Program Evaluation and Review Technique (PERT)

Abstract

The focal point of this article will be the simplified Program Evaluation and Review Technique (PERT), which is a project management tool used for the planning, scheduling and control of complex projects. The U.S. Navy originated PERT in 1958 as a tool for scheduling the development of a complete weapons system . It is a network-based technique that uses a flow diagram to represent the interdependencies of tasks in a project.

This article starts with a brief introduction to the project management concept and the planning and estimating procedures. After the tool's description, this article's outline will follow with the importance of this technique in project management and the advantages of the simplified method. The goal of PERT is to provide project managers with a visual representation of the project timeline and to help identify the critical path and critical tasks, which must be completed on time for the entire project to be on schedule and meet the assigned deadline. In addition, PERT provides project managers with a way to estimate the total duration time and identify potential bottlenecks and risks in the project itinerary.

Subsequently, this article will thoroughly explain how to apply the simplified PERT, including its terminology and an example for further illustration, and when its application will be accurate within the estimation of a project. To build a PERT diagram, specific steps must be followed to allocate resources and ensure that the project stays on track.

Moreover, PERT also has advantages and limitations that will be covered in this composition. For instance, this method has dependency limitations, meaning that activity durations are assumed to be independent . Despite these disadvantages, which will be addressed below, PERT remains a valuable tool for project management and can be used effectively when its limitations are considered. Finally, this article will propose new approaches and tools for project estimation that will help overcome some PERT limitations.

Introduction

Project Management

• What is a project?

To better understand what project management entails, the concept of a project should be explained in advance. Therefore, projects can be defined as temporary efforts to create value through unique products, services, and processes. However, this is a broad definition of the term at hand. When analysed in-depth and broken down into smaller pieces, a project consists of a series of tasks and activities that must be completed in a structured and careful way in order to produce the desired deliverables or outcomes.

• What does project management entail?

Project management is the implementation of knowledge, skills, tools and techniques to the project's tasks, with the purpose of meeting or fulfilling the needs and expectations of the entities and organisations involved in the said project. To deliver the project on time, within budget, and with the intended quality, entails managing resources, timelines, budgets, and risks. Along with recognising and managing possible risks and impediments that can appear over the project's life cycle, effective project management also includes interacting with and communicating with stakeholders to make sure their demands are addressed.

Project management has grown in importance recently as firms have realised the necessity for more organised and effective methods of project delivery. In fact, according to the PMI, companies that give project management a high priority enjoy a 35% rise in their project success rates.

Planning and estimating in project management

• The planning process of a project

When it comes to project planning, there are several steps that must be followed during this process to guarantee that it is finished on schedule and within budget. One such procedure entails defining the activities that form the project, calculating their duration, identifying the connections or relationships between them, drawing a network diagram, identifying the critical path, and balancing the project.

1. The activities are defined. Identifying the project's activities is the first step in the planning process. In order to do this, the project must be divided into smaller, easier-to-manage tasks or activities.

2. Each activity's duration and cost are estimated. This step comes next after the activities have been defined. It entails estimating the time needed to finish each task, taking into account the resources available, the difficulty of the assignment, and the abilities of the project members who will be working on the project. In this process of resource planning, it is essential to be familiar with the activities to properly assign the resources needed to each activity, both physical (infrastructure, equipment, materials and components) and human resources. Then, the cost of the activities is estimated based on the previous information.

3. The sequence and connections between activities are identified. Finding the order and the dependency relationships between activities comes next, meaning that it is necessary to figure out which tasks can be handled concurrently and which ones require the completion of other tasks.

4. A network diagram is drawn. The following step is to create a project network diagram using the data acquired in the preceding sections. This diagram serves as a visual representation of the project plan and helps in highlighting the connections between the tasks.

5. The duration and critical path are calculated. The longest succession of interdependent tasks that must be finished in order to complete the project on schedule is known as the critical path. Finding the critical path is crucial since it aids in identifying the activities that are most crucial to the project's success and those that have the biggest influence on its time frame.

6. Project balance is achieved. The project team can balance the project after determining the critical path and duration. To guarantee that the project is finished on time and within the allocated budget entails verifying and adjusting the resources and duration of the tasks as the project evolves.

In conclusion, there are various processes involved in the planning process for a project, each of which is essential to its success.

• The estimation process

As mentioned in the previous section, planning entails developing estimates for work effort, duration, costs, people, and physical resources. Estimates are a quantitative assessment of the likely amount or outcome of a variable, such as project costs, resources, effort, or duration. As the project evolves, the estimates can change based on current information and circumstances (PMI, 2021).

Different techniques can be applied to create an estimation of the work, time, or cost associated with a project.

