How PERT builds up on CPM - Revision history

Tkokotas at 13:58, 18 December 2018

2018-12-18T13:58:00Z

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			''Developed by Olöf Run Sigurjonsdottir''


	In project management it is necessary to use a tool which states how the project is going. The project manger faces the challenge of planning, coordinating and monitoring the project, which can be difficult if no tool is at hand <ref name=''begin''> CareerProfile.info. (n.d.) ''The Project Management Interview.'' Retrieved 08.09.2016 from http://www.careerprofiles.info/project-management-interview.html </ref>. Therefore, project managers often use the '''Critical Path Method (CPM)''' and '''Program Evaluation Review Technique (PERT)''' to do those things. The tools give a good overview of how a project progresses. Over the years, CPM and PERT have been used in a wide range of projects. For example, in building constructions, maintenance of equipment, design and installation of management systems, organizing transportation projects and so on. <ref name=''math''> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://www.math.csusb.edu/faculty/prakash/611/Project_Management.ppt.pdf </ref>		In project management it is necessary to use a tool which states how the project is going. The project manger faces the challenge of planning, coordinating and monitoring the project, which can be difficult if no tool is at hand <ref name=''begin''> CareerProfile.info. (n.d.) ''The Project Management Interview.'' Retrieved 08.09.2016 from http://www.careerprofiles.info/project-management-interview.html </ref>. Therefore, project managers often use the '''Critical Path Method (CPM)''' and '''Program Evaluation Review Technique (PERT)''' to do those things. The tools give a good overview of how a project progresses. Over the years, CPM and PERT have been used in a wide range of projects. For example, in building constructions, maintenance of equipment, design and installation of management systems, organizing transportation projects and so on. <ref name=''math''> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://www.math.csusb.edu/faculty/prakash/611/Project_Management.ppt.pdf </ref>

S150964: /* Example of PERT */

2016-09-26T21:17:58Z

Example of PERT

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	First of all, a diagram is drawn and the critical path is found with the duration of the normal time, m. Since, this is the same example as for the CPM, the critical path has already been computed, A-B-D-F-G. On the diagram below the critical path have been marked with green arrows between tasks.		First of all, the expected activity time, <math>t_e\,</math>, is calculated with Equation 4. When the expected time have been computed the diagram is drawn. Then, the table will be:


	~~[[File:ExamplePERT.jpg]]~~


	~~Next~~, the expected activity time, <math>t_e\,</math>, is calculated with Equation 4. Then, the table will be:

	{\| class="wikitable"		{\| class="wikitable"
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	\| G \|\| ''F, E'' \|\| 3 \|\| 5 \|\| 8 \|\| 5.17		\| G \|\| ''F, E'' \|\| 3 \|\| 5 \|\| 8 \|\| 5.17
	\|}		\|}

			Next, a diagram is drawn and the critical path is found with the expected task time, <math>t_e\,</math>. That is done with the forward pass and the backward pass from the CPM, so please look at that for further demonstration. When CPM have been applied the diagram will have the critical path which can be seen with the green arrows.


			[[File:ExamplePERT.jpg]]


	Now, with Equation 5 compute the variance of the task completion time, <math>\sigma^2\,</math>, and add it to the table.		Now, with Equation 5 compute the variance of the task completion time, <math>\sigma^2\,</math>, and add it to the table.

S150964: /* The Critical Path Method */

2016-09-26T20:58:37Z

The Critical Path Method

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	[[File:Note.jpg\|thumb\|''Figure 1:'' Indicates how notes build up.]]		[[File:Note.jpg\|thumb\|''Figure 1:'' Indicates how notes build up.]]

