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© 2007 Hulett & Associates, LLC. 1
Integrated Cost / Schedule Risk Analysis
A presentation to the PM Challenge
February 6-7, 2007Moody Gardens, Galveston, TX
David T. Hulett, Ph.D.Hulett & Associates, LLC
Los Angeles, CA(310) 476-7699 / [email protected]
www.projectrisk.com
© 2007 Hulett & Associates, LLC. 2
Agenda
• Schedule Risk Analysis– One-path schedule, two paths and the “merge bias”– Highest risk path – risk criticality– Probabilistic branching
• Integrated Cost – Schedule Risk Analysis– Basics – risks in time-related and time-independent
costs– Schedule in Project, Costs in Excel– Resources in the schedule – integrated simulations
using Monte Carlo and Pertmaster on Primavera P3 schedules
© 2007 Hulett & Associates, LLC. 3
Risk of an Individual Activity
• Simple activity duration estimates are risky
Design Unit 1
30d
© 2007 Hulett & Associates, LLC. 4
Probability Distributions Available
Uniform Triangular
Date: 1/13/2003 5:18:35 PMSamples: 3000Unique ID: 3Name: Design Unit
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
7/26/21 7/15
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Triangular Distribution
Date: 1/13/2003 5:21:27 PMSamples: 3000Unique ID: 3Name: Design Unit
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
7/36/21 7/15
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Uniform Distribution
© 2007 Hulett & Associates, LLC. 5
Probability Distributions Available (continued)
Normal BETA
Date: 7/10/2002 3:19:37 PMSamples: 3000Unique ID: 3Name: Design Unit
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
7/36/21 7/15
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.040.06
0.080.10
0.12
0.140.16
0.180.20
Normal Distribution
Date: 7/10/2002 3:20:30 PMSamples: 3000Unique ID: 3Name: Design Unit
Completion DateFr
eque
ncy
Cum
ulat
ive
Prob
abilit
y
7/16/21 7/13
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.03
0.05
0.08
0.10
0.13
0.15
0.17
0.20
0.22
Beta Distribution
© 2007 Hulett & Associates, LLC. 6
Comparison of Four Distributions
• The three distributions have different characteristics– The uniform expresses most risk (mean, Standard deviation)– Triangular is fairly conservative– The Beta is the least risky
Mean Standard DeviationUniform 33d 7.2dTriangular 32d 5.1dNormal 33d 4.1dBeta 31d 3.4d
Comparison of Probability Distributions(20d, 30d, 45d)
© 2007 Hulett & Associates, LLC. 7
Risk Along a Contiguous Schedule Path
• Path risk is the combination of the risks of its activities
StartDesign Unit
Build Unit Finish
Test Unit
© 2007 Hulett & Associates, LLC. 8
Really Simple Schedule
• This schedule finishes on September 3– 7-day weeks, like a model changeover, refinery turnaround
• If we can get into trouble with this simple schedule, we can get into trouble with real project schedules
ID Task Name Duration Start Finish1 Project 95 d 6/1 9/32 Start 0 d 6/1 6/13 Design Unit 30 d 6/1 6/304 Build Unit 40 d 7/1 8/95 Test Unit 25 d 8/10 9/36 Finish 0 d 9/3 9/3
6/16/1 6/30
7/1 8/98/10 9/3
9/3
May June July August Septembe
© 2007 Hulett & Associates, LLC. 9
Add Duration Risk to the Schedule using Triangular Distributions
ID Task Name Rept ID Min Rdur ML Rdur Max Rdur Curve1 Project 2 0 d 0 d 0 d 02 Start 0 0 d 0 d 0 d 03 Design Unit 0 20 d 30 d 45 d 24 Build Unit 0 35 d 40 d 50 d 25 Test Unit 0 20 d 25 d 50 d 26 Finish 0 0 d 0 d 0 d 0
© 2007 Hulett & Associates, LLC. 10
What is a Simulation?