  1. Analogous estimation: the length or expense of an activity or project is estimated using historical data from previous iterations of the 
  same activity or project.
  2. Multiple-point estimation: when there is uncertainty with the individual activity estimations, multi-point estimating evaluates cost or 
  duration by applying an average or weighted average of optimistic, pessimistic, and most likely estimates. This technique is also known as 
  three-point estimation or PERT.
  3. Single-point estimation: this technique provides a single value that represents a best-guess estimate. This type of estimation contrasts 
  with a range estimate, which takes into account both the best and worst-case scenarios.
  4. Parametric estimation: with the use of an algorithm, parametric estimating determines cost or duration based on past data and 
  project parameters.
  5. Relative estimation: by comparing results to a similar amount of work and taking effort, complexity, and uncertainty into account, 
  relative estimating is used to provide estimates. Absolute units of cost or time are not always used in relative estimation. In relative 
  estimating, story points are a typical unitless unit of measurement.

PERT in project management

PERT technique

• Description of the tool

The U.S. Navy developed PERT in 1958 as a tool for planning the establishment of an entire weapons system, specifically to support the launch of the Polaris mobile submarine project.

PERT stands for Program Evaluation and Review Technique, which is a network-modeling tool used for planning the activities required to complete large, complex and nonrepetitive projects. The method views a project as an acyclic network of activities and events. To calculate the duration of a project, a system flow plan takes into account the expected value and variance of each task's length. The critical path consists of a series of activities that cannot be delayed without endangering the project as a whole. PERT can be used to calculate the likelihood that a project or a specific activity will be finished by a given deadline.

Moreover, this method makes the assumption that activity durations follow a beta distribution in order to deal quantitatively with uncertain and imprecise durations. In order to approximate the mean and variance of the beta probability density function, three estimates of each activity duration—the optimistic, the most likely, and the pessimistic estimates—are supposed.

• Importance of performing PERT

The performance of this method is important for several reasons in project management. Among the main reasons, the following can be found:

1. Improvement of the project's planning. With PERT, project managers can divide a project into smaller, easier-to-manage tasks and design a network diagram that shows how the tasks are interconnected. This makes it easier for project managers to plan and schedule the work, ensuring that all activities are finished within the anticipated time range. Also, it allows them to identify the critical path, which is crucial because then they can concentrate their efforts and resources on the most crucial tasks.

2. Risk management. PERT entails assigning each activity time estimates, which are used to determine the project's total duration and to pinpoint areas of risk and uncertainty, making it possible to anticipate possible issues before they arise and create solutions.

3. Resource allocation. By identifying the tasks that are most critical to the project's success, PERT aids project managers in allocating resources more efficiently and achieving what is called a balance of resources . This enables project managers to concentrate their efforts on the most crucial activities and guarantee the project's timely and economical completion.

4. Improved Communication. PERT gives a visual representation of the activities and their dependencies, making it simpler to update stakeholders on the project's status.

• Simplification of the conventional PERT

In this section of the article, a simplified version of the PERT method is introduced, where the number of estimations needed for activity durations is reduced from three, in traditional PERT, to two. To achieve this, it is required to apply a normal distribution with the "most likely" and the "pessimistic" estimates to the duration of an activity, rather than the beta distribution. After having estimated the expected duration of the activities and the variances, the rest of the simplified PERT approach has no differences from that of traditional PERT.

As this technique minimises the time and effort required to complete it and produces values similar to those of the conventional PERT when activity duration distributions are not highly skewed , then the remainder of the paper will concentrate on this condensed version.

Application of the simplified PERT

This approach can be implemented for large and complex projects, as it was stated in the description of the tool. This is due to the fact that PERT assumes that the project has a large number of activities for the normal distributions to be assumed. As a result, the analysis may be biased when there are few activities. For this reason, in comparison to standard PERT, this condensed version may be more easily and quickly employed in industry, particularly in the planning of large-scale, intricate construction projects.

In today's digital age, the use of hardware and software is no longer a barrier to project management. Many project management tools, including Microsoft Project and Oracle Primavera, now feature PERT graphs as a standard feature. PERT graphics are very effective in demonstrating the interdependencies between the many project-related activities. PERT is useful when combined with the Gantt diagram, a highly efficient and simple approach to compare the actual progress made on each task of the project to the progress that was originally predicted for each one. Even more popular than PERT graphics are Critical Path diagrams because they provide a more user-friendly representation as the nodes stand in for the activities, not the events.

Terminology

Several terms and parameters are used in drawing and applying the PERT technique. Therefore, there are detailed below:

- Activity: this term refers to a specific task or set of tasks that must be completed within a defined time frame to achieve the project's objectives. Activities are typically described in detail in the project plan, including their start and end dates, dependencies on other activities, and the resources required to complete them . In the PERT diagram, they are represented by continuous lines.

- Fictional activity: an activity with a time duration of zero that resolves complex dependencies and is represented by a discontinuous line.

