PERT and CPM

Abstract

Program Evaluation and Review Technique, known as PERT, is a powerful tool used by project managers to plan and execute complex projects. PERT breaks down complicated projects into smaller and more tangible tasks and develops a network diagram with the tasks. The network diagram describes the relation and dependencies between each task and durations for each individual task is estimated. The time estimate of tasks can be calculated through a simple formula taking both a pessimistic, most-likely and optimistic estimations into account, providing an improved projection of the project timeline and deliverables. ^[1]

A critical path is identified and determined within the network diagram, which is the path of tasks the project must complete on time for the entirety of the project to finish on time. ^[2] Thus, the critical path determines the time duration of the entire complex project. If tasks on the critical path is delayed, the entirety of the project will be behind schedule. The critical path highlights the tasks that focus for the project to become a succus. Mangers using PERT can include a risk management of the individual tasks to identify problem areas and create a plan to deal with the potential of these problems.

PERT visualizes the tasks needed to complete to finish the project. ^[3] This can greatly help managers to improve communication, planning and scheduling, identify project stakeholders and improve the execution of the project. PERT is an extremely flexible tools which can be tailored to help the project managers with their specific need, for them to best deliver on their goal or project. This article will provide a guide for project managers to implement PERT when tackling complex projects and a thought example of a project where PERT and CPM is applied to estimate the duration.

Big Idea

Project managers are often tasked with generating a projection of the estimated time of a projected to be completed. Complex projects can easily be too complex to comprehend and estimate a realistic timeline. In addition, a proper planning of a complex project is often needed to ensure a high-quality deliverable for the project manager. This is where the tool/method PERT shines and can help the project manager to provide project owners with a realistic timeline, plan, and schedule for the project.

PERT is a method or tool to digest advanced and complex project into smaller, more tangible tasks. The goal of PERT is to use the tasks to better estimate, plan and execute the desires project. By visualizing the decomposed tasks in a network diagram, managers are provided with an overview of the entirety of a project.

Managers in collaboration with their team can use PERT to better estimate the duration of project, to help them deliver on time and risk asses the tasks within the project. Each tasks duration in the network diagram is estimated and a critical path can be established. The critical path in the network diagram is the path through the essential tasks that requires on time completion for the project to complete on time. The duration of tasks in the critical path can summarized to provide the manager with a more realistic estimate of the project.

Tasks durations is estimated through multiple factors. Firstly, an optimistic, most-likely and pessimistic estimation of the singular task is estimated. Secondly, the estimations are then calculated with statistical methods to provide the manager with the best possible time estimation.

Application

When faced with a big/complex project, project managers can benefit from applying PERT. To provide an overview of the method, a sequence of task is listed below for managers to follow when implementing PERT. This description of PERT below is inspired by Jean-Michel Réveillac^[4].

Identify tasks
1. Sequence of tasks with relationships and dependences
2. Building a network diagram
Estimation and calculation of tasks durations
1. Estimation: Pessimistic, optimistic and most-likely
Identification of the critical path
1. Calculation of estimated project completion time
Risk management
1. Identify potential risks to the project

Identify tasks

When assigned with a complex project, the first step when using PERT is to divide the project into smaller tasks.

Sequence of tasks with relationships and dependences

When tasks have been defined, the sequence of the completion of tasks should be set by the manager. Usually, a number is given to each task or activity. The start tasks are numbered with a 0, to indicate the starting point. No tasks or activity can be a predecessor to task 0. A table of the relationship and dependences of each task, also called predecessors and successors, is setup within a table. Often when applying the sequence table, an additional column describing the activity is included to provide overview for the engaged actors.

It is important that there is only one start and end task ^[4]. Projects should start with a single task to provide a clear indication of the beginning of the project. Likewise, a single end task is necessary to ensure a clear common understanding of the end goal of a project.

Tasks	Predecessors	Successors
0	NA	1
1	0	2; 3
2	1	4
3	1	4
4	2; 3	5
5 (end task)	4	NA

Building a network diagram

With tasks defined and predecessors and successors determined, it now time to build the network diagram of the complex project. It is important that the arrows drawn follow the direction of the order of which the tasks are done. It is important to be vary of tasks which can be done parallel or if a certain task needs to finish before the next can start ^[4]. In the table shown, tasks 2 and 3 are parallel tasks as these can be performed simultaneously by the team. Whereas task 0 needs to be done for task 1 to start.

