ESD.36 System Project Management

Instructor(s)

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- Probabilistic Scheduling

Prof. Olivier de Weck

Dr. James Lyneis

Lecture 9

October 4, 2012

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Today’s Agenda

Probabilistic Task Times

PERT (Program Evaluation and Review Technique)

Monte Carlo Simulation

Signal Flow Graph Method

System Dynamics

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Task Representations

Tasks as Nodes of a Graph Circles

Boxes

Tasks as Arcs of a Graph Tasks are uni-directional arrows

Nodes now represent “states” of a project

Kelley-Walker form

ID:A

ES EF

Dur:5

LS LF

A,5

broken A, 5

fixed

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Task Times Detail - Task i

ES(i) EF(i)

Duration t(i)

LS(i) LF(i)

Duration t(i) Total Slack TS(i)

ES(j) j>i

j is the immediate successor of i with the smallest ES

FS(i)

Free Slack

Free Slack (FS) is the amount a job can be delayed without delaying the Early Start (ES) of any other job.

FS<=TS always

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How long does a task take?

Conduct a small in-class experiment

Fold MIT paper airplane Have sheet & paper clip ready in front of you

Paper airplane type will be announced, e.g. A1-B1-C1-D1

Build plane, focus on quality rather than speed

Note the completion time in seconds +/- 5 [sec]

Plot results for class and discuss Submit your task time online , e.g. 120 sec

We will build a histogram and show results

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- MIT Paper Airplane

Credit: Steve Eppinger 6

Courtesy of Steven D. Eppinger. Used with permission.

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- Concept Question 1

How long did it take you to complete your paper airplane (round up or down)? 25 sec

50 sec

75 sec

100 sec

125 sec

150 sec

175 sec

200 sec

225 sec

> 225 sec

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- MIT Class Results (2008)

Beta Distribution parameters: a=2.27, b=5.26

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Discussion Point 1

Job task durations are stochastic in reality

Actual duration affected by

Individual skills

Learning curves … what else?

Why is the distribution not symmetric (Gaussian)?

Project Task i

0

5

10

15

10 15 20 25 30 35 40

completion time [days]

Fre

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cy

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Today’s Agenda

Probabilistic Task Times

PERT (Program Evaluation and Review Technique)

Monte Carlo Simulation

Signal Flow Graph Method

System Dynamics

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- PERT

PERT invented in 1958 for U.S Navy Polaris Project (BAH)

Similar to CPM

Treats task times probabilistically

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Original PERT chart used “activity-on-arc” convention

50t=3 mo

t=3 mo

t=3 mo

t=4 mo

A

B C

E

D Ft=1 mo

t=2 mo30

40

10

20

Image by MIT OpenCourseWare.

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CPM vs PERT

Difference how “task duration” is treated:

CPM assumes time estimates are deterministic

Obtain task duration from previous projects

Suitable for “implementation”-type projects

PERT treats durations as probabilistic

PERT = CPM + probabilistic task times

Better for “uncertain” and new projects

Limited previous data to estimate time durations

Captures schedule (and implicitly some cost) risk

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PERT -- Task time durations are treated as uncertain

A - optimistic time estimate

minimum time in which the task could be completed

everything has to go right

M - most likely task duration

task duration under “normal” working conditions

most frequent task duration based on past experience

B - pessimistic time estimate

time required under particularly “bad” circumstances

most difficult to estimate, includes unexpected delays

should be exceeded no more than 1% of the time

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- A-M-B Time Estimates

Project Task i

0

5

10

15

10 15 20 25 30 35 40

completion time [days]

Fre

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Range of Possible Times

times

Time A

Time M

Time B

Assume a Beta-distribution

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Beta-Distribution

All values are enclosed within interval

As classes get finer - arrive at b-distribution

Statistical distribution

,t A B

0,1x

pdf:

Beta function:

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- MIT Class Results (2008)

Beta Distribution parameters: a=2.27, b=5.26

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Expected Time & Variance Estimated Based on A, M & B

Mean expected Time (TE)

Time Variance (TV)

Early Finish (EF) and Late Finish (LF) computed as for CPM with TE

Set T=F for the end of the project

Example: A=3 weeks, B=7 weeks, M=5 weeks --> then TE=5 weeks

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A M BTE

2

2

6t

B ATV

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- What Can We Do With This?

