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1. Overview
The **Program Evaluation and Review Technique (PERT)** is a project management tool used to analyze and represent the tasks involved in completing a project. It helps managers:

• Plan and schedule project timelines.
• Identify critical paths and potential delays.
• Optimize resource allocation and task sequencing.

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2. Key Features of PERT
Task Representation: Tasks are represented as nodes or arrows in a flowchart-style diagram. 
Focus on Uncertainty: PERT incorporates uncertainty by using probabilistic time estimates for tasks. 
Critical Path Method (CPM): Identifies the sequence of tasks that determine the project's minimum completion time.

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3. PERT Time Estimates
PERT uses three time estimates for each task to account for uncertainty:

• Optimistic Time (O): The minimum time required to complete the task under ideal conditions.
• Most Likely Time (M): The best estimate of the time required to complete the task under normal conditions.
• Pessimistic Time (P): The maximum time required to complete the task under adverse conditions.

Formula for Expected Time (TE):
TE = (O + 4M + P) / 6

Variance of Task Time (σ²):
Variance = [(P - O) / 6]²

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4. Steps in PERT Analysis
1. **Identify Tasks and Dependencies:** 
   - Break down the project into individual tasks.
   - Determine the sequence of tasks and dependencies.

2. **Estimate Time for Each Task:** 
   - Use optimistic, most likely, and pessimistic time estimates to calculate expected time.

3. **Construct the PERT Diagram:** 
   - Represent tasks as nodes and dependencies as arrows.

4. **Determine the Critical Path:** 
   - Identify the longest path through the network (tasks with zero slack).

5. **Update as Needed:** 
   - Adjust estimates and dependencies as the project progresses.

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5. Benefits of PERT

• Enhanced Planning: Provides a structured framework to manage complex projects.
• Risk Identification: Highlights potential bottlenecks and delays.
• Flexibility: Easily updated as new information becomes available.
• Resource Optimization: Ensures efficient allocation of resources.

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6. Example PERT Diagram
A PERT diagram typically includes:

• Tasks (represented by nodes).
• Dependencies (represented by arrows).
• Estimated time for each task.
• Critical path (highlighted to indicate tasks that directly impact the project duration).

Illustration:
Task A --> Task B --> Task C
   \          /
    --> Task D
- Task A leads to Tasks B and D, which converge into Task C.

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7. Limitations of PERT

• Complexity: Can become complicated for large projects with many tasks.
• Subjectivity: Time estimates are based on judgment and may not always be accurate.
• Focus on Time Only: Does not account for cost or resource limitations directly.

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8. Applications of PERT
PERT is widely used in:

• Construction and engineering projects.
• Software development and IT projects.
• Manufacturing and product development.
• Research and development (R&D) projects.

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9. Conclusion
The **Program Evaluation and Review Technique (PERT)** is a powerful tool for managing projects with uncertain timelines. By combining structured task representation with probabilistic time estimates, PERT enables effective planning, scheduling, and monitoring of complex projects.

Key Takeaway: PERT is ideal for projects where uncertainty is high, helping managers anticipate risks and ensure timely completion.

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1. What is PERT?

The **Program Evaluation and Review Technique (PERT)** is a project management methodology used to plan, schedule, and control complex tasks. It was developed in the 1950s by the U.S. Navy for managing the Polaris missile program.

Purpose of PERT:

• Identify and evaluate the time required for each task in a project.
• Determine the most efficient sequence of tasks to minimize delays.
• Manage uncertainties and risks in project timelines.

Core Characteristics of PERT:

• Probabilistic Approach: Accounts for uncertainties by using three time estimates for each task.
• Graphical Representation: Represents tasks and their dependencies in a network diagram.
• Critical Path Focus: Identifies the sequence of tasks that determines the minimum project duration.

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2. Key Components of PERT

A. Tasks/Activities:
- The work or actions required to complete the project. Each task is represented as a node in the PERT diagram.

