Understanding Gantt Charts and CPM/PERT Terminology

Gantt Charts and Project Status

Gantt charts are bar graphs that immediately show the status of implementation within a project, identifying any delays or advances. They attempt to represent the duration of each of the activities into which the project is divided. A drawback to their use is that they do not permit cross-connections showing directly how one activity depends on or influences another.

CPM / PERT Terminology Definitions

Activity

Each element of the project or program represented by an arc in CPM. This arc sometimes represents a time duration or a connection between two events of the graph. An activity cannot begin while the preceding event has not occurred.

Event

An event in the project or CPM that marks the beginning or end of an activity. These are the nodes or vertices of the graph.

Network Diagram (Red)

A graphical representation of all activities or events in a sequence diagram.

Time Estimates (PERT)

• Time Optimistic (a): The minimum estimate of the duration of an activity. It is unlikely to occur.
• Time Pessimistic (b): The maximum duration of an activity. It is unlikely to occur.
• Time Likely (m): The most realistic estimate of how long the execution of an activity might take.
• Estimated Time: The expected time required to carry out an activity.

Scheduling Dates

• Earliest Start Date (T_E): The first date on the calendar where an event is expected to occur or the performance of an activity is achieved.
• Latest Permissible Date (T_L): The latest calendar date on which an event can occur without delaying the scheduled completion of the program.

Float and Path Analysis

Clearance (Slack)

The clearance (slack) can be:

• Positive: Indicating an excess of time for the execution time.
• Negative: Indicating insufficient time has been allotted for the event to take place.
• Zero: Indicating the activity belongs to the critical path.

Critical Path

The path that has the longest duration among all paths sharing the same initial and final events. The determination of the critical path involves following the events that form a path from the initial event to the end and have no slack.

Margin (Float)

This is the excess time available to carry out an activity, relative to the expected execution time. We differentiate between:

• Free Margin: Calculated when an activity starts as soon as possible and is delayed as much as possible.
• Total Margin (Net Total): Considered when the initial activity is set as early as possible, and the final activity is set at the last allowable date.