Mitigating Risk in Schedules
                      Quantitative Methods in Project Management




                        ...
About Confidence

• Likelihood an event will occur within a range
• A number from 0 to 1
• Cumulative summation of probabi...
Confidence ―S‖ Curve




                                                                              1
                 ...
Confidence ―S‖ Curve


                        1. 68% confidence: value between -1 to +1
                        2. 16% co...
Generating Confidence


                                             Probability Distribution

                           ...
Sum & Plot area increments



                                                              F(v) = 1 is the limiting value...
Schedule Network Architecture 1




                                                               What is to be expected ...
Schedule Network Architecture 1



                                                                                       ...
Schedule Network Architecture 1




                                                                     0.3

            ...
Monte Carlo simulation


       Date 1/1                                    1/21
                                   1.1
  ...
Monte Carlo simulation


                       Date 1/1                                    1/21
                         ...
Monte Carlo simulation


                       Date 1/1                                    1/21
                         ...
Budgets?


• Are the effects on budget totals any different when adding up a
  string of $budgets from the WBS work packag...
Schedule Network Architecture 2




                                                                  What happens at the ...
Schedule Network Architecture 2




                                                          What happens at the mileston...
Schedule Network Architecture 2


                                         Durations, d1 and d2


                        ...
Schedule Network Architecture 2


                                         Durations, d1 and d2


                        ...
Schedule Network Architecture 2


                                   Durations, d1 and d2


                              ...
Monte Carlo Simulation



                                      1/21                                                      ...
Monte Carlo Simulation



                                                                                              3/...
Event Chain Methodology


• Extension of Monte Carlo simulation method.
• Events occur at probabilistic nodes
• Probabilis...
Build a path

                80 days for the path shown
                Task Duration is shown in days (#):

            ...
Build a network schedule

   A(12)        Every network at least one Critical Path
                CP = 80 days; Additiona...
Critical path shifts with variation

   B(11)        Critical path is 81.5 days
                Former path at 50%; new pa...
Critical path shifts with variation

                Three milestones will shift the END & change CP probabilities


     ...
―Critical Chain‖ buffers uncertainty


                      10 days                                                      ...
―Critical Chain‖ buffers uncertainty
                                                              1           2

        ...
Resources on the CP



            Rule # 1: CP work begins at project beginning

        Task 1                  20d     ...
Resources on the CP



            Rule # 2: Resource CP first and then level

        Task 1              Mary 20d       ...
CP responds to constraints



            Rule # 3: Reorganize the network logic

                                        ...
Resource consequences


• Resource dependencies
  lengthen the schedule
• In fact, any loss of
  independence from any
  c...
Project manager’s mission:
To defeat an unfavorable forecast and deliver
customer value, taking reasonable risks to do so
...
Graphic Earned Schedule, ES




Value
Cumulative


                                                                 ES Var...
Graphic Earned Schedule, ES

                   • ES will never be 0 for a late project
                   • EV schedule v...
What‘s been learned?


• Confidence expresses probability over a range
• Confidence is based on the cumulative probability...
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Quantitative methods schedule

