Poor Man s Approach to Monte Carlo

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1 Poor Man s Approach to Monte Carlo Based on the PMI PMBOK Guide Fourth Edition 20 IPDI has been reviewed and approved as a provider of project management training by the Project Management Institute (PMI). 1 Version 4.1 Monte Carlo Answers the Question: What is the probability of this project being successful? Monte Carlo: Uses project models and simulations that translates the uncertainties specified at a detailed level into their potential impact on objectives that are expressed at the level of the total project Or, put another way: How likely are you to stay out of trouble on your project? 2 Version 4.1 Integrated Process Developers, Inc. Page: 1 For permissions and other rights

2 Monte Carlo Monte Carlo uses probability distributions based on historical information to predict the probability of potential outcomes The basic steps of the Monte Carlo technique 1. Determine the probability distribution for the variables being considered (duration and work/) 2. For each variable within its specific range, select a value randomly within the probability distribution. 3. Run a deterministic analysis using the combination of values selected for each one of the variables 4. Repeat steps 2 and 3 a statistically significant number of times to obtain the probability distribution of the result 3 Version 4.1 Monte Carlo A Example Based on a Project of 60 days Analysis Indicates 1 Standard Deviation = 10 days Probability of Occurrence 98% 84% 50% 16% 2.27% Project Duration 40 days -2σ 50 days 60 days 70 days 80 days -1σ u +1σ +2σ Adapted from PMBOK Guide Fourth Edition, pg. 300, Fig Version 4.1 Integrated Process Developers, Inc. Page: 2 For permissions and other rights

3 Monte Carlo A Example Based on a Project Estimate of $600,000 Analysis Indicates 1 Standard Deviation = $25,000 Probability of Occurrence 98% 84% 50% 16% 2% Project (,000) $550-2σ $575 $600 $625 $650-1σ u +1σ +2σ Adapted from PMBOK Guide Fourth Edition, pg. 300, Fig Version 4.1 vs. Duration Monte Carlo Analysis Pessimistic (98%) Most Likely (50%) Optimistic (2%) 6 Version 4.1 Integrated Process Developers, Inc. Page: 3 For permissions and other rights

4 vs. Duration Monte Carlo Analysis -2σ -1σ u +1σ +2σ $650 $625 $600 $575 $550 Project (,000) uncertainty Baseline without Risk Responses (Plan meets Scope Statement & Requirements +2σ Scope Reqmt. Project Plan with Risk Responses ( Contingencies and Buffers Scope Reqmt. +2σ uncertainty Project Duration (days) 40-2σ σ u +1σ +2σ 7 Version 4.1 vs. Duration Monte Carlo Analysis $650 $625 $600 $575 $550 Scope Reqmt. Project (,000) Scope Reqmt. Project Duration (days) Version 4.1 Integrated Process Developers, Inc. Page: 4 For permissions and other rights

5 vs. Duration Monte Carlo Analysis $650 $625 $600 $575 $550 Project (,000) uncertainty Baseline without Risk Responses (Plan meets Scope Statement & Requirements Scope Reqmt. Project Plan with Risk Responses ( Contingencies and Buffers Scope Reqmt. uncertainty Project Duration (days) Version 4.1 Poor Man s Monte Carlo Analysis B O = 6 M.L. = 10 P = 17 C O = 12 M.L. = 15 P = 20 A O = 3 M.L. = 5 P = 10 E O = 12 M.L. = 15 P = 20 D F G O = 4 M.L. = 10 P = 12 H O = 3 M.L. = 5 P = 9 O = 4 M.L. = 5 P = 8 O = 3 M.L. = 5 P = 12 A - Analytical Design B - Develop Design C - Build Parts D - Assemble Prototypes E - Determine Test Requirements F - Calibrate Test Equipment G - Perform & Analyze Tests H - Update Design 10 Version 4.1 Integrated Process Developers, Inc. Page: 5 For permissions and other rights

