Portfolio Analysis in the Cost-Efficiency Evaluation of Weapon Systems
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Helsinki University of Technology Systems Analysis Laboratory
Portfolio Analysis in thePortfolio Analysis in theCost-Efficiency Evaluation of Cost-Efficiency Evaluation of
Weapon SystemsWeapon Systems
7 July 2009
23rd European Conference on Operational Research in Bonn
Jussi Kangaspunta, Juuso Liesiö and Ahti Salo
Systems Analysis Laboratory
Helsinki University of Technology
P.O. Box 1100, 02015 TKK, Finland
firstname.lastname@tkk.fi
Helsinki University of Technology Systems Analysis Laboratory
Challenges in the Evaluation of Weapon SystemsChallenges in the Evaluation of Weapon Systems
Cost-efficiency of weapon systems depends on both impacts and costs
Several impact dimensions must be accounted for– Enemy and own casualties, mission success probability, combat duration etc.
Impacts depend on the context– Mission (attack/defense), weather conditions, enemy strategies etc.
There are strong interactions among weapon systems– How should joint impacts be attributed to constituent systems ?
– Earlier research mainly focused on individual systems
Impacts are often non-linear– 16 artillery guns may not be twice as effective as 8 guns
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Helsinki University of Technology Systems Analysis Laboratory
Impact Assessment ModelImpact Assessment Model
Estimates from an independent combat simulator of Defense Forces– Operating situation with pre-specified enemy, terrain, mission and strategies
– Some of own forces kept at a constant level but others are varied
– Numerous simulations with different portfolios of selected weapon systems
– Simulation results could be extended by appropriate mathematical methods (e.g. interpolation)
Kangaspunta, Liesiö and Salo: Portfolio Analysis in the Cost-Efficiency Evaluation of Weapon Systems 3
Criterion 1
Criterion 2
Criterion n
Overall impact of the portfolio
Impact model
...
Combat simulator
Operating
situation
Enem
yOwn forces
portfolio
Helsinki University of Technology Systems Analysis Laboratory
Modeling of Weapon SystemsModeling of Weapon Systems
Weapon system portfolio= number of different weapon systems
= number of weapon systems of the jth type in portfolio
= cost of portfolio
Feasible portfolios satisfy all relevant constraints– E.g. budget constraints, 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
Kangaspunta, Liesiö and Salo: Portfolio Analysis in the Cost-Efficiency Evaluation of Weapon Systems 4
Helsinki University of Technology Systems Analysis Laboratory
Incomplete Information and DominanceIncomplete Information and Dominance
Instead of point-estimate criterion weights, a set of feasible weights
– E.g. rank-ordering for criterion importance
Portfolio x1 dominates x2 if it has greater or equal overall impact for all feasible weights
Kangaspunta, Liesiö and Salo: Portfolio Analysis in the Cost-Efficiency Evaluation of Weapon Systems 5
Helsinki University of Technology Systems Analysis Laboratory
Cost-Efficient PortfoliosCost-Efficient Portfolios
Feasible portfolios that are not dominated by any less or equally expensive portfolio
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Helsinki University of Technology Systems Analysis Laboratory
Numerical Example Based on Realistic DataNumerical Example Based on Realistic Data
Three weapon systems
– Only unit costs
Three impact criteria measuring different types of enemy casualties
Incomplete information on the value (i.e. relevance) of the impacts
Analysis of different budget levels with a focus on cost-efficient portfolios
Kangaspunta, Liesiö and Salo: Portfolio Analysis in the Cost-Efficiency Evaluation of Weapon Systems 7
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Helsinki University of Technology Systems Analysis Laboratory
Simulated and Interpolated Impact FunctionsSimulated and Interpolated Impact Functions
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Helsinki University of Technology Systems Analysis Laboratory
Impacts of Weapon System PortfoliosImpacts of Weapon System Portfolios
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Helsinki University of Technology Systems Analysis Laboratory
Composition of Cost-Efficient PortfoliosComposition of Cost-Efficient Portfolios
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Helsinki University of Technology Systems Analysis Laboratory
ConclusionsConclusions
Portfolio approach is necessitated by strong interactions
→ Evaluation of individual weapon systems makes little sense
These interactions are captured by the combat simulator results
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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Helsinki University of Technology Systems Analysis Laboratory
ReferencesReferences
Brown, G.G., Dell, R.F., Newman, A.M. (2004). Optimizing Military Capital Planning, Interfaces Vol. 34, No. 6, pp. 415-425.
Bunn, D.W., Salo, A.A. (1993). Forecasting with Scenarios, European Journal of Operational Research, Vol. 68, pp. 291-303.
Fox, P. (1965). A Theory of Cost-Effectiveness for Military Systems Analysis, Operations Research, Vol. 13, No. 2, pp. 191-201.
Liesiö, J., Mild, P., Salo, A. (2007) Preference Programming for Robust Portfolio Modeling and Project Selection,European Journal of Operational Research, Vol. 181., No. 3., pp. 1488-1505.
Liesiö, J., Mild, P., Salo, A. (2008) Robust Portfolio Modeling with Incomplete Cost Information and Project Interdependencies, European Journal of Operational Research, Vol. 190, pp. 679-695.
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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Helsinki University of Technology Systems Analysis Laboratory
Questions and Comments ?Questions and Comments ?
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Helsinki University of Technology Systems Analysis Laboratory
Extensions and Further ResearchExtensions and Further Research
Considering multiple operating situations
– Cost-efficiency is highly context dependent
– Can be integrated to model for instance using probabilities
– Risk and/or robustness measures for portfolios can be formed
Complementing simulation data with expert evaluations
– Simulations can be augmented with judgmental expert evaluations of impacts
– Experimental design of simulations and/or expert evaluations
Considering cost-efficiency using core indices
– “What proportion of evaluations supports that a given portfolio is cost-efficient?”
– “What proportion of possible operating situations supports that a given portfolio is cost-efficient?”
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Helsinki University of Technology Systems Analysis Laboratory
Multiple Operating SituationsMultiple Operating Situations
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...
Overall expected impact of portfolio
Weapon system
portfolio
p2
pm
p1
...
Helsinki University of Technology Systems Analysis Laboratory
CostCost-Efficiency Using Core Indices 1/2-Efficiency Using Core Indices 1/2
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Helsinki University of Technology Systems Analysis Laboratory
CostCost-Efficiency Using Core Indices 2/2-Efficiency Using Core Indices 2/2
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