors and predecessors.

PERT also monitors activities and their subdivisions:

PERT activity: a task that consumes time and resources such as labor, materials, or equipment; it represents work progressing from one event to another. This activity cannot commence until its predecessor event has taken place.
PERT sub-activity: an activity broken down into smaller components (for example, A1 divided into A1.1, A1.2, A1.3), each with defined predecessor and successor events; these can be further subdivided as needed.

Time

PERT utilizes four distinct time estimates for project activities:

optimistic time (o): the shortest possible duration under ideal circumstances.
pessimistic time (p): the longest expected duration assuming unfavorable conditions, excluding major disasters.
most likely time (m): the best guess for duration under typical conditions.
expected time (te): a weighted average that accounts for uncertainty, computed as:

The total expected duration along a path is:

standard deviation of time (σ): quantifies the variability in activity or path durations:

<math>

\begin{align} & \sigma_{te} = \frac{p - o}{6} \\[8pt] & \sigma_{TE} = \sqrt{\sum_{i=1}^n {\sigma_{te_i}}^2} \end{align} </math>

Management tools

PERT offers various management instruments to clarify project parameters, such as:

float or slack: indicates the surplus time and resources available to complete an activity without delaying subsequent tasks (free float) or the overall project completion (total float). A positive float signifies being ahead of schedule, a negative float means behind schedule, and zero float indicates being on schedule.
critical path: the longest uninterrupted sequence of activities from initiation to completion, establishing the project's minimum duration. Any delay along this path results in postponing project delivery.
critical activity: an activity with zero total float. Note that zero free float does not necessarily imply that an activity lies on the critical path.
lead time: the earliest point at which a predecessor event must finish to enable subsequent tasks to start promptly.
lag time: the minimum waiting period required before a successor event can commence following a specific predecessor event.
fast tracking: performing critical activities simultaneously to reduce overall project length.
crashing critical path: shortening durations of critical tasks, often incurring higher expenses.

Implementation

Scheduling a project begins by determining essential tasks and their order. Some sequences are straightforward—for example, preparing the ground must precede foundation work—while others involve constraints like limited equipment availability. Time estimates generally represent normal durations but can be compressed if necessary, typically at additional cost or potential quality trade-offs.

Example

Imagine seven tasks labeled from A to G. Certain tasks occur simultaneously (such as A and B), whereas others depend on prior completions (e.g., C starts only after A). Each task is assigned three time estimates: optimistic (o), most likely (m), and pessimistic (p). The expected time (te) is calculated using the formula (o + 4×m + p) ÷ 6.

Activity	Predecessor	Opt. (o)	Normal (m)	Pess. (p)	Expected time
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 tasks and their durations are established, project managers can develop Gantt charts or network diagrams to illustrate schedules and identify critical paths.

Creating network diagrams manually or with software

Network diagrams may be constructed either by hand or through the use of specialized diagramming tools, typically employing one of two formats: activity on arrow (AOA) or activity on node (AON). Among these, AON diagrams tend to be simpler to develop and interpret. When assembling an AON diagram, it is customary to begin with a start node that has zero duration, from which activities lacking predecessors (such as a and b) are linked. Subsequent tasks are then connected based on their predecessor dependencies, ultimately converging at a finish node that joins all terminal activities.

Although a basic network diagram can resemble a Gantt chart, it can be enriched by incorporating essential project parameters such as:

Activity identifier
Estimated duration
Early start (ES)
Early finish (EF)
Late start (LS)
Late finish (LF)
Slack

These metrics are derived assuming known durations for each activity. The ES for any task is determined as the highest EF among its predecessors or zero if it is the first activity; EF is calculated by adding the activity’s duration to its ES. For instance:

The start node has both ES and EF set at zero.
Activities like a and b commence at zero, with their EF values establishing the ES for subsequent tasks.
The ES and EF for later activities follow this logic, respecting predecessor constraints.
The total project length corresponds to the EF of the finish node—in this example, 19.51 working days.

Following this, LS and LF are computed by working backward from the project completion point. LF is assigned as the lowest LS among successor tasks or equals EF for the final activity; LS is found by subtracting the activity’s duration from its LF. This backward pass identifies slack time within activities, indicating where scheduling flexibility exists.

Applying these systematic calculations enables project managers to refine schedules, optimize resource distribution, and effectively control timelines to fulfill organizational goals.

Identifying critical path and calculating slack

The subsequent phase involves pinpointing the critical path along with any activities possessing slack. The critical path represents the longest chain of dependent tasks that establishes the shortest possible project duration. To determine it, sum the durations along each potential path. Activities with slack can experience delays without extending the overall project timeline. Slack is computed either as slack = LF − EF or slack = LS − ES. Tasks on the critical path consistently have zero slack.

Path adf: 14.83 working days
Path aceg: 19.51 working days
Path beg: 15.67 working days

Here, the critical path is identified as aceg, lasting 19.51 working days. It is important to recognize that in more complex projects multiple critical paths may exist or shift if task durations change. For example, if activities d and f reach their pessimistic time estimates, the critical path shifts to adf, extending to 22 working days. Conversely, shortening activity c by one day reduces aceg to 15.34 days, making beg (15.67 days) the new critical path.

Assuming stable durations without such adjustments, slack times for each activity are:

Milestones such as start and finish inherently have zero slack.
All activities on the critical path have zero slack:
- LF_a − EF_a = 0
- LF_c − EF_c = 0
- LF_e − EF_e = 0
- LF_g − EF_g = 0
Activity b shows a slack of 3.84 working days (LF=9.17, EF=5.33)
Activity d has a slack of 4.68 working days (LF=15.01, EF=10.33)
Activity f also possesses a slack of 4.68 working days (LF=19.51, EF=14.83)

Therefore, activity b can be postponed by nearly four workdays without affecting overall completion, while activities d and f can each be delayed up to approximately 4.68 days individually or share this allowance between them.

Preventing cycles

Cycles like A -> B -> C -> A may cause algorithms to enter an endless loop during critical path computations. One method to handle this is to flag visited nodes and remove these flags once processing concludes. Alternatively, a more straightforward technique involves tracking the sum of activity durations; if the earliest finish (EF) surpasses the entire project length, halt the calculation and examine recent nodes to pinpoint the cycle's origin.

Benefits

PERT diagrams clearly represent and illustrate precedence relationships among elements within the work breakdown structure (WBS).
The method emphasizes the critical path, facilitating task prioritization.
It determines early start, late start, and slack times for individual activities.
By enhancing understanding of dependencies, PERT can shorten project timelines through optimized task overlap.
It consolidates complex project information into visual diagrams that assist in decision-making processes.
PERT provides estimates regarding the likelihood of completing the project within a specified timeframe.

Limitations

Projects with extensive scope may contain hundreds or thousands of tasks and dependencies.
Due to its complexity, PERT is less suitable for smaller-scale projects.
Network diagrams can become excessively large and cumbersome, often necessitating multiple pages or specialized paper formats.
Many PERT/CPM charts do not explicitly display timeframes, which complicates progress monitoring; applying color-coding schemes can partially mitigate this issue.

Scheduling uncertainty

Project execution often deviates from original plans because of uncertainties stemming from subjective estimations and unexpected risks. These uncertainties in scheduling can considerably diminish the reliability of PERT’s predicted project completion times.

To improve resilience, proactive scheduling integrates contingency buffers within the baseline schedule to absorb potential delays. Nonetheless, it is impractical to account for every possible disruption. Therefore, reactive scheduling establishes protocols to manage disturbances that exceed the baseline’s buffer capacity.

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