6 Poor Man s Monte Carlo Analysis A O ML P B C D E F G H Version 4.1 Poor Man s Work/ Monte Carlo Analysis A O ML P O ML P 4 hrs 6 hrs 8 hrs $ 400 $ 600 $ 800 B 5 hrs 6 hrs 10 hrs $ 500 $ 600 $ 1,000 C 1 hrs 2 hrs 3 hrs $ 100 $ 200 $ 300 D 3 hrs 4 hrs 8 hrs $ 300 $ 400 $ 800 E 4 hrs 6 hrs 8 hrs $ 400 $ 600 $ 800 F 6 hrs 7 hrs 11 hrs $ 600 $ 700 $ 1,100 G 5 hrs 8 hrs 20 hrs $ 500 $ 800 $ 2,000 H 4 hrs 6 hrs 8 hrs $ 400 $ 600 $ 800 TOTAL: 32 hrs 45 hrs 76 hrs $ 3,200 $ 4,500 $ 7, Version 4.1 Integrated Process Developers, Inc. Page: 6 For permissions and other rights

7 vs. Duration Monte Carlo Analysis Project $ Pessimistic Optimistic Duration (days) 13 Version 4.1 Most Likely Poor Man s Monte Carlo Analysis Probability distributions PERT Duration & Analysis Uses a weighted average estimate to calculate duration and estimates Differs from CPM in that it uses the mean instead of the most likely duration Number of Occurrences Most Likely (Used in original CPM calculations) Shorter (50%) Optimistic (Can achieve this dur. 10% of the time) Possible Durations PERT Weighted Average = (Optimistic + 4 X Most Likely + Pessimistic) 6 Beta Distribution Pessimistic (Can achieve this dur. 90% of the time) Longer 14 Version 4.1 Integrated Process Developers, Inc. Page: 7 For permissions and other rights

8 Poor Man s Monte Carlo Analysis Based on the three sets of project data points All Optimistic All Most Likely All Pessimistic X days Y days Z days $ A $ B $ C Calculate the project Mean and the Standard Deviation PERT Weighted Average (50% point) = (Optimistic + 4 X Most Likely + Pessimistic) 6 PERT Standard Deviation = (Pessimistic Optimistic) 6 15 Version 4.1 Example: 16 Version 4.1 Poor Man s Monte Carlo Analysis All Optimistic All Most Likely All Pessimistic 100 days 130 days 220 days $200,000 $280,000 $440,000 PERT Weighted Average Duration = (100+4* )/6 = 140 days (50% Prob.) PERT Standard Deviation = ( )/6 = 20 days PERT Weighted Average = (200+4* )/6 = $293,000 (50% Prob.) PERT Standard Deviation = ( )/6 = $40,000 Integrated Process Developers, Inc. Page: 8 For permissions and other rights

9 Poor Man s Monte Carlo Analysis Example, cont. Wt. Average Std Dev 140 days 20 days $293,000 $40,000 Probability -2 Std Dev -1 Std Dev Wt. Average +1 Std Dev +2 Std Dev 2% 16% 50% 84% 98% 100 days 120 days 140 days 160 days 180 days $213,000 $253,000 $293,000 $333,000 $373, Version 4.1 Exercise: Risk Game! RISK GAME by Integrated Process Developers, Inc. Ver 4.1 B: E: H: K: N: $ $ $ $ $ A: C: F: I: L: O: $ $ $ $ $ $ End of Project Milestone D: G: J: M: P: $ $ $ $ $ 18 Version 4.1 Integrated Process Developers, Inc. Page: 9 For permissions and other rights

10 Duration Distribution Number of Rolls Duration Distribution $10,000 $10,200 $10,400 $10,600 $10,800 $11,000 $11,200 $11,400 $11,600 $11,800 $12,000 $12,200 $12,400 $12,600 $12,800 Number of Rolls $13,000 $13,200 $13,400 $13,600 $13,800 $14,000 $14,200 $14,400 $14,600 $14,800 $15,000 $15,200 $15,400 $15,600 $15,800 $16,000 $16,200 $16,400 $16,600 $16,800 $17,000 $17,200 $17,400 $17,600 $17,800 $18,000 $18,200 $18,400 $18,600 $18,800 $19,000 $19,200 Project 19 Version 4.1 Questions? 20 Version 4.1 Integrated Process Developers, Inc. Page: 10 For permissions and other rights