What does PERT mean?

PERT stands for Program Evaluation and Review Technique. The PERT method was developed in the 1960s by the United States Department of Defense. Initially the method was used during large military programs, but later it was more increasingly used in civilian projects as well.

The PERT method is usually used when conducting large and complex projects that involve sequences of tasks or that run in parallel with other projects.

What is the PERT method based on?

The PERT method is based on the creation of an arrow diagram. The diagram takes into account the relationship between individual tasks and the primacy of tasks over each other. The diagram is created using the so-called AoN (Activity on Nodes) notation, which involves representing tasks as rectangles connected by arrows. Instead of AoN, the AoA (Activity on Arrows) notation can also be used. However, in practice, the AoN notation is far more commonly used.

In the rectangle symbolizing the task, we put information such as:

• Task identification number and its description.
• Earliest and latest start date (ES-Early Start and EF-Early Finish).
• Earliest and latest completion date (LS-Late Start and LF-Late Finish).
• Duration of the task (D-Duration).
• Total time reserve (F-Float).

Why calculate the duration of each task?

The calculation of the duration of individual tasks and the analysis of the PERT diagram is used to determine the shortest time to complete the project (taking into account any logistical constraints and connections). In addition, determining the duration of individual tasks has a disciplinary function for project team members. Those who have a predetermined time to complete certain activities feel obligated to meet it.

Calculating the duration of tasks

To calculate the duration of each task you need to determine certain values. They are:

• t_a – the shortest possible (optimistic variant) duration of a given activity (will occur under conditions that are particularly favorable for the implementation of the task),
• t_b – the longest possible (pessimistic variant) duration of a given activity (will occur in the case of a number of difficulties that cause delay in the implementation of the task),
• t_m – the most likely (realistic variant) duration of a given activity (ta < tm < tb).

Having determined the above values, we can proceed to calculate the expected execution time of the task. We substitute the estimated values into the selected formula.

We can use the beta distribution of the probability density curve:

This calculation method is based mainly on intuition and subjective evaluation of project team members. It should be noted that depending on the composition of the evaluating group – the results may vary. However, this does not detract from its high practical value.

We can also use the beta distribution and substitute the values into the formula below:

And then calculate the standard deviation and time variance of the task by substituting the values into the formulas below:

Standard deviation:

Variance:

We put all the calculated parameters in a table and assign them to individual tasks. This facilitates later analysis by the project group.

Development of a PERT diagram

If the table of results is already completed, we can proceed to develop a PERT diagram. The diagram resembles a flowchart, which indicates the order in which the various tasks in the project are carried out. In practice, a Gantt chart is often used to develop the graphical form of the diagram. In addition to describing the activities and determining their order, the diagram should include information such as the time of implementation of tasks in the optimistic, realistic and pessimistic variants.

Example of a PERT diagram

What next?

If we already have the diagram worked out then we move to the next step, which is to calculate the earliest completion date of the project. In practice, this means calculating this parameter for the last task in the diagram (looking from left to right). We start with the earliest start of task 1 (that is, 0) and add the expected duration of this task. The result is the earliest possible end time for the task, which is also the earliest possible start time for the next task. We follow the same process until we reach the last task in the diagram.

Traditionally, “1” was entered as the start time of the first task (the first day of the project). However, this caused some complications in further calculations, so nowadays it is more common to use the designation “0”.

The next step is to determine the time reserve for each task. The total time reserve is the amount of time by which we can delay the start of a particular task without causing a delay for the next task in the project. Remember that the first and last tasks always have zero time reserve.

This time we start the calculation with the last task. The earliest task completion time (calculated in the previous step) is also the latest task completion time. From this value we subtract the expected duration of the task. The result is the latest start time. We proceed similarly with subsequent tasks, moving along the logical links, from right to left, until we reach the starting task.

The critical path

After calculating the earliest possible completion date for the project and determining the time reserves for individual tasks, at least one chain of activities with zero time reserve appears – this is the so-called critical path. The critical path is formed by activities of strategic importance to the execution of the entire project. A delay in the execution of strategic activities causes a delay in the completion of the entire project. Therefore, it is crucial for the project to be completed on schedule to meet the deadlines for “critical” activities.

In the picture above, the critical path is marked with bold arrows.

Advantages of the PERT method:

• Making the planning process easier during large and complex projects.
• Use of simple calculation methods.
• Ability to clearly present the results in a graphical form.
• Making the process of task time control and assessing the risk of project delays easier.
• Helping the project team become more disciplined (by clearly setting deadlines for tasks) and increasing motivation for action.
• Ability to estimate the time completion of individual tasks in the project.
• Possibility of estimating the completion date of the entire project.

Disadvantages of the PERT method:

• Subjectivity of evaluators in estimating the times for completing individual tasks.
• At the initial stage of the project, the possibility of discouraging team members from taking action (by breaking down tasks into factors, their number can seem overwhelming).
• Low flexibility of the method during the project – due to the deterministic nature of the network.
• A large amount of time in the initial phase of the project is required.