• How do you find total project results?– Cannot add distributions– Must combine distributions
• Combining distributions using simulation– Almost all possible combinations of durations– “Perform” the project many times
© 2007 Hulett & Associates, LLC. 11
Combine Distributions by Simulation
• Monte Carlo simulation– Very General– 50-year old method
• Computer “performs” project many times– Exercise is a “simulation”– Each calculation is an “iteration”
• Brute force solution– All combinations of possible costs or durations
© 2007 Hulett & Associates, LLC. 12
Monte Carlo Simulation Results for Really Simple Schedule
Date: 2/18/2006 3:56:56 PMS am ples : 3000Unique ID: 2Nam e: P rojec t
Com pletion S td Deviation: 8.75 d95% Confidence Interval: 0.31 dEach bar represents 3 d
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
9/138/21 10/10
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14 Com pletion P robability Table
P rob ProbDate Date0.05 8/310.10 9/20.15 9/40.20 9/60.25 9/70.30 9/80.35 9/100.40 9/110.45 9/120.50 9/13
0.55 9/140.60 9/160.65 9/170.70 9/180.75 9/190.80 9/210.85 9/230.90 9/250.95 9/291.00 10/10
CPM date is not even the most likely – That’s about 9/10
CPM date is <15% Likely to be met80% Target is
9/21
© 2007 Hulett & Associates, LLC. 13
Risk at Merge Points:The “Merge Bias”
• Many parallel paths merge in a real schedule• Finish driven by the latest converging path • Merge Bias has been understood for 40 years
FinishStart
Test Unit 1Build Unit 1Design Unit 1
Design Unit 2 Build Unit 2 Test Unit 2
© 2007 Hulett & Associates, LLC. 14
This Schedule has Three Parallel Paths
ID Task Name Rept ID Min Rdur ML Rdur Max Rdur Curve1 Project 2 0 d 0 d 0 d 02 Start 0 0 d 0 d 0 d 03 Unit 1 1 0 d 0 d 0 d 04 Design Unit 0 20 d 30 d 45 d 25 Build Unit 1 0 35 d 40 d 50 d 26 Test Unit 1 0 20 d 25 d 50 d 27 Unit 2 1 0 d 0 d 0 d 011 Unit 3 1 0 d 0 d 0 d 015 Finish 0 0 d 0 d 0 d 0
6/1
6/1 6/307/1 8/9
8/10 9/3
9/3
May June July August Septemb
Two paths are collapsedEach path has exactly the same structure
© 2007 Hulett & Associates, LLC. 15
Evidence of the Merge BiasDate: 2/18/2006 3:56:56 PMSamples: 3000Unique ID: 2Name: Project
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
9/138/21 10/10
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Date: 2/18/2006 4:04:12 PMSamples: 3000Unique ID: 2Name: Project
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
9/218/31 10/14
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
One Path ProjectThree Path Project
© 2007 Hulett & Associates, LLC. 16
Evidence of Merge Bias (continued)
Three Path Schedule One Path Schedule
C om plet ion S td Devia t ion: 6 .95 d95% Confidenc e In terva l: 0 .25 dE ac h bar repres ents 3 d
C om plet ion P robability Tab le
P rob P robD ate Date0.05 9/100.10 9/130.15 9/140.20 9/150.25 9/160.30 9/170.35 9/180.40 9/190.45 9/200.50 9/21
0.55 9/220.60 9/230.65 9/240.70 9/250.75 9/260.80 9/270.85 9/290.90 10/10.95 10/31.00 10/14
C om ple t ion S td D evia t ion : 8 .93 d95% C onfidenc e In te rva l: 0 .32 dE ac h bar repres en ts 3 d
C om ple t ion P robab ility Tab le
P rob P robD ate D ate0 .05 8 /310 .10 9 /30 .15 9 /40 .20 9 /60 .25 9 /70 .30 9 /80 .35 9 /90 .40 9 /110 .45 9 /120 .50 9 /13
0 .55 9 /140 .60 9 /150 .65 9 /170 .70 9 /180 .75 9 /200 .80 9 /210 .85 9 /230 .90 9 /250 .95 9 /291 .00 10/15
© 2007 Hulett & Associates, LLC. 17
Graphical Evidence of the Merge Bias
The "Merge Bias"
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
8/11 8/21 8/31 9/10 9/20 9/30 10/10 10/20
Date
Cum
.Pro b
.
