Hulett david

Integrated Cost / Schedule Risk Analysis

A presentation to the
PM Challenge
February 6-7, 2007
Moody Gardens, Galveston, TX

David T. Hulett, Ph.D.
Hulett & Associates, LLC
Los Angeles, CA
(310) 476-7699 / info@projectrisk.com
www.projectrisk.com

© 2007 Hulett & Associates, LLC. 1

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. 2

Risk of an Individual Activity
• Simple activity duration estimates are risky

30d

Design Unit 1


Probability Distributions Available
Date: 1/13/2003 5:21:27 PM Date: 1/13/2003 5:18:35 PM
Samples: 3000 Samples: 3000
Unique ID: 3 Unique ID: 3
Name: Design Unit Name: Design Unit
0.09 1.0 0.16 1.0
0.08 0.9 0.9
0.14

Cumulative Probability

0.07 0.8 0.8
0.12
0.7 0.7
0.06
Frequency

Frequency
0.6 0.10 0.6
0.05
0.5 0.08 0.5
0.04
0.4 0.06 0.4
0.03 0.3 0.3
0.02 0.04
0.2 0.2
0.01 0.1 0.02 0.1

6/21 7/3 7/15 6/21 7/2 7/15
Completion Date Completion Date
Uniform Distribution Triangular Distribution

Uniform Triangular


Probability Distributions Available
(continued)
Date: 7/10/2002 3:19:37 PM Date: 7/10/2002 3:20:30 PM
Name: Design Unit Name: Design Unit

0.20 1.0 0.22 1.0
0.18 0.9 0.20 0.9


0.16 0.8 0.17 0.8
0.14 0.7 0.7
Frequency

Frequency
0.15
0.12 0.6 0.6
0.13
0.10 0.5 0.5
0.10
0.08 0.4 0.4
0.3 0.08 0.3
0.06
0.04 0.2 0.05 0.2
0.02 0.1 0.03 0.1

6/21 7/3 7/15 6/21 7/1 7/13
Normal Distribution Beta Distribution

Normal BETA


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

Comparison of Probability Distributions
(20d, 30d, 45d)
Mean Standard Deviation
Uniform 33d 7.2d
Triangular 32d 5.1d
Normal 33d 4.1d
Beta 31d 3.4d

Risk Along a Contiguous Schedule Path

• Path risk is the combination of the risks of its
activities

Design Build Test
Start Finish
Unit Unit Unit


Really Simple Schedule
• This schedule finishes on September 3
– 7-day weeks, like a model changeover, refinery turnaround
ID Task Name Duration Start Finish May June July August Septembe
1 Project 95 d 6/1 9/3
2 Start 0d 6/1 6/1 6/1
3 Design Unit 30 d 6/1 6/30 6/1 6/30
4 Build Unit 40 d 7/1 8/9 7/1 8/9
5 Test Unit 25 d 8/10 9/3 8/10 9/3
6 Finish 0d 9/3 9/3 9/3

• If we can get into trouble with this simple schedule, we can
get into trouble with real project schedules

Add Duration Risk to the Schedule
using Triangular Distributions

ID Task Name Rept ID Min Rdur ML Rdur Max Rdur Curve
1 Project 2 0d 0d 0d 0
2 Start 0 0d 0d 0d 0
3 Design Unit 0 20 d 30 d 45 d 2
4 Build Unit 0 35 d 40 d 50 d 2
5 Test Unit 0 20 d 25 d 50 d 2
6 Finish 0 0d 0d 0d 0


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


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

Monte Carlo Simulation Results
for Really Simple Schedule
CPM date is not even the most likely – That’s about 9/10
Date: 2/18/2006 3:56:56 P M Com pletion S td Deviation: 8.75 d
S am ples : 3000 95% Confidenc e Interval: 0.31 d
Unique ID: 2 E ac h bar repres ents 3 d
Nam e: P rojec t

0.14 1.0 Com pletion P robability Table
0.9

0.12 P rob Date P rob Date
0.8
0.05 8/31 0.55 9/14
0.10 0.7 0.10 9/2 0.60 9/16
Frequency

0.6 0.15 9/4 0.65 9/17
0.08
0.5 0.20 9/6 0.70 9/18
0.06 0.4 0.25 9/7 0.75 9/19
0.3 0.30 9/8 0.80 9/21
0.04
0.35 9/10 0.85 9/23
0.2
0.02 0.40 9/11 0.90 9/25
0.1 0.45 9/12 0.95 9/29
8/21 9/13 10/10
0.50 9/13 1.00 10/10
C o mp le tio n D a te

80% Target is
CPM date is&<15% Likely to be met
© 2007 Hulett Associates, LLC. 9/21 12

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

Design Unit 1 Build Unit 1 Test Unit 1

Start
Finish
Design Unit 2 Build Unit 2 Test Unit 2


This Schedule has
Three Parallel Paths

ID Task Name Rept ID Min Rdur ML Rdur Max Rdur Curve May June July August Septemb
1 Project 2 0d 0d 0d 0
2 Start 0 0d 0d 0d 0 6/1
3 Unit 1 1 0d 0d 0d 0
4 Design Unit 0 20 d 30 d 45 d 2 6/1 6/30
5 Build Unit 1 0 35 d 40 d 50 d 2 7/1 8/9
6 Test Unit 1 0 20 d 25 d 50 d 2 8/10 9/3
7 Unit 2 1 0d 0d 0d 0
11 Unit 3 1 0d 0d 0d 0
15 Finish 0 0d 0d 0d 0 9/3