  1. 1. Mitigating Risk in Schedules Quantitative Methods in Project Management Produced by Square Peg Consulting, LLC John C. Goodpasture Managing Principal www.sqpegconsulting.com Copyright 2010, John C Goodpasture, All Rights Reserved 1
  2. 2. About Confidence • Likelihood an event will occur within a range • A number from 0 to 1 • Cumulative summation of probabilities within the range Copyright 2010, John C Goodpasture, All Rights Reserved
  3. 3. Confidence ―S‖ Curve 1 Cumulative Probability 0.75 0.5 0.25 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Normalized value Value / Standard deviation, σ Normalized cumulative probability from ‗bell‘ curve Copyright 2010, John C Goodpasture, All Rights Reserved
  4. 4. Confidence ―S‖ Curve 1. 68% confidence: value between -1 to +1 2. 16% confidence: value > 1 3. 84% confidence: value < 1 2 1 Cumulative Probability 0.75 0.5 1 0.25 0 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 3 1 2 Copyright 2010, John C Goodpasture, All Rights Reserved
  5. 5. Generating Confidence Probability Distribution f(v) Area = Height (probability) X Probability p f(v) width (Δ Value) Δ value 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Normalized random variable value Calculate each ―Area increment‖ Δ value x p Copyright 2010, John C Goodpasture, All Rights Reserved
  6. 6. Sum & Plot area increments F(v) = 1 is the limiting value f(v)Δv F(v) Area increments summed Value F(v) is the area under the f(v) curve Copyright 2010, John C Goodpasture, All Rights Reserved
  7. 7. Schedule Network Architecture 1 What is to be expected at the milestone? 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  8. 8. Schedule Network Architecture 1 EV 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 7 8 9 10 11 12 Convolved task probabilities 0.45 0.4 0.35 0.3 EV 0.25 0.2 EVmilestone = Sum (EV in tandem) 0.15 0.1 0.05 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  9. 9. Schedule Network Architecture 1 0.3 0.25 0.2 0.15 0.1 0.05 0 1.2 1 2 3 4 5 6 7 8 9 10 11 12 1 0.8 0.6 1.2 0.4 1 0.2 0.8 0 0.6 1 2 3 4 5 6 0.4 0.2 0 Value = 1 2 3 4 5 6 7 8 9 10 11 12 Sum values at a constant confidence Copyright 2010, John C Goodpasture, All Rights Reserved
  10. 10. Monte Carlo simulation Date 1/1 1/21 1.1 1.2 2/12 1.3 3/15 12 weeks, 60 work days 1.4 3/25 Risk Parameters for each Task: • Risk distribution: Triangular • Most optimistic: -10% of ML duration • Most pessimistic: +25% of ML duration • ML finish dates shown Copyright 2010, John C Goodpasture, All Rights Reserved
  11. 11. Monte Carlo simulation Date 1/1 1/21 1.1 1.2 2/12 1.3 3/15 Includes effects of non- 1.4 3/25 working days 10:30:27 PM Date: 3/9/99 Name: Task 1.4 170 1.0 1.0 Completion Std Deviation: 2.4d Cumulative Probability 153 0.9 Each bar represents 1d. 136 0.8 119 0.7 102 0.6 Completion Probability Table Sample Count 85 0.5 0.5 Prob Date Prob Date 0.05 3/25/99 0.55 3/31/99 68 0.4 0.10 3/25/99 0.60 3/31/99 51 0.3 0.15 3/26/99 0.65 4/1/99 34 0.2 0.20 3/26/99 0.70 4/1/99 0.25 3/29/99 0.75 4/1/99 17 0.1 0.30 3/29/99 0.80 4/2/99 3/23/99 3/31/99 4/9/99 0.35 3/29/99 0.85 4/2/99 3/23 3/31 4/9 0.40 3/30/99 0.90 4/5/99 0.45 3/30/99 0.95 4/6/99 Completion Date range 0.50 3/30/99 1.00 4/9/99 Copyright 2010, John C Goodpasture, All Rights Reserved
  12. 12. Monte Carlo simulation Date 1/1 1/21 1.1 1.2 2/12 1.3 3/15 1.4 3/25 Date: 3/9/99 10:30:27 PM Name: Task 1.4 170 1.0 1.0 Cumulative Probability 153 0.9 136 0.8 Risk Evaluation: 3/25 CPM date is 119 0.7 about 10% probable 102 0.6 Sample Count 85 0.5 0.5 68 0.4 51 0.3 34 0.2 17 0.1 3/23/99 3/31/99 3/31 4/9/99 3/23 4/9 Completion Date range Copyright 2010, John C Goodpasture, All Rights Reserved
  13. 13. Budgets? • Are the effects on budget totals any different when adding up a string of $budgets from the WBS work packages? Copyright 2010, John C Goodpasture, All Rights Reserved
  14. 14. Schedule Network Architecture 2 What happens at the milestone? 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  15. 15. Schedule Network Architecture 2 What happens at the milestone? Lots of combinations—36 possible outcomes 0.2 0.18 0.16 0.14 0.12 0.1 Series1 0.08 0.06 0.04 0.02 0 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 Duration value ‗12‘ combo  milestone value could be 4 or 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  16. 16. Schedule Network Architecture 2 Durations, d1 and d2 Milestone, m What happens at the milestone? •Confidence at the milestone is the product of the confidences of the joining paths 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  17. 17. Schedule Network Architecture 2 Durations, d1 and d2 Milestone, m What happens at the milestone? Confidence degrades Shift right to recover confidence 1.2 1 0.8 1.2 0.6 1 0.8 0.4 0.6 0.2 0.4 0 0.2 1 2 3 4 5 6 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  18. 18. Schedule Network Architecture 2 Durations, d1 and d2 Milestone, m What happens at the milestone? Probability ‗center of gravity‘ shifts right EV increases from 3.6 to 4.2 Critical path may change 0.6 0.5 EV 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 Copyright 2010, John C Goodpasture, All Rights Reserved