OnePathThreePath
Merge Bias
© 2007 Hulett & Associates, LLC. 18
Cost and Schedule Risk Integration
“Burn Rate” Time Independent Costs
Time Dependent Costs
Project Schedule Risk
Cost Risk
Risk
Time
Project Cost Risk
© 2007 Hulett & Associates, LLC. 19
Cost Estimating Basics
• Cost estimates can be constructed by multiplying:– Workers assigned – Daily rate– Duration of task
• Uncertainty in any of these variables leads to uncertainty in project cost estimates
• Cost risk estimating can be more accurate and the reasons for risk better illuminated when time and cost factors are addressed individually rather than as one cost uncertainty distribution
© 2007 Hulett & Associates, LLC. 20
Cost / Schedule Risk Using a Schedule
• Simple schedule• Starts June 1, finishes without risk on September 6
ID Task Name Duration Start Finish0 Integrated Cost-Sched 98 d 6/1 9/61 Start 0 d 6/1 6/12 Design 28 d 6/1 6/283 Build 45 d 6/29 8/124 Test 25 d 8/13 9/65 Finish 0 d 9/6 9/6
6/16/1 6/28
6/29 8/128/13 9/6
9/6
May June July August SeptembO
© 2007 Hulett & Associates, LLC. 21
Add Resources to the Simple Schedule
• Designers, builders and testers are assigned and cost data are specified
ID Task Name Duration Start Finish Resource Names0 Integrated Cost-Schedule 98 d 6/1 9/61 Start 0 d 6/1 6/12 Design 28 d 6/1 6/28 Designers[5]3 Build 45 d 6/29 8/12 Builders[10]4 Test 25 d 8/13 9/6 Testers[8]5 Finish 0 d 9/6 9/6
$105/hrWorkTesters$80/hrWorkBuilders$90/hrWorkDesigners
RateType of ResourceResource Name
© 2007 Hulett & Associates, LLC. 22
Computing Schedule Risk when Time and Resources are in MS Project
• Using Risk+, simulate the MS Project schedule, collecting cost results for the project
• Inputs– 3-point estimates for duration of tasks
• Outputs– Pairs of cost and date for each iteration
• Note: the cost of each resource per time period is fixed in this method
© 2007 Hulett & Associates, LLC. 23
Inputs to Schedule Risk Analysis
ID Task Name Rept Min Rd ML Rdu Max Rd Curve0 Integrated Cost- 2 0 d 0 d 0 d 01 Start 0 0 d 0 d 0 d 02 Design 0 20 d 28 d 40 d 23 Build 0 35 d 45 d 60 d 24 Test 0 15 d 25 d 40 d 25 Finish 0 0 d 0 d 0 d 0
© 2007 Hulett & Associates, LLC. 24
Schedule Risk Analysis: Dates
Date: 2/18/2006 9:49:40 AMSamples: 3000Unique ID: 0Name: Integrated Cost-Schedule
Completion Std Deviation: 8.25 d95% Confidence Interval: 0.29 dEach bar represents 3 d
Completion Date
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
9/118/17 10/7
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.04
0.06
0.08
0.10
0.12
0.14 Completion Probability Table
Prob ProbDate Date0.05 8/290.10 8/310.15 9/20.20 9/40.25 9/50.30 9/70.35 9/80.40 9/90.45 9/100.50 9/11
0.55 9/120.60 9/130.65 9/140.70 9/160.75 9/170.80 9/180.85 9/200.90 9/220.95 9/251.00 10/7
Sept. 6 is 25 – 30% likely. 80th percentile is Sept. 20 for a 2-week contingency
Source: Risk+®
© 2007 Hulett & Associates, LLC. 25
All Resource Types are “Work”
• Each resource is assumed to work on a daily basis– Baseline cost is $556,800– Each extra day of work is extra cost, dollar for dollar
• Cost risk is determined by uncertain durations onlyID Task Name Duration Total Cost0 Integrated Cost-Schedule 98 d $556,8001 Start 0 d $02 Design 28 d $100,8003 Build 45 d $288,0004 Test 25 d $168,0005 Finish 0 d $0
