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Easy steps to network construction and critical path determination

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Dr. Mahmoud Al-Naimi

Project Management, Easy steps to network construction and critical path determination

Engineering
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Easy Steps to Network Construction and Critical Path Determination Project Management Dr. Mahmoud Abbas Mahmoud Asst. Prof. 2016
Easy Steps to Network Construction and Critical Path Determination Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG Example: For the activities given in the table: i) Draw the (AOA) network diagram. ii) Find the critical activities. iii) Find the critical path (CP). iv) Find project completion time. We will illustrate these steps with the following Example. Dr. Mahmoud Abbas Mahmoud
Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG
Note: Practically, nodes numbering can be start by (0) or (1). Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 1
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G ???????But (G) depend on both (D) and (E)
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G Use Dummy !
A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G Dummy
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 (AOA) Network Drawing is Completed
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Critical Path Calculations
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass:
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass: Calculating the Earliest Start Time (ES):
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass: Calculating the Earliest Start Time (ES): Earliest Start Time (ES)j=Max [ (ES)i + Dij ]
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 Earliest Start Time (ES) for Start Event = (0) NOTE: (ES) for any Start Event = (0)
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 10[0+10]= 10 0
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 Max [(0+7) , (10+5)] = Max [7,15]= 15
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 [10+ 6]= 16
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 Max [(15+9) , (16+0)] = Max [24,16]= 24
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Max [(16+8) , (24+12)] = Max [24,36]= 36
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Therefore, Project completion time is: 36 weeks
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Backward Pass:
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36 Calculating the Latest Completion Time (LC):
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36 Calculating the Latest Completion Time (LC): Latest Completion Time (LC)i=Min [ (LC)j - Dij ]
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 24 36 36 36 – 12 = 24
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 24 16 24 24 36 36 Min [(36-8),(24-0)= Min[28,24] = 24
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 15 24 16 24 24 36 36 24 – 9 = 15
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 10 15 15 24 16 24 24 36 36 Min [(24-6),(15-5)= Min[18,10] = 10
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 0 10 10 15 15 24 16 24 24 36 36 Min [(15-7),(10-10)= Min[8, 0] = 0
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36
A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 How to find the Critical Activities and the Critical Path ???
Dr. Mahmoud Abbas Mahmoud Remember that only a critical activity can have a Zero Total Float (TF)
Dr. Mahmoud Abbas Mahmoud Therefore, we will calculate the Total Floats for all activities and each activity has a ZERO Total Float (TF) will be a critical activity.
Total Float (TF) calculations Dr. Mahmoud Abbas Mahmoud TFij = (LC)j – (ES)i – Dij A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity A B C D E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A B C D E F G Dummy For activity A (1, 2) TF = 10 – 0 – 10 = 0*
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A B C D E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B C D E F G Dummy For activity B (1, 3) TF = 15 – 0 – 7 = 8
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B C D E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C D E F G Dummy For activity C (2, 3) TF = 15 – 10 – 5 = 0*
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C D E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D E F G Dummy For activity D (3, 4) TF = 24 – 10 – 6 = 8
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E F G Dummy For activity E (3, 5) TF = 24 – 15 – 9 = 0*
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F G Dummy For activity F (4, 6) TF = 36 – 16 – 8 = 12
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G Dummy For activity G (5, 6) TF = 36 – 24 – 12 = 0*
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy For Dummy activity (4, 5) TF = 24 – 16 – 0 = 8
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy
Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy The Critical Activities are: (A, C, E, G) Critical Path is: (A C E G) Project completion time is: 36 weeks
Dr. Mahmoud Al-Naimi

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Easy steps to network construction and critical path determination