	Before starting to use the CPM it is crucial to make a chart. The first thing is to list all tasks in the project. In the list it is needed to specify the task, the description, predecessors and the estimated time. Then, make a graph with notes, indicating each task, and arrows which indicate the connection between them. All arrows go from left to right and they begin at the first task, which has no predecessor, and go all the way to the last task, which has no successor. <ref name="mindtools"> Mind Tools Editorial Team. (n.d.) ''Critical Path Analysis and PERT Charts.'' Retrieved 14.09.2016 from https://www.mindtools.com/critpath.html </ref> The notes have to include space for the EST, EFT, LST, LFT and slack, as shown in ~~figure~~ 1. When the graph has been made the CPM can be computed.		Before starting to use the CPM it is crucial to make a chart. The first thing is to list all tasks in the project. In the list it is needed to specify the task, the description, predecessors and the estimated time. Then, make a graph with notes, indicating each task, and arrows which indicate the connection between them. All arrows go from left to right and they begin at the first task, which has no predecessor, and go all the way to the last task, which has no successor. <ref name="mindtools"> Mind Tools Editorial Team. (n.d.) ''Critical Path Analysis and PERT Charts.'' Retrieved 14.09.2016 from https://www.mindtools.com/critpath.html </ref> The notes have to include space for the EST, EFT, LST, LFT and slack, as shown in Figure 1. When the graph has been made the CPM can be computed.

S150964: /* How PERT builds upon CPM */

2016-09-26T20:58:10Z

How PERT builds upon CPM

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	== How PERT builds upon CPM ==		== How PERT builds upon CPM ==

	Now, ~~it have been~~ gone through both the CPM and PERT. From that it can be seen that they are closely connected, have similar methodology. They both begin on creating a diagram, which indicates connections between tasks in a project. As mentioned above, to use PERT it is necessary to find the critical path first. That can be done by using the forward pass and the backward pass, as is done with CPM. When the critical path ~~have~~ been computed PERT can be applied. Hence, in someways it can be said that PERT builds upon CPM. As shown with the examples, where the critical path from the CPM example was used to start the example for PERT.		Now, the article has gone through both the CPM and PERT. From that it can be seen that they are closely connected, have similar methodology. They both begin by creating a diagram, which indicates connections between tasks in a project. As mentioned above, to use PERT it is necessary to find the critical path first. That can be done by using the forward pass and the backward pass, as is done with CPM. When the critical path has been computed PERT can be applied. Hence, in someways it can be said that PERT builds upon CPM, because it uses forward and backward pass to calculate the critical path. As shown with the examples, where the critical path from the CPM example was used to start the example for PERT.

	== Annotated bibliography ==		== Annotated bibliography ==

S150964: /* Program Evaluation and Review Technique */

2016-09-26T20:55:11Z

Program Evaluation and Review Technique

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	== Program Evaluation and Review Technique ==		== Program Evaluation and Review Technique ==

	When the period of a task is uncertain the ~~critical path method~~ cannot be used. However, in those cases ~~program evaluation and review technique~~ analysis can be applied <ref name="book" />. When the method is ~~applied~~ it is necessary to use diagram, corresponding to the CPM diagram. Then, from the diagram the critical path can be computed and used later on in the calculations. The PERT analysis depends on three types of estimated duration for a task, as in CPM there is only single value <ref name="book" />:		When the period of a task is uncertain the CPM cannot be used. However, in those cases PERT analysis can be applied <ref name="book" />. When the method is computed it is necessary to use a diagram, corresponding to the CPM diagram. Then, from the diagram the critical path can be computed and used later on in the calculations. The PERT analysis depends on three types of estimated duration for a task, as in CPM there is only single value <ref name="book" />:

	1. The '''optimistic duration a''' indicates the time which a task will take under the best conditions.		1. The '''optimistic duration a''' indicates the time which a task will take under the best conditions.
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	PERT analysis provides answers for question about the critical path(s), the beginning and finish times of tasks, project’s expected completion time and it takes in to account variability of the completion time for the project. Furthermore, estimates whether or not the project will be on time. Also, the analysis can estimate with a given probability how long the completion time is in the project. <ref name="book" />		PERT analysis provides answers for question about the critical path(s), the beginning and finish times of tasks, project’s expected completion time and it takes in to account variability of the completion time for the project. Furthermore, estimates whether or not the project will be on time. Also, the analysis can estimate, with a given probability, how long the completion time is in the project. <ref name="book" />


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	Next, the expected activity time, <math>t_e\,</math>, is calculated with ~~equation~~ 4. Then, the table will be:		Next, the expected activity time, <math>t_e\,</math>, is calculated with Equation 4. Then, the table will be:

	{\| class="wikitable"		{\| class="wikitable"
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	\|}		\|}

	Now~~, compute~~, with ~~equation~~ 5, the variance of the task completion time, <math>\sigma^2\,</math>, and add it to the table.		Now, with Equation 5 compute the variance of the task completion time, <math>\sigma^2\,</math>, and add it to the table.

