Post on 24-Aug-2021
11/13/2012 1
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A Portfolio Approach to System-of-Systems
Acquisition and Architecture
NDIA Conference 26-OCTOBER-2012
Dr. Daniel DeLaurentis
Dr. Navindran Davendralingam davendra@purdue.edu
School of Aeronautics & Astronautics Center for Integrated Systems in Aerospace
Purdue University
This material is based upon work supported, in whole or in part, by
the U.S. Department of Defense through the Systems Engineering
Research Center (SERC) under Contract H98230-08-D-0171. SERC
is a federally funded University Affiliated Research Center managed
by Stevens Institute of Technology.
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Presentation Outline
• Motivation: Defense Acquisitions and Systems Engineering
• SoS Architecting and Acquisition: Wave Model context
• An Investment Portfolio Approach
―Mean Variance Approach
―Mean-Variance: A Robust Version
• Concept Problem: Simple Littoral Combat Ship (LCS)
―Robust Portfolio application
―Multiple risk measures
―Operational Robustness using Bertsimas-Sim method
• Future Work
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Motivation: Acquisitions and Systems Engineering
Image from: Presentation slides by RDML Vic Guillory of
OPNAV at Mine Warfare Association Conference (titled
“Littoral Combat Ship”, 08-May-07)
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The Big Picture
Bayesian & FDNA Approach
Stand-In Redundancy
Petri-Nets
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SoS Architecture Development
How do we support these actions for SoS acquisitions?
*adapted from Dahmann et. al, “Integrating Systems Engineering and Test & Evaluation in
System of Systems Development” IEEE Vancouver, 2011
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SoS Acquisition and Architecture
• How to leverage acquiring capabilities against associated risk?
• What about system interdependencies?
• What about performance/development uncertainty considerations?
• Can I exploit architectural connectivity for robustness?
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A Portfolio Approach: Background
• Classical Mean-Variance optimization among techniques adopted by financial engineering and operations research.
• Balance expected profit (performance) against risk (variance) in investments
• Generates efficiency frontier of optimal portfolios given investor risk averseness
• Systems (nodes) can be modeled as potential investment assets how do we invest?
Nodes = systems
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• Model individual system as
‘nodes’
• Functional & Physical
representation
• Rules for node connectivity
• Compatibility between
nodes
• Bandwidth of linkages
• Supply (Capability)
• Demand (Requirements)
• Relay capability
Portfolio Approach: SoS Modelling Additions
Capability Requirement
Relay Bandwidth
Compatibility.
Inputs
Outputs
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Mean-Variance Portfolio Approach
Portfolio Fraction
Portfolio Total Budget
Requirements Satisfaction
Selection Rules (Compatibility)
Uncertainty in Covariance
(Interdependencies)
Capability Cost Risk
Co
nstr
ain
ts
Objective
Maximize Performance Index
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Extension to SoS Interconnectivities
max
s.t.
B
ic i c
i
c
B
cij j rj
i
B
cij j rj
i
S w X R
R
X X S
X X S
1
0
0
n
cij ij
c
X X
X X M
0
0
cij ij
c
B
cij cij j rj
i j
B
i
M X X
X X X S
X
Limit
0 capability
TB
ij i critical
cij cij
cij
X
X
X c
, binary {0,1}
ij ij
L U
ij
B
cij jX X
Maximize Capability Performance
Index
Sufficient Capabilities Supplied
Individual System Requirements met
Connectivity Rules Obeyed
(Big-M formulation)
Risk Tolerance (per measure of risk)
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Portfolio Uncertainty
• Sources of uncertainty
―System Capability: Actual performance of system individually and as a whole SoS entity
―System Interdependence: Interdependency variances/covariances?
• Addressing uncertainty
―Operations Research/Financial Engineering Methods to address uncertainty measures
―Introduce uncertainty in interdependencies and individual asset performances
―Introduce SoS connectivity in portfolio space
System 1
System 2
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Mean-Variance Portfolio: A Robust Approach
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Robust Portfolio Case Study: Simple LCS Portfolio
Diagonal : System Variance
Off Diagonal : System
Interdependency
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Robust Portfolio Case Study: Simple LCS Portfolio
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Portfolio Approach: LCS Multiple Risk Measures
Weapon Variance (Risk)
Constraint
Comm. Variance (Risk)
Constraint
• Layered measure of
risk (e.g. weapons
vs. communications
layer).
• Separate covariance
for each measure of
risk
01
23
45
67
89
10
0
2
4
6
8
10
0
0.5
1
1.5
2
2.5
3
3.5
4
x 106
Variance Risk Measure (Weapons)Variance Risk Measure (Comm)
Perf
orm
an
ce In
dex [
no
n-d
im]
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Bertsimas-Sim Method: Adjust
conservatism Γi term to control
probability of constraint violation
Portfolio Robust Operational
Constraints
Conservatism Added
(This can be converted to an LP ==
easy to solve even for large
problems)
Constraint Rules for
Connectivity & Operations
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5
0.505
0.51
0.515
0.52
0.525
Pro
bab
ilit
y o
f V
iola
tio
n
Level of Conservatism
Portfolio Robust Operational Constraint
Important Operational
Constraint (e.g.)
Package Bandwith Req
ASW Variable Depth 3.54
Multi Fcn Tow 60
Lightweight tow 33.99
MCN RAMCS II 24.25
ALMDS (MH-60) 76.8
SUW N-LOS Missiles 11.07
Griffin Missiles 42.68
Seaframe Package System 1 91.54
& Combat Package System 2 55.06
Management Package System 3 63.85
Subject to some
uncertainty (+/-)
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Future Work: Portfolio Approach
• Semi Definite Programming (SDP) – can be hard to solve/implement
― Conic and Linear Programming versions well developed open solvers
• Extend to multi-period portfolio dynamic programming
• Agent-Based Simulation (e.g. for covariance estimation, CVaR)
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Summary/Conclusion
• RMVO promising framework to leverage SoS performance against risk
• Considers uncertainty and system interdependencies explicitly in portfolio construction
• Develop further towards analytic workbench objectives