Compute probability distribution for project finish

Determine likelihood of making a specific target date

Identify paths for buffers and reserves

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- Probability Distribution for Finish Date

PERT treats task times as probabilistic

Individual task durations are b-distributed

Simplify by estimating A, B and C times

Sums of multiple tasks are normally distributed

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Time

Normal Distribution for F

E[EF(n)]=F

See draft textbook Chapter 2, second half, for details of calculations.

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Probability of meeting target ?

Many Projects have target completion dates, T Interplanetary mission launch windows 3-4 days

Contractual delivery dates involving financial incentives or penalties

Timed product releases (e.g. Holiday season)

Finish construction projects before winter starts

Analyze expected Finish F relative to T

Time E[EF(n)]=F

Normal Distribution for F

T Probability that project will be done at or before T

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Probabilistic Slack

Time SL(i)

Normal (Gaussian) Distribution for Slack SL(i)

Target date for a tasks is not met when SL(i)<0, i.e. negative slack occurs

Put buffers in paths with high probability of negative slack

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Experiences with PERT?

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Today’s Agenda

Probabilistic Task Times

PERT (Program Evaluation and Review Technique)

Monte Carlo Simulation

Signal Flow Graph Method

System Dynamics

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- Project Simulation (from Lecture 5)

PanelDesign

DieDesign

ManufacturabilityEvaluation

PrototypeDie

ProductionDie

SurfaceModeling

PanelData

VerificationData

SurfaceData

Analysis Results

SurfaceData

SurfaceData

AnalysisResults

DieGeometry

DieGeometry

VerificationData

Highly Iterative Process • how often is each task carried out ? • how long to complete?

Image removed due to copyright restrictions.

Die Design and Manufacturing

Steven D. Eppinger, Murthy V. Nukala, and Daniel E. Whitney. "Generalised Models of Design Iteration Using Signal Flow Graphs", Research in Engineering Design. vol. 9, no. 2, pp. 112-123, 1997.

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Signal Flow Graph Model: Stamping Die Development

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Computed Distribution of Die Development Timing

0 20 40 60 80 100 1200

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10

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20

25

30

Project Duration [days]

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Simulation: 100 Runs

36.97

Estimate likely completion time

What else can we do with the simulation?

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Process Redesign/Refinement

. 1 432 5 6

7

8 9 10

Init. Surf.M odeling

Final Surf.M odeling

0.75 z 2z 2

z 20.25

z 1

z0.25 1

z1

0.1

z 30.9

z7Finish

0.5

Start

0 .7 5z2

z0 . 5

z 3z 3

Final M fg.Eval.

Prelim . M fg.Eval.-1

Prelim . M fg.Eval.-2

D ieDesign-1

DieDesign-2

D ieDesign-3

1

Most likely path

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What-if analysis

Spend more time on die design (1):

Increase time spent on initial die design (1) from 3 to 6 days

Increase likelihood of going to Initial Surface Modeling (7) from 0.25 to 0.75

Is this worthwhile doing?

Original E[F]=37 days

New E[F]= 37 days – no real effect ! Why?

Spend more time on final surface modeling (8):

Increase time for that task from 7 to 10 days

Increase likelihood of Finishing from 0.5 to 0.75

New E[F] = 30.8 days

Why is this happening?

