Critical Path Method [CPM] - Steps and Introduction | Network Analysis | Operation Research
Watch videoWhen studying Critical Path Method we should keep the following points in mind:
- Every project has its pre-assumed time for completion.
- Project constitute of many different activities, and those activities have their own pre-assumed completion time.
- By summing up the completion time of all the activities we get the project completion time (pre-assumed).
It is important to note that, the total completion time also have a buffer time added up to compensate any un-assumed delay occurs - in real life scenarios (real life projects).
Types of Activities in a project
Based on estimation of completion time activities are classified as:
- Deterministic Activities
- Variable Activities
Deterministic Activities
If completion time of any activity can be estimated perfectly, then the activity is called as Deterministic Activity.
To evaluate network (of a particular project), that has all activities as deterministic activities, the technique used is "Critical Path Method (CPM)"
Variable Activities
If the activity is performed for the first time, the uncertainty is high, so the estimated completion time may vary on any side. These activities are called as Variable Activities.
To evaluate network having variable activities, the technique used is "Project Evaluation and Review Technique (PERT)".
Critical Path Method (CPM)
The Critical Path Method technique includes the following steps for the evaluation of project completion time.
Step 1: Calculate time for each activity
In this step we need to determine the starting time by which the activity must begin and finishing time at which the activity must be finished.
Using the starting and finishing time we can find the Earliest Start Time (EST), Earliest Finish Time (EFT), Latest Start Time (LST) and Latest Finish Time (LFT).
Earliest Start Time (EST)
It is the time at which an activity can begin at the earliest.
For EST, it is assumed that all preceding activities are finished before starting that activity.
It may be possible that, many times an activity depends on more than one activities, so until and unless both the preceding activities are not completed, the depending activity cannot be started.
To calculate EST easily, following way is used:
- If only one activity converges on an event, its EST is calculated by adding the EST's of the tail event of the activity and the time duration of that activity.
Fig-1: Tail event, Head event, EST, LFT and time duration
- If more than one activity converges on it, EST's via all paths would be calculated and the highest value is chosen and termed as EST.
Fig-2: EST - more than one activity converges
Latest Finish Time (LFT)
It is the time by which the activity must be finished and the project cannot be delayed more than that.
This is calculated by moving backwards from end event of the network to the start event.
Calculation begins from end event, considering that the LFT is equal to the EST.
LFT for all other events are calculated as follows:
- If only one activity branches from an event, then calculate LFT by subtracting activity duration from the LFT of its head event.
Fig-3: Calculate LFT
- If more than one activity branches out from an event, then calculate its LFT's via all the paths and lowest value is selected and is termed as LFT for that event.
Fig-4: Calculate LFT more than one branches
Step 2: Calculate EFT and LST
- EFT and LST of different events can be found using EST and LFT values found in step 1.
Step 3: Calculate the float in various activities of the project
Total Float: It is the difference between the start times or finish times. Mathematically,
Moreover, practically we can understand total float as indication of maximum time up to which an activity can be delayed and its in such a way that it will not affect the project completion time.
Total time is calculated after considering the sequence of the project and the time required to complete each activity.
Step 4: Identify critical activities and find Critical Path
Critical Activities: Those activities that must be started on time and must be completed on time are called Critical Activities. We cannot delay such activities otherwise the project may get delayed.
Critical Path: The network path joining all critical activities is called as critical path. The critical path is the longest path of the project.
Fig-5: Calculate critical path
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In the above figure, the activities that have EST and LFT values equal are called critical activities.
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These activities must be started on time and must be completed on time.
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The critical activities in the given network are: 1, 3, 5 and 6.
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Hence the path joining these activities is the critical path and you can find that it is the longest path.
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To find the longest path, add up the time duration along these paths of the network from start to end.
For example:
We found that C.P. 1-3-5-6 is the longest one.
- Also, the time found at the tail event is considered as the total project completion time.
Note that: To check if your network and time calculation is correct or not, simply check the value of start and end event. The values of start and end events must be equal and start event values must be (0,0) after whole calculation of times.
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Transportation Model - Introduction
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