1. Project Scheduling: Networks, Duration estimation, and Critical Path

2. Project Scheduling Terms Successors Predecessors Network diagram Serial activities Concurrent activities E D C B A F

3. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-3 Project Scheduling Terms E D C B A F Merge activities Burst activities Node Path Critical Path

4. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-4 Network Diagrams Show interdependence Facilitate communication Help schedule resources Identify critical activities Determine project completion Show start & finish dates

5. AOA vs. AON The same mini-project is shown with activities on arrow… C E D B F E C D B F …and activities on node.

6. Node Labels Early Start Activity Float Activity Descriptor Late Start ID Number Activity Duration Late Finish Early Finish

7. Duration Estimation Methods Past experience Expert opinion Mathematical derivation – Beta distribution –Most likely (m) –Most pessimistic (b) –Most optimistic (a)

8. TaskPredecessoramb A--7815 BA131619 CA141822 DB, C121416 ED1413 FD61014 GF, E111419 1.Sketch the network described in the table. 2.Determine the expected duration and variance of each activity.

9. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-9 Constructing the Critical Path Forward pass – an additive move through the network from start to finish Backward pass – a subtractive move through the network from finish to start Critical path – the longest path from end to end which determines the shortest project length

10. Rules for Forward/Backward Pass Forward Pass Rules (ES & EF) –ES + Duration = EF –EF of predecessor = ES of successor –Largest preceding EF at a merge point becomes EF for successor Backward Pass Rules (LS & LF) –LF – Duration = LS –LS of successor = LF of predecessor –Smallest succeeding LS at a burst point becomes LF for predecessor

11. TaskPredecessorTime A--4 BA9 CA11 DB5 EB3 FC7 GD, F3 HE, G2 KH1 1.Sketch the network described in the table. 2.Determine the ES, LS, EF, LF, and slack of each activity

12. Laddering Activities Project ABC can be completed more efficiently if subtasks are used A(3)B(6)C(9) ABC=18 days Laddered ABC=12 days A 1 (1)A 2 (1)A 3 (1) B 1 (2)B 2 (2)B 3 (2) C 1 (3)C 2 (3)C 3 (3)

13. Hammock Activities Used as summaries for subsets of activities 0 A5 0 55 5 B15 5 1015 15 C18 15 318 0 Hammock18 01818 Useful with a complex project or one that has a shared budget

14. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-14 Reducing the Critical Path Eliminate tasks on the CP Convert serial paths to parallel when possible Overlap sequential tasks Shorten the duration on critical path tasks Shorten –early tasks –longest tasks –easiest tasks –tasks that cost the least to speed up

15. Chapter 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-15

16. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-16 Lags in Precedence Relationships The logical relationship between the start and finish of one activity and the start and finish of another activity. Four logical relationships between tasks 1.Finish to Start 2.Finish to Finish 3.Start to Start 4.Start to Finish

17. Finish to Start Lag Most common type of sequencing Shown on the line joining the modes –Added during forward pass –Subtracted during backward pass 0 A 6 Spec Design 6 6 B 11 Design Check 5 15 C 22 Blueprinting 7 Lag 4 This lag is not the same as activity slack

18. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-18 Finish to Finish Lag Two activities share a similar completion point –The mechanical inspection cannot happen until wiring, plumbing, and HVAC installation are complete 10 B 16 Plumbing 6 16 C 24 HVAC 5 24 D 25 Inspection 1 15 A 21 Wiring 6 Lag 3

19. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-19 Start to Start Lag Logic must be maintained by both forward and backward pass 31 B 32 Plumbing 1 33 C 36 HVAC 5 36 D 37 Inspection 1 30 A 36 Wiring 6 Lag 3

20. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-20 Start to Finish Lag Least common type of lag relationship Successor’s finish dependent on predecessor’s start 22 B 28 Plumbing 6 28 C 33 HVAC 5 33 D 34 Inspection 1 30 A 36 Wiring 6 Lag 3

21. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-21 Gantt Charts Establish a time-phased network Can be used as a tracking tool Benefits of Gantt charts 1.Easy to create and comprehend 2.Identify the schedule baseline network 3.Allow for updating and control 4.Identify resource needs

22. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-22 Create a Gantt chart based on the activities listed in the table. TaskTimePred A8-- B5A C8A D4B,CB,C E5D

23. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-23 Crashing The process of accelerating a project Principal methods for crashing  Improving existing resources’ productivity  Changing work methods  Increasing the quantity of resources

24. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-24 Managerial Considerations Determine activity fixed and variable costs The crash point is the fully expedited activity Optimize time-cost tradeoffs Shorten activities on the critical path Cease crashing when –the target completion time is reached –the crashing cost exceeds the penalty cost

25. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-25 What is the lowest cost to complete this project in 52 weeks? Times are in weeks and costs in dollars. Plot the AON & AOA networks and the GANTT chart. ActivityPredNormal Time Min Time Normal Cost Crash Cost A--1495001500 BA5210001600 CA10820002900 DB, C8510002500 ED661600 FD9615003000 GE, F746001800 HG151116003600

26. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-26 Activity on Arrow Networks Activities represented by arrows Widely used in construction Event nodes easy to flag Forward and backward pass logic similar to AON Two activities may not begin and end at common nodes Dummy activities may be required

27. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-27 1.Use AOA to sketch the network that represents the project as described in the table. 2.Calculate early and late event times for all activities. ActivityTimePredActivityTimePred A4--F15E B2AG4E C10AH7D,F,G D3BI11H E15B,C

28. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-28 Activity on Arrow Network AH F D E C B I G

29. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-29 Controversies in the Use of Networks  Networks can be too complex  Poor network construction creates problems  Networks may be used inappropriately  When employing subcontractors –The master network must be available to them –All sub-networks must use common methods  Positive bias exists in PERT networks