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New Project Duration

20 30 40 50 60 70 80 90 100 110 1200

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100

150

200

250

300

350

400

450

500

Project Duration [days]

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Simulation: 1000 Runs

30.796

New distribution of Finish time

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Applying Project Simulation to HumLog Distribution Center Project (From Lecture 4)

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Simulation Application to HumLog DC

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1 2

3

4

5

6 7 8 9 10 11

12

17 15 16

18

20 21 22

13

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14 Start

0 4

2

2

8

4 2 1 2 2 3

4

6

2

2 2 1

3 1

4

1

0 4

4 6

4 6 6 14

14 18

44 44

23 29

34 36

32 34 28 32

25 28 20 21 18 20 21 23 23 25

34 36 34 35

36 39

39 43 43 44

29 30

A-Planning (14)

B-Contracting (9) C-Construction (11)

D-Staffing (7)

E-Installation (5)

F-Commissioning (5)

Simplify project into 7 major steps

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- Signal Flow Graph (with iterations)

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A

B

C D

D E

Start

End

z14

Planning

Contracting

z9

0.5z7

0.25z7

Staffing Construction

0.25z11

z5

Installation

0.2z3

0.8z5

z11

Commissioning

Add uncertain rework loops

re-planning loop

fix construction errors loop

sequential staffing

state in red 1

2

3

4 5

6 7

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- HumLog Simulation Results

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Shortest Duration: 44 weeks

Expected Duration: 56 weeks

In some cases duration can exceed 100 weeks !

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- Concept Question 2

What is your opinion of these “long tails” in project schedule distributions?

I don’t think they are real. This is a simulation artifact.

Yes, they exist. I have experienced this.

This is only relevant for projects that deal with very new products or extreme environments.

I’m not sure.

I don’t care.

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- System Dynamics Simulation

Can carry out Monte-Carlo Simulations with System Dynamics

Vary key model parameters such as fraction correct and complete, productivity, rework discovery fraction, number of staff etc…

Assume distributions for these parameters

Obtain insights into potential distribution of

Time to completion, required staffing levels, error rates, project cost …

Improve planning and adaptation of projects, and confidence in “claim” numbers

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- Example

Model without project control from last class and HW#3

Probabilistic Simulations:

Normal Productivity uniform distribution (0.9 – 1.1)

Normal Fraction Correct and Complete uniform distribution (0.75 – 0.95)

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- Results for project finish …

Individual simulations

Class3 Q on Q ProbabilisticWork Done1,000

750

500

250

00 15 30 45 60

Time (Month)

Confidence bounds

Class3 Q on Q Probabilistic50% 75% 95% 100%Work Done1,000

750

500

250

00 15 30 45 60

Time (Month)

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Distribution skewed to later finish

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- Results for project cost …

Individual simulations

Class3 Q on Q ProbabilisticCumulative Effort Expended4,000

3,000

2,000

1,000

00 15 30 45 60

Time (Month)

Confidence bounds

Class3 Q on Q Probabilistic50% 75% 95% 100%Cumulative Effort Expended4,000

3,000

2,000

1,000

00 15 30 45 60

Time (Month)

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- Monte Carlo and SD

Use in planning and adaptation:

Size and timing (fraction compete) of buffers

Timing of project milestones

Important use in specifying confidence bands in a “claim” situation for distribution of cost overrun due to client (owner)

“Fit” constrained – only simulations which fit the data can be accepted

Graham AK, Choi CY, Mullen TW. 2002. Using fit-constrained Monte Carlo trials to quantify confidence in simulation model outcomes. Proceedings of the 35th Annual Hawaii Conference on Systems Sciences. IEEE: Los Alamitos, Calif. (Available on request)

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- Usefulness of PERT and Simulation

Account for task duration uncertainties

Optimistic Schedule

Expected Schedule

Pessimistic Schedule

Helps set time reserves (buffers)

Compute probability of meeting target dates when talking to management, donors

Identify and carefully manage critical parts of the schedule

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Reading List

Project Management Book

Systems Engineering: Principles, Methods and Tools for System Design and Management

de Weck, Crawley and Haberfellner (eds.), Springer 2010

(draft) textbook to support SDM core classes at MIT

About 200 pages

Selected Article Steven D. Eppinger, Murthy V. Nukala, and Daniel E. Whitney. "Generalised

Models of Design Iteration Using Signal Flow Graphs", Research in Engineering Design. vol. 9, no. 2, pp. 112-123, 1997.

For this lecture, please read:

Chapter Network Planning Techniques Second Half of Chapter

MIT OpenCourseWarehttp://ocw.mit.edu

ESD.36 System Project ManagementFall 2012

For inforation about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.