Beginning

These three principles must always be respected when drawing a PERT mesh:.

• - Principle of successive designation: the vertices are named according to the natural numbers, so that they are not assigned numbers until all those from which edges originate and end up at them have been named.

• - Principle of uniqueness of the initial and final state: the existence of more than one initial or final vertex is prohibited. There is only one start situation and one end situation for the project.

• - Univocal designation principle: There cannot be two edges that have the same source and destination nodes. Typically, activities are named by the pair of vertices they join. If this principle is not respected, two edges may receive the same name.

Duration of an Activity

To estimate the expected duration of each activity, it is also desirable to have previous experience performing similar tasks. In project planning and programming, it is estimated that the expected duration of an activity is a random variable with a unimodal Beta probability distribution of parameters (o, m, p) where:.

= It is defined as the optimistic time, the shortest time that an activity can last.

= It is the most likely time that an activity could last.

= This is the pessimistic time, or the longest time an activity can last.

= Corresponds to the expected time for an activity (This corresponds to the CPM time, assuming that the calculations are exact).

NOTE: It is assumed that each Task follows an Euler distribution law.

The expected value (or time) in this distribution. This is expressed in the following formula:

whose variance is given by:.

and one standard deviation:.

Drawing of a PERT mesh

There are two accepted methodologies for drawing a PERT mesh, “Activity in the Arc” and “Activity in the Node”, the latter being the most used currently given that it is the one used by most of the computer applications specializing in this topic.

In a drawing of a PERT mesh we can distinguish "Vertex (graph theory)" nodes and "Edge (graph theory)" arcs, the nodes represent instants in time. Specifically, they represent the start time of one or several activities and simultaneously the end time of several other activities. The arcs, for their part, represent the activities, they have an initial node and another end node where it arrives at the arrowhead. Associated with each arc is the expected duration of the activity.

More information from an activity diagram is to represent these with a complexity rating to minimize the effect of bottleneck&action=edit&redlink=1 "Bottleneck (production) (not yet written)").

Each node contains the following information about the activity:

• - Name of the activity;

• - Expected duration of the activity (t);.

• - Earliest Start Time (ES = Earliest Start);

• - Earliest Finish Time (EF = Earliest Finish);

Another way to represent the PERT network.

• - Latest start time (LS = Latest Start);

• - Latest Finish Time (LF = Latest Finish);

• - Activity Slack (H);.

By convention, arcs are always drawn facing right, towards the project termination node, never going backwards.

Drawing a PERT mesh starts at the project start node. From it, activities are drawn that do not have preceding activities, that is, those that do not have to wait for other activities to finish before they can start.

Next, the remaining activities are drawn, taking care to respect the precedence between them.

At the end of the drawing of the preliminary mesh, there will be several blind nodes, terminal nodes that reach those activities that are not predecessors of any other, that is, those that do not influence the start date of any other, these are the terminal activities and therefore attend the end node of the project.

Calculating Earliest Start and Finish Times

The earliest start time “ES” (Early Start) and earliest completion time “EF” (Early finish) for each project activity are calculated from the start node to the project completion node according to the following relationship: The expected duration of the project (T) is equal to the greatest of the EF times of all the activities that lead to the completion or termination node of the project.

Calculating Latest Start and Finish Times

The latest start time “LS” (Latest Start) and latest finish time “LF” (Latest finish) for each project activity are calculated from the finish node back to the project start node according to the following relationship:

Slacks, critical activities and critical paths

The Slack of an activity is the time that is available to either be delayed in its start date or extended in its expected execution time, without causing any delay in the end date of the project.

• - Critical activities.

• - Critical routes.

• - ADM.

• - CPM.

• - PDM.

• - Gantt chart.

• - Milestone Diagram.

• - Beta Distribution.

• - PERT distribution.

• - Critical path method.

How to get the duration of a project with PERT

Example PERT - Program Review and Evaluation Technique.

