Multidisciplinary System
Design Optimization (MSDO)
Design for Value
Lecture 19
Karen Willcox
Olivier de Weck
Select figures courtesy of Jacob Markish and Ryan Peoples. Used with permission.
1
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Today’s Topics
•
•
•
•
•
•
2
An MDO value framework
Lifecycle cost models
Value metrics & valuation techniques
Value-based MDO
Aircraft example
Spacecraft Example
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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?
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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?
manufacturing cost?
aircraft demand?
aircraft price?
•
•
•
•
4
•
aerodynamics?
structural dynamics?
tooling?
environmental impact?
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?
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
What about market Engineering
uncertainty?
Systems Division and Dept. of Aeronautics and Astronautics
Value Optimization Framework
Manufacturing
Tooling
Design
Operation
Aerodynamics
Structures
Weights
Mission
Stability & Control
Market factors
Fleet parameters
Competition
5
Cost
Module
Performance
Module
“Value” metric
“Optimal”
design
Revenue
Module
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Challenges
•
•
•
•
•
•
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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
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Cost Model
Cost
Module
Performance
Module
Revenue
Module
7
“Value” metric
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.
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Lifecycle Cost
95%
0
Disposal
20
Operation
and support
40
Manufacturing
and acquisition
60
Detailed design
65%
Preliminary design,
system integration
85%
80
Conceptual
design
Impact on LCC (%)
100
Time
8
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
9
Tooling
Engineering
- airframe design/analysis
- configuration control
- systems engineering
Tooling
- design of tools and fixtures
- fabrication of tools and fixtures
Other
- development support
- flight testing
Other
Cost incurred one time only:
Engineering
Non-Recurring Cost
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Development Cost Model
• Cashflow profiles based on beta curve:
c(t ) Kt 1 (1 t ) 1
• Typical development time ~6 years
• Learning effects captured – span, cost
0.06
Support
0.05
normalized cost
Tool Fab
0.04
Tool Design
ME
0.02
(from Markish)
Engineering
0.01
0
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
10
normalized time
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
11
Material
Support
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
Recurring Cost
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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.
Yx
Y0 x
n
Yx = number of hours to produce unit x
n = log b/log 2
b = learning curve factor (~80-100%)
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Learning Curve
Cost of unit
1
0.8
0.6
0.4
b=0.9
0.55
0.2
Every time
production
doubles,
cost is
reduced by
a factor of
0.9
0
0
10
20
30
40
50
Unit number
Typical LC slopes: Fab 90%, Assembly 75%, Material 98%
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Airplane Related Operating Costs
CAPITAL COSTS:
Financing
Insurance
Depreciation
Capital
Costs
CAROC
40%
60%
CASH AIRPLANE RELATED
OPERATING COSTS:
Crew
Fuel
Maintenance
Landing
Ground Handling
GPE Depreciation
GPE Maintenance
Control & Communications
CAROC is only 60% - ownership costs are significant!
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Value Metric
Need to provide a
quantitative metric that
incorporates cost,
performance and
revenue information.
Cost
Module
Performance
Module
“Value” metric
In optimization, need to
be especially carefully
about what metric we
choose...
Revenue
Module
15
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
Demand
Revenue
Price
EBIT
Schedule
Product
Quality
System
Design
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From Markish,
Fig. 1, pg 20
Economic
Value
Added
Cost
Shareholder
Value
Customer value derived from
quality, timeliness, price.
Shareholder value derived
from cost and revenue, which
is directly related to customer
satisfaction.
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Value Metrics
Traditional Metrics
Augmented Metrics
performance
weight
speed
cost
revenue
profit
quietness
emissions
commonality
...
The definition of value will vary depending on your system
and your role as a stakeholder, but we must define a
quantifiable metric.
17
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
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C0
C1
1 r
C2
1 r
CT
2
1 r
T
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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%
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NPV =
$18,400
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Risk-Adjusted Discount Rate
•
•
DCF analysis assumes a fixed schedule of cash flows
What about uncertainty?
•
•
Common approach: use a risk-adjusted discount rate
The discount rate is often used to reflect the risk
associated with a project: the riskier the project, use a
higher discount rate
Typical discount rates for commercial aircraft programs:
12-20%
•
•
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Issues with this approach?
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Net Present Value (NPV)
T
NPV
t
Ct
t
0 (1 r )
1500
500
29
27
25
23
21
19
17
15
13
11
9
7
5
3
0
1
Cashflow, Pt [$]
1000
Cashflow
DCF (r=12%)
-500
-1000
-1500
Program Time, t [yrs]
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Discounted payback
•
Payback criterion modified to account for the time
value of money
– Cash flows before cut-off date are discounted
25
•
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
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
NPV
C0
C1
1 IRR
C2
1 IRR
CT
2
1 IRR
T
0
• 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
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Return on Investment (ROI)
• Return of an action divided by the cost
of that action
ROI
revenue cost
cost
• Need to decide whether to use actual or
discounted cashflows
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Decision Tree Analysis (DTA)
• NPV analysis with different future scenarios
• Weighted by probability of event occurring
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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)
29
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Dynamic Programming:
Problem Formulation
•
•
•
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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?
