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(Aoa) and (aon) networks

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(AOA) and (AON) Network Construction and Critical Path Determination

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(Aoa) and (aon) networks

  1. 1. Project Management Dr. Mahmoud Abbas Mahmoud Asst. Prof. 2016 - 2017 Activity on Arrow (AOA) and Activity on Node (AON) Networks 1
  2. 2. Identify for Each Activity: • Which other activities must be completed previously (predecessors) ? • How long time required for completion ? • What are the required resources ? Dr. Mahmoud Abbas Mahmoud 2
  3. 3. Project Scheduling Commonly used techniques: • Gantt Chart • Critical Path Method (CPM) • Program Evaluation and Review Technique (PERT) Dr. Mahmoud Abbas Mahmoud 3
  4. 4. Drawing the Project Network • AOA – Activity on Arrow: networks show each activity as an arrow, and the nodes represent the starting and ending points • AON – Activity on Node: networks show each activity as a node and arrows show the immediate predecessor activities Dr. Mahmoud Abbas Mahmoud 4
  5. 5. A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA) A comes before B, which comes before C (i) A B C BA C A and B must both be completed before C can start (ii) A C C B A B B and C cannot begin until A is completed (iii) B A C A B C Dr. Mahmoud Abbas Mahmoud 5
  6. 6. A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA) C and D cannot begin until both A and B are completed (iv) A B C D B A C D C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA (v) CA B D Dummy activity A B C D Dr. Mahmoud Abbas Mahmoud 6
  7. 7. A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA) B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA. (vi) A C DB A B C D Dummy activity Dr. Mahmoud Abbas Mahmoud 7
  8. 8. Example: Activity Immediate Predecessors A — B — C A D A, B E C F C G D, E H F, G Dr. Mahmoud Abbas Mahmoud
  9. 9. AOA Network Dr. Mahmoud Abbas Mahmoud 9
  10. 10. AON Network Dr. Mahmoud Abbas Mahmoud 10
  11. 11. Example: General Foundry • Have 16 weeks to install a complex air filter system on its smokestack • May be forced to close if not completed within 16 weeks due to environmental regulations • Have identified 8 activities Dr. Mahmoud Abbas Mahmoud 11
  12. 12. Dr. Mahmoud Abbas Mahmoud 12
  13. 13. AON Network for General Foundry Dr. Mahmoud Abbas Mahmoud 13
  14. 14. Activity Time Estimates Dr. Mahmoud Abbas Mahmoud 14
  15. 15. Determining the Project Schedule • Some activities can be done simultaneously so project duration should be less than 25 weeks (the total time of all activities) • Critical path analysis is used to determine project duration • The critical path (CP) is the longest path through the network Dr. Mahmoud Abbas Mahmoud 15
  16. 16. Critical Path Analysis Need to find the following for each activity: • Earliest Start Time (ES) • Earliest Finish Time (EF) • Latest Start Time (LS) • Latest Finish Time (LF) Dr. Mahmoud Abbas Mahmoud 16
  17. 17. Performing a Critical Path Analysis Activity Description Time (weeks) A Build internal components 2 B Modify roof and floor 3 C Construct collection stack 2 D Pour concrete and install frame 4 E Build high-temperature burner 4 F Install pollution control system 3 G Install air pollution device 5 H Inspect and test 2 Total Time (weeks) 25 Earliest start (ES) = earliest time at which an activity can start, assuming all predecessors have been completed Earliest finish (EF) = earliest time at which an activity can be finished (completed) Latest start (LS) = latest time at which an activity can start so as to not delay the completion time of the entire project Latest finish (LF) = latest time by which an activity has to be finished (completed) so as to not delay the completion time of the entire project AON Network for General Foundry Dr. Mahmoud Abbas Mahmoud
  18. 18. A Activity Name or Symbol Earliest Start ES Earliest FinishEF Latest Start LS Latest Finish LF Activity Duration 2 Dr. Mahmoud Abbas Mahmoud
