Multidisciplinary System Design Optimization (MSDO) · Multidisciplinary System Design Optimization...

1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox

Engineering Systems Division and Dept. of Aeronautics and Astronautics

Design for Value

Lecture 19

Karen Willcox

Olivier de Weck

Multidisciplinary System

Design Optimization (MSDO)

Select figures courtesy of Jacob Markish and Ryan Peoples. Used with permission.



Today’s Topics

• An MDO value framework

• Lifecycle cost models

• Value metrics & valuation techniques

• Value-based MDO

• Aircraft example

• Spacecraft Example



Optimal Design

• Traditionally, design has focused on performance

e.g. for aircraft design

optimal = minimum weight

• Increasingly, cost becomes important

• 85% of total lifecycle cost is locked in by the end of

preliminary design.

• But minimum weight minimum cost maximum value

• What is an appropriate value metric?



Design Example• We need to design a particular portion of the wing

• Traditional approach: balance the aero & structural requirements,

minimize weight

• We should consider cost: what about an option that is very cheap to

manufacture but performance is worse?

aerodynamics?

• How do we trade performance and cost?

• How much performance are we willing to give up for $100 saved?

• What is the impact of the low-cost design on price and demand of

this aircraft?

• What is the impact of this design decision on the other aircraft I

build?

• What about market uncertainty?

structural dynamics?

manufacturing cost?

aircraft demand?

aircraft price?tooling?

environmental impact?



Cost

Module

“Value” metricPerformance

Module

Aerodynamics

Structures

Weights

Mission

Stability & Control

Revenue

Module

Value Optimization Framework

Manufacturing

Tooling

Design

Operation

Market factors

Fleet parameters

Competition

“Optimal”

design



Challenges

• Cost and revenue are difficult to model

– often models are based on empirical data

– how to predict for new designs

• Uncertainty of market

• Long program length

• Time value of money

• Valuing flexibility

• Performance/financial groups even more uncoupled

than engineering disciplines



Cost Model

Need to model the lifecycle

cost of the system.

Life cycle :

Design - Manufacture -

Operation - Disposal

Lifecycle cost :

Total cost of program over

life cycle

85% of Total LCC is locked

in by the end of preliminary

design.

Cost

Module


Module

Revenue

Module



Lifecycle Cost

0

20

40

60

80

100

65%

Co

ncep

tua

l

desig

n

Pre

lim

inary

desig

n,

syste

m i

nte

gra

tio

n

Deta

iled

de

sig

n

Man

ufa

ctu

rin

g

an

d a

cq

uis

itio

n

Op

era

tio

n

an

d s

up

po

rt

Dis

po

sal

Time

Impact on L

CC

(%

)

85%

95%



Non-Recurring Cost

Cost incurred one time only:

Engineering

- airframe design/analysis

- configuration control

- systems engineering

Tooling

- design of tools and fixtures

- fabrication of tools and fixtures

Other

- development support

- flight testing

Engin

eeri

ng

Toolin

gO

ther



Development Cost Model

• Cashflow profiles based on beta curve:

• Typical development time ~6 years

• Learning effects captured – span, cost

11 )1()( tKttc

0

0.01

0.02

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

normalized time

Support

Tool Fab

Tool Design

ME

Engineering

no

rmalized

co

st

(from Markish)



Recurring Cost

Cost incurred per unit:

Labor

- fabrication

- assembly

- integration

Material to manufacture

- raw material

- purchased outside production

- purchased equipment

Production support

- QA

- production tooling support

- engineering support

Labor

Mate

rial

Support



Learning Curve

As more units are made, the recurring cost per

unit decreases.

This is the learning curve effect.

e.g. Fabrication is done more quickly, less

material is wasted.

n

x xYY 0

Yx = number of hours to produce unit x

n = log b/log 2

b = learning curve factor (~80-100%)



Learning Curve

0.55

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Unit number

Co

st

of

un

it

b=0.9

Typical LC slopes: Fab 90%, Assembly 75%, Material 98%

Every time

production

doubles,

cost is

reduced by

a factor of

0.9



CASH AIRPLANE RELATED

OPERATING COSTS:

Crew

Fuel

MaintenanceLanding

Ground Handling

GPE Depreciation

GPE Maintenance

Control & Communications

Airplane Related Operating Costs

CAROC is only 60% - ownership costs are significant!

