Project Scheduling: Lagging, Crashing and Activity Networks

1. Project Scheduling: Lagging, Crashing and Activity Networks Chapter 10

2. Learning Goals • Apply lag relationships to project activities. • Construct and comprehend Gantt charts. • Understand the trade-offs required in the decision to crash project activities. • Develop activity networks using Activity-on-Arrow techniques. • Understand the differences in AON and AOA and recognize the advantages and disadvantages of each technique.

3. 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 • Finish to Start • Finish to Finish • Start to Start • Start to Finish

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

5. 30 R 36 Wiring 6 39 U 45 Interior Const. 6 31 S 33 Plumbing 2 33 T 39 HVAC 3 Finish-to-Finish (FF) Lag • Two activities share a similar completion point • The interior construction cannot happen until wiring, plumbing, and HVAC installation are complete Lag 3 days

6. 30R 36 Wiring 6 Lag 3 36 U 42 Inspection 6 33T 36 HVAC 3 31 S 33 Plumbing 2 Start-to-Start (SS) Lag • Often two or more activities must start at the same time • Logic must be maintained by both forward and backward pass

7. Lag 3 Start-to-Finish (SF) Lag • Least common type of lag relationship • Successor’s finish dependent on predecessor’s start 30R 36 Wiring 6 22 S 28 Plumbing 6 33 U 34 Inspection 1 28 T 33 HVAC 5

8. Gantt Charts • A graphical representation of the project schedule that illustrates how work flows over time • Shows activity start and end dates and durations • Links project activities to a project schedule baseline • Can be used as a tracking tool Benefits of Gantt charts • Easy to create, read, and comprehend • Identify the project network and schedule baseline • Allows for updating and control • Useful to identify resource needs and assigning resources to tasks

9. Example • Create a Gantt chart based on the activities listed in the table.

10. Gantt Chart Example from MSExcel http://office.microsoft.com/en-us/excel/HA102382531033.aspx

11. Sample Tracking Gantt Chart With Critical Path A-C-D-F-H Critical path in red

12. Crashing Projects Accelerating a project by committing more resources. Principal options for crashing • Improving existing resources’ productivity • Changing work methods used • Increasing the quantity of resources

13. Crashing Projects – Under What Conditions? • The initial schedule may be too optimistic. • Market needs change and the project is in demand earlier than anticipated. • The project has slipped considerably behind schedule. • The contractual situation provides even more incentive to avoid schedule slippage.

14. Compute the crash cost per time period. If crash costs are linear over time: (Crash cost – Normal cost) (Normal time – Crash time) Crash cost per period = Steps in Project Crashing • Using current activity times, find the critical path and identify the critical activities.

15. Steps in Project Crashing • If there is only one critical path, then select the activity on this critical path that • can still be crashed, and • has the smallest crash cost per period. • If there is more than one critical path, then select one activity from each critical path such that • each selected activity can still be crashed, and • the total crash cost of all selected activities is the smallest. Note: the same activity may be common to more than one critical path.

16. Steps in Project Crashing • Update all activity times. • If the desired due date has been reached, stop. If not, return to Step 2.

17. Activity Cost Crash Point $34,000 — $33,000 — $32,000 — $31,000 — $30,000 — — Crash Cost – Normal Cost Normal Time – Crash Time Crash Cost/Wk = $34,000 – $30,000 3 – 1 Crash Cost = $4,000 2 Wks = = $2,000/Wk Normal Point Normal Cost | | | 1 2 3 Time (Weeks) Crash Time Normal Time Time-Cost Tradeoffs for Crashing Activities How far do you need to speed up the process?

18. Crashing Activities – An Example Formula Slope = crash cost – normal cost normal time – crash time Example – calculating the cost of crashing Suppose: Normal activity duration = 8 weeks Normal cost = $14,000 Crashed activity duration = 5 weeks Crashed cost = $23,000 The activity cost slope = 23,000 – 14,000 or, $9,000 = $3,000 per week 8 – 5 3

19. 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 crash cost exceeds the penalty cost

20. Crash Example

21. Crash Example • What is the lowest cost to complete this project in 53 weeks? Times are in weeks and costs in dollars.

22. Activity on Arrow (AOA) Networks • Activities represented by arrows • 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 Earliest Event Time (ES) Event label Latest Event Time (LF) Task Description Duration

23. Sample AOA Network Diagram Figure 10.18

24. Activity on Arrow (AOA) Network E B H A F C D K G

25. A comes before B, which comes before C A C (a) B A B C A A A and B must both be completed before C can start (b) C C B B B B and C cannot begin until A is completed B A (c) A C C A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA)

26. C and D cannot begin until both A and B are completed A C B A C (d) D B D C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA A C A C (e) Dummy activity B D B D A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA)

27. B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA. A B D B A Dummy activity C (f) C D A Comparison of AON and AOA Network Conventions Activity on Activity Activity on Node (AON) Meaning Arrow (AOA)

28. Discussion Questions • Please give examples of circumstances in which a project would employ lag relationships between activities using: • Finish to start • Finish to finish • Start to start • Start to finish • The advantage of Gantt Charts lies in their linkage to the project schedule baseline. Explain this concept. • What are the advantages in the use of Gantt charts over PERT diagrams? In what ways might PERT diagrams be advantageous? • Under what circumstances might you wish to crash a project?

29. Discussion Questions • In crashing a project, we routinely focus on those activities that lie on the critical path, not activities with slack time. Explain why this is the case. • What are some of the advantages in the use of AOA notation as opposed to AON? Under what circumstances does it seem better to apply AON methodology in network development? Explain the concept of a “dummy variable.” Why are they employed in AOA notation? Why is there no need to use dummy variables in an AON network? • Explain the concept of a “dummy variable.” Why are they employed in AOA notation? Why is there no need to use dummy variables in an AON network?