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.

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.

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

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

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

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

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

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.

9 (a) activity-on-the-arrow (b) precedence (activity-on-the-node) Fig. 5-6: Foundation Operation A B C D E F G ABCDEFGdummy early finish = largest of 30 & late start = smallest of 8 &5 50 FF TF IF

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:

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

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.

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.

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.

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

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