CAROC

60%40%

Capital

Costs

CAPITAL COSTS:

Financing

Insurance

Depreciation



Value Metric

Need to provide a

quantitative metric that

incorporates cost,

performance and

revenue information.

In optimization, need to

be especially carefully

about what metric we

choose...

Cost

Module


Module

Revenue

Module



What is Value?

• Objective function could be different for each stakeholder

e.g. manufacturer vs. airline vs. flying public

• Program related parameters vs. technical parameters

cost, price, production quantity, timing

• Traditionally program-related design uncoupled from

technical design

Customer

Value

Shareholder

Value

Product

Quality

Schedule

Cost

Economic

Value

Added

Demand

Revenue

EBIT

System

Design

Price

From Markish,

Fig. 1, pg 20

Customer value derived from

quality, timeliness, price.

Shareholder value derived

from cost and revenue, which

is directly related to customer

satisfaction.



Value Metrics

performance

weight

speed

Traditional Metrics

cost

revenue

profit

quietness

emissions

commonality

...

Augmented Metrics

The definition of value will vary depending on your system

and your role as a stakeholder, but we must define a

quantifiable metric.



Valuation Techniques

Investor questions:

• How much will I need to invest?

• How much will I get back?

• When will I get my money back?

• How much is this going to cost me?

• How are you handling risk & uncertainty?

Investment Criteria

• Net present value

• Payback

• Discounted payback

• Internal rate of return

• Return on investment



Net Present Value (NPV)

• Measure of present value of various cash flows in different

periods in the future

• Cash flow in any given period discounted by the value of a

dollar today at that point in the future

– “Time is money”

– A dollar tomorrow is worth less today since if properly

invested, a dollar today would be worth more tomorrow

• Rate at which future cash flows are discounted is

determined by the “discount rate” or “hurdle rate”

– Discount rate is equal to the amount of interest the

investor could earn in a single time period (usually a

year) if s/he were to invest in a “safer” investment



Discounted Cash Flow (DCF)

• Forecast the cash flows, C0, C1, ..., CT of the project

over its economic life

– Treat investments as negative cash flow

• Determine the appropriate opportunity cost of capital

(i.e. determine the discount rate r)

• Use opportunity cost of capital to discount the future

cash flow of the project

• Sum the discounted cash flows to get the net present

value (NPV)

NPV C0

C1

1 r

C2

1 r2

CT

1 rT



DCF example

Period Discount Factor Cash Flow Present Value

0 1 -150,000 -150,000

1 0.935 -100,000 -93,500

2 0.873 +300000 +261,000

Discount rate = 7% NPV = $18,400



Risk-Adjusted Discount Rate

• DCF analysis assumes a fixed schedule of cash flows

• What about uncertainty?

• Common approach: use a risk-adjusted discount rate

• The discount rate is often used to reflect the risk

associated with a project: the riskier the project, use a

higher discount rate

• Typical discount rates for commercial aircraft programs:

12-20%

• Issues with this approach?



Net Present Value (NPV)

0 (1 )

Tt

tt

CNPV

r

-1500

-1000

-500

0

500

1000

1500

1 3 5 7 9

11

13

15

17

19

21

23

25

27

29

Cashflow

DCF (r=12%)

Program Time, t [yrs]

Cashflow

, P

t[$

]



Payback Period

• How long it takes before entire initial investment is

recovered through revenue

• Insensitive to time value of money, i.e. no

discounting

• Gives equal weight to cash flows before cut-off date

& no weight to cash flows after cut-off date

• Cannot distinguish between projects with different

NPV

• Difficult to decide on appropriate cut-off date



Discounted payback

• Payback criterion modified to account for the time

value of money

– Cash flows before cut-off date are discounted

• Overcomes objection that equal weight is given to

all flows before cut-off date

• Cash flows after cut-off date still not given any

weight



Internal rate of return (IRR)

• Investment criterion is “rate of return must be greater than the opportunity cost of capital”

• Internal rate of return is equal to the discount rate for which the NPV is equal to zero

• IRR solution is not unique

– Multiple rates of return for same project

• IRR doesn’t always correlate with NPV

– NPV does not always decrease as discount rate increases

NPV C0

C1

1 IRR

C2

1 IRR2

CT

1 IRRT

0



Return on Investment (ROI)

• Return of an action divided by the cost

of that action

• Need to decide whether to use actual or

discounted cashflows

revenue cost

costROI



Decision Tree Analysis (DTA)

