Definitions Used In Project Evaluation and Review Technique (PERT) :

Event

It is the start of completion of a task. It is represented by a circle and does not consume time and resources.

Activity

An activity is the actual performance of a task. It consumes time and resources such as manpower, materials etc. and it is represented by the line and arrow.

For example,

Start Machine installation : An event

Machine installation : Activity

Completion of machine installations : An event

Successor Event

Successor event is an event which immediately follows another event.

Predecessor Event

Predecessor event is an event which takes place immediately before a particular event.

Earliest Expected Time (T_e)

It is the earliest expected time of the project and is equal to the sum of the expected times of all the activities, along with the longest path at the project.

Latest Allowable Time (T_L)

It is the largest possible time that event can take without causing delay in the final completion date.

T_L  for an event = Total expected time for the end of an event of a project from the longest path – Total expected time for the event under consideration from the longest path.

Slack (T_L – T_e)

Slack is the difference between the latest allowable time (T_L) and the Earliest Expected Time (T_e). It is the span of time available for the performance of an activity without any delay in the completion date of the project. This value of slack indicates how critical that event is and how much stress given on that activity.

Critical Path

This is a path on the network along which no slippage is allowed. In this path, slack is either negative or zero.

Example

Show the earliest and the latest expected time on the following network and indicate the Critical Path on it.

Solution

The Earliest and the Latest times are shown on the network given in the figure below in this network, the Critical Path will be the path along the events 1, 2, 5 and 6 because on this whole path T_e = T_L i.e. slack is always equal to zero.