	{\| class="wikitable"		{\| class="wikitable"
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	\|}		\|}

	Then, ~~equation~~ 6 is used to ~~compute~~ the expected completion time of the project, <math>\mu_p\,</math>.		Then, Equation 6 is used to calculate the expected completion time of the project, <math>\mu_p\,</math>.


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	~~And~~ with ~~equation~~ 7 the variability of the project, <math>\sigma_p\,</math>, is calculated.		Lastly, with Equation 7 the variability of the project, <math>\sigma_p\,</math>, is calculated.


	&ensp; &ensp; <math>\sigma_p = \sqrt{\mbox{0.444 + 1 + 1 + 0.694 + 0.694}} = 1.958</math>		&ensp; &ensp; <math>\sigma_p = \sqrt{\mbox{0.444 + 1 + 1 + 0.694 + 0.694}} = 1.958</math>

	From the equations above it can be seen that expected completion time of the project is 25.333 weeks and the standard deviation is 1.958. Therefore, it is 68.2% probability that the duration of the project will be in the range of 23.375 weeks to 27.291 weeks.		From the equations above it can be seen that expected completion time of the project is 25.333 weeks and the standard deviation is 1.958 weeks. Therefore, it is 68.2% probability that the duration of the project will be in the range of 23.375 weeks to 27.291 weeks.

	=== PERT's advantages ===		=== PERT's advantages ===

	~~To know methods advantages~~ is necessary ~~for everyone how are going~~ to ~~practice them~~. When the advantages are ~~know~~ the calculation and solution will be understandable and the usage of the method will be easier. PERT is no exception of that and therefore some of PERT's advantages have been listed below.		Before practicing a method it is necessary to know the method's advantages. When the advantages are known the calculation and solution will be understandable and the usage of the method will be easier. PERT is no exception of that and therefore some of PERT's advantages have been listed below.

	1. Makes the management think carefully if the various tasks are pertinent for the project. <ref name="alPERT"> Kalpana R. (n.d.) ''(PERT): Origin, Methodology, Advantages and Limitations.'' Retrieved 14.09.2016 from http://www.businessmanagementideas.com/business/pert-origin-methodology-advantages-and-limitations/535 </ref> Since, the project manager has to estimate what time interval each task takes he is able to determine if a task is suitable for the project.		1. Makes the management think carefully if the various tasks are pertinent for the project. <ref name="alPERT"> Kalpana R. (n.d.) ''(PERT): Origin, Methodology, Advantages and Limitations.'' Retrieved 14.09.2016 from http://www.businessmanagementideas.com/business/pert-origin-methodology-advantages-and-limitations/535 </ref> Since, the project manager has to estimate what time interval each task takes he is able to determine if a task is suitable for the project.

	2. ~~Can easily be used and understood~~. <ref name="lPERT" > All Syllabus. (n.d.) ''Advantages and Limitations of PERT/CPM.'' Retrieved 14.09.2016 from http://www.allsyllabus.com/aj/note/Computer_Science/Operations%20Research/Unit6/Advantages%20and%20Limitations%20of%20PERT%20CPM.php#.V9qsfJh9600 </ref>		2. Makes it possible to predict time of a project. <ref name="lPERT" > All Syllabus. (n.d.) ''Advantages and Limitations of PERT/CPM.'' Retrieved 14.09.2016 from http://www.allsyllabus.com/aj/note/Computer_Science/Operations%20Research/Unit6/Advantages%20and%20Limitations%20of%20PERT%20CPM.php#.V9qsfJh9600 </ref> Because the method depends on three different types of duration times it is more likely that the duration will be estimated correctly.