• NPV analysis with different future scenarios

• Weighted by probability of event occurring



Real Options Valuation Approach

In reality:

Cashflows are uncertain

Ability to make decisions as future unfolds

View an aircraft program as a series of investment decisions

Spending money on development today gives the option to build and sell aircraft at a later date

Better valuation metric: expected NPV from dynamic programming algorithm (Markish, 2002)



Dynamic Programming:

Problem Formulation

• The firm:

– Portfolio of designs

– Sequential development phases

– Decision making

• The market:

– Sale price is steady

– Quantity demanded is unpredictable

– Units built = units demanded

• Problem objective:

– Which aircraft to design?

– Which aircraft to produce?

– When?

Dynamic Programming:Dynamic Programming:Problem ElementsProblem ElementsProblem ElementsProblem Elements

1. State variables stt

2. Control variables ut

3. Randomness

4 Profit function4. Profit function

5. Dynamics

• Solution: [ ]⎭⎬⎫

⎩⎨⎧

++= ++ )(

11),(max)( 11 ttttttutt sFE

russF

t

π

• Solve recursively

31 © Massachusetts Institute of Technology - Prof. de Weck and Prof. WillcoxEngineering Systems Division and Dept. of Aeronautics and Astronautics



Dynamic Programming:

Operating Modes

How to model decision making?



BWB-450

BWB-250C

Fuselage bays

Inner wing

Outer wing

Example: BWB

• Blended-Wing-Body (BWB):

– Proposed new jet transport

concept

• 250-seat, long range

• Part of a larger family sharing common centerbody bays, wings, ...



BWB Example: Simulation Run

-4,000,000

-3,000,000

-2,000,000

-1,000,000

0

1,000,000

2,000,000

3,000,000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

time (years)

cash

flo

w (

$K

)

0123456789

10111213141516

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

time (years)

op

era

tin

g m

od

e

0

20

40

60

80

100

120

qu

an

tity

dem

an

ded

per

yea

r

mode

demand



BWB Example:

Importance of Flexibility

-10

-5

0

5

10

15

20

25

3 5 7 11 18 28 44 69 108 171 270

initial annual demand forecast

pro

gra

m v

alu

e (

$B

)

dynamic programming

deterministic NPV

At baseline of 28 aircraft, DP value is $2.26B versus deterministic value of $325M



Traditional Design Optimization

Objective function: usually minimum weight

Design vector: attributes of design, e.g. planform geometry

Performance model: contains several engineering disciplines

Performance

Model

Optimizer

Design

vector x

Objective

function J(x)



Coupled MDO Framework

Performance

Model

Cost

Revenue

Optimizer

Valuation

Market

Price,

Demand

Cost

Design

vector xObjective

function J(x)

Objective function: value

metric, e.g. NPV

Simulation model:

performance and financial

Stochastic element



Value-Based Optimization Results

Boeing BWB case study

475 passengers, 7800 nmi range

Baseline: optimized for minimum GTOW

Outcomes

Comparison of min GTOW and max E[NPV]

designs

Traditional NPV vs. stochastic E[NPV]

Effect of range requirement on program value

Effect of speed requirement on program value



Different Objectives, Different Designs

New objective results in tradeoff:Lower structural weight, lower

cost

Higher fuel burn, lower price

Net result

2.3% improvement in value

Overall design very similarConstrained to satisfy design

requirements

Unable to move dramatically in design space

Minimum-GTOW planform

Maximum-value planform



Deterministic vs. Stochastic Valuation

• Discount rates: 12% and 20%– Computational expense reduced, but NPV results are

negative

– E[NPV] for 12% design = 0.58% decrease

– E[NPV] for 20% design = 3.7% decrease

• High-rd drives design to reduce development costs

• Traditional NPV not

appropriate

– As valuation metric

– As optimization

objective

relative to

max-E[NPV] design

-10

-8

-6

-4

-2

0

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Program Year

Rela

tive C

ash

Flo

w

r_d = 12%

r_d = 20%



Range Specification

• Comparison of min-GTOW and max-E[NPV] design

solutions

• E[NPV] for varying ranges relative to max-E[NPV] design

Design decisions based on understanding of E[NPV] impact

0

0.2

0.4

0.6

0.8

1

1.2

5000 5500 6000 6500 7000 7500 8000 8500 9000 9500 10000

Range (nmi)