  19. 19. Forward Pass Begin at starting event and work forward Earliest Start Time Rule:  If an activity has only a single immediate predecessor, its ES equals the EF of the predecessor  If an activity has multiple immediate predecessors, its ES is the maximum of all the EF values of its predecessors ES = Max {EF of all immediate predecessors} Dr. Mahmoud Abbas Mahmoud
  20. 20. Forward Pass Begin at starting event and work forward Earliest Finish Time Rule:  The earliest finish time (EF) of an activity is the sum of its earliest start time (ES) and its activity time EF = ES + Activity time Dr. Mahmoud Abbas Mahmoud
  21. 21. ES / EF Calculations Start 0 0 ES 0 EF = ES + Activity time + = Dr. Mahmoud Abbas Mahmoud
  22. 22. ES / EF Calculations Start 0 0 0 A 2 2 EF of A = (ES of A) + 2 0 ES of A Dr. Mahmoud Abbas Mahmoud
  23. 23. B 3 ES / EF Calculations Start 0 0 0 A 2 20 3 EF of B = (ES of B) + 3 0 ES of B Dr. Mahmoud Abbas Mahmoud
  24. 24. C 2 2 4 ES / EF Calculations B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud
  25. 25. C 2 2 4 ES / EF Calculations B 3 0 3 Start 0 0 0 A 2 20 D 4 73 = Max (2, 3)2 3 Dr. Mahmoud Abbas Mahmoud
  26. 26. D 4 3 7 C 2 2 4 ES / EF Calculations B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud
  27. 27. E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 D 4 3 7 C 2 2 4 ES / EF Calculations B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud
  28. 28. Backward Pass Begin with the last event and work backwards Latest Finish Time Rule:  If an activity is an immediate predecessor for just a single activity, its LF equals the LS of the activity that immediately follows it  If an activity is an immediate predecessor to more than one activity, its LF is the minimum of all LS values of all activities that immediately follow it LF = Min {LS of all immediate following activities} Dr. Mahmoud Abbas Mahmoud
  29. 29. Backward Pass Begin with the last event and work backwards Latest Start Time Rule:  The latest start time (LS) of an activity is the difference of its latest finish time (LF) and its activity time LS = LF – Activity time Dr. Mahmoud Abbas Mahmoud
  30. 30. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 LF = EF of Project Dr. Mahmoud Abbas Mahmoud 15
  31. 31. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud 13 LS = LF – Activity time
  32. 32. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud 13 13
  33. 33. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 10 13 8 13 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 Dr. Mahmoud Abbas Mahmoud 84
  34. 34. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 10 13 8 13 4 8 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 LF = Min(4, 10) 42 Dr. Mahmoud Abbas Mahmoud
  35. 35. LS / LF Calculations E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 10 13 8 13 4 8 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 42 84 20 41 00 Dr. Mahmoud Abbas Mahmoud
  36. 36. Computing Slack Time After computing the ES, EF, LS, and LF times for all activities, compute the slack or free time for each activity  Slack is the length of time an activity can be delayed without delaying the entire project Slack = LS – ES or Slack = LF – EF Dr. Mahmoud Abbas Mahmoud
  37. 37. Computing Slack Time Earliest Earliest Latest Latest On Start Finish Start Finish Slack = Critical Activity ES EF LS LF (LS – ES) = (LF – EF) Path A 0 2 0 2 0 Yes B 0 3 1 4 1 No C 2 4 2 4 0 Yes D 3 7 4 8 1 No E 4 8 4 8 0 Yes F 4 7 10 13 6 No G 8 13 8 13 0 Yes H 13 15 13 15 0 Yes Dr. Mahmoud Abbas Mahmoud
  38. 38. Critical Path E 4 F 3 G 5 H 2 4 8 13 15 4 8 13 7 13 15 10 13 8 13 4 8 D 4 3 7 C 2 2 4 B 3 0 3 Start 0 0 0 A 2 20 42 84 20 41 00 Dr. Mahmoud Abbas Mahmoud
  39. 39. Critical Path A – C – E – G – H Completion Time = 15 weeks Dr. Mahmoud Abbas Mahmoud
  40. 40. Dr. Mahmoud Al-Naimi

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