Critical Path method (CPM)

The Critical Path Method, abbreviated CPM, or critical path analysis, is a mathematically based algorithm for scheduling a set of project activities. It is an important tool for effective project management

The essential technique for using CPM is to construct a model of the project that includes the following:

1. A list of all activities required to complete the project (also known as Work breakdown structure),
2. The time (duration) that each activity will take to completion, and
3. The dependencies between the activities.

The activities lying on the CP are called critical activities (CA'S) and remaining activities are called non critical activities (non CA'S)

Critical activities on any account shouldn't be delayed, if delayed the project completion time will be extended.

Non critical activities can be delayed to a certain extent so that the project divination is not affected. This can be stated as the earlier completion of critical activities will result in earlier completion of the project. Similarly delay in the completion of critical activities will cause delay in completion of the project

TERMS associated with the study of CPM

• Earliest start time(EST): It is the earliest possible time in which the activity can be started. For eg A is an activity which needs 10 days to complete. If this activity is to be completed from April 1st to April 30th, then the EST of A is April 1st
• Earliest finish time (EFT): The earliest possible time in which the activity can be completed is called finish time. in the above example EFT of A is April 10th.

                     So EFT= (EST+ duration)

• Latest start time (LST): The latest possible time in which the activity can be started is called LST. if the activity is started beyond LST, then it cannot be completed within the specified time limit. In the above eg LST of A is 21St April.
• Latest Finish time (LFT): The latest possible time in which the activity can be completed within the specified limit is called LFT. in the above example April 30th is the LFT
• Total Float (TF): The additional time or spare time which is available for the activity so that we can delay the activity then the completion time of the project is not affected. In the above eg the total float for A is 20 days. Total float can be interpreted as maximum delay that can be made on the activity without affecting the project duration is called total float

Method of calculation of EST, LST

1. Draw the NWD for the given project
2. Identify the critical path & its duration
3. Indicate EST=0 for the 1st node add the duration of the activities emanating from it. The result is the EST for the head note. 

If 2 or more activities converge to a node then calculate EST for each pair of nodes. Among them select the highest, consider the diagram

Indicate the project duration as LFT for the finish node. Subtract the durations from the LFT, the result is the LST for the tail node. 

If 2 or more activities emanating from the node then deduct the duration of each activity from the LFT of the head node. Among the result select the lowest.

With the help of EST , LFT we can calculate EFT, LST, TF

TF=LST-EST  or  LFT-EFT

A schedule indicating the activities duration EST,EFT,LST, LFT, TF is called activity schedule. This indicates that which activity can it be delayed and how long can it be delayed. The total float of each critical activity is 0 indicating that critical activity has no spare time nor additional time.

Non critical activities always have float. Hence they can be delayed to the extent of total float.