Rela

tive E

[NP

V]

max E[NPV]

min GTOW



Speed Specification

• Comparison of E[NPV] and other metrics for varying

speeds

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92

Cruise Mach number

Re

lati

ve

me

tric

va

lue

E[NPV]

M*L/D

M*P/D

M*P*R/GTOW



Lecture Summary

• Designing for value is crucial: for a program to be

successful, we cannot focus exclusively on performance

• The definition of value is flexible, and will vary depending

on the application and on your interest as a stakeholder

• Financial metrics can be used to quantifying value, but

use caution in your choice of value objective function

• Cost and revenue are difficult to model – often use

empirical data

• It is important that uncertainty and risk are handled

appropriately

• There is much work to be done on this issue



References

Brealey, R. & Myers, S., Principles of Corporate Finance, 7th Edition,

McGraw-Hill, NY 2003

Markish, J., “Valuation Techniques for Commercial Aircraft Program

Design”, Masters Thesis, MIT Dept. of Aeronautics & Astronautics, June

2002.

Markish, J. and Willcox, K., “Value-Based Multidisciplinary Techniques

for Commercial Aircraft System Design”, AIAA Journal, Vol. 41, No. 10,

October 2003, pp. 2004-12.

Peoples, R. and Willcox, K., “Value-Based Multidisciplinary Optimization

for Commercial Aircraft Design and Business Risk Assessment,” Journal

of Aircraft, Vol. 43, No. 4, July-August, 2006, pp. 913-921.

Roskam, J., Airplane Design Part VIII, 1990.

Raymer, D., Aircraft Design: A Conceptual Approach, 3rd edition, 1999.

Schaufele, R., The Elements of Aircraft Preliminary Design, 2000.



System Cost Modeling

This section will:

- present a process for obtaining system

cost estimates, particularly for space systems

- provide cost-estimating relationships

- describe how to assess uncertainty in cost estimates

- provide a specific example: optical systems cost

dWo, 5-6-2002



Cost Breakdown Structure (CBS)

Organizational Table that collects costs, covers:

- research, development, test and evaluation (RDT&E)

- production, including learning curve effects

- launch and deployment

- operations

- end-of-life (EOL) disposal

Space

Mission

Architecture

Program

Level Costs

Space

Segment

Launch

Segment

Ground

Segment

Operations

and Support

• Management

• Systems Eng

• Integration

• Payload

• Spacecraft

• Software

• “Systems”

• Launch Vhc

• Launch Ops

• S/C-L/V

integration

• Facilities

• Equipment

• Software

• etc

• Personnel

• Training

• Maintenance

• Spares

RDT&E

ProductionOperations



Cost Estimating Methods

Basic techniques to develop Cost Models:

(1) Detailed bottom-up estimating

- identify and specify lower level elements

- estimated cost of system is of these

- time consuming, not appropriate early, accurate

(2) Analogous Estimating

- look at similar item/system as a baseline

- adjust to account for different size and complexity

- can be applied at different levels

(3) Parametric Estimating

- uses Cost Estimation Relationships (CER’s)

- needed to find theoretical first unit (TFU) cost



Parametric Cost Models

Are most appropriate for trade studies:

Advantages:• less time consuming than traditional bottom-up estimates

• more effective in performing cost trades

• more consistent estimates

• traceable to specific class of (space) systems

Major Limitations:• applicable only to parametric range of historical data

• lacking new technology factors, adjust CER to account for new technology

• composed of different mix of “things” in element to be costed

• usually not accurate enough for a proposal bid



Process for developing CER’s

Subsystem A

Subsystem B

Subsystem N….

Cost/parametric data

Constant Year Costs

Regression

Analysis

Preferred Form

(Cost Model Assumption)

Subsystem A

Subsystem B

Subsystem N….

$

Weight - kg

$ bAW

Computer

Software

Step 1

Develop Database

File

Step 2

Apply Regression

Analysis

Step 3

Obtain CER’s and

Error Statistics

Key statistics: R2,

Standard Error: RMS



Adjustment to constant-year dollars

It is critical that cost estimated be based on a

constant-year dollar bases. Reason: INFLATION

Y Y NC R C

E.g. All costs are adjusted to FY92 (“Fiscal Year 1992”)

Past Years

Future Years

Use actual inflation numbers

Use forecasted inflation numbers

e.g. 3.1% yearly inflation in U.S.