Two paths are collapsed
Each path has exactly the same structure


Evidence of the Merge Bias
Date: 2/18/2006 4:04:12 PM Date: 2/18/2006 3:56:56 PM
Name: Project Name: Project

0.16 1.0 0.14 1.0
0.9 0.9
0.14


0.12
0.8 0.8
0.12
0.7 0.10 0.7
Frequency

Frequency
0.10 0.6 0.6
0.08
0.08 0.5 0.5
0.4 0.06 0.4
0.06
0.3 0.04 0.3
0.04
0.2 0.2
0.02 0.02
0.1 0.1

8/31 9/21 10/14 8/21 9/13 10/10

Three Path Project One Path Project

Evidence of Merge Bias (continued)
C o m p le t io n S t d D e via t io n : 6 . 9 5 d C o m p le t io n S t d D e via t io n : 8 . 9 3 d
9 5 % C o n fid e n c e In t e rva l: 0 . 2 5 d 9 5 % C o n fid e n c e In t e rva l: 0 . 3 2 d
E a c h b a r re p re s e n t s 3 d E a c h b a r re p re s e n t s 3 d

C o m p le t io n P ro b a b ilit y Ta b le C o m p le t io n P ro b a b ilit y Ta b le
P ro b D ate P ro b Date P ro b D ate P ro b D ate
0.05 9/10 0.55 9/22 0.05 8/31 0.55 9/14
0.10 9/13 0.60 9/23 0.10 9/3 0.60 9/15
0.15 9/14 0.65 9/24 0.15 9/4 0.65 9/17
0.20 9/15 0.70 9/25 0.20 9/6 0.70 9/18
0.25 9/16 0.75 9/26 0.25 9/7 0.75 9/20
0.30 9/17 0.80 9/27 0.30 9/8 0.80 9/21
0.35 9/18 0.85 9/29 0.35 9/9 0.85 9/23
0.40 9/19 0.90 10/1 0.40 9/11 0.90 9/25
0.45 9/20 0.95 10/3 0.45 9/12 0.95 9/29
0.50 9/21 1.00 10/14 0.50 9/13 1.00 10/15

Three Path Schedule One Path Schedule

Graphical Evidence of the Merge Bias

The "Merge Bias"

100%

90%

80%

70% One
60% Path
b.
Cum.Pro

Three
50% Path
40% Merge Bias
30%

20%

10%

0%
8/11 8/21 8/31 9/10 9/20 9/30 10/10 10/20
Date


Cost and Schedule Risk Integration

Risk

Project Schedule Cost Risk
Risk
“Burn Rate” Time Independent
Time Costs

Time Dependent Project
Costs Cost Risk

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

Cost / Schedule Risk Using a Schedule
• Simple schedule
• Starts June 1, finishes without risk on September 6

ID Task Name Duration Start Finish May June July August SeptembO
0 Integrated Cost-Sched 98 d 6/1 9/6
1 Start 0d 6/1 6/1 6/1
2 Design 28 d 6/1 6/28 6/1 6/28
3 Build 45 d 6/29 8/12 6/29 8/12
4 Test 25 d 8/13 9/6 8/13 9/6
5 Finish 0d 9/6 9/6 9/6


Add Resources to the Simple Schedule
• Designers, builders and testers are assigned and cost
data are specified
ID Task Name Duration Start Finish Resource Names
0 Integrated Cost-Schedule 98 d 6/1 9/6
1 Start 0d 6/1 6/1
2 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 0d 9/6 9/6

Resource Name Type of Resource Rate

Designers Work $90/hr
Builders Work $80/hr
Testers Work $105/hr

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

Inputs to Schedule Risk Analysis

ID Task Name Rept Min Rd ML Rdu Max Rd Curve
0 Integrated Cost- 2 0d 0d 0d 0
1 Start 0 0d 0d 0d 0
2 Design 0 20 d 28 d 40 d 2
3 Build 0 35 d 45 d 60 d 2
4 Test 0 15 d 25 d 40 d 2
5 Finish 0 0d 0d 0d 0


Schedule Risk Analysis: Dates
Date: 2/18/2006 9:49:40 AM Completion Std Deviation: 8.25 d
Samples: 3000 95% Confidence Interval: 0.29 d
Unique ID: 0 Each bar represents 3 d
Name: Integrated Cost-Schedule

0.14 1.0 Completion Probability Table
0.9

0.12 Prob Date Prob Date
0.8
0.05 8/29 0.55 9/12
0.10 0.7 0.10 8/31 0.60 9/13
Frequency

0.6 0.15 9/2 0.65 9/14
0.08
0.5 0.20 9/4 0.70 9/16
0.06 0.4 0.25 9/5 0.75 9/17
0.3 0.30 9/7 0.80 9/18
0.04
0.35 9/8 0.85 9/20
Source: 0.2
0.40 9/9 0.90 9/22
0.02
Risk+® 0.1 0.45 9/10 0.95 9/25
8/17 9/11 10/7
0.50 9/11 1.00 10/7
Completion Date

