PERT and CPM

Latest revision as of 21:27, 26 February 2023

[edit] 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.

[edit] 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.

[edit] 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

[edit] Identify tasks

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

[edit] 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

[edit] 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

[edit] Estimation and calculation of tasks durations

[edit] 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].

[edit] Identification of the critical path

[edit] 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].

[edit] Risk management

[edit] 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].

[edit] 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.

[edit] Identify tasks

First, the necessary tasks in order to built a car prototype is identified. The project will only focus on a frame, interior and chassis design. A real life project would be extensively more complex than the showcased example. The identified tasks in order to complete the project is given a task number and the predecessors and successors are determined. The results are presented in the table.

Task name	Task number	Predecessors	Successors
Kick off	0	NA	1
Spec requirements	1	0	2
Initial Frame Design	2	1	3,4
Initial interior design	3	2	5
Initial chassis design	4	2	8
Customer feedback	5	3	6
Revised interior design	6	5	9
Revised frame design	7	2	10
Revised chassis design	8	4	10
Final interior design	9	6	12
Assembly	10	7,8	11
Prototype	11	10	12
Final approval	12	9,11	NA

With the tasks numbered and the predecessors and successors determined, a network diagram can now be drawn to show the connections and dependencies of the tasks. Here the network diagram will include the tasks names, one could include both the name and number for a more visual representation of the project.

Network diagram with task names

[edit] Estimation and calculation of task durations

With the tasks identified and network diagram drawn. It is time to estimate the optimistic, most-likely and pessimistic duration of each of the tasks. The estimations are given in expected days of work. The table will include the calculations of the standard deviation and mean duration, based on the equations provided earlier in the article.

	Task number	Optimistic	Most likely	Pessimistic	Standard deviation	Mean
Kick off	0	0	0	0	0.000	0.0
Spec requirements	1	5	9	15	1.667	9.3
Initial Frame Design	2	5	10	18	2.167	10.5
Initial interior design	3	2	5	12	1.667	5.7
Intial chasis design	4	4	12	25	3.500	12.8
Customer feedback	5	1	3	6	0.833	3.2
Revised interior design	6	1	4	9	1.333	4.3
Revised frame design	7	2	5	7	0.833	4.8
Revised chasis design	8	3	7	12	1.500	7.2
Final interior design	9	1	2	4	0.500	2.2
Assembly	10	5	8	9	0.667	7.7
Prototype	11	3	9	18	2.500	9.5
Final approval	12	0	0	0	0.000	0.0

[edit] Identification of the critical path

With the estimations and calculations done for the tasks in the project, it is time to identify the critical path. It is seen the network diagram, that there are three important aspect of the project which are the interior, frame and chassis design. The critical path can in this instance help determine which is the limiting constraint when it comes to working days required.

To help visualize the critical path, the network diagram is redrawn with the mean time of each task. The critical path is determined by summing the task and the highest path from start to finish is the critical path. On the figure the critical path is highlighted by red arrows.

Critical path of thought example

The most time consuming path throughout the network diagram is summarized to be 57 working days and involves primarily the chassis. Thus, reveling that the chassis in this specific imaginary project is a potential focus for the project manager. The project manager is given the duration estimation of the entire project to be 57 days. It is possible for the project manager to use the standard deviation and variance to get an percentage chance of the deviation from the total estimated time. By summing the variance of the tasks on the critical path, the standard deviation from the summed variance can be calculated. In this instance it comes out to be 5.4 working days. Thus, the project manager knows the chance of finishing the project within one standard deviation (51.6 to 62.4 days) is 68%. The probability within two standard deviations is 95%.

[edit] Risk management

With the critical path identified, it could be useful for the project manager to see if it possible to lower the working days needed to complete the chassis design. To ensure the project would be finished by the estimated time the project manager could investigate if there could be preventive methods applied to ensure the chassis design does not pass the estimated duration.

[edit] Advantages of PERT and CPM method

PERT - Overview of complex projects
PERT is a great tool to provide project managers and other employees with a great overview of complex projects^[5]. By breaking down projects into tasks and mapping their connections a visual representation of an otherwise difficult to comprehend project is made easier.