	3. ~~Makes it possible to predict time~~ of a project. <ref name="alPERT" /> ~~Because the method depends on three different types of duration times it is more likely that the time will be right.~~		3. Finds the probability of the duration, both for each task and the whole project, and therefore enable determination of that. <ref name="alPERT" />

	4. ~~Finds the probability of the duration, both for each task and the whole~~ project~~, and therefore enable determination of that~~. <ref name="alPERT" />		4. Helps coordinate various tasks in a project. <ref name="alPERT" /> Because the PERT diagram shows visual the relation between tasks and therefore managers can see where the project are in the process.

	5. Helps coordinate various tasks in a project. <ref name="alPERT" /> Because the PERT diagram shows visual the relation between tasks and therefore managers can in see where the project are in the process.

	~~6. Shows if there are any delays or ahead of schedule in a project. <ref name="lPERT" />~~

	=== PERT's limitation ===		=== PERT's limitation ===

	All methods have some limits and the ~~critical path method and~~ PERT are no exception of that. To know them is crucial to be able to see the gaps in the method and respond accordingly. In this section ~~it will be demonstrated~~ PERT's limitations.		All methods have some limits and the PERT are no exception of that. To know them is crucial to be able to see the gaps in the method and respond accordingly. In this section PERT's limitations will be demonstrated.

	1. Depends on that all tasks are known beforehand. In some projects, such as in research and development, that is not possible. <ref name="alPERT" /> When the complexity of a project is not fully understood in the beginning of a project, it is impossible to know which tasks are necessary for ~~the~~ project.		1. Depends on that all tasks are known beforehand. In some projects, such as in research and development, that is not possible. <ref name="alPERT" /> When the complexity of a project is not fully understood in the beginning of a project, it is impossible to know which tasks are necessary for a project.

	2. Assumes that tasks can be sub-divided into pre known and separate tasks, but in reality this is not always possible. <ref name="alPERT" />		2. Assumes that tasks can be sub-divided into pre known and separate tasks, but in reality this is not always possible. <ref name="alPERT" />
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	5. Requires frequent updating and recalculating, which is expansive and time consuming. Because of the updating and recalculations there is need for highly trained staff. <ref name="alPERT" />		5. Requires frequent updating and recalculating, which is expansive and time consuming. Because of the updating and recalculations there is need for highly trained staff. <ref name="alPERT" />

	6. Depends on that relationships between tasks should be known beforehand. As mentioned above, all tasks cannot always ~~been~~ known before a project starts therefore the relationships of those tasks cannot be known. Also, some tasks are difficult to put on one particular place. <ref name="lPERT" />		. Depends on that relationships between tasks should be known beforehand. As mentioned above, all tasks cannot always be known before a project starts therefore the relationships of those tasks cannot be known. Also, some tasks are difficult to put on one particular place. <ref name="lPERT" />

	7. Focuses too much on the critical path but not the other tasks, which are not a part of the critical path. Hence, the tasks, which are not critical, may be forgotten in the process. <ref name="lPERT" />		7. Focuses too much on the critical path but not the other tasks, which are not a part of the critical path. Hence, the tasks, which are not critical, may be forgotten in the process. <ref name="lPERT" />

S150964: /* The Critical Path Method */

2016-09-26T20:39:03Z

The Critical Path Method

Show changes

S150964: /* Definitions */

2016-09-26T20:16:28Z

Definitions

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	== Definitions ==		== Definitions ==

	To be able to understand the ~~critical path method~~ it is necessary to define some key concepts. In a project there are couple of '''paths''', which are a sequence of connected tasks from the beginning of the project until the end. The sum of the time, which the tasks in the path take, is the '''length of the path'''. <ref name="book" /> The longest sequence of tasks, which has to be ~~complete~~ so a project can be finished, is the '''critical path'''. Hence, a task on the critical path cannot begin before its predecessors have been completed. Therefore, if there is a delay in one of the tasks, which is on the critical path, the project will also delay. <ref name="cp"> Business Dictionary. (n.d.) ''critical path.'' Retrieved 14.09.2016 from http://www.businessdictionary.com/definition/critical-path.html </ref> ~~Project~~ can have more than one critical path but all critical paths, in it, have the same length. <ref name="book" /> Later in the ~~essay~~, will be shown an example of a critical path.		To be able to understand the CPM it is necessary to define some key concepts. In a project there are couple of '''paths''', which are a sequence of connected tasks from the beginning of the project until the end. The sum of the time, which the tasks in the path take, is the '''length of the path'''. <ref name="book" /> The longest sequence of tasks, which has to be completed so a project can be finished, is the '''critical path'''. Hence, a task on the critical path cannot begin before its predecessors have been completed. Therefore, if there is a delay in one of the tasks, which are on the critical path, the project will also delay. <ref name="cp"> Business Dictionary. (n.d.) ''critical path.'' Retrieved 14.09.2016 from http://www.businessdictionary.com/definition/critical-path.html </ref> A project can have more than one critical path but all critical paths, in a project, have the same length. <ref name="book" /> Later in the article, will be shown an example of a critical path.