Network diagram

Estimation and calculation of tasks durations

Estimation: Pessimistic, optimistic and most-likely

To provide a timeline for the project, the manager needs to estimate the time of the tasks involved. Using the PERT method, a project manager can potentially the team is to estimate the optimistic, pessimistic and most-likely time a task can be completed on^[3]. From those, the standard deviation of the task duration is calculated, together with the mean time a task is taken to be completed.

The following annotations for the time estimation of tasks are used^[3]:

Name	Annotation
Optimistic	$l_a$
Pessimistic	$u_a$
Most likely	$m_a$
Standard deviation	$\sigma_2$
Mean	$\mu_2$

To calculate the standard deviation and mean, the following mathematic equations are to be followed^[3]:

$\sigma_a = 1/6 (u_a - l_a)$

$\mu_a = (l_a+4*m_a+u_a)/6$

With the estimations and calculation done, it can be beneficial to list these next to their task in a table. This can help the project manager with an overview of the importance of certain tasks. An example of such a table is shown below:

	Optimistic	Most likely	Pessimistic	Standard deviation	Mean
Task 0	$l_a$	$m_a$	$u_a$	$\sigma_2$	$\mu_2$
Task 1	$l_a$	$m_a$	$u_a$	$\sigma_2$	$\mu_2$

It can also be beneficial to add float and total float to the table. Float is the amount of time a task can be delayed without affecting the duration of the next tasks. Total float is identical, but the amount of time before a task delay affects the project deadline ^[5].

Identification of the critical path

Calculation of estimated project completion time

With the prior steps done, it is possible to calculate the critical path of a project. The critical path is determined from the mean duration of each task. The highest sum of mean time duration on a path through the network diagram is determined to be the critical path^[3]. Thus, the critical path will provide the manager with a time estimation of the planned project. The duration of the project can be calculated by the sum of mean duration of the tasks on the critical path. The critical path is to be highlighted on the network diagram, to give an easy overview of which task are the most time critical^[6].

If tasks located on the critical path is to be delayed or shortened by a certain time, the overall project duration will be influenced the same^[7].This can help project managers with an easy overview of the total time duration.

The standard deviation of the entire project can also be calculated. This is done by finding the variance of each task located on the critical path. Then the variance of the task is summarized, and the square root of the sum is taken to identify the standard deviation of the entire duration of the critical path and thereby also the entire project ^[8].

$\sigma_{cp} = \sqrt{\sum{\sigma_i^2}}$

The standard deviation of the entire critical path describes the chances of a project being completed by the estimated time. The chances of a project being completed within one standard deviation both positively and negatively of the entire critical path is 68%. Within two standard deviations the chances are 95% and within three there is 99.7% chance that it will be done^[8].

Risk management

Identify potential risks to the project

With the critical path highlighted in the network diagram, it can help the project manager to which task is valuable to focus on before project start. Specific tasks located on the critical path could be subjected to time reducing effort from the project management and/or the team. Thus, helping to bring the overall time of the project down^[5]. However, following time reduction efforts, it is important to continuously update and revise the critical path as it could change as a consequence from such actions. Time reduction efforts should only be focused on tasks that are critical to the project duration. Reducing the time on tasks which are not critical, would not bring down the total project duration^[5].

Another subject for project managers to look into in order to identify the risk to the project deadline is float and total float. These can provide an overview of which task are flexible and which are very time constrained^[5]. Taking effort into improving the float time of specific task, may help the project manager to decrease the chance of delays to the entire project.

The manager can through the work of PERT and CPM analyze the tasks in the network diagram to reduce project deadline or improve the resilience of possible delays to the deadline. Some of these methods could be to brainstorm new work method or tools to a use on a certain task. The project manager could use resource management to increase, decrease, or allocate resources given to certain tasks. Take effort into reducing the duration of critical tasks^[5].

Thought example of applying PERT and CPM

To showcase how to use PERT and CPM a thought example of building a car prototype will be demonstrated. This is a very simplified and minimalistic process but included in the article to give an example of using PERT and CPM on a project.