© 2007 Hulett & Associates, LLC. 26
All Resource Types are “Work” (2)
Date: 2/18/2006 9:49:40 AMSamples: 3000Unique ID: 0Name: Integrated Cost-Schedule
Cost Standard Deviation: $49,64595% Confidence Interval: $1,777Each bar represents $25,000
Cost
Freq
uenc
y
Cum
ulat
ive
Prob
abilit
y
$583,479$432,397 $736,369
0.1
0.2
0.30.4
0.5
0.60.7
0.8
0.91.0
0.02
0.040.06
0.08
0.100.12
0.140.16
0.180.20 Cost Probability Table
Prob ProbCost Cost0.05 $503,3290.10 $519,5410.15 $530,8950.20 $539,7060.25 $547,1950.30 $555,0410.35 $562,1380.40 $569,2100.45 $575,9550.50 $583,082
0.55 $589,1110.60 $595,7930.65 $602,9670.70 $610,3970.75 $617,8770.80 $626,7050.85 $636,6460.90 $649,9000.95 $667,0441.00 $736,369
Cost risk results differ because activity duration risks differ
© 2007 Hulett & Associates, LLC. 27
With Work-Type Resources, Cost and Time are Highly Correlated
Scatter Plot of Time and Cost for Work-Type Resources
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
800,000
8/11 8/21 8/31 9/10 9/20 9/30 10/10
Date
Cos
t
© 2007 Hulett & Associates, LLC. 28
Uncertainty in the “Burn Rate”
• Usually resources are found in a spreadsheet • This enables us to deal with uncertain burn rates• Cost estimates are often at a less detailed level
than the schedule• We also will often need schedule risk analysis for a
summary task
© 2007 Hulett & Associates, LLC. 29
Cost Estimates are in a Spreadsheet / Schedules are in Scheduling Package
• Process when schedule is in MS Project and costs are in MS Excel
• Use schedule risk results from Risk+ for Project and Crystal Ball for Excel– Simulate MS Project with Risk+ for duration, not dates– Read the detailed iteration results into a spreadsheet– Estimate the Crystal Ball function that fits the best– Use that function in the cost estimate to represent
uncertain duration in Crystal Ball simulation of cost risk
© 2007 Hulett & Associates, LLC. 30
The Cost Estimate may be at a Higher Level than the Schedule
556,800Total Cost
98Days
8Hours/Day
88Hourly Rate
8Average Workers
ValueCost Element
Summary Cost Estimate
© 2007 Hulett & Associates, LLC. 31
Determine the Best Crystal Ball Distribution for the Uncertain Schedule Risk Duration: Beta
Source: Crystal Ball®
© 2007 Hulett & Associates, LLC. 32
Distribution Parameters
© 2007 Hulett & Associates, LLC. 33
Insert Uncertain Burn Rate into Cost Model
556,800Total Cost
Fitted Beta Distribution98Days
8Hours/Day
100888488Hourly Rate
12868Average Workers
MaximumMost LikelyMinimumValueCost Element
Summary Cost Estimate
© 2007 Hulett & Associates, LLC. 34
Adding Uncertainty in Burn Rate
Uncertain Duration, Workers and Rate per Hour
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
8/11 8/21 8/31 9/10 9/20 9/30 10/10
Date
Cos
t
More Scatter, Less Tightly Correlated due to Uncertain Burn Rate
© 2007 Hulett & Associates, LLC. 35
Consider More Realism: Time-Independent Resources
• Some resources’ costs are not determined by time– E.g., test equipment, materials
• These are “use-type” or “material-type” resources• Their costs may not be known with certainty but
they are not determined by activity durations
© 2007 Hulett & Associates, LLC. 36