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	• The '''latest start time (LST)''' means the latest time a task can start if there will not be a delay in the project.		• The '''latest start time (LST)''' means the latest time a task can start if there will not be a delay in the project.

	• The '''latest finish time (LFT)''' is the latest time a task can finish if there will not be a delay in the project.		• The '''latest finish time (LFT)''' is the latest time a task can finish if there will not be a delay in the project.


	== The Critical Path Method ==		== The Critical Path Method ==

S150964: /* Improvements of the CPM */

2016-09-26T20:10:55Z

Improvements of the CPM

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	=== Improvements of the CPM ===		=== Improvements of the CPM ===

	Since the development of the ~~critical path method there~~ have been made ~~couple of improvements~~ on it. First there was the Theory of Constraints which was formulated in the 1980s by the physicist Eliyahu Goldratt. <ref name="history" /> The theory is a methodology to analyse which factor is most likely to cause delay and then to improve that factor until it is no longer a bottleneck. <ref name="lean"> Vorne Industries Inc. (n.d.) ''WHAT IS THE THEORY OF CONSTRAINTS?'' Retrieved 14.09.2016 from http://www.leanproduction.com/theory-of-constraints.html </ref> Then in 1997 the concept of the Critical Chain was introduced by Goldratt, when he published a book with that name. This improved method says to keep a project on schedule it is necessary to emphasize on its resources and the flexibility required in the resources. Also, the method adds uncertainty buffers to the project schedule so it can be ready for unpredictable problems which may arise. <ref name="history" />		Since the development of the CPM, a couple of improvements have been made on it. First there was the Theory of Constraints which was formulated in the 1980s by the physicist Eliyahu Goldratt. <ref name="history" /> The theory is a methodology to analyse which factor is most likely to cause delay and then to improve that factor until it is no longer a bottleneck. <ref name="lean"> Vorne Industries Inc. (n.d.) ''WHAT IS THE THEORY OF CONSTRAINTS?'' Retrieved 14.09.2016 from http://www.leanproduction.com/theory-of-constraints.html </ref> Then in 1997 the concept of the Critical Chain was introduced by Goldratt, when he published a book with that name. This improved method says to keep a project on schedule, it is necessary to emphasize on its resources and the flexibility required in the resources. Also, the method adds uncertainty buffers to the project schedule so it can be ready for unpredictable problems which may arise. <ref name="history" />


	== Definitions ==		== Definitions ==

S150964: /* History */

2016-09-26T20:05:50Z

History

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	=== History ===		=== History ===

	The history of project management tools like the ~~critical path method~~ can be traced back to ancient Egypt. For example, when ancient Egyptians build the Great Pyramid of Giza, which stands near Cairo. That project was more than 5.000 years ago. The pyramid was built out of more than two million blocks of ~~stone~~. The pyramid took over 20 years in building and needed much manpower which was divided into four construction teams. <ref name="history"> Kielmas, Maria. (n.d.) ''History of the Critical Path Method.'' Retrieved 14.09.2016 from http://smallbusiness.chron.com/history-critical-path-method-55917.html </ref>		The history of project management tools like the CPM can be traced back to ancient Egypt. For example, when ancient Egyptians build the Great Pyramid of Giza, which stands near Cairo. That project was more than 5.000 years ago. The pyramid was built out of more than two million blocks of stones. The pyramid took over 20 years in building and needed much manpower which was divided into four construction teams. <ref name="history"> Kielmas, Maria. (n.d.) ''History of the Critical Path Method.'' Retrieved 14.09.2016 from http://smallbusiness.chron.com/history-critical-path-method-55917.html </ref>


