Network analysis by PERT and CPM

Construction of Network Diagram in PERT and CPM. Fulkerson's rule for numbering the nodes. Illustrative problem on CPM

1. “Solving Problems on PERT/CPM” By Dr. Rajendrakumar V Kadi Associate Professor Dept of Mechanical Engg Tontadarya College of Engineering, GADAG TONTADARYA COLEGE OF ENGINEERING GADAG, Karnataka VIDEO LECTURE SERIES ON OPERATIONS RESEARCH

2. Construction of Network Diagram Some of the terms commonly used in Network. Activity : It is physically identifiable part of a project which requires time and resources for its execution. In conventional method an activity is represented by an arrow, the tail of which represents the start and the head finish of the activity. Shape, size and direction of the arrow has no relation to the size of the activity. Event: The event is happening such as start and finish. The Start of an activity and end of an activity is represented as event. Event does not consume any resource. In conventional method event is represented by circle (or Node). Path : An unbroken chain of activity arrows connecting the initial event to some other event is called path. Network: It is graphical representation of logically and sequentially connected arrows and nodes representing activities and events of a project. Networks are also called arrow diagram.

3. Construction of Network Diagram Network diagram may be drawn in two methods. They are: 1. AOA (Activity-On-Arrow) Diagram: A network with activities represented on arrows and events on node. Often dummy arrow is needed to Establish precedence relationship which makes the network a little cumbersome and requires greater computation. But is easily understandable. It is also called as conventional arrow diagram. A B 3 5 2. AON (Activity-On-Node ): A network with activities represented on nodes. Arrows indicate only the interdependencies between them. The use of dummy activities can be avoided. A, 3 B, 5

4. Example 1: The dependency relationship between various activities of a project are given below. Draw the AOA (arrow) and AON diagrams. AOA (Activity-On-Arrow) Diagram: A D B E C F Construction of Network Diagram Activity A B C D E F Immediate Predecessor -- -- -- A, B B B,C

5. Construction of Network Diagram Example 1: The dependency relationship between various activities of a project are given below. Draw the AOA (arrow) and AON diagrams. AON (Activity-On-Node) Diagram: A D Start B E End F C Activity A B C D E F Immediate Predecessor -- -- -- A, B B B,C

6. Construction of Network Diagram Activity A B C D E F Immediate Predecessor -- A A B C D, E A B D C F E A B C F E D AOA AON S E S E E

7. Fulkerson’s Rule for Numbering the Events The initial event which has all outgoing arrows with no incoming arrow is numbered “1”. Delete all the arrows coming out from node “1”. This will convert some more nodes (at least one) in to initial events. Number these events 2,3,…. Delete all the arrows going out from these numbered events to create more initial events. Assign next numbers to these events. Continue until final or terminal node, which has all arrows coming in with no arrow going out, is numbered.

8. Fulkerson’s Rule for Numbering the Events a c g j h e b f k d i Illustrative Example

9. Fulkerson’s Rule for Numbering the Events 1 a c g j h e b f k d i

10. Fulkerson’s Rule for Numbering the Events 3 2 1 c g j h e f k d i

11. Fulkerson’s Rule for Numbering the Events 5 3 2 4 1 g j h k i

12. Fulkerson’s Rule for Numbering the Events 5 3 2 4 7 6 1

13. Fulkerson’s Rule for Numbering the Events 5 3 2 4 7 6 1 8

14. Fulkerson’s Rule for Numbering the Events 5 3 2 1 4 7 6 8 a c g j h e b f k d i

15. Activity After Node Numbering a 1-2 b 1-3 c 2-4 d 2-5 e 3-5 f 3-7 g 4-6 h 5-8 i 5-7 j 6-8 k 7-8

16. Difference between PERT and CPM

17. Benefits of PERT/CPM Useful at many stages of project management Mathematically simple Give critical path and slack time Provide project documentation Useful in monitoring costs

18. Limitations of PERT/CPM Clearly defined, independent and stable activities Specified precedence relationships Over emphasis on critical paths

19. Applications of CPM / PERT Construction of a dam or a canal system in a region Construction of a building or highway Maintenance or overhaul of airplanes or oil refinery Space flight Cost control of a project using PERT / CPM Designing a prototype of a machine Development of supersonic planes

20. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 Illustrative Probem on CPM

21. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES LF ES LF ES LF ES LF ES LF ES LF ES LF ES LF ES LF

22. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES LF ES LF ES LF ES LF ES LF ES LF ES LF ES LF ES 00 LF

23. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES LF ES LF ES LF ES LF ES LF ES LF ES LF ES 00 LF

24. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES LF ES LF ES LF ES LF ES LF ES LF ES 00 LF

25. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES LF ES LF ES LF ES LF ES 12 LF ES LF ES 00 LF

26. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES LF ES LF ES LF ES LF ES 12 LF ES 16 LF ES 00 LF

27. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES LF ES LF ES LF ES 12 LF ES 16 LF ES 00 LF

28. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES LF ES LF ES 19 LF ES 12 LF ES 16 LF ES 00 LF

29. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES 27 LF ES LF ES 19 LF ES 12 LF ES 16 LF ES 00 LF

30. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES 27 LF ES 30 LF ES 19 LF ES 12 LF ES 16 LF ES 00 LF

31. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES 27 LF ES 30 LF 30 ES 19 LF ES 12 LF ES 16 LF ES 00 LF

32. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES 27 LF 27 ES 30 LF 30 ES 19 LF ES 12 LF ES 16 LF ES 00 LF

33. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF ES 16 LF ES 00 LF

34. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF ES 16 LF ES 00 LF

35. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF ES 16 LF 22 ES 00 LF

36. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF 12 ES 16 LF 22 ES 00 LF

37. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF ES 10 LF 16 ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF 12 ES 16 LF 22 ES 00 LF

38. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF 02 ES 10 LF 16 ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF 12 ES 16 LF 22 ES 00 LF

39. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF 02 ES 10 LF 16 ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF 12 ES 16 LF 22 ES 00 LF 00

40. ACTIVITY DURATION (DAYS) START TIME FINISH TIME TOTAL FLOAT (LS-ES) OR (LF-EF) FREE FLOAT (TF-Head event slack ) REMARK ES LS (LF-DURATION) EF (ES+DURATION) LF 0-1 2 2 2 C 1-2 8 2 8 10 16 6 NC 1-3 10 2 2 12 12 C 2-4 6 10 16 16 22 6 NC 2-5 3 10 22 13 25 12 NC 3-4 3 12 19 15 22 7 1 NC 3-6 7 12 12 19 19 C 4-7 5 16 22 21 27 6 6 NC 5-7 2 13 25 15 27 12 12 NC 6-7 8 19 19 27 27 C 7-8 3 27 27 30 30 C

41. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 ES 02 LF 02 ES 10 LF 16 ES 13 LF 25 ES 27 LF 27 ES 30 LF 30 ES 19 LF 19 ES 12 LF 12 ES 16 LF 22 ES 00 LF 00

42. 4 3 2 5 6 7 8 3 8 3 10 7 6 1 5 2 2 8 3 CRITICAL PATH: 0-1-3-6-7-8 PROJECT DURATION: 30 DAYS