The Network Diagram and Critical Path

1. DEVELOPMENT OF THE NETWORK DIAGRAM AND CRITICAL PATH Acknowledgement - A Practical Introduction to Management Science 4 th edition

2. BUILDING A HOUSE THE NETWORK DIAGRAM IS ABOUT CREATING RELATIONSHIPSBETWEEN ACTIVITIES

3. BUILDING A HOUSE RELATIONSHIPS ARE ALSO REFERRED TO AS DEPENDENCIES – THE MOST BASIC IS “FINISH TO START”

4. BUILDING A HOUSE THUS THE BASIC QUESTION IS WHICH ACTIVITIES MUST BE FINISHED BEFORE WHICH ACTIVITIES CAN START

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. 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. 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. 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. Task 1 Is to Create These Dependencies By Indicating the Predecessors For Each Activity

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. 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. Task 2 TEST THE LOGIC BY CONSTRUCTING THE NETWORK DIAGRAM

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

15. Task 3 DETERMINE DURATIONS FOR EACH ACTIVITY

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. Task 4 FILL EACH NODE AS FOLLOWS

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. Task 5 CALCULATE THE FORWARD AND THE BACKWARD PASS

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

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. Task 6 DETERMINE THE CRITICAL PATH

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