	However, modern project management did not begin until 1900s when the Gantt chart was created. It was Henry Gantt and Fredrick Taylor that designed a graphical method to plan and control a work schedule and recording its progress. Over the years Gantt charts have been used, for example in 1931 when Hoover Dam was ~~in build~~. It is still in use today because the chart can be easily understood. <ref name="history" />		However, modern project management did not begin until 1900s when the Gantt chart was created. It was Henry Gantt and Fredrick Taylor that designed a graphical method to plan and control a work schedule and recording its progress. Over the years Gantt charts have been used, for example in 1931 when Hoover Dam was being built. It is still in use today because the chart can be easily understood. <ref name="history" />


	Furthermore, in 1956 the ~~critical path method~~ was used to deal with the interrelationships of separate tasks in a project schedule. The Dupont chemical company and Remington Rand Univac, a computer firm, thought up the method because they had a joint venture. However, it was not until 1958 that the method was first tested. It was on a construction project of a new chemical plant. The ~~critical path method~~ was then used again in 1959 to shutdown a plant at Louisville, Kentucky. <ref name="history" />		Furthermore, in 1956 the CPM was used to deal with the interrelationships of separate tasks in a project schedule. The Dupont chemical company and Remington Rand Univac, a computer firm, thought up the method because they had a joint venture. However, it was not until 1958 that the method was first tested. It was on a construction project of a new chemical plant. The CPM was then used again in 1959 to shutdown a plant in Louisville, Kentucky. <ref name="history" />


	Independent of the ~~critical path method~~, in 1958, the U.S Navy’ Special Projects Office, along with Lockheed Missile System and Booz Allen & Hamilton developed ~~Program Evaluation Review Technique (~~PERT) for a missile program called Polaris. The reason why the U.S. government wanted to develop the tool was to ensure that the Polaris program was completed. Also, the U.S. government had ~~concern~~ about the number of nuclear weapons which the Soviet Union was manufacturing. CPM and PERT both were designed to deal with the relationship between tasks in a project. However, PERT aimed to control over 3.000 contractors on the missile program but really the tool showed visually the major tasks and their relationship. As for the difference in function of the methods, PERT just showed the time interval but did not tackle the cost and quality issues faced by commercial firms. <ref name="history" />		Independent of the CPM, in 1958, the U.S Navy’ Special Projects Office, along with Lockheed Missile System and Booz Allen & Hamilton developed PERT for a missile program called Polaris. The reason why the U.S. government wanted to develop the tool was to ensure that the Polaris program was completed. Also, the U.S. government had concerns about the number of nuclear weapons which the Soviet Union was manufacturing. CPM and PERT both were designed to deal with the relationship between tasks in a project. However, PERT aimed to control over 3.000 contractors on the missile program but really the tool showed visually the major tasks and their relationship. As for the difference in function of the methods, PERT just showed the time interval but did not tackle the cost and quality issues faced by commercial firms. <ref name="history" />


