Program Evaluation and Review Technique (PERT) is a vital project management tool used to schedule, organize, and coordinate tasks within a project. PERT is especially useful for projects with task durations that have uncertainty, allowing project managers to estimate the overall project duration with greater accuracy. This guide explains PERT, its key formulas, and definitions, along with a summary table for quick reference.
What is PERT?
PERT helps estimate project durations by incorporating variability in task durations. It is ideal for complex projects with tasks that are non-repetitive and have uncertain time frames.
PERT Time Estimates
PERT uses three time estimates for each task:
- Optimistic Time (O): The shortest time a task can be completed under ideal conditions.
- Most Likely Time (M): The best estimate of the time required under normal conditions.
- Pessimistic Time (P): The longest time a task might take under challenging conditions.
PERT Formula for Expected Time
The expected time (TE) for a task is calculated using the following weighted average formula:
$$TE = \frac{O + 4M + P}{6}$$
where:
- O is the Optimistic Time
- M is the Most Likely Time
- P is the Pessimistic Time
PERT Variance and Standard Deviation
To assess the uncertainty in task durations, PERT calculates the variance and standard deviation:
Variance (V):
$$V = \left(\frac{P - O}{6}\right)^2$$
Standard Deviation (σ):
$$\sigma = \frac{P - O}{6}$$
These calculations help project managers understand the potential risk associated with the project timeline.
Example of PERT Calculation
Assume the following task data:
| Task | Optimistic Time (O) | Most Likely Time (M) | Pessimistic Time (P) |
|---|---|---|---|
| A | 4 days | 5 days | 8 days |
| B | 2 days | 3 days | 4 days |
| C | 1 day | 2 days | 5 days |
Calculations for Expected Time (TE) and Variance (V):
Task A:
- Expected Time:
$$TE_A = \frac{4 + 4(5) + 8}{6} = 5.33 \text{ days}$$
- Variance:
$$V_A = \left(\frac{8 - 4}{6}\right)^2 = 0.444 \text{ days}^2$$
Task B:
- Expected Time:
$$TE_B = \frac{2 + 4(3) + 4}{6} = 3 \text{ days}$$
- Variance:
$$V_B = \left(\frac{4 - 2}{6}\right)^2 = 0.111 \text{ days}^2$$
Task C:
- Expected Time:
$$TE_C = \frac{1 + 4(2) + 5}{6} = 2.5 \text{ days}$$
- Variance:
$$V_C = \left(\frac{5 - 1}{6}\right)^2 = 0.444 \text{ days}^2$$
Summary Table for PERT Calculations
| Task | TE (Expected Time) | Variance (V) | Standard Deviation (σ\sigmaσ) |
|---|---|---|---|
| A | 5.33 days | 0.444 days^2 | 0.667 days |
| B | 3 days | 0.111 days^2 | 0.333 days |
| C | 2.5 days | 0.444 days^2 | 0.667 days |
Conclusion
The Program Evaluation and Review Technique (PERT) is an effective project management tool for estimating project completion time while considering uncertainty in task durations. By using the PERT formula for expected time, variance, and standard deviation, project managers can better plan, allocate resources, and anticipate risks, ensuring a realistic project schedule.