**Method Description**

**The critical path method (CPM) is used to find the longest path for a sequence of planned activities from the start to the end of a project and what the earliest and latest starting and finishing time for each activity is without extending the total time taken.**

The objective of the analysis is to determine which activities are critical and determine the path of these critical activities (i.e. the critical path). It is also used to determine which would have a total float higher than zero, which indicates that these activities can be delayed without interrupting the overall critical time for the process.

The objective of the analysis is to determine which activities are critical and determine the path of these critical activities (i.e. the critical path). It is also used to determine which would have a total float higher than zero, which indicates that these activities can be delayed without interrupting the overall critical time for the process.

**Important terms:****Node:**represents an event

**Arcs:**represents the activities

__Early and Late Event Time__**ET(i):**The

**early event time**for node i, is the earliest time at which the event corresponding to node i can occur.

ET(i

ET(i

**current) = ET(iprevious) + ticurrenti**

**previous**

***ticurrentiprevious = duration between activity i and j**

**LT(i):**The

**late event time**for node i, is the latest time at which the event corresponding to node i can occur without delaying the completion of the project.

**LT(icurrent) = LT(iprevious) - ticurrentiprevious**

**Total float and Free Float**The

**total float (or slack)**, representing activity (i, j), represented by TF(i, j) is the amount by which the activity could be delayed beyond its earliest possible starting time without delaying the completion of the project. One can say that the total float is a measure of the flexibility in the duration of an activity. Any activity with a total float of zero is a

**critical activity**, as any delay in the start of the activity will delay the completion of the project.

TF(i, j) = LT(j) – ET(i) - tij

TF(i, j) = LT(j) – ET(i) - tij

A path from node 1 to the finish node that consists entirely of critical activities is called a

**critical path**.

The

**free float**of the activity corresponding to arc (i, j), denoted by FF(i, j), is the amount by which the starting time of the activity corresponding to arc (i, j) can be delayed without delaying the start of any later activity beyond its earliest possible starting time.

FF(i, j) = ET(j) – ET(i) - tij

FF(i, j) = ET(j) – ET(i) - tij