Effect of planning changes
With the overview and calculations of durations for task and entire projects, PERT and CPM provides the project manager with great insights into the process of a project. It can also provide excellent knowledge of the effects of changing the flow of tasks within a project and its effects^[2].

Ease of implementation
PERT and CPM are two relatively simple tools. This results in it is easily adaptable for project managers with no prior knowledge. Resulting in project managers can integrate PERT and CPM in their planning of project, without the need to study the methods intensely^[2].

Improved coordination'
Using PERT and CPM in conjunction can lead to better coordination and team work between individual actors and departments. The visual aspect of PERT can help to identify when it is necessary for teams or departments to work together and to show what tasks are dependent on different departments. Such insights before a project are started can help to coordinate cross-functional work^[9].

[edit] Limitations of PERT and CPM method

Subjective estimation of task duration
With the need for project managers and their teams to estimate the three factors of task duration (optimistic, pessimistic, and most-likely), a common criticism against the tool is that estimation is subjective^[1]. This results in inaccurate estimation as these are based on personal assumptions instead of a factual estimation. It is difficult for people to estimate such factors accurately, especially if the tasks estimated are new to the team, so they have no prior knowledge to build their knowledge upon.

Time as the only constraint
When using PERT the only constraint factor taken into account is time. Although, PERT does a great job at this, there are still factors to affect the project time, scope and planning. The exclusion of such factors as resources, money, and employees can lead to the project manager to assess the project incorrectly. An example, if two parallel tasks can be completed in 3 days individual but there are not enough employees available to complete the tasks in the given time ^[10].

Lack of near critical-path inclusion
PERT and the CPM method does takes only the critical path into account. Meaning that near critical paths, which are not inconsequential to the project are left out^[1]. If these path were to become significant or critical in a project, it could catch project mangers of guard and lead to further delays in the project. This problem is exaggerated for each parallel task in the network diagram^[1].

[edit] Annotated bibliography

SIMPLIFIED PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) Cottrell, Wayne D., 1999, JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT

- This article provides an simplified version of PERT and uses a normal distribution instead of the normal beta-distribution.

A distributionally robust analysis of the program evaluation and review technique Roos, Ernst and Hertog, Dick den, 2020, European Journal of Operational Research

- This article goes in depth with the math used within the PERT method, as well as trying to provide a better method to calculate the statistics

Optimization Tools for Logistics Réveillac, Jean-Michel, (2015), “Optimization Tools for Logistics”, iste press

- This article dives deeper into PERT in combination with CPM. THe author explains how to use the methods and provides examples

[edit] References

↑ ^1.0 ^1.1 ^1.2 ^1.3 [SIMPLIFIED PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)] Cottrell, Wayne D., 1999, JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT
↑ ^2.0 ^2.1 ^2.2 [M-PERT. A manual project duration estimation technique for teaching scheduling basics] Ballesteros-Pérez, P. (2017), Journal of Construction Engineering and Management.
↑ ^3.0 ^3.1 ^3.2 ^3.3 ^3.4 [A distributionally robust analysis of the program evaluation and review technique] Roos, Ernst and Hertog, Dick den, 2020, European Journal of Operational Research
↑ ^4.0 ^4.1 ^4.2 [“Optimization Tools for Logistics”] “Réveillac, Jean-Michel, (2015), “Optimization Tools for Logistics”, iste press“
↑ ^5.0 ^5.1 ^5.2 ^5.3 ^5.4 ^5.5 [“Production Planning and Control] Kiran, D.R, (2019), “Production Planning and Control”, Butterworth-Heinemann
↑ [“FUZZY CRITICAL PATH METHOD”] Nasution, Sofjan H., (1994), “FUZZY CRITICAL PATH METHOD”, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
↑ [“Popularizing Mathematical Methods in the People’s Republic of China] Wang, Yuan and Hua, Loo-Keng, (Edited by Heijmans, J.G.C), (1989), “Popularizing Mathematical Methods in the People’s Republic of China, BIRKHÄUSER
↑ ^8.0 ^8.1 [“https://www.linkedin.com/pulse/what-pert-how-can-we-use-dave-fourie-pmp-prince2-”] Nasution, Sofjan H., (1994), Fourie, Dave, 2015, What is PERT and how can we use it?
↑ [“https://www.projectmanager.com/blog/pert-and-cpm] Landau, Peter, 2022, PERT and CPM: Their Differences and How to Use Them Together
↑ [“Phantom Float] Kyunghwan, Kim, and Garza, Jesus M. de la, (2003), “Phantom Float”, JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT

[Wayne_D..2C_1999-0] 1.0 ^1.1 ^1.2 ^1.3 [SIMPLIFIED PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)] Cottrell, Wayne D., 1999, JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT

[Ballesteros-P.C3.A9rez.2C_P..2C_2017-1] 2.0 ^2.1 ^2.2 [M-PERT. A manual project duration estimation technique for teaching scheduling basics] Ballesteros-Pérez, P. (2017), Journal of Construction Engineering and Management.

[Roos.2C_Ernst.2C_et._al.-2] 3.0 ^3.1 ^3.2 ^3.3 ^3.4 [A distributionally robust analysis of the program evaluation and review technique] Roos, Ernst and Hertog, Dick den, 2020, European Journal of Operational Research

[R.C3.A9veillac.2C_Jean-Michel.2C_2015-3] 4.0 ^4.1 ^4.2 [“Optimization Tools for Logistics”] “Réveillac, Jean-Michel, (2015), “Optimization Tools for Logistics”, iste press“

[Kiran.2C_D.R.2C_.282019.29-4] 5.0 ^5.1 ^5.2 ^5.3 ^5.4 ^5.5 [“Production Planning and Control] Kiran, D.R, (2019), “Production Planning and Control”, Butterworth-Heinemann

[Nasution.2C_Sofjan_H..2C_.281994.29-5] [“FUZZY CRITICAL PATH METHOD”] Nasution, Sofjan H., (1994), “FUZZY CRITICAL PATH METHOD”, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

[Wang.2C_Yuan_and_Hua.2C_Loo-Keng.2C_.28Edited_by_Heijmans.2C_J.G.C.29-6] [“Popularizing Mathematical Methods in the People’s Republic of China] Wang, Yuan and Hua, Loo-Keng, (Edited by Heijmans, J.G.C), (1989), “Popularizing Mathematical Methods in the People’s Republic of China, BIRKHÄUSER

[Fourie.2C_Dave.2C_2015-7] 8.0 ^8.1 [“https://www.linkedin.com/pulse/what-pert-how-can-we-use-dave-fourie-pmp-prince2-”] Nasution, Sofjan H., (1994), Fourie, Dave, 2015, What is PERT and how can we use it?

[Landau.2C_Peter.2C_2022-8] [“https://www.projectmanager.com/blog/pert-and-cpm] Landau, Peter, 2022, PERT and CPM: Their Differences and How to Use Them Together

[Kyunghwan.2C_Kim.2C_and_Garza.2C_Jesus_M._de_la.2C_.282003.29-9] [“Phantom Float] Kyunghwan, Kim, and Garza, Jesus M. de la, (2003), “Phantom Float”, JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT

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@@ Line 9: / Line 9: @@
 PERT visualizes the tasks needed to complete to finish the project. <ref name="Roos, Ernst, et. al.">[''A distributionally robust analysis of the program evaluation and review technique''] ''Roos, Ernst and Hertog, Dick den, 2020, European Journal of Operational Research '' </ref> 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.
 __TOC__
 == Big Idea ==

PERT and CPM

Latest revision as of 21:27, 26 February 2023

[edit] Abstract

Contents

[edit] Big Idea

[edit] Application

[edit] Identify tasks

[edit] Sequence of tasks with relationships and dependences

[edit] Building a network diagram

[edit] Estimation and calculation of tasks durations

[edit] Estimation: Pessimistic, optimistic and most-likely

[edit] Identification of the critical path

[edit] Calculation of estimated project completion time

[edit] Risk management

[edit] Identify potential risks to the project

[edit] Thought example of applying PERT and CPM

[edit] Identify tasks

[edit] Estimation and calculation of task durations

[edit] Identification of the critical path

[edit] Risk management

[edit] Advantages of PERT and CPM method

[edit] Limitations of PERT and CPM method

[edit] Annotated bibliography

[edit] References

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