- Event: the moment that indicates the start or completion of one or more activities. There are two types of events, a predecessor event and a successor one. The former occurs just before another event without any other events coming in between. One event could precede several other activities or the other way around. On the other hand, a successor event happens right after another event without any other events coming in between. Once more, one event can come after several activities or vice versa.

- Dependencies between activities: this term refers to the relationship and order in which the activities must be completed to achieve the project's objectives. The project's critical path—the sequence of tasks that must be completed by the due date to prevent delays and jeopardise the entire project—is established by these dependencies between the activities. There are four kinds of dependence relationships between activities:

   1. Finish-to-Start (FS): The predecessor activity must be completed before the successor activity can begin.
   2. Start-to-Start (SS): The predecessor activity must begin first for the successor activity to begin.
   3. Finish-to-Finish (FF): The predecessor activity must finish before the successor activity can.
   4. Start-to-Finish (SF): The predecessor activity must begin for the successor activity to begin.

- Most likely duration (m): the most accurate way to estimate how long it will take to complete an activity. It is believed that everything will go according to plan.

- Pessimistic duration (b): the longest time necessary to complete an activity. Everything that could possibly go wrong must be taken for granted. This estimation assumes all unfavourable circumstances, the occurrence of all potential risks, and the absence of any risk mitigation.

- Expected duration (Te): the most accurate estimation of the amount of time needed to complete a task, taking into consideration potential obstacles. It is considered the PERT weighted average duration.

- Variance (σ^2(Te)): the variance in the length of time required to complete an activity.

- Earliest start time (EST): the earliest time an activity can begin due to its dependencies on the other activities of the project. Calculated by the forward pass performed on the network.

- Earliest finish time (EFT): the earliest time an activity can be completed due to its dependencies on the other activities of the project. Also, calculated by the forward pass performed on the network.

- Latest start time (LST): the latest time an activity can begin due to its dependencies on the other activities of the project. Calculated by the backward pass performed on the network.

- Latest finish time (LFT): the latest time an activity can be completed due to its dependencies on the other activities of the project. Also, calculated by the backward pass performed on the network.

- Float (also known as slack): the difference between the latest start time and the earliest start time (F=LST-EST). Every activity on a critical path has a float of zero. On the other hand, by looking for arcs with zero float, the critical path can be found.

Guide on how to build a simplified PERT

Figure 1. Steps for the application of PERT

As discussed in the planning process, to be able to begin implementing the simplified PERT, the first step is to identify and compile a list of the project's activities.

The next step is to assign two time estimates—the most likely time estimate (m) and the pessimistic time estimate (b)—for each activity. These time estimations must be used as inputs to calculate the expected value and variance of an activity's duration, which is step three of building PERT. The only alternative is to presume that a duration's distribution is symmetric, or normal, rather than beta. Thus, any two points on one side of the curve can be used to define a unique normal distribution. Using m and b is the more cautious course of action. Given normal distribution, the mode, or m, in this case, equals the mean. In the simplified PERT model, an activity's expected duration can be calculated as follows: Te = m. Meanwhile, the variance can be computed as shown in the following equation: 𝜎_90^2(Te) = [(b-m)/1,625]^2.

The fourth step entails defining the chronological sequence of the activities from the beginning of the project to its end and the dependency relationships between them . Fifth, similar to the commonly used critical path method, forward and backward passes over the network are made to determine the earliest start and finish time, the latest start and finish time, the floats, and, as a result, the critical path of this network.

The last step is to draw the PERT diagram to provide a visual representation of the project's activities and its dependencies.

Example

In this section of the article, an example of the application of the simplified PERT will be developed.

A company has decided to buy and implement an Enterprise Resource Planning (ERP) in order to optimise its operations. Therefore, the Project's Director has been tasked with evaluating the different alternatives on the market and selecting the best one for the company.

As it is described in the previous section of the article, the first step is to identify the activities. In the ERP project, eleven activities are identified and assigned two time estimates, the most likely and the pessimistic estimate. This is due to the fact that, for this particular project, the company does not have a history of similar projects, leading to the conclusion that a probabilistic approach with a normal distribution is required. As a result, the expected durations, which are the ones used to build the PERT and determine the total duration of the project, and variances of the activities are calculated. Subsequently, the order and the dependencies of the activities are defined.

The following table compiles all of the findings.

Table 1. ERP Project's activities

Figure 2. PERT diagram with the activities and their dependencies

With the previous inputs, the forward and backward passes are determined for all the events and activities through the network, as it is shown for activity 7 in Figure 3. After completing the aforementioned passes, the total duration of the project and the critical path are estimated. In the ERP project, the total duration is 14 weeks, being both the earliest and the latest finish time of the project, and the critical path is formed by the following activities: A1-A2-A3-A6-A9-A10-A11. These activities cannot be delayed if the project must be completed in fourteen weeks.

