Node

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Node

  1. 1. CPM Network Computation Activity Depends on t AOA AON 1-2 A ─ 3 2-3 B A 4Spring 2008, Activity on Node 1King Saud University Dr. Khalid Al-Gahtani
  2. 2. AOA A ct ivit y N a m e 1 3 A B 3 4 2 A ct ivit y D urat io n AON 3 4 A BSpring 2008, Activity on Node 2King Saud University Dr. Khalid Al-Gahtani
  3. 3. Drawing CPM Networks• Prerequisites: Before drawing a CPM network, we must have: – List of all activities comprising the project – Order of precedence of each activity – Duration estimate of each activitySpring 2008, Activity on Node 3King Saud University Dr. Khalid Al-Gahtani
  4. 4. Example: Depends on Duration (Day) Activity (Immediate Predecessor(s)) (Time to perform) a ─ 14 b ─ 3 c ─ 7 d a, b 4 e b, c 10Spring 2008, Activity on Node 4King Saud University Dr. Khalid Al-Gahtani
  5. 5. Activity on arrow Solution a d b D um m y c eSpring 2008, Activity on Node 5King Saud University Dr. Khalid Al-Gahtani
  6. 6. Activity-on-node Solution a d ST A RT b F IN IS H e cSpring 2008, Activity on Node 6King Saud University Dr. Khalid Al-Gahtani
  7. 7. Class work#1:Draw AON Network for the fowling project: Activity Depends upon Activity Depends upon A G F B A I F F A J H H A K I, J, F C B, A L G, D, E D B M K E C N L, M Spring 2008, Activity on Node 7 King Saud University Dr. Khalid Al-Gahtani
  8. 8. “Activity on Node”• Nodes = Activities• Links = Precedence Relationships• Dummy activities are not required ES t ES Activity Name LS TF LFSpring 2008, Activity on Node 8King Saud University Dr. Khalid Al-Gahtani
  9. 9. Example Activity Depends on Duration (Days) A 5 B A 15 C A 10 D B 15 E B, C 10 F D, E 5Spring 2008, Activity on Node 9King Saud University Dr. Khalid Al-Gahtani
  10. 10. AON ES t EF N am e B D LS TF LF F FIN ISHST A R T A C ESpring 2008, Activity on Node 10King Saud University Dr. Khalid Al-Gahtani
  11. 11. AON ES t EF N am e 5 15 20 20 15 35 B D LS TF LF 5 20 20 35 35 5 40 40 0 400 0 0 0 5 5 F FIN ISH ST A R T A 35 40 40 400 0 0 5 5 10 15 20 10 30 C E 15 25 25 35Spring 2008, Activity on Node 11King Saud University Dr. Khalid Al-Gahtani
  12. 12. Constraints with Lead/lag timeSpring 2008, Activity on Node 12King Saud University Dr. Khalid Al-Gahtani
  13. 13. Finish-to-Start (FSij):• FSij is equal to the minimum number of time units that must transpire from the completion of the predecessor (i) prior to the start of the successor (j).• The time between the finish of one activity and the start of its successor is called “Lag”.Spring 2008, Activity on Node 13King Saud University Dr. Khalid Al-Gahtani
  14. 14. Finish-to-Start (FSij):• If the relationship is not listed on the dependency arrow, FS is assumed with Lag= 0.• Example: a planner may wish to have an activity of removing formwork from a new building component follow the concrete pour by some pre-defined lag period to allow setting.Spring 2008, Activity on Node 14King Saud University Dr. Khalid Al-Gahtani
  15. 15. Start-to-Start (SSij):• SSij is equal to the minimum number of time units that must be complete on the preceding activity (i) prior to the start of the successor (j).Spring 2008, Activity on Node 15King Saud University Dr. Khalid Al-Gahtani
  16. 16. Start-to-Start (SSij):• “Lag” is always applied to SS relation.• Example: parallel in starting of Installing and Finishing the walls activity of 100 rooms on a project must be 10 days difference (SS=10 days). – You don’t have to wait installing 100 wall’s room to start doing the finishing work.Spring 2008, Activity on Node 16King Saud University Dr. Khalid Al-Gahtani
  17. 17. Finish-to-Finish (FFij):• FFij is equal to the minimum number of time units that must remain to be completed on the successor (j) after the completion of the predecessor (i).• It is applied as productivity control.Spring 2008, Activity on Node 17King Saud University Dr. Khalid Al-Gahtani
  18. 18. Finish-to-Finish (FFij):• The finish date of Installing and Finishing walls’ activity of 100 rooms on a project must have 10 days difference in order to control productivity (FF=10 days). – In this example, the productivity of installing the walls’ activity might be less than finishing the rooms’ activity.• “Lag” is always applied to FF relation as buffer between the two activities.Spring 2008, Activity on Node 18King Saud University Dr. Khalid Al-Gahtani
  19. 19. Start-to-Finish (SFij):• SFij is equal to the minimum number of time units that must transpire from the start of the predecessor (i) to the completion of the successor (j).• It is applied also for controlling productivitySpring 2008, Activity on Node 19King Saud University Dr. Khalid Al-Gahtani
  20. 20. Start-to-Finish (SFij): Example: The start date of Installing 100 rooms’ wall’s activity and the finish date of Finishing same walls’ activity of a project must maintain 30 days difference to control productivity (SF=30 days). “Lag” is always applied to SF relation as buffer between the two activities.• It is not recommended to use by planner.Spring 2008, Activity on Node 20King Saud University Dr. Khalid Al-Gahtani
  21. 21. Start-to-Start and Finish-to-Finish (ZZij):• ZZij is a combination of two constraints. i.e., a start-to-start and finish-to-finish relationship. It is written with the SSij time units first, followed by the FFij time units.• These two relations are used combined to maintain buffer between the start and finish of two activities.Spring 2008, Activity on Node 21King Saud University Dr. Khalid Al-Gahtani
  22. 22. Forward Pass Computations Initial T im e E Fi F S ij E S j = M ax all i ESi SS ij E Fi F F ij Dj ESi SF ij Dj EFj = ESj + DjSpring 2008, Activity on Node 22King Saud University Dr. Khalid Al-Gahtani
  23. 23. Backward Pass Computation T erm inal T im e LS j F S ij L F i = M in all j LF j F Fij LSi SS ij Di LF j SFij Di LSi = LFi DjSpring 2008, Activity on Node 23King Saud University Dr. Khalid Al-Gahtani
  24. 24. Example 2 2 6 B FS 4 C SF 5 D SS 3 FF 1 SF 5 4 1 3 6 A F SF 4 L E 5 1 2 ES D EF K G FS 4 H A ctivity LS F LFSpring 2008, Activity on Node 24King Saud University Dr. Khalid Al-Gahtani
  25. 25. Example Solution 4 2 6 10 2 12 9 6 15 B FS 4 C SF 5 D 5 1 7 SS 3 11 1 13 10 1 16 FF 1 SF 50 4 4 4 1 5 9 3 12 16 6 22 A F SF 4 L E0 0 4 10 6 11 11 2 14 16 0 22 ES D EF 4 5 9 9 1 10 14 2 16 A ctivity K G FS 4 H LS F LF 4 0 9 9 0 10 14 0 16 Spring 2008, Activity on Node 25 King Saud University Dr. Khalid Al-Gahtani

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