  • 1. Easy Steps to Network Construction and Critical Path Determination Project Management Dr. Mahmoud Abbas Mahmoud Asst. Prof. 2016
  • 2. Easy Steps to Network Construction and Critical Path Determination Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG Example: For the activities given in the table: i) Draw the (AOA) network diagram. ii) Find the critical activities. iii) Find the critical path (CP). iv) Find project completion time. We will illustrate these steps with the following Example. Dr. Mahmoud Abbas Mahmoud
  • 3. Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG
  • 4. Note: Practically, nodes numbering can be start by (0) or (1). Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 1
  • 5. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG
  • 6. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2
  • 7. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B
  • 8. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3
  • 9. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C
  • 10. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D
  • 11. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4
  • 12. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E
  • 13. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5
  • 14. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F
  • 15. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6
  • 16. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G
  • 17. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G ???????But (G) depend on both (D) and (E)
  • 18. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G Use Dummy !
  • 19. A 1 Dr. Mahmoud Abbas Mahmoud Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 2 B 3 C D 4 E 5 F 6 G Dummy
  • 20. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0
  • 21. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 (AOA) Network Drawing is Completed
  • 22. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Critical Path Calculations
  • 23. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass:
  • 24. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass: Calculating the Earliest Start Time (ES):
  • 25. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 Forward Pass: Calculating the Earliest Start Time (ES): Earliest Start Time (ES)j=Max [ (ES)i + Dij ]
  • 26. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 Earliest Start Time (ES) for Start Event = (0) NOTE: (ES) for any Start Event = (0)
  • 27. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0
  • 28. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 10[0+10]= 10 0
  • 29. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 Max [(0+7) , (10+5)] = Max [7,15]= 15
  • 30. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 [10+ 6]= 16
  • 31. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 Max [(15+9) , (16+0)] = Max [24,16]= 24
  • 32. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Max [(16+8) , (24+12)] = Max [24,36]= 36
  • 33. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Therefore, Project completion time is: 36 weeks
  • 34. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 Backward Pass:
  • 35. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36
  • 36. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36
  • 37. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36 Calculating the Latest Completion Time (LC):
  • 38. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 36 36 Calculating the Latest Completion Time (LC): Latest Completion Time (LC)i=Min [ (LC)j - Dij ]
  • 39. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 16 24 24 36 36 36 – 12 = 24
  • 40. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 24 16 24 24 36 36 Min [(36-8),(24-0)= Min[28,24] = 24
  • 41. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 15 15 24 16 24 24 36 36 24 – 9 = 15
  • 42. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 10 10 15 15 24 16 24 24 36 36 Min [(24-6),(15-5)= Min[18,10] = 10
  • 43. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 Duration (week) Preceding Activity Activity 10-A 7-B 5AC 6AD 9B, CE 8DF 12D, EG 0 0 0 10 10 15 15 24 16 24 24 36 36 Min [(15-7),(10-10)= Min[8, 0] = 0
  • 44. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36
  • 45. A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 Dr. Mahmoud Abbas Mahmoud G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 How to find the Critical Activities and the Critical Path ???
  • 46. Dr. Mahmoud Abbas Mahmoud Remember that only a critical activity can have a Zero Total Float (TF)
  • 47. Dr. Mahmoud Abbas Mahmoud Therefore, we will calculate the Total Floats for all activities and each activity has a ZERO Total Float (TF) will be a critical activity.
  • 48. Total Float (TF) calculations Dr. Mahmoud Abbas Mahmoud TFij = (LC)j – (ES)i – Dij A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36
  • 49. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity A B C D E F G Dummy
  • 50. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A B C D E F G Dummy For activity A (1, 2) TF = 10 – 0 – 10 = 0*
  • 51. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A B C D E F G Dummy
  • 52. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B C D E F G Dummy For activity B (1, 3) TF = 15 – 0 – 7 = 8
  • 53. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B C D E F G Dummy
  • 54. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C D E F G Dummy For activity C (2, 3) TF = 15 – 10 – 5 = 0*
  • 55. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C D E F G Dummy
  • 56. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D E F G Dummy For activity D (3, 4) TF = 24 – 10 – 6 = 8
  • 57. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D E F G Dummy
  • 58. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E F G Dummy For activity E (3, 5) TF = 24 – 15 – 9 = 0*
  • 59. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E F G Dummy
  • 60. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F G Dummy For activity F (4, 6) TF = 36 – 16 – 8 = 12
  • 61. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F G Dummy
  • 62. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G Dummy For activity G (5, 6) TF = 36 – 24 – 12 = 0*
  • 63. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G Dummy
  • 64. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy For Dummy activity (4, 5) TF = 24 – 16 – 0 = 8
  • 65. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy
  • 66. Dr. Mahmoud Abbas Mahmoud A= 10 B= 7 1 2 3 C= 5 D= 6 E= 9 4 5 6Dummy F= 8 G= 12 0 0 0 10 10 15 15 24 16 24 24 36 36 CriticalTotal FloatActivity Yes0A No8B Yes0C No8D Yes0E No12F Yes0G No8Dummy The Critical Activities are: (A, C, E, G) Critical Path is: (A C E G) Project completion time is: 36 weeks