Sept. 6 is 25 – 30% likely. 80th percentile is Sept. 20 for a 2-week contingency

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 only
ID Task Name Duration Total Cost
0 Integrated Cost-Schedule 98 d $556,800
1 Start 0d $0
2 Design 28 d $100,800
3 Build 45 d $288,000
4 Test 25 d $168,000
5 Finish 0d $0

All Resource Types are “Work” (2)
Date: 2/18/2006 9:49:40 AM Cost Standard Deviation: $49,645
Samples: 3000 95% Confidence Interval: $1,777
Unique ID: 0 Each bar represents $25,000
Name: Integrated Cost-Schedule

0.20 1.0 Cost Probability Table
0.18 0.9

Prob Cost Prob Cost
0.16 0.8
0.05 $503,329 0.55 $589,111
0.14 0.7 0.10 $519,541 0.60 $595,793
Frequency

0.12 0.6 0.15 $530,895 0.65 $602,967
0.10 0.5 0.20 $539,706 0.70 $610,397
0.08 0.4 0.25 $547,195 0.75 $617,877
0.06 0.3 0.30 $555,041 0.80 $626,705
0.35 $562,138 0.85 $636,646
0.04 0.2
0.40 $569,210 0.90 $649,900
0.02 0.1 0.45 $575,955 0.95 $667,044
$432,397 $583,479 $736,369
0.50 $583,082 1.00 $736,369
Cost

Cost risk results differ because activity duration risks differ

With Work-Type Resources,
Cost and Time are Highly Correlated
Scatter Plot of Time and Cost for Work-Type Resources

800,000

700,000

600,000

500,000
Cost

400,000

300,000

200,000

100,000

0
8/11 8/21 8/31 9/10 9/20 9/30 10/10
Date

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


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

The Cost Estimate may be at a
Higher Level than the Schedule
Summary Cost Estimate

Cost Element Value

Average Workers 8

Hourly Rate 88

Hours/Day 8

Days 98

Total Cost 556,800


Determine the Best Crystal Ball Distribution
for the Uncertain Schedule Risk Duration: Beta

Source: Crystal Ball®

Distribution Parameters


Insert Uncertain Burn Rate into Cost Model

Cost Element Value Minimum Most Likely Maximum

Average Workers 8 6 8 12

Hourly Rate 88 84 88 100

Hours/Day 8

Days 98 Fitted Beta Distribution

Total Cost 556,800


Adding Uncertainty in Burn Rate
Uncertain Duration, Workers and Rate per Hour

1,200,000

1,000,000

800,000
Cost

600,000

400,000

200,000
More Scatter, Less
Tightly Correlated due
0
8/11 8/21 8/31 9/10 9/20 9/30 10/10
to Uncertain Burn Rate Date


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


Add Test Equipment @ $200,000
Time and Material Resources

Resource Type Hourly Rate Rate per Use

Designers Work $90/hr N/A
Builders Work $80/hr N/A
Testers Work $105/hr N/A
Test Equipment Material N/A $200,000

ID Task Name Duration Start Finish Cost Resource Names
0 Integrated Cost-Schedule 98 d 6/1 9/6 $756,800
1 Start 0d 6/1 6/1 $0
2 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 Equipme
5 Finish 0d 9/6 9/6 $0


Add Risky Materials Cost
Independent of Time

Cost Element Value Minimum Most Likely Maximum

Average Workers 8 6 8 12

Hourly Rate 88 84 88 100

Hours/Day 8

Days 98 Beta Distribution

Time-Related Cost 556,800

Test Equipment 200,000 160,000 200,000 280,000

Total Cost 756,800


Adding Materials with Time-Independent Risk
Adding Time-Independent Equipment Cost Risk

1,400,000

1,200,000

1,000,000

800,000
Cost

Series1
600,000

400,000

More Scatter, 200,000 tightly
Less
Correlated due to0
Uncertain Burn Rate and 8/21
8/11 8/31 9/10 9/20 9/30 10/10
Date
Risky Time-Independent
Material Cost

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


Hardware / Software Build and Integrate

Build the Schedule in Primavera Project Planner (P3)

Modern Approach to Integrated C/S Risk:
Import P3 Schedule to Pertmaster


Pertmaster Risk from P3 Schedules

Duration Risk Range


Pertmaster Risk from P3 Schedules (2)

Time-Independent Risk Range Burn Rate Risk Range


Integrated Cost and Schedule Risk Results

Overrun both
Cost and
Schedule

Date and Cost Scatter plot from Pertmaster® schedule risk software

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)


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


Integrated Cost / Schedule Risk Analysis

A presentation to the
PM Challenge
February 6-7, 2007
Moody Gardens, Galveston, TX

David T. Hulett, Ph.D.
Hulett & Associates, LLC
Los Angeles, CA
(310) 476-7699 / info@projectrisk.com
www.projectrisk.com


Hulett david

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