	=== Improvements of the CPM ===		=== Improvements of the CPM ===

S150964 at 19:59, 26 September 2016

2016-09-26T19:59:23Z

← Older revision		Revision as of 19:59, 26 September 2016
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	In project management it is necessary to use a tool which states how the project is going. The project manger ~~face~~ the challenge of planning, coordinating and monitoring the project, which can be difficult if no tool is at hand <ref name=''begin''> CareerProfile.info. (n.d.) ''The Project Management Interview.'' Retrieved 08.09.2016 from http://www.careerprofiles.info/project-management-interview.html </ref>. Therefore, project managers often use the '''Critical Path Method (CPM)''' and '''Program Evaluation Review Technique (PERT)''' to do those things. The tools give a good overview of how a project progresses. Over the years, CPM and PERT have been used in a ~~white~~ range of projects. For example, in building constructions, maintenance of equipment, design and installation of management systems, organizing transportation projects and so ~~many more~~. <ref name=''math''> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://www.math.csusb.edu/faculty/prakash/611/Project_Management.ppt.pdf </ref>		In project management it is necessary to use a tool which states how the project is going. The project manger faces the challenge of planning, coordinating and monitoring the project, which can be difficult if no tool is at hand <ref name=''begin''> CareerProfile.info. (n.d.) ''The Project Management Interview.'' Retrieved 08.09.2016 from http://www.careerprofiles.info/project-management-interview.html </ref>. Therefore, project managers often use the '''Critical Path Method (CPM)''' and '''Program Evaluation Review Technique (PERT)''' to do those things. The tools give a good overview of how a project progresses. Over the years, CPM and PERT have been used in a wide range of projects. For example, in building constructions, maintenance of equipment, design and installation of management systems, organizing transportation projects and so on. <ref name=''math''> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://www.math.csusb.edu/faculty/prakash/611/Project_Management.ppt.pdf </ref>


	The ~~critical path method~~ organizes project’s tasks, which need to be done to complete a project, and ~~estimate~~ how much time it will take. Also, the method shows what tasks are sensitive in a project because these tasks may take more time. <ref name=''characteristics''> Thompson, Scott. (n.d.) ''Characteristics of the Critical Path Method.'' Retrieved 08.09.2016 from http://smallbusiness.chron.com/characteristics-critical-path-method-66136.html </ref> This method shows visually how the tasks relate to one and another. <ref name=''definition''> Business Dictionary. (n.d.) ''critical path method (CPM).'' Retrieved 08.09.2016 from http://www.businessdictionary.com/definition/critical-path-method-CPM.html </ref> Therefore, the key essence of the ~~critical path method~~ is to compute the shortest time, which a project can take, by valuating task according to its predecessors.		The CPM organizes project’s tasks, which need to be done to complete a project, and estimates how much time it will take. Also, the method shows what tasks are sensitive in a project because these tasks may take more time. <ref name=''characteristics''> Thompson, Scott. (n.d.) ''Characteristics of the Critical Path Method.'' Retrieved 08.09.2016 from http://smallbusiness.chron.com/characteristics-critical-path-method-66136.html </ref> This method shows visually how the tasks relate to one and another. <ref name=''definition''> Business Dictionary. (n.d.) ''critical path method (CPM).'' Retrieved 08.09.2016 from http://www.businessdictionary.com/definition/critical-path-method-CPM.html </ref> Therefore, the key essence of the CPM is to compute the shortest time, which a project can take, by valuating a task according to its predecessors.


	As for ~~program evaluation review technique~~, the method also shows visually how the tasks relate to one and another as CPM does. However, PERT takes into account that the duration of a task is not always known. So, the method uses three estimated ~~time~~ to calculate most likely duration of a ~~tasks~~ and hence the project as a whole. <ref name="book"> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://learngroup.org/uploads/2015-01-02/Lecture_-_Project_Management_%28Overview%29.pdf </ref>		As for the PERT, the method also shows visually how the tasks relate to one and another as CPM does. However, PERT takes into account that the duration of a task is not always known. So, the method uses three estimated times to calculate most likely duration of a task and hence the project as a whole. <ref name="book"> Anon. (n.d.) ''Project Scheduling: PERT/CPM.'' Retrieved 08.09.2016 from http://learngroup.org/uploads/2015-01-02/Lecture_-_Project_Management_%28Overview%29.pdf </ref>


	~~In this~~ article will ~~first go~~ through the history of the methods and how the ~~critical path method~~ has been improved over the years. Then, some key concepts will be described and defined. Furthermore, the ~~critical path method~~ and PERT will be explained and an example taken and calculated to see how the methods work. Advantages and limitations of ~~these methods~~ will be listed and described. In the end, will be gone through how PERT builds up on CPM.		This article will begin by going through the history of the methods and how the CPM has been improved over the years. Then, some key concepts will be described and defined. Furthermore, the CPM and PERT will be explained and an example taken and calculated to see how the methods work. Advantages and limitations of each method will be listed and described. In the end, will be gone through how PERT builds up on CPM.

	== Overview ==		== Overview ==