hulett david

© 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


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


Risk of an Individual Activity

• Simple activity duration estimates are risky

Design Unit 1

30d


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


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


Probability Distributions Available (continued)

Normal BETA


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


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


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)


Risk Along a Contiguous Schedule Path

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

StartDesign Unit

Build Unit Finish

Test Unit


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


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


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

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


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


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


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


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


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


Cost and Schedule Risk Integration

“Burn Rate” Time Independent Costs

Time Dependent Costs

Project Schedule Risk

Cost Risk

Risk

Time

Project 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 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


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


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 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


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+®


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


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


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


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

556,800Total Cost

98Days

8Hours/Day

88Hourly Rate

8Average Workers

ValueCost Element

Summary Cost Estimate


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

556,800Total Cost

Fitted Beta Distribution98Days

8Hours/Day

100888488Hourly Rate

12868Average Workers

MaximumMost LikelyMinimumValueCost Element



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


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

$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


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



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


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

Date and Cost Scatter plot from Pertmaster® schedule risk software

Overrun both Cost and Schedule


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, 2007Moody Gardens, Galveston, TX

David T. Hulett, Ph.D.Hulett & Associates, LLC

Los Angeles, CA(310) 476-7699 / [email protected]

www.projectrisk.com

hulett david

Technology

hulett associates

path schedule

design unit30 d

agenda schedule risk

duration risk

risk mean

schedule finishes

d25 d50 d