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Understanding Project Management: A Guide to Network Diagrams and Critical Paths

This project management guide focuses on key concepts such as Activity-on-Node (A-O-N) and Activity-on-Arrow (A-O-A) network diagrams, detailing how they represent activities and paths in a project. It covers essential definitions like critical path, slack time, earliest and latest start and finish times, as well as relevant algorithm formulas. You will learn how to identify critical activities and estimate project duration effectively. With practical examples, this guide enhances your ability to manage complex projects efficiently.

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Understanding Project Management: A Guide to Network Diagrams and Critical Paths

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  1. Project Management

  2. Definitions • Activity-on-Node (A-O-N) - Network diagram convention in which nodes designate activities • Activity-on-Arrow (A-O-A) - Network diagram convention in which arrows designate activities Activity (arrow)

  3. Definitions • Path - a sequence of activities that leads from the starting node to the finishing node. Activity A Activity B Event 1 Event 2 Event 3

  4. How many paths are in this network? C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  5. 1-2-5-6 C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  6. C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  7. 1-2-4-6 C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  8. 1-3-4-5-6 C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  9. 1-3-4-6 C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3)

  10. Critical Path - The longest path - determines the project duration. C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 1-2-5-6 (10) 1-2-4-5-6 (10) 1-2-4-6 (11) 1-3-4-6 (9) 1-3-4-5-6 (8) E (3)

  11. Critical Activities - activities on the critical path C (3) Event 5 Event 2 A (5) H (2) Event 1 F (1) D (2) Event 6 Event 4 B (2) G (4) Event 3 E (3) A-D-G

  12. Definitions • Slack - Allowable slippage for a path; the difference between the length of a path and the length of the critical path.

  13. Algorithm Definitions • Earliest Start (ES) - the earliest time an activity can start, assuming all preceding activities start as early as possible • Earliest Finish (EF) - the earliest time an activity can finish • Latest Start (LS) - the latest time the activity can start and not delay the project • Latest Finish (LF) - the latest time the activity can finish and not delay the project

  14. Algorithm Formulas EF = ES + t EF ES t

  15. 6 4 2 8 11 3 1 5 1 6 4 9 3

  16. 8 0 0 Example 2 6 4 2 11 1 5 1 6 4 9 3

  17. 8 8 0 0 4 6 4 2 11 1 5 1 6 4 9 3

  18. 8 8 0 8 0 4 4 Example 2 8 6 4 2 11 1 5 1 6 4 9 3

  19. 8 8 0 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  20. 3 8 8 14 0 6 8 0 13 19 10 4 4 Example 2 14 8 6 4 2 11 1 5 1 6 4 9 3

  21. 3 8 17 8 14 0 6 8 0 13 19 10 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  22. 3 8 17 8 14 0 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  23. 3 8 17 8 14 0 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 19 9 3

  24. 3 8 17 8 14 0 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 19 20 9 3

  25. Algorithm Formulas EF = ES + t LS = LF - t LS LF EF ES t

  26. 3 8 17 8 14 0 20 19 20 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  27. 3 8 17 8 14 0 19 20 19 20 8 0 13 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  28. 3 19 8 17 8 14 0 19 20 19 19 20 8 0 13 19 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  29. 3 19 16 8 17 8 14 0 19 20 8 19 19 20 8 0 13 19 10 19 4 4 14 8 6 4 2 11 1 5 1 6 4 9 3

  30. 3 19 16 8 17 8 14 0 19 20 8 19 19 20 8 0 13 19 10 19 10 4 4 16 14 8 6 4 2 11 1 5 1 6 4 9 3

  31. 3 19 16 8 17 8 14 0 19 20 8 6 19 19 20 8 0 13 19 10 19 10 4 4 16 10 14 8 6 4 2 11 1 5 1 6 4 9 3

  32. 3 19 16 8 17 8 14 0 19 20 8 6 19 19 20 8 0 13 19 10 19 10 4 4 16 10 14 8 6 4 2 11 1 5 1 6 4 9 3

  33. 3 19 16 8 17 8 14 0 19 20 8 6 19 19 20 8 0 13 19 10 19 10 4 4 16 10 14 8 6 4 2 8 11 1 5 1 6 4 9 3

  34. 3 19 16 8 17 8 14 0 19 20 8 6 19 19 20 8 0 13 19 10 19 10 4 4 16 10 14 8 6 4 2 8 0 11 1 5 1 6 4 9 3

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