Beginning

These three principles must always be respected when drawing a PERT mesh:.

• - Principle of successive designation: the vertices are named according to the natural numbers, so that they are not assigned numbers until all those from which edges originate and end up at them have been named.

• - Principle of uniqueness of the initial and final state: the existence of more than one initial or final vertex is prohibited. There is only one start situation and one end situation for the project.

• - Univocal designation principle: There cannot be two edges that have the same source and destination nodes. Typically, activities are named by the pair of vertices they join. If this principle is not respected, two edges may receive the same name.

Duration of an Activity

To estimate the expected duration of each activity, it is also desirable to have previous experience performing similar tasks. In project planning and programming, it is estimated that the expected duration of an activity is a random variable with a unimodal Beta probability distribution of parameters (o, m, p) where:.

= It is defined as the optimistic time, the shortest time that an activity can last.

= It is the most likely time that an activity could last.

= This is the pessimistic time, or the longest time an activity can last.

= Corresponds to the expected time for an activity (This corresponds to the CPM time, assuming that the calculations are exact).

NOTE: It is assumed that each Task follows an Euler distribution law.

The expected value (or time) in this distribution. This is expressed in the following formula:

whose variance is given by:.

and one standard deviation:.

Drawing of a PERT mesh

There are two accepted methodologies for drawing a PERT mesh, “Activity in the Arc” and “Activity in the Node”, the latter being the most used currently given that it is the one used by most of the computer applications specializing in this topic.

In a drawing of a PERT mesh we can distinguish "Vertex (graph theory)" nodes and "Edge (graph theory)" arcs, the nodes represent instants in time. Specifically, they represent the start time of one or several activities and simultaneously the end time of several other activities. The arcs, for their part, represent the activities, they have an initial node and another end node where it arrives at the arrowhead. Associated with each arc is the expected duration of the activity.

More information from an activity diagram is to represent these with a complexity rating to minimize the effect of bottleneck&action=edit&redlink=1 "Bottleneck (production) (not yet written)").

Each node contains the following information about the activity:

• - Name of the activity;

• - Expected duration of the activity (t);.

• - Earliest Start Time (ES = Earliest Start);

• - Earliest Finish Time (EF = Earliest Finish);

Another way to represent the PERT network.

• - Latest start time (LS = Latest Start);

• - Latest Finish Time (LF = Latest Finish);

• - Activity Slack (H);.

By convention, arcs are always drawn facing right, towards the project termination node, never going backwards.

Drawing a PERT mesh starts at the project start node. From it, activities are drawn that do not have preceding activities, that is, those that do not have to wait for other activities to finish before they can start.

Next, the remaining activities are drawn, taking care to respect the precedence between them.

At the end of the drawing of the preliminary mesh, there will be several blind nodes, terminal nodes that reach those activities that are not predecessors of any other, that is, those that do not influence the start date of any other, these are the terminal activities and therefore attend the end node of the project.

Calculating Earliest Start and Finish Times

The earliest start time “ES” (Early Start) and earliest completion time “EF” (Early finish) for each project activity are calculated from the start node to the project completion node according to the following relationship: The expected duration of the project (T) is equal to the greatest of the EF times of all the activities that lead to the completion or termination node of the project.

Calculating Latest Start and Finish Times

The latest start time “LS” (Latest Start) and latest finish time “LF” (Latest finish) for each project activity are calculated from the finish node back to the project start node according to the following relationship:

Slacks, critical activities and critical paths

The Slack of an activity is the time that is available to either be delayed in its start date or extended in its expected execution time, without causing any delay in the end date of the project.

• - Critical activities.

• - Critical routes.

• - ADM.

• - CPM.

• - PDM.

• - Gantt chart.

• - Milestone Diagram.

• - Beta Distribution.

• - PERT distribution.

• - Critical path method.

How to get the duration of a project with PERT

Example PERT - Program Review and Evaluation Technique.