Portfolio and Scenario Analysis in the Evaluation of Cost-Efficient Weapon Systems

1. Portfolio and Scenario Analysis in the Evaluation of Cost-Efficient Weapon Systems Jussi Kangaspunta, Juuso Liesiö and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, 02015 TKK, Finland http://www.sal.tkk.fi firstname.lastname@tkk.fi

2. Contents • Challenges in the evaluation of weapon systems • Multi-criteria portfolio model for weapon systems • Numerical example and future research • Conclusions

3. Challenges in the evaluation of weapon systems • Cost-efficiency of weapon systems depends on both impacts and costs • Several impact dimensions (i.e. criteria) 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. • Impacts are often very non-linear • 16 artillery guns may not be twice as effective as 8 guns • There are strong interactions among systems • How should joint impacts be attributed to constituent systems? • Earlier work mainly focused on individual systems

4. Impact assessment model • Estimates from ground battle simulator of Defense Forces • Battle scenario with pre-specified enemy, terrain and mission • 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 interpolation or regression methods Battle simulator Scenario Criterion 1 Own forces portfolio Enemy Overall impact of the portfolio Impact model Criterion 2 ... Criterion n

5. 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 captured by an additive value function

6. Incomplete information and dominance • Feasible weight set • E.g. rank-ordering for criterion importance • Portfolio x1 dominates x2if it has greater or equal overall impact for all feasible weights two criteria; w1≥w2 V(x1,w) V1 V2 V(x2,w) w1=1 w2=0 w1=0 w2=1 w1=.5 w2=.5

7. Cost-efficient portfolios • Feasible portfolios that are not dominated by any less or equally expensive portfolio

8. Numerical 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

9. Simulated and interpolated impact functions

10. Impacts of weapon system portfolios

11. Composition of cost-efficient portfolios

12. Extensions and future research • 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 multiple battle scenarios • 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 • Considering cost-efficiency using core indices • “What proportion of evaluations supports that a given portfolio is cost-efficient?” • “What proportion of possible scenarios supports that a give portfolio iscost-efficient?”

13. Multiple battle scenarios 1 p1 Overall expected value of the portfolio Weapon system portfolio p2 2 ... ... ps s

14. Cost-efficiency using core indices 1/2

15. Cost-efficiency using core indices 2/2

16. Conclusions • Portfolio approach is necessitated by strong interactions • Evaluation of individual weapon systems makes little sense • These interactions are captured by the battle 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

17. References • 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.

18. Questions and comments?