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The Network Diagram and Critical Path

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The Network Diagram and Critical Path

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The Network Diagram and Critical Path

  1. 1. DEVELOPMENT OF THE NETWORK DIAGRAM AND CRITICAL PATH Acknowledgement - A Practical Introduction to Management Science 4 th edition
  2. 2. BUILDING A HOUSE THE NETWORK DIAGRAM IS ABOUT CREATING RELATIONSHIPSBETWEEN ACTIVITIES
  3. 3. BUILDING A HOUSE RELATIONSHIPS ARE ALSO REFERRED TO AS DEPENDENCIES – THE MOST BASIC IS “FINISH TO START”
  4. 4. BUILDING A HOUSE THUS THE BASIC QUESTION IS WHICH ACTIVITIES MUST BE FINISHED BEFORE WHICH ACTIVITIES CAN START
  5. 5. BUILDING A HOUSE THE USE OF AN ARROW (SPECIFICALLY IN THE NOTATION USED IN THIS EXAMPLE) SHOWS THIS RELATIONSHIP Activity A Must Be Finished Before B Can Start A B
  6. 6. BUILDING A HOUSE THE USE OF AN ARROW (SPECIFICALLY IN THE NOTATION USED IN THIS EXAMPLE) SHOWS THIS RELATIONSHIP But Activity E, F and G Don’t Have to Wait for Each Other D E F G Frame HVAC Rough Electric H Sheet Rock
  7. 7. BUILDING A HOUSE THE USE OF AN ARROW (SPECIFICALLY IN THE NOTATION USED IN THIS EXAMPLE) SHOWS THIS RELATIONSHIP Note That E, F and G Don’t Have to Start and Finish At The Same Time D E F G Frame HVAC Rough Electric H Sheet Rock
  8. 8. BUILDING A HOUSE THE USE OF AN ARROW (SPECIFICALLY IN THE NOTATION USED IN THIS EXAMPLE) SHOWS THIS RELATIONSHIP TheY However Need to Be Finished Before H Can Start D E F G Frame HVAC Rough Electric H Sheet Rock
  9. 9. Task 1 Is to Create These Dependencies By Indicating the Predecessors For Each Activity
  10. 10. SUMMARY OF ACTIVITIES Time Immediate Required Predecessor Activity Description (in days) Activities A Excavate B Lay foundation C Rough plumbing D Frame E Finish exterior F Install HVAC G Rough electric H Sheet rock I Install cabinets J Paint K Final plumbing L Final electric M Install flooring
  11. 11. SUMMARY OF ACTIVITIES Time Immediate Required Predecessor Activity Description (in days) Activities A Excavate -- B Lay foundation A C Rough plumbing B D Frame B E Finish exterior D F Install HVAC D G Rough electric D H Sheet rock C, E, F, G I Install cabinets H J Paint H K Final plumbing I L Final electric J M Install flooring K, L
  12. 12. Task 2 TEST THE LOGIC BY CONSTRUCTING THE NETWORK DIAGRAM
  13. 13. An Activity-On-Node (AON) Network Install Cabinets A B C D E F G H I J K L M Excavate Lay Foundation Rough Plumbing Frame Finish Exterior HVAC Rough Electric Sheet Rock Paint Final Plumbing Final Electric Install Flooring
  14. 14. Basic Rules for Constructing the Network Diagram <ul><li>Networks typically flow from left to right; </li></ul><ul><li>An activity cannot begin until all of its preceding activities are complete; </li></ul><ul><li>Arrows indicate precedence and flow and can cross over each other; </li></ul><ul><li>Identify each activity with a unique number ; this number must be greater than its predecessors; </li></ul><ul><li>Looping is not allowed; </li></ul><ul><li>Conditional statements are not allowed; </li></ul><ul><li>Use unique start and stop nodes. </li></ul>
  15. 15. Task 3 DETERMINE DURATIONS FOR EACH ACTIVITY
