Helsinki University of Technology Systems Analysis Laboratory

Portfolio and Scenario Analysis in Portfolio and Scenario Analysis in

the Cost-Effectiveness Evaluation of the Cost-Effectiveness Evaluation of

Weapon Systems Weapon Systems

Jussi Kangaspunta, Ahti Salo and Juuso LiesiöSystems Analysis Laboratory

Helsinki University of Technology

P.O. Box 1100, 02015 TKK, Finland

http://www.sal.tkk.fi

firstname.lastname@tkk.fi

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ContentsContents

Finnish Defense Forces

Challenges in the evaluation of weapon systems

Multi-criteria portfolio model for weapon systems

Numerical example and future research

Conclusions

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Finnish Defense ForcesFinnish Defense Forces

Key statistics– Annual budget ~ 2.3€ (~$2.8) billion

– About 1.3% of GNP (in USA ~4.5%)

– Peacetime strength » 13,000 regulars» 27,000 conscripts» 30,000 reservists trained annually

– Wartime strength 430,000» Population of Finland ~5.2 million

Tasks– Territorial surveillance

– Safeguarding territorial integrity

– Defense of national sovereignty in all situations

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Challenges in the evaluation of weapon systemsChallenges in the evaluation of weapon systems

Several impact dimensions must be accounted for – E.g. enemy and own casualties, mission success probability

Impacts depend on the context– Mission (attack/defence), weather conditions, enemy strategies etc.

There are strong interactions among systems – How can joint impacts be best attributed to constituent systems?

– Yet earlier work mainly focused on individual systems

Impacts are often very non-linear– 16 artillery guns may not be twice as effective as 8 guns

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Modelling of weapon systems Modelling of weapon systems

Weapon system portfolio– = number of different weapon systems

– = number of weapon systems of the jth type in portfolio x

– = cost of portfolio x

– Feasible portfolios satisfy all relevant constraints» E.g. budget constraints C(x) ≤ B, logical constraints (incompatibilities etc.)

Impact assessment criteria– Portfolios evaluated with regard to different impact criteria

» Enemy casualties, own casualties etc.

– Overall impacts approximated by an additive value function

1( ,..., ) mmx x x

jx

( )C x

m

n

0

1 1

( , ) ( ), { | 1}n n

ni i w i

i i

V x w wV x w S w w

mFX

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Estimates from ground battle simulator of Defense Forces– Battle scenario with pre-specified enemy, terrain and mission

– Numbers of own weapon systems varied according to an experimental design

– Numerous simulations with different portfolios of selected weapon systems

– Simulation results extended by interpolation

Impact assessment modelImpact assessment model

Criterion 1

Criterion 2

Criterion n

Overall impact of the portfolio

Impact model

...

Battle simulator

1( ) [ ( ), ( )]TnV x V x V x

Scenario

Ene

myOwn

weapon system

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Feasible weight set– E.g. rank-ordering for criterion importance

Portfolio x’ dominates x if it has greater or

equal overall impact for all feasible weights

Incomplete information and dominanceIncomplete information and dominance

w1=1w2=0

w1=0w2=1

w1=.5w2=.5

V2

0w wS S

01 2{ | ... }w w nS w S w w w

V1

two criteria; w1≥w2

( ', ) ( , )'

( ', ) ( , )w

wS

w

V x w V x w w Sx x

V x w V x w w S

for allfor some

V(x’,w)

V(x,w)

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Feasible portfolios that are not dominated by any less or

equally expensive portfolio

Cost-efficient portfoliosCost-efficient portfolios

{ | ' s.t. ' , ( ') ( )}wE F F SX x X x X x x C x C x

V1 V2 COST

Cost-efficient portfoliosInefficient portfolios

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Numerical example based on realistic dataNumerical example based on realistic data

Three weapon systems– Additive costs

Three impact criteria for different types of enemy

casualties

Incomplete information on the value (i.e relevance) of the

impacts

Analysis at different budget levels with the aim of identifying

cost-efficient portfolios

1 2 3{0,1,..., 24}, {0,1,...,8}, {0,1}x x x 3

1

( ) j jj

C x c x

03 1 2{ | }w wS w S w w w

1 2 3, ,V V V

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Simulated and interpolated impact functions Simulated and interpolated impact functions

x3=0

x3=1

1( )V x 3( )V x2 ( )V x

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Impacts of weapon system portfoliosImpacts of weapon system portfolios

Cost-efficient portfolios ~25%

Inefficient portfolios ~75%

1( )V x

3( )V x

2 ( )V x

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Composition of cost-efficient portfolios (1/2)Composition of cost-efficient portfolios (1/2)

Cost-efficient portfolios

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Composition of cost-efficient portfolios (2/2)Composition of cost-efficient portfolios (2/2)

Cost-efficient portfolios

Inefficient portfoliosx3=1

x3=0

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Extensions and future researchExtensions and future research

Complementing simulation data with expert evaluations – Simulations can be augmented with judgmental expert evaluations of impacts

– This helps overcome the ”curse of dimensionality” with more weapon systems

– Experimental design of simulations and/or expert evaluations

Considering multiple battle scenarios– Cost-efficiency is highly context dependent many scenarios are needed for

comprehensiveness

– These can be integrated with the MAVT model using probabilities

– Risk and/or robustness measures for weapon portfolios can also be formed

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Multiple battle scenariosMultiple battle scenarios

Overall expected

value of the portfolio

Optimization

Weapon system

portfolio

1

......

p1

p2

pm

2

m

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ConclusionsConclusions

Portfolio approach is necessitated by strong interactions Evaluation of individual weapon systems makes little sense

These interactions are captured by the battle simulator

Multi-criteria model aggregates several impact dimensions – Contextual importance of impacts captured through incomplete information

Cost-efficiency depends on both impacts and costs Focus on the computation of cost-efficient portfolios

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References References » Liesiö, J., Mild, P., Salo, A. (2007) Preference Programming for Robust

Portfolio Modelling and Project Selection, European Journal of Operational Research, forthcoming

» Liesiö, J., Mild, P., Salo, A. (2007) Robust Portfolio Modeling with Incomplete Cost and Budget Information, European Journal of Operational Research, forthcoming.

» Stafira, S., Parnell, G., Moore, J., (1997). A Methodology for Evaluating Military Systems in a Counterproliferation Role, Management Science, Vol. 43, No. 10, pp. 1420-1430.

» Parnell, G., et. al. (1998). Foundations 2025: A Value Model for Evaluating Future Air and Space Forces, Management Science, Vol. 44, No. 10, pp. 1336-1350.

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Questions and comments?Questions and comments?