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Dynamic Programming:
Problem Elements
1. State variables
2. Control variables
st
ut
3. Randomness
4 Profit function
4.
5. Dynamics
1
⎧
⎫
Ft ( st ) = max ⎨π t ( st , ut ) +
Et [Ft +1 ( st +1 )]⎬
ut
1+ r
⎩
⎭
•
Solution:
•
Solve recursively
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Dynamic Programming:
Operating Modes
How to model decision making?
32
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Example: BWB
Fuselage bays
BWB-450
• Blended-Wing-Body (BWB):
– Proposed new jet transport
concept
• 250-seat, long range
• Part of a larger family sharing
common centerbody bays,
wings, ...
BWB-250C
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Inner wing
Outer wing
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
operating mode
16
120
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
mode
demand
100
80
60
40
20
quantity demanded
per year
BWB Example: Simulation Run
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
18
20
22
24
26
28
30
time (years)
3,000,000
2,000,000
cash flow ($K)
1,000,000
0
0
2
4
6
8
10
12
14
16
-1,000,000
-2,000,000
-3,000,000
-4,000,000
time (years)
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
BWB Example:
Importance of Flexibility
25
dynamic programming
program value ($B)
20
deterministic NPV
15
10
5
0
-5
3
5
7
11
18
28
44
69
108 171 270
-10
initial annual demand forecast
At baseline of 28 aircraft, DP value is $2.26B versus
deterministic value of $325M
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Traditional Design Optimization
 Objective function:
usually minimum
weight
 Design vector:
attributes of design,
e.g. planform
geometry
 Performance model:
contains several
engineering
disciplines
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Performance
Model
Objective
function J(x)
Design
vector x
Optimizer
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Coupled MDO Framework
Objective function: value
metric, e.g. NPV
Simulation model:
performance and financial
Market
Stochastic element
Cost
Performance
Model
Cost
Valuation
Revenue
Price,
Demand
Design
vector x
Optimizer
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Objective
function J(x)
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
38
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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 similar
Minimum-GTOW planform
 Constrained to satisfy design
requirements
 Unable to move dramatically in
design space
Maximum-value planform
39
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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 relative to
max-E[NPV] design
– E[NPV] for 20% design = 3.7% decrease
• High-rd drives design to reduce development
costs
• Traditional NPV not
appropriate
2
0
– As valuation metric
– As optimization
objective
Relative Cash Flow
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
-2
r_d = 12%
-4
r_d = 20%
-6
-8
-10
40
Program Year
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Range Specification
• Comparison of min-GTOW and max-E[NPV] design
solutions
• E[NPV] for varying ranges relative to max-E[NPV] design
Relative E[NPV]
1.2
1
0.8
0.6
max E[NPV]
0.4
min GTOW
0.2
0
5000
5500
6000
6500
7000
7500
8000
8500
9000
9500
10000
Range (nmi)
41
Design decisions
based on understanding
of- Prof.
E[NPV]
impact
© Massachusetts
Institute of Technology
de Weck
and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Speed Specification
• Comparison of E[NPV] and other metrics for varying
speeds
1.1
Relative metric value
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.78
E[NPV]
M*L/D
M*P/D
M*P*R/GTOW
0.8
0.82
0.84
0.86
0.88
0.9
0.92
Cruise Mach number
42
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
43
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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.
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© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
45
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
Operations
- end-of-life (EOL) disposal
Production
RDT&E
Space
Mission
Architecture
Program
Level Costs
• Management
• Systems Eng
• Integration
46
Space
Segment
Launch
Segment
Ground
Segment
Operations
and Support
• Payload
• Launch Vhc • Facilities
• Personnel
• Spacecraft • Launch Ops • Equipment • Training
• Software
• Software
• S/C-L/V
• Maintenance
• etc
• “Systems”
integration
Spares
© Massachusetts Institute
of Technology
- Prof. de Weck•and
Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Cost Estimating Methods
Basic techniques to develop Cost Models:
47
(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 ©toMassachusetts
find theoretical
first unit (TFU) cost
Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
48
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Process for developing CER’s
Computer
Software
Subsystem N
….
Subsystem B
Subsystem A
Cost/parametric data
Constant Year Costs
Regression
Analysis
Preferred Form
$
Step 1
Develop Database
File
49
AW b
Step 2
Apply Regression
Analysis
Subsystem N
….