  16. 16. SUMMARY OF ACTIVITIES Time Immediate Required Predecessor Activity Description (in days) Activities A Excavate 3 -- B Lay foundation 4 A C Rough plumbing 3 B D Frame 10 B E Finish exterior 8 D F Install HVAC 4 D G Rough electric 6 D H Sheet rock 8 C, E, F, G I Install cabinets 5 H J Paint 5 H K Final plumbing 4 I L Final electric 2 J M Install flooring 4 K, L
  17. 17. Task 4 FILL EACH NODE AS FOLLOWS
  18. 18. Information Recorded for Each Node t i = DURATION required to perform activity i EST i = earliest possible start for activity i EFT i = earliest possible finish for activity i LST i = latest possible start for activity i LFT i = latest possible finish for activity i i t i EST i EFT i LST i LFT i
  19. 19. Task 5 CALCULATE THE FORWARD AND THE BACKWARD PASS
  20. 20. <ul><li>A Forward Pass through the network determines the earliest times each activity can start and finish – ALSO DETERMINE THE TOTAL DURATION OF THE PROJECT </li></ul><ul><li>A Backward Pass through the network determines the latest times each activity can start and finish without delaying completion of the project – WITH THIS INFORMATION WE CAN DETERMINE WHERE WE CAN DELAY ACTIVITIES (HAVE SLACK) AND WHERE WE CANNOT </li></ul>
  21. 21. The Forward Pass <ul><li>The earliest start (EST) for the initial activity in a project is “time zero”; </li></ul><ul><li>The EST of an activity is equal to the latest (or maximum) early finish of the activities directly preceding it; </li></ul><ul><li>The EFT of an activity is equal to its EST plus the duration required to perform the activity. </li></ul>
  22. 22. Results of the Forward Pass 25 33 8 33 38 5 0 3 3 7 17 10 3 7 4 Note: EST H =MAX(EFT C ,EFT E ,EFT F ,EFT G )=25 H E 17 25 8 J 33 38 5 I K 38 42 4 L 38 40 2 M 42 46 4 A F 17 21 4 G 17 23 6 D C 7 10 3 B
  23. 23. The Backward Pass <ul><li>The latest finish (LFT) for the final activity in a project is equal to its EFT as determined by the forward pass; </li></ul><ul><li>The LFT for any other activity is equal to the earliest (or minimum) LST of the activities directly following (or succeeding) it; </li></ul><ul><li>The LST of an activity is equal to its LFT minus the time required to perform the activity. </li></ul>
  24. 24. Results of the Backward Pass Note: LFT H =MIN(LST I ,LST J )=33 LFT D =MIN(LST E ,LST F ,LST G )=17 LFT B =MIN(LST C ,LST D )=7 25 33 8 0 3 3 7 17 10 3 7 4 0 3 3 7 22 25 17 7 17 25 21 25 25 19 25 33 33 38 35 40 42 42 40 42 46 38 3 H E 17 25 8 J 33 38 5 I 33 38 5 K 38 42 4 L 38 40 2 M 42 46 4 A F 17 21 4 G 17 23 6 D C 7 10 3 B
  25. 25. Task 6 DETERMINE THE CRITICAL PATH
  26. 26. Determining The Critical Path <ul><li>Critical activities have zero slack and cannot be delayed without delaying the completion of the project; </li></ul><ul><li>The slack for non-critical activities represents the amount of time by which the start of these activities can be delayed without delaying the completion of the entire project (assuming that all predecessor activities start at their earliest start times); </li></ul><ul><li>The longest path on the network; </li></ul><ul><li>Could also be those activities with the least slack. </li></ul>
  27. 27. The Critical Path Note: Slack = LST i -EST i and LFT i -EFT i 25 33 8 M 42 46 4 7 17 10 0 3 3 7 22 25 17 7 17 25 21 25 25 19 25 33 33 38 35 40 42 42 40 42 46 38 Slack=0 Slack=0 Slack=0 Slack=15 Slack=0 Slack=4 Slack=2 Slack=0 Slack=0 Slack=0 Slack=2 Slack=2 Slack=0 H E 17 25 8 J 33 38 5 I 33 38 5 K 38 42 4 L 38 40 2 A 0 3 3 F 17 21 4 G 17 23 6 D C 7 10 3 B 3 7 4

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