PERT is a project management technique used to plan, schedule, and control complex projects. This Workspirited article discusses what the PERT formula is, and how it is used to estimate a project duration, with examples.
A project is a set of interrelated activities that must be executed in a certain logical sequence to complete the entire task. Every activity in a project requires time and resources for its completion. It cannot be initiated unless the other preceding activities are completed.
Managing an entire project is a challenging job performed by a project manager; however, before the project goes on the floor, he has to perform a crucial task of providing an estimation of the project cost and duration to the client. For doing this, the PERT (Program Evaluation and Review Technique) comes to the rescue. We shall discuss what is PERT, and how it is used to calculate the expected project completion time.
PERT is a project scheduling technique which uses three estimates per activity to get the final estimate for the project duration.
- Pessimistic (Tp): the longest time that an activity might require to complete
- Optimistic (To): the shortest time in which an activity can be completed
- Most likely (Tm): the completion time of an activity having the highest probability
The PERT technique is used in conjunction with the Critical Path Method (CPM), therefore, it is also referred to as the PERT-CPM method. Before we begin to use PERT, we need to be familiar with the following keywords:
Also known as the PERT diagram, it is a pictorial representation of all the activities involved in the project. The diagram is easy to understand, since it describes the logical relationships among the activities and the milestones they reach upon completion. The activities are denoted by arrows, while the milestones are denoted by nodes on the network diagram. Generally, the activities are named alphabetically, while the milestones are named numerically.
It is the longest time path on the network, which indicates that it is the longest time it takes to complete a project. Delay in any activity along the critical path will delay the project completion time. All activities on this path have a slack time of zero.
It is the amount of time an activity can be delayed before the project finish date is delayed. Formula to calculate the slack time is:
- S < 0: indicates the amount of time that must be saved so that the project finish date is not delayed.
- S > 0: indicates the acceptable delay so that the project finish date is not delayed.
- S = 0: indicates that the activity is a critical task.
The estimated time to complete a project can be computed if we have the pessimistic (Tp), optimistic (To), and most likely (Tm) estimates of all the activities involved in the project. The estimated time for an activity to be completed can be calculated using the following PERT equation:
The PERT equation is a weighted average, where the most likely estimate is weighted 4 times more heavily than the optimistic and pessimistic estimates. This prevents the PERT output from being too heavily inclined in one direction.
Similarly, you can calculate the standard deviation, variance, and estimated time to complete an entire project. The formulae are given below.
Once you have the aforementioned values related to a project, i.e., TE and σE, you can calculate the chances of meeting a specific project scheduled time (TS) using the probability theory formula:
Using the computed Z, refer to the standard probability table for normal distribution functions to determine the probability of meeting the scheduled time TS.
- Identify the activities in the project.
- Determine the logical sequence of the activities.
- Construct a network diagram.
- Calculate Te and Ve for every activity.
- Determine the critical path.
- Calculate TE by adding up the values of Te for every activity on the critical path. This value is the overall expected completion time for the project.
- Similarly, calculate the VE by adding up the values of Ve for every activity on the critical path. This value is the variance for the entire project.
- Calculate the standard deviation of the project (σE), which is equal to the square root of the variance (VE).
- Calculate the project completion time with the desired probability by using the normal probability distribution.
The following calculator will enable you to compute the PERT estimate value.