2. 1 5. P RECEDENCE N ETWORK D EVELOPMENT AND A NALYSIS Objective: To understand the principles of developing precedence networks and using them as the basis for time analysis. Summary: 5.1 Basics of Precedence Network Development 5.2 Basic Time Analysis with Precedence Networks 5.3Delays, Including Lead and Lag Times, and Ladder Constructs.

3. 2 5.1 B ASICS OF P RECEDENCE N ETWORK D EVELOPMENT The basic tenets are: –representation of the activity as a node, and –the use of arrows to indicate dependencies. Advantage: –dependencies are simpler to represent, largely removing the need for dummy activities. Disadvantage: –the network cannot be graphically time scaled.

4. 3 Show activity on the node rather than activity on the arrow Fig. 5-1: Comparison of Alternative Representations of Activities (a) activity-on-the-arrow (b) precedence d A start event finish event early event time late event time A d early start time early finish time late start time late finish time

5. 4 Compare how dependencies are represented Fig. 5-2: Merging Activities (a) activity-on-the-arrow (b) precedence A B C A B C

6. 5 Fig. 5-3: Bursting Activities (a) activity-on-the-arrow (b) precedence A B C AB C

7. 6 Fig. 5-4: Merge-Burst Activities (a) activity-on-the-arrow (b) precedence A B D C ABDC

8. 7 Fig. 5-5: Activity D has Subset of Activity C’s Dependencies (a) activity-on-the-arrow (b) precedence A BC D dummy activity A B D C no dummy required

9. 8 5.2 B ASIC T IME A NALYSIS WITH P RECEDENCE N ETWORKS Foundation operation example: Network Structure: Original dummies not required. Dummies sometimes required to tie ends together.

10. 9 (a) activity-on-the-arrow (b) precedence (activity-on-the-node) Fig. 5-6: Foundation Operation 5 7 10 6 5 7 12 3 4 5 6 7 0 5 12 15 25 32 27 25 15 5 0 A B C D E F G ABCDEFGdummy 5 7 10 6 5 7 0 0 early finish = 0 + 5 5 512 515 1218 1525 30 2532 largest of 30 & 32 32 late start = 32 - 0 32 27 3225 2721 2515 8 5 smallest of 8 &5 50 FF TF IF 0 3 0 9 0 2 0 0 0 0 0 7 0 2 0 0 0 0 4 0 0 0

11. 10 5.3 D ELAYS, I NCLUDING L EAD AND L AG T IMES AND L ADDER C ONSTRUCTS Precedence networks provide a convenient mechanism for representing delays:

12. 11 Fig. 5-7: Delay Between the Finish of A and Start of B (a) activity-on-the-arrow (b) precedence A dummy   = delay B A  B

13. 12 Fig. 5-8: Lead Time (Delay Between the Start of A and Start of B) (a) activity-on-the-arrow (b) precedence A dummy   = delay B A  B Note the subtle difference in the logic: in (a), the delay is from the earliest A can start; in (b), the delay is from the actual time A starts; as a lead time, the precedence is more accurate.

14. 13 Fig. 5-9: Lag Time (Delay Between the Finish of A and Finish of B) (a) activity-on-the-arrow (b) precedence A dummy   = delay B A  B Note, the logic is identical.

15. 14 Fig. 5-10: Delay Between the Start of A and Finish of B (a) activity-on-the-arrow (b) precedence A dummy   = delay B A  B Note the subtle difference in the logic as for Fig. 5-8.

16. 15 Fig. 5-11: Ladder Construction (a) activity-on-the-arrow (b) precedence A   B   C ABC    

17. 16 Fig. 5-12: Time Calculations on Precedence Ladders add the lead time to the early start: 0+1 largest of 5 + 2 (via the lag) and 1 + 7 (through the activity) subtract the lag: 10 - 2 smallest of: 4 - 2 (via the lead) and 8 - 7 (through the activity) Total Floats are calculated as before: LF - ES - d Total Floats are calculated as before: LF - ES - d A C B 7 6 5 1 2 2 2 05 06 18 8 310 4 1 0 1 1 Total Float on a link: TF=LF(of link)–ES (of link)–d (of link) TF=4-1-2=0