Subsystem B
Subsystem A
$
Weight - kg
Key statistics: R2,
Standard Error: RMS
Step 3
Obtain CER’s and
Error Statistics
© Massachusetts
Institute
of Technology - Prof. de Weck and Prof. Willcox
(Cost Model
Assumption)
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Adjustment to constant-year dollars
It is critical that cost estimated be based on a
constant-year dollar bases. Reason: INFLATION
E.g. All costs are adjusted to FY92 (“Fiscal Year 1992”)
CY
R CY
N
Past Years
R
Use actual inflation numbers
1.040 1.037 1.034
FY 92
FY 93
Future Years
R
50
1 iRATE
N
1.115
Convert Oct-1991 cost
to Oct-1994 costs
FY 94
Use forecasted inflation numbers
e.g. 3.1% yearly inflation in U.S.
$ 1M in FY 1980 corresponds to
$ 2.948M in FY 2005 (projected)
See Table 20-1 ©
onMassachusetts
handout Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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
relay
optics
object
k-th aperture
beam
combiner
B
lk
k
b
Lk
Dk
51
dk
sub-telescope plane
combiner plane
focal plane
(input ©
pupil)
(exit
pupil)
(image
Massachusetts Institute of Technology - Prof.
depupil)
Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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:
52
S
0.37 D 2.58 [M$] (1980)
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Cost Modeling Approach
Monolithic System
Modular Golay System
(A)
Sub-telescope
(B)
Relay optics and
none
combiner
(C)
Detector
Total Cost:
53
Does not include
development
© Massachusetts Institute of Technology
- Prof. de Weck and cost
Prof. Willcox
total = CA + CB +CC
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Cost Estimation Relationships
(A) Optical Telescope Assy:
Modular array telescope:
CA
CA
B 1
(C) Detector: CCD:
54
LA D
NB
TFU
(includes learning curve)
(B) Relay & Combining Optics:
LA D
log 100% / S / log 2
Use ARGOS cost database
Cc
Lc
n pix
Next Step: Need to determine coefficients based
© Massachusettspricing
Institute of Technology
- Prof. de Weck and Prof. Willcox
on available commercial
data
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Small Amateur Telescopes (I)
Telescope Comparison
14000
12000
DHQ f/5
DHQ f/4.5
D Truss f/5
Obsession f/4.5
Celestron G-f/10
Price [US$]
10000
8000
6000
4000
2000
0
55
0
10
20
30
40
50
Diameter Size[cm]
60
70
80
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
8
Telescope Purchase Cost C [2001$]
Cumulative Weighted Fitting Error
Small Amateur Telescopes (II)
Telescope CER fitting
x 10
7
6
5
4
3
2
1
0 1
2
3
4
5
6
7
8
Power Coefficient
9
x 10
3
4
2.76
Telescope Cost CER (Aperture): C=28917*D
2.5
2
1.5
1
0.5
10
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Telescope Diameter D [m]
1
Minimum yields best CER fit
exponent =2.76
56
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Professional Telescope OTA cost
4
x 10
5
3.5
CERs for
Ritchey-Chretien
Ritchey-Chretien
Classical Cassegrain
OTA Cost [2001 $]
3
CRC
2.5
376000 D2.80
Classical Cassegrain
2
CCC
1.5
322840 D2.75
1
0.5
0
0
57
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Aperture Diameter D [m]
0.8
0.9
1
Remarkable Result:
virtually identical
power law across
completely different
product lines.
Company: Optical Guidance Systems
(http:www.opticalguidancesystems.com)
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
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:
$ 32,874.Passive Optics: Collimators, Combiner, etc
Active Optics: FSM, Fold Mirrors etc...
$ 18,859.-
58
ma = 10
About:
$ 50,000.-
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
CCD Cost Models
4
3
Polynomial Fit of Compiled Data
x 10
Least Squares Polynomial Fit
Compiled Data
2.5
Price [US$]
2
1.5
AP-9 (KAF-6303E)
1
CCCD
0.5
0
0
500
1000
1500 2000 2500 3000 3500
Square Root of Numbers of Pixels
4000
4500
0.68
n pix
1.23
5000
It appears that CCD cost also depends on
factors other than raw pixel count. Need to investigate.
59
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
Break-Even Analysis
4
x 10
5
Break Even Cost Analysis
3.5
Optical Systems Cost [2001 $]
Assumptions:
N=3
npix = 2048
Monolithic
Golay-3
3
Relay optics
and combiner
costs fixed
2.5
2
1.5
ARGOS
1
0.5
0
0.1
60
0.2
0.3
0.4
0.5
0.6
0.7
Equivalent Aperture D [m]
0.8
0.9
1
Preliminary
Analysis
suggest
crossover
around 0.7 m
© Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox
Engineering Systems Division and Dept. of Aeronautics and Astronautics
MIT OpenCourseWare
http://ocw.mit.edu
ESD.77 / 16.888 Multidisciplinary System Design Optimization
Spring 2010
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