Figure 3. Forward and Backward passes

Lastly, the PERT diagram can be fully drawn, with all the information acquired beforehand.

Figure 4. Complete PERT diagram

Discussion

Advantages

• Benefits of the simplified version versus the standard PERT

Since the early 1960s, a number of PERT criticisms and suggested adjustments have been published in the literature. As a result, in this section of the article, a number of traditional PERT's drawbacks that are overcome or lessened by the basic PERT will be discussed.

As previously discussed, one of PERT's main disadvantages is the need for several time estimates, which can take months to generate, making this process time-consuming and complex. The simplification of PERT reduces the amount of work and time necessary to implement PERT and the amount of activity duration knowledge that is needed. Also, it delivers results similar to those obtained with conventional PERT but with less work if the activities do not have severely skewed duration distributions.

The time estimations of the activity duration are difficult to predict with accuracy for project engineers and managers. Subjective estimates of a, m and b are based on judgment and may not be closely related to statistical sampling of the real times. This subjectivity is exacerbated by the fact that the distribution of the activity duration is also hypothesised. However, it can be reduced by decreasing the number of time estimates from three to two.

Limitations

Some of the drawbacks of this tool are the same as the ones from the original PERT. The real mean and variance of the distribution are estimated from the mean and variance of an activity duration as determined by the formulas presented in the section on how to build a PERT. The difference between the estimated and actual equations results in a significant error in the estimations.

In addition, when calculating the probability that a project will be completed on time, both PERT approaches solely take the critical path into account. The approach disregards near-critical routes with a high likelihood of going critical.

However, as it is explained in the advantages, one of the biggest shortcomings of the simplified version is a high skewness in the activity duration. This skewness can appear if there are factors that make it more likely for the activity to take longer than average, such as unexpected delays or complications. When the actual distribution's skewness is larger than 0,28 or less than -0,48, simplified PERT durations are susceptible to errors of more than 10%.

Other scheduling tools

In addition to PERT, the Critical Path Method (CPM) is the method most frequently used for project scheduling. Since both of these network strategies highlight a project's critical path, which includes activities that cannot be postponed without increasing the project's completion time, and also indicate activities with slack (or float), they do not significantly differ from one another. The CPM, on the other hand, is a deterministic method rather than a stochastic one and enables resource allocation. The method is intended to control project time and expense factors, especially time/cost trade-offs. As a result, activities can be expedited at an additional expense to reduce completion times.

Another widely recognised project management scheduling technique is the Monte Carlo Simulation, which is "a process which generates hundreds or thousands of probable performance outcomes based on probability distributions for cost and schedule on individual tasks. The outcomes are then used to generate a probability distribution for the project as a whole” (Project Management Institute, 2013, p. 547). Since the time is predicted using more than just simple weighted averages and it is able to handle different activity duration probability distributions, the Monte Carlo simulation is more accurate than the PERT. Additionally, the technique can account for the impact of critical path sensitivity since the Monte Carlo Simulation employs time estimates for all of the project's tasks rather than just the critical path task weighted averages. However, this technique is computationally harder to implement and takes more time and effort than PERT.

Annotated bibliography

• Project Management Institute, Inc. (2021). Project Management: A guide to the Project Management Body of Knowledge (PMBOK guide). 7th Edition and The Standard for Project Management - The Standard for Project Management. https://findit.dtu.dk/en/catalog/2702860479

- This book is an essential resource for efficient project management across all industries as it contains an exhaustive list of pertinent procedures, best practises, standards, and terminologies. Section 4 of the book gives an in-depth description of some common methods that are helpful for project management, such as the Multipoint estimating technique.

• Cottrell, Wayne D. (1999). SIMPLIFIED PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT). Journal of Construction Engineering and Management, 125(1), 16-22. https://doi.org/10.1061/(ASCE)0733-9364(1999)125:1(16)

- This article provides a detailed explanation of the simplified version of the PERT while comparing both techniques. The paper supplies the reader with a study of PERT-related issues in the literature, and, therefore, introduces the presentation of the simplified PERT. Testing and evaluation of the simplified technique using both activity duration mean and a set of project networks are included and contrasted with those from traditional PERT.

• Poveda Bautista, R. (2021). Apuntes y transparencias del curso. 11489 Proyectos, Lección 4: Conceptos básicos. Planificación, Universidad Politécnica de Valencia (UPV) (Spanish)

- These slides of the lecture regarding the planning process are extremely helpful in learning the following concepts of management, planning, scheduling, Work Breakdown Structure (WBS), and project plans. They also aid in developing the ability to handle tools and management techniques. Moreover, it is a crucial resource to understand the most employed project planning and management techniques and the significance of using them to ensure the project's success.