See Table 20-1 on handout

92 93 94

1.040 1.037 1.034 1.115

FY FY FY

R Convert Oct-1991 cost

to Oct-1994 costs

1N

RATER i$ 1M in FY 1980 corresponds to

$ 2.948M in FY 2005 (projected)



Case: Modular Optics Cost Modeling

• Investigate economical viability of modular

optics given performance constraints

• Focus on monolithic Cassegrain telescopes

versus Golay-3 design

• Use real data and experience from ARGOS

k

Lk

B

Dk

lk b

dk

sub-telescope plane

(input pupil)

combiner plane

(exit pupil)focal plane

(image pupil)

object

k-th aperture

beam

combiner

relay

optics



Literature Search

Kahan, Targrove, “Cost modeling of large

spaceborne optical systems”, SPIE, Kona, 1998

Humphries, Reddish, Walshaw,”Cost scaling laws

and their origin: design strategy for an optical array

telescope”, IAU, 1984

Meinel, “Cost-scaling laws applicable to very large

optical telescopes”, SPIE, 1979

Meinel’s law: 2.580.37 [M$] (1980)S D



Cost Modeling Approach

Monolithic System Modular Golay System

(A)Sub-telescope

Total Cost: total = CA + CB +CC

(B)

Relay optics and

combiner

(C)

Detector

Does not include

development cost

none



Cost Estimation Relationships

A AC L D

Next Step: Need to determine coefficients based

on available commercial pricing data

(A) Optical Telescope Assy:

(B) Relay & Combining Optics:

(C) Detector: CCD:

Modular array telescope:

TFU

1 log 100% / / log 2

B

A AC L D N

B S

c c pixC L n

(includes learning curve)

Use ARGOS cost database



Small Amateur Telescopes (I)

0 10 20 30 40 50 60 70 800

2000

4000

6000

8000

10000

12000

14000Telescope Comparison

Diameter Size[cm]

Price

[U

S$

]

DHQ f/5

DHQ f/4.5

D Truss f/5

Obsession f/4.5

Celestron G-f/10



Small Amateur Telescopes (II)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3x 10

4

Telescope Diameter D [m]Te

lesco

pe P

urc

ha

se

Co

st

C [

20

01

$] Telescope Cost CER (Aperture): C=28917*D

2.76

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7x 10

Power Coefficient

Cum

ula

tive

Weig

hte

d F

ittin

g E

rro

r

Telescope CER fitting8

Minimum yields best CER fit

exponent =2.76



Professional Telescope OTA cost

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

Aperture Diameter D [m]

OT

A C

ost [2

00

1 $

]

Ritchey-Chretien

Classical Cassegrain

Company: Optical Guidance Systems

(http:www.opticalguidancesystems.com)

CERs for

Ritchey-Chretien

Classical Cassegrain

Remarkable Result:

virtually identical

power law across

completely different

product lines.

2.80376000RCC D

2.75322840CCC D



Relay and Combining Optics

Cost of relay optics depends on:

• number and type of actuators: ODL, FSM, active

translation stages, active pyramid mirrors

• sensing elements (CCD, quad cells etc)

• aperture magnification ma

• Quality requirements (RMS WFE)

As interim solution use ARGOS cost database:

Passive Optics: Collimators, Combiner, etc

Active Optics: FSM, Fold Mirrors etc...

ma = 10

$ 32,874.-

$ 18,859.-

About: $ 50,000.-



CCD Cost Models

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

0.5

1

1.5

2

2.5

3x 10

4 Polynomial Fit of Compiled Data

Square Root of Numbers of Pixels

Price [

US

$]

Least Squares Polynomial Fit

Compiled Data

1.23

0.68CCD pixC n

It appears that CCD cost also depends on

factors other than raw pixel count. Need to investigate.

AP-9 (KAF-6303E)



Break-Even Analysis

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

Equivalent Aperture D [m]

Op

tical S

yste

ms C

ost [2

00

1 $

]Break Even Cost Analysis

Monolithic

Golay-3

ARGOS

Preliminary

Analysis

suggest

crossover

around 0.7 m

Assumptions:

N=3

npix = 2048

Relay optics

and combiner

costs fixed

MIT OpenCourseWarehttp://ocw.mit.edu

ESD.77 / 16.888 Multidisciplinary System Design Optimization

Spring 2010

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