How PERT builds up on CPM
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 [1]. Therefore, project managers often use the Critical Path Method (CPM) to do those things. The tool gives a good overview of how a project progresses. Over the years, CPM has 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. [2]
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. [3] This method shows visually how the tasks relate to one and another. [4]
In this article will first go through the history of the critical path method and how the 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 what the differences are of CPM and PERT.
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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. [5]
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. [5]
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. [5]
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. [5]
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. [5] 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. [6] 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. [5]
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. [7] 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. [8] Project can have more than one critical path but all critical paths, in it, have the same length. [7] Later in the essay, will be shown an example of a critical path.
To find the earliest and latest schedules to avoid delays in the project are crucial. Hence, the following information is calculated for each task in the project.
• The earliest start time (EST) which means the earliest time a task can start if there will not be a delay in the project.
• The earliest finish time (EFT) indicates the earliest time a task can end 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. [7]
The Critical Path Method
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Before starting to use the critical path method 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, description, predecessors and 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. [9] The notes have to include space for the EST, EFT and LFT, as shown in figure XXX. When the graph has been made the critical path method can be started.
The critical path method depends on EST, EFT, LST and LFT. The EST and EFT are calculated with a forward pass, but on the other hand the LST and LFT with a backward pass. In the forward pass a time is computed from the starting task to the finish one. As for the backward pass it is gone from the finish task to the starting one. How this is done will be explained in the upcoming paragraphs and an example taken in the next section. [7]
The basic of a forward pass is that all the predecessors connected to the task must be finished before it can begin. Let t be duration of a task and then it is possible to calculate EFT of a task if there is no delay with EFT = EST + t here after called Equation 1. [7]
As a result from the equation above the EFT of the latest task is the EST for the next, called the EST rule. This will be shown below in the example section. The forward pass may be formulated as follows: [7]
1. All tasks which has know predecessor get EST = 0.
2. All tasks which have known EST, compute EFT using Equation 1.
3. Apply the EST rule to get EST for next task.
4. Repeat step 2 and 3 until all tasks have EST and EFT. [7]
The basic of a backward pass is a task can begin at the latest time if and just if all its predecessors are finished, it is called the LFT rule. Therefore, each task has the latest finish time equal to the smallest latest start times of the task which follows. Hence, the latest start time can be computed from equation LST = LFT – t, if there is no delay in the project. The LST equation will here after been referenced to as Equation 2. The backward pass starts when the EFT for the last task has be found with the forward pass and then calculated from the end task to the first task. The backward pass can be formulated as follows: [7]
1. Set LFT equal to EFT at the finish task and at all tasks which do not have successors.
2. For all tasks where LFT value is known, compute LST using Equation 2.
3. The LST from the successor becomes the LFT for every new task, the LFT rule.
4. Repeat step 2 and 3 until all tasks have LFT and LST. [7]
The length of time which do not delay a project is the slack time. It is necessary calculate the slack time to identify the critical path(s), either with the start times or the finish times. If the slack time is equal to zero the task is part of the critical path. This can be done with following equation: Slack = LST – EST or LFT – EFT, Equation 3 here after. [7]
Example of CPM
As mentioned in the section above, here will be taken an example with the critical path method. In the example, the critical path will be found and the duration of the project. In reality the project manager would list the tasks, its predecessor and duration of each task. However, in this case that has already been done in the table below.
| Task | Predecessor | Time |
| A | – | 4 |
| B | A | 5 |
| C | A | 5 |
| D | B | 6 |
| E | B, C | 5 |
| F | D | 4 |
| G | F, E | 5 |
First of all it is necessary to draw a diagram then the procedure of the project becomes visual. Also, it becomes easier to calculate the EST, EFT, LST, LFT and slack for each task. Therefore, the diagram for this specific project will be:
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Then, start to calculate EST and EFT for each tasks starting on the first task until all EST and EFT have been computed, use Equation 1. Here it is good to remember that the EST for the first task, here task A, equals 0 and the EST of the successor is the EFT of the task before. If the task depends on two previous tasks the EFT which is higher is chosen.
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When forward pass has been applied it can be seen that the total duration of the project is 24. To find the critical path, it is necessary to find the LST and LFT. To do so, the backward pass is used. Task G has the EFT = 24 therefore LFT = 24, as explained in the method section. When that is known, equation 2 can be applied to find LST and LFT for each task. Remember that LFT is equal to the LST of the successor. If the task has two or more successors the lowest number is chosen.
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Now, the slack of each task is found by using Equation 3. In the diagram the slack is marked in red.
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From the diagram above it can be seen that the critical path is the path A-B-D-F-G, since tasks C and E both have 1 in slack.
To sum the solution up, the forward pass gave the solution of the project time, which was 24, and when finished applying the backward pass and slack the critical path was found, which was A-B-D-F-G.
Limitation
Reference
- ↑ http://www.careerprofiles.info/project-management-interview.html
- ↑ http://www.math.csusb.edu/faculty/prakash/611/Project_Management.ppt.pdf
- ↑ http://smallbusiness.chron.com/characteristics-critical-path-method-66136.html
- ↑ http://www.businessdictionary.com/definition/critical-path-method-CPM.html
- ↑ 5.0 5.1 5.2 5.3 5.4 5.5 http://smallbusiness.chron.com/history-critical-path-method-55917.html
- ↑ http://www.leanproduction.com/theory-of-constraints.html
- ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Project Scheduling: CPM/PERT, file:///C:/Users/%C3%93l%C3%B6fR%C3%BAn/Downloads/sampleChapter8%20(1).pdf
- ↑ http://www.businessdictionary.com/definition/critical-path.html
- ↑ https://www.mindtools.com/critpath.html