B. Events/Milestones:
- Specific points in the project that indicate the start or completion of a task.

C. Dependencies:
- Relationships between tasks. A task may depend on the completion of one or more other tasks.

D. Critical Path:
- The longest path through the network diagram. Tasks on this path directly affect the project duration.

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3. Time Estimates in PERT

PERT uses three time estimates for each task to account for uncertainties:

• Optimistic Time (O): The shortest time in which the task can be completed under ideal conditions.
• Most Likely Time (M): The time required to complete the task under normal conditions.
• Pessimistic Time (P): The longest time the task might take under adverse conditions.

Expected Time (TE):
To calculate the expected time for a task, the following weighted average formula is used:
TE = (O + 4M + P) / 6

Variance of Task Time (σ²):
The formula to calculate variance is:
Variance = [(P - O) / 6]²

Example Calculation:
- Optimistic Time (O): 4 days
- Most Likely Time (M): 6 days
- Pessimistic Time (P): 10 days

Expected Time (TE):
TE = (4 + 4(6) + 10) / 6 = 6.33 days

Variance:
Variance = [(10 - 4) / 6]² = 1

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4. Steps to Create a PERT Diagram

Step 1: Define the Tasks
- List all tasks required to complete the project.
- Identify dependencies (tasks that must be completed before others can begin).

Step 2: Estimate Time for Each Task
- Use optimistic, most likely, and pessimistic time estimates for each task.

Step 3: Construct the PERT Diagram
- Represent tasks as nodes (circles or rectangles).
- Connect tasks with arrows to indicate dependencies.

Step 4: Determine the Critical Path
- Calculate the total time for all paths through the diagram.
- The critical path is the longest path and determines the project duration.

Step 5: Monitor and Update
- Regularly update the PERT diagram as tasks are completed or delayed.

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5. Critical Path and Slack Time

Critical Path:
- The sequence of tasks that directly affects the project duration.
- Any delay in tasks on the critical path will delay the entire project.

Slack Time:
- The amount of time a task can be delayed without affecting the overall project timeline.
- Slack is calculated as:
Slack = Latest Start Time (LST) - Earliest Start Time (EST)

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6. Benefits of PERT

• Improved Planning: Helps managers visualize the entire project and its components.
• Time Management: Identifies critical tasks and potential delays.
• Flexibility: Can be updated and adjusted as the project progresses.
• Risk Reduction: Accounts for uncertainty through probabilistic time estimates.
• Resource Optimization: Ensures efficient use of resources by identifying task priorities.

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7. Limitations of PERT

• Complexity: Can become complicated for large projects with many tasks and dependencies.
• Subjectivity: Time estimates are based on judgment and may not always be accurate.
• Focus on Time Only: Does not directly account for costs or resource availability.

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8. Applications of PERT

Common Uses:

• Engineering and construction projects.
• Software development and IT projects.
• Manufacturing and production planning.
• Research and development (R&D) initiatives.

Real-World Example:
- Developing a new product:
  - Tasks: Market research, prototype design, testing, production setup.
  - Dependencies: Prototype testing must be completed before production setup.
  - Critical Path: Identifies which tasks directly impact the product launch date.

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9. PERT Diagram Example

Simple PERT Diagram:
Task A --> Task B --> Task C
   \          /
    --> Task D

Details:
- Task A leads to Tasks B and D.
- Tasks B and D converge into Task C.
- Critical Path: The longest path (e.g., A --> B --> C).

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10. Conclusion

The **Program Evaluation and Review Technique (PERT)** is an essential tool for managing complex projects with uncertainties. By visualizing tasks and their dependencies, PERT enables better planning, monitoring, and control of project timelines.

Key Takeaways:

• PERT provides a probabilistic approach to managing projects with uncertain timelines.
• Critical path analysis ensures focus on tasks that directly impact the project completion date.
• PERT is ideal for projects requiring detailed scheduling and flexibility.