Managing Projects

1. Managing Projects

2. Project Management Questions • What activities are required to complete a project and in what sequence? • When should each activity be scheduled to begin and end? • Which activities are critical to completing the project on time? • What is the probability of meeting the project completion due date? • How should resources be allocated to activities?

3. Tennis Tournament Activities ID Activity Description Network Immediate Duration Node Predecessor (days) 1 Negotiate for Location A - 2 2 Contact Seeded Players B - 8 3 Plan Promotion C 1 3 4 Locate Officials D 3 2 5 Send RSVP Invitations E 3 10 6 Sign Player Contracts F 2,3 4 7 Purchase Balls and Trophies G 4 4 8 Negotiate Catering H 5,6 1 9 Prepare Location I 5,7 3 10 Tournament J 8,9 2

4. Notation for Critical Path Analysis Item Symbol Definition Activity duration t The expected duration of an activity Early start ES The earliest time an activity can begin if all previous activities are begun at their earliest times Early finish EF The earliest time an activity can be completed if it is started at its early start time Late start LS The latest time an activity can begin without delaying the completion of the project Late finish LF The latest time an activity can be completed if it is started at its latest start time Total slack TS The amount of time an activity can be delayed without delaying the completion of the project

5. Scheduling Formulas ES = EFpredecessor (max) (1) EF = ES + t (2) LF = LSsuccessor (min) (3) LS = LF - t (4) TS = LF - EF (5) TS = LS - ES (6) or

6. Tennis Tournament Activity on Node Diagram TS ES EF LS LF A2 C3 D2 G4 START E10 I3 J2 B8 F4 H1

7. Early Start Gantt Chart for Tennis Tournament ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required 2 2 2 2 2 3 3 3 3 3 3 2 1 1 1 2 1 1 1 1 Critical Path Activities Activities with Slack

8. Resource Leveled Schedule for Tennis Tournament ID Activity Days Day of Project Schedule 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A Negotiate for 2 Location B Contact Seeded 8 Players C Plan Promotion 3 D Locate Officials 2 E Send RSVP 10 Invitations F Sign Player 4 Contracts G Purchase Balls 4 and Trophies H Negotiate 1 Catering I Prepare Location 3 J Tournament 2 Personnel Required 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 1 1 Critical Path Activities Activities with Slack

9. Incorporating Uncertainty in Activity times F(D) P(D<A) = .01 P(D>B) = .01 TIME A M D B optimistic most pessimistic likely

10. Formulas for Beta Distribution of Activity Duration Expected Duration Variance Note: (B - A )= Range or

11. Activity Means and Variances for Tennis Tournament Activity A M B D V A 1 2 3 B 5 8 11 C 2 3 4 D 1 2 3 E 6 9 18 F 2 4 6 G 1 3 11 H 1 1 1 I 2 2 8 J 2 2 2

12. Uncertainly Analysis Assumptions 1. Use of Beta Distribution and Formulas For D and V 2. Activities Statistically Independent 3. Central Limit Theorem Applies ( Use “student t” if less than 30 activities on CP) 4. Use of Critical Path Activities Leading Into Event Node Result Project Completion Time Distribution is Normal With: For Critical Path Activities For Critical Path Activities

13. Completion Time Distribution for Tennis Tournament Critical Path ActivitiesDV A 2 4/36 C 3 4/36 E 10 144/36 I 3 36/36 J 20 = 20 188/36 = 5.2 =

14. Question What is the probability of an overrun if a 24 day completion time is promised? Days 24 P (Time > 24) = .5 - .4599 = .04 or 4%

15. Costs for Hypothetical Project Total Cost Indirect Cost • Cost Opportunity Cost Direct Cost (0,0) Duration of Project Schedule with Minimum Total Cost

16. Activity Cost-time Tradeoff Cost Crash C* Slope is cost to expedite per day Normal C D* D Activity Duration (Days)

17. Cost-Time Estimates for Tennis Tournament Time Estimate Direct Cost Expedite Cost Activity Normal Crash Normal Crash Slope A 2 1 5 15 B 8 6 22 30 C 3 2 10 13 D 2 1 11 17 E 10 6 20 40 F 4 3 8 15 G 4 3 9 10 H 1 1 10 10 I 3 2 8 10 J 2 1 12 20 Total 115

18. Progressive Crashing Project Activity Direct Indirect Opportunity Total Duration Crashed Cost Cost Cost Cost 20 Normal 115 45 8 168 19 41 6 18 37 4 17 33 2 16 29 0 15 25 -2 14 21 -4 13 17 -6 12 13 -8 Normal Duration After Crashing Activity Project Paths Duration A-C-D-G-I-J 16 A-C-E-I-J 20 A-C-E-H-J 18 A-C-F-H-J 12 B-F-H-J 15

19. Applying Theory of Constraints to Project Management • Why does activity safety time exist and is subsequently lost?1. Dependencies between activities cause delays to accumulate.2. The “student syndrome” procrastination phenomena.3. Multi-tasking muddles priorities. • The “Critical Chain” is the longest sequence of dependent activities and common resources. • Replacing safety time with buffers- Feeding buffer (FB) protects the critical chain from delays.- Project buffer (PB) is a safety time added to the end of the critical chain to protect the project completion date.- Resource buffer (RB) ensures that resources (e.g. rental equipment) are available to perform critical chain activities.

20. Accounting for Resource Contention Using Feeding Buffer NOTE: E and G cannot be performed simultaneously (same person) FB=7 G4 A2 C3 D2 START E10 I3 J2 FB=5 B8 F4 H1 Set feeding buffer (FB) to allow one day total slack Project duration based on Critical Chain = 24 days

21. Incorporating Project Buffer NOTE: Reduce by ½ all activity durations > 3 days to eliminate safety time FB=2 G2 A2 C3 D2 J2 PB=4 START E5 I3 FB=3 B4 F2 H1 Redefine Critical Chain = 17 days Reset feeding buffer (FB) values Project buffer (PB) = ½ (Original Critical Chain-Redefined Critical Chain)