Chapter III: Project Scheduling - PERT and MPM Methods

Mastering Project Planning and Control

Learn how to plan, schedule, and manage complex projects using two powerful network-based methods: PERT (Program Evaluation and Review Technique) and MPM (Méthode des Potentiels Metra / Precedence Diagram Method). From building bridges to launching software, these techniques help ensure projects finish on time!

Project scheduling is the process of defining project activities, their durations, dependencies, and determining when each activity should start and finish to complete the project as efficiently as possible.

🏗️ Where Are PERT and MPM Used?

• Construction: Building projects, infrastructure development
• Manufacturing: Product development, production line setup
• Software Development: Complex software projects, system implementations
• R&D: Research projects, drug development
• Event Planning: Conferences, weddings, festivals
• Aerospace: Aircraft design, space missions
• Government: Defense projects, public works

📜 The Birth of PERT (1958)

🇫🇷 Development of MPM (1960s)

What is PERT?

PERT is a network-based technique that uses an Activity-on-Arrow (AOA) representation where:

• Nodes (circles) represent events (milestones)
• Arrows represent activities (work tasks)
• Activity durations are shown on arrows

1. Each activity is represented by one and only one arrow
2. Each event (node) has a unique identifier
3. No two activities can have the same start and end events (use dummy if needed)
4. Network flows from left to right (time progression)
5. No loops allowed (can't go backward in time)
6. One start event and one end event for the entire project
7. Every event (except start) must have at least one incoming activity
8. Every event (except end) must have at least one outgoing activity

🔧 Step 1: List All Activities

Create a table with all project activities and their properties:

🔧 Step 2: Identify Precedence Relationships

Determine which activities must be completed before others can start:

• A and B can start immediately (no predecessors)
• C and D require A to be completed first
• E requires both B and C to be completed

🔧 Step 3: Draw the Network

Process:

1. Start with a single start event (Event 1)
2. Draw activities with no predecessors from start event
3. Progress through activities in logical order
4. Use dummy activities if needed to maintain correct logic
5. End with a single finish event

Step 1: The Forward Pass (Earliest Times)

1. Start at the first event: Set its earliest time (ES or t₀) = 0.
2. For each subsequent event: Earliest time is
   t_i = max(t_j + d_j→i), for all predecessors j, where d_j→i is the duration of the activity from j to i.
3. Continue until all nodes are labeled with earliest occurrence times.
4. The project duration is the earliest time at the final event (exit node).

Step 2: The Backward Pass (Latest Times)

1. Start at the final event: Set its latest time (LF = EF = project duration).
2. For each preceding event: The latest time is
   t'_j = min(t'_i - d_j→i), for all successors i.
3. Proceed backwards until all nodes are labeled with latest allowable occurrence times.

Step 3: Determining Floats and Critical Path

• Total float of an activity (i → j): TF = t'_j - t_i - d_i→j
• Critical activities: Those with TF = 0; together, these form the critical path.
• Critical path: The sequence of activities from start to finish with zero total float; determines project duration.

Given:

• Activity List:
  • A (3 days), no predecessors
  • B (4 days), no predecessors
  • C (2 days), after A
  • D (3 days), after A
  • E (4 days), after B and C

Question:

Find:

• Earliest Start and Finish times for each activity
• Latest Start and Finish times for each activity
• All floats and identify the critical path
• Total project duration

• Project duration = 9 days (longest path: A→C→E)
• Critical Path: A-C-E

What is MPM?

MPM is a node-based project scheduling method where:

• Boxes (nodes) represent activities, not events
• Arrows show dependencies (Finish-to-Start logic, unless otherwise specified)
• All timing (earliest/latest starts/finishes, floats) are shown directly on each activity box for easy reading
• No dummy activities needed (unlike classic PERT)

MPM is widely used in engineering, construction software (e.g., MS Project), and research.

Example: MPM (AON/PDM) Network

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Example 1: Small Network Calculation

• Draw PERT and AON networks.
• Compute early/late times, floats, and critical path.
• Check with at least two students/colleagues, compare answers.

Exercise 1: Network Drawing and Analysis

Given the following table, draw the PERT and MPM networks and find the critical path, project duration, and all floats.

Tip: Practice both hand-drawn and software-generated diagrams.

Self-Check Questions

• What is the difference between total float and free float?
• Why do modern project managers prefer AON/PDM over classic PERT?
• Can a project have multiple critical paths? Under what circumstances?
• How does activity duration uncertainty affect the use of PERT?
• What are dummy activities, and why are they avoided in the MPM method?
• How would you explain the critical path to a non-technical stakeholder?
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📖 Key Textbooks

• Introduction to Operations Research, by Hillier & Lieberman (extensive PERT/CPM/MPM chapters, examples, and exercises)
• Project Management: A Systems Approach, by Harold Kerzner (in-depth project scheduling, real-world cases)
• Operations Research: Applications and Algorithms, by Wayne Winston (well-explained critical path, float, network algorithms)
• CPM and PERT: A Practical Guide, by Joseph Moder & Cecil Phillips (classic focused text on network scheduling)
• Fundamentals of Project Management, by Joseph Heagney (practical primer for new project managers)

🌐 Online Resources

• MIT OpenCourseWare: Search "Critical Path Method", "PERT", or "Project Scheduling"
• Coursera (Project Management Principles and Practices Specialization, UC Irvine; Fundamentals of Project Planning and Management, University of Virginia)
• edX (Project Management MicroMasters, RIT; Construction Scheduling, Columbia University)
• YouTube playlists: "PERT and CPM Explained", "Critical Path in MS Project"
• PMI (Project Management Institute): pmi.org, standards and articles
• Lucidchart, Draw.io: Free templates for network diagrams
• ProjectLibre: https://www.projectlibre.com/
• GanttProject: https://www.ganttproject.biz/
• OR-Exchange Q&A: or.stackexchange.com (scheduling, algorithms, practice questions)

✔️ Chapter Complete: Project Scheduling Mastery

With PERT and MPM/Precedence Diagram methods, you are ready to analyze and optimize the timing of any project. These practical tools are essential for engineers, developers, and project managers.

Next: Try modeling and analyzing your own scheduling challenge—or explore further with advanced topics such as resource-constrained scheduling and probabilistic network analysis!