Add Test Equipment @ $200,000
$200,000 N/AMaterialTest Equipment
N/A$105/hrWorkTesters
N/A$80/hrWorkBuilders
N/A$90/hrWorkDesigners
Rate per UseHourly RateTypeResource
Time and Material Resources
ID Task Name Duration Start Finish Cost Resource Names0 Integrated Cost-Schedule 98 d 6/1 9/6 $756,8001 Start 0 d 6/1 6/1 $02 Design 28 d 6/1 6/28 $100,800 Designers[5]3 Build 45 d 6/29 8/12 $288,000 Builders[10]4 Test 25 d 8/13 9/6 $368,000 Testers[8],Test Equipme5 Finish 0 d 9/6 9/6 $0
© 2007 Hulett & Associates, LLC. 37
Add Risky Materials Cost Independent of Time
756,800Total Cost
280,000200,000160,000200,000Test Equipment
556,800Time-Related Cost
Beta Distribution98Days
8Hours/Day
100888488Hourly Rate
12868Average Workers
MaximumMost LikelyMinimumValueCost Element
Summary Cost Estimate
© 2007 Hulett & Associates, LLC. 38
Adding Materials with Time-Independent Risk
Adding Time-Independent Equipment Cost Risk
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
8/11 8/21 8/31 9/10 9/20 9/30 10/10
Date
Cos
t
Series1
More Scatter, Less tightly Correlated due to
Uncertain Burn Rate and Risky Time-Independent
Material Cost
© 2007 Hulett & Associates, LLC. 39
Computing Schedule Risk when Cost and Schedule are in the Scheduling Program
• Resources are identified and their hourly or daily cost are input into the scheduling software
• Resources are assigned to tasks and costs of those tasks and the total project are computed
• Uncertainty can be added by:– Probability distribution of the duration– Probability distribution of the burn rate– Use or material resources can also be risky and their costs varied
• Jointly simulate the cost and schedule in the program
© 2007 Hulett & Associates, LLC. 40
Hardware / Software Build and Integrate
Build the Schedule in Primavera Project Planner (P3)
© 2007 Hulett & Associates, LLC. 41
Modern Approach to Integrated C/S Risk:Import P3 Schedule to Pertmaster
© 2007 Hulett & Associates, LLC. 42
Pertmaster Risk from P3 Schedules
Duration Risk Range
© 2007 Hulett & Associates, LLC. 43
Pertmaster Risk from P3 Schedules (2)
Time-Independent Risk Range Burn Rate Risk Range
© 2007 Hulett & Associates, LLC. 44
Integrated Cost and Schedule Risk Results
Date and Cost Scatter plot from Pertmaster® schedule risk software
Overrun both Cost and Schedule
© 2007 Hulett & Associates, LLC. 45
Summary of Main Principles
• Schedule Risk depends on the schedule logic and uncertainty in the activity durations
• Monte Carlo simulation is the accepted method of estimating the uncertainty from all risks simultaneously
• Simulation software allows Monte Carlo for schedules in several packages (e.g. Project, P3)
© 2007 Hulett & Associates, LLC. 46
Summary of Main Principles (2)
• Cost risk depends in large part on elements of schedule uncertainty– The cost estimate is not secure if the schedule is
slipping• Uncertain burn rates for time-dependent costs• Uncertain costs for time-independent costs
© 2007 Hulett & Associates, LLC. 47
Integrated Cost / Schedule Risk Analysis
A presentation to the PM Challenge
February 6-7, 2007Moody Gardens, Galveston, TX
David T. Hulett, Ph.D.Hulett & Associates, LLC
Los Angeles, CA(310) 476-7699 / [email protected]
www.projectrisk.com