11/13/2012 1

[Replace With Your Logo Here]

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.

11/13/2012 2

[Replace With Your Logo Here]

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

11/13/2012 3

[Replace With Your Logo Here]

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)

11/13/2012 4

[Replace With Your Logo Here]

The Big Picture

Bayesian & FDNA Approach

Stand-In Redundancy

Petri-Nets

11/13/2012 5

[Replace With Your Logo Here]

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

11/13/2012 6

[Replace With Your Logo Here]

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?

11/13/2012 7

[Replace With Your Logo Here]

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

11/13/2012 8

[Replace With Your Logo Here]

• 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

11/13/2012 9

[Replace With Your Logo Here]

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

11/13/2012 10

[Replace With Your Logo Here]

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)

11/13/2012 11

[Replace With Your Logo Here]

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

11/13/2012 12

[Replace With Your Logo Here]

Mean-Variance Portfolio: A Robust Approach

11/13/2012 13

[Replace With Your Logo Here]

Robust Portfolio Case Study: Simple LCS Portfolio

Diagonal : System Variance

Off Diagonal : System

Interdependency

11/13/2012 14

[Replace With Your Logo Here]

Robust Portfolio Case Study: Simple LCS Portfolio

11/13/2012 15

[Replace With Your Logo Here]

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]

11/13/2012 16

[Replace With Your Logo Here]

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

11/13/2012 17

[Replace With Your Logo Here]

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 (+/-)

11/13/2012 18

[Replace With Your Logo Here]

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)

11/13/2012 19

[Replace With Your Logo Here]

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