Quantitative methods schedule

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

―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

―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

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

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

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

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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Quantitative methods schedule

by John Goodpasture on May 04, 2010

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