  19. 19. Monte Carlo Simulation 1/21 3/15 1/1 2/12 3/25 3/15 1/21 2/12 Date: 3/9/99 10:30:27 PM 3/25 Name: Task 1.4 170 1.0 1.0 • Milestone distribution for each Cumulative Probability 153 0.9 136 0.8 119 102 0.7 0.6 independent path Sample Count 85 0.5 0.5 • 50% confidence of 3/30 completion 68 0.4 51 0.3 34 0.2 17 0.1 3/23/99 3/31/99 3/31 4/9/99 3/23 4/9 Completion Date range Copyright 2010, John C Goodpasture, All Rights Reserved
  20. 20. Monte Carlo Simulation 3/15 3/25 Probability of 3/30 = Join independent 0.5 x 0.5 = 0.25, or less 3/15 paths at milestone 3/25 Date: 3/8/99 9:31:06 PM Number of Samples: 2000 Unique ID: 12 Name: Finish Milestone 1.0 Completion Probability Table 0.9 Cumulative Probability Prob Date Prob Date 0.8 0.05 3/29/99 0.55 4/1/99 0.7 0.10 3/29/99 0.60 4/1/99 0.15 3/30/99 0.65 4/2/99 0.6 0.20 3/30/99 0.70 4/2/99 0.5 0.25 3/30/99 0.75 4/2/99 0.4 0.30 3/31/99 0.80 4/2/99 0.35 3/31/99 0.85 4/5/99 0.3 0.40 3/31/99 0.90 4/5/99 0.2 0.45 3/31/99 0.95 4/6/99 0.1 0.50 4/1/99 1.00 4/12/99 3/24/99 4/1/99 4/12/99 Completion Date Copyright 2010, John C Goodpasture, All Rights Reserved
  21. 21. Event Chain Methodology • Extension of Monte Carlo simulation method. • Events occur at probabilistic nodes • Probabilistic nodes can be in the middle of the task and lead to task delay, restart, cancellation • Events can cause other events and generate event chains p = 0.2 Probabilistic node Alternative p = 0.8 Baseline outcome Copyright 2010, John C Goodpasture, All Rights Reserved
  22. 22. Build a path 80 days for the path shown Task Duration is shown in days (#): C(15) G(20) I(8) A(12) Float = 25d D(21) J(13) L(12) H(3) O(9) Start End E(15) K(21) M(14) B(11) Float = 33d F(18) N(20) Copyright 2010, John C Goodpasture, All Rights Reserved
  23. 23. Build a network schedule A(12) Every network at least one Critical Path CP = 80 days; Additional paths are 49, 57, or 63, 73 days < 82 days C(15) G(20) I(8) A(12) Float = 25d D(21) J(13) L(12) H(3) O(9) Start End E(15) K(21) M(14) B(11) Float = 33d F(18) N(20) Copyright 2010, John C Goodpasture, All Rights Reserved
  24. 24. Critical path shifts with variation B(11) Critical path is 81.5 days Former path at 50%; new path at 80% C(15) G(20) I(8) A(12) Float = 25d D(21) J(13) L(12) H(3) O(10) Start End E(17) K(23) M(16) B(12) Float = 33d F(18) N(20) Copyright 2010, John C Goodpasture, All Rights Reserved
  25. 25. Critical path shifts with variation Three milestones will shift the END & change CP probabilities C(15) G(20) I(8) A(12) Float = 25d D(21) J(13) L(12) H(3) O(10) Start End E(17) K(23) M(16) B(12) Float = 33d F(18) N(20) Copyright 2010, John C Goodpasture, All Rights Reserved
  26. 26. ―Critical Chain‖ buffers uncertainty 10 days Project Buffer Project buffer 15 days 10 days protects final milestone from variation Task on the critical path Critical chain is a concept developed in the book Critical Chain (Goldratt, 1997) Copyright 2010, John C Goodpasture, All Rights Reserved
  27. 27. ―Critical Chain‖ buffers uncertainty 1 2 10 days 11 days 12 days Buffer Project Buffer Path buffer mitigates 15 days 10 days “shift right” at the milestone of joining path Task on the critical path Task with risky duration, not on critical path Critical chain is a concept developed in the book Critical Chain (Goldratt, 1997) Copyright 2010, John C Goodpasture, All Rights Reserved
  28. 28. Resources on the CP Rule # 1: CP work begins at project beginning Task 1 20d 30d Critical Path = 50d Task 2 5d 15d Copyright 2010, John C Goodpasture, All Rights Reserved
  29. 29. Resources on the CP Rule # 2: Resource CP first and then level Task 1 Mary 20d John 30d Critical Path = 65d Mary John 15d Task 2 5d Float Copyright 2010, John C Goodpasture, All Rights Reserved
  30. 30. CP responds to constraints Rule # 3: Reorganize the network logic Mary 20d John 30d Critical Path = 55d Task 1 Mary Task 2 John 15d 5d Work does not begin first on the CP Copyright 2010, John C Goodpasture, All Rights Reserved
  31. 31. Resource consequences • Resource dependencies lengthen the schedule • In fact, any loss of independence from any cause will lengthen the schedule! • Resource constraints may require work begin off the CP Copyright 2010, John C Goodpasture, All Rights Reserved
  32. 32. Project manager’s mission: To defeat an unfavorable forecast and deliver customer value, taking reasonable risks to do so Copyright 2010, John C Goodpasture, All Rights Reserved
  33. 33. Graphic Earned Schedule, ES Value Cumulative ES Variance Schedule AT = actual time ES = earned schedule Copyright 2010, John C Goodpasture, All Rights Reserved
  34. 34. Graphic Earned Schedule, ES • ES will never be 0 for a late project • EV schedule variance, EV – PV, will always be 0 for a completed project EV = PV Value Cumulative ES Variance Schedule AT ES Copyright 2010, John C Goodpasture, All Rights Reserved
  35. 35. What‘s been learned? • Confidence expresses probability over a range • Confidence is based on the cumulative probability, a.k.a. the ‗area under the curve‘ • Confidence is constant in tandem strings, whether budget or schedule, but degrades rapidly at a parallel join • Monte Carlo simulations give results very close to calculated ‗ideals‘ • Earned schedule will not have a 0 variance when all value is earned Copyright 2010, John C Goodpasture, All Rights Reserved

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