Helsinki University of Technology Systems Analysis Laboratory Determining cost-effective portfolios of weapon systems Juuso Liesiö, Ahti Salo and Jussi Kangaspunta Systems Analysis Laboratory Helsinki University of Technology P.O. Box 1100, TKK, Finland

Helsinki University of Technology Systems Analysis Laboratory 2 Contents n Finnish Defense Forces n Challenges in the cost-efficiency analysis of weapon systems n Multi-criteria portfolio model for weapon systems n A realistic example n Conclusions

Helsinki University of Technology Systems Analysis Laboratory 3 Finnish Defense Forces n Key statistics –Annual budget ~ 2.8 billion USD –About 1.3% of GDP –Peacetime strength: »13,000 regulars » 27,000 conscripts and 30,000 reservists trained annually –Wartime strength: 430,000 n Tasks –Territorial surveillance –Safeguarding territorial integrity –Defending national sovereignty in all situations

Helsinki University of Technology Systems Analysis Laboratory 4 Cost efficiency analysis of weapon systems n Challenges in the impact assessment of weapon systems –Several relevant measures and interpretations »E.g. enemy losses, mission success probability, own losses –Individual systems difficult to evaluate due to interactions among systems »How to attribute impacts of artillery to guns and target acquisition? –Impacts may be highly non-linear »Are 16 artillery pieces twice as effective as 8? –Impacts contingent on mission (attack/defense), conditions (summer/winter) etc. n Earlier work based on expert evaluations –Air Force 2025 (Parnell et al. 1998) –Systems for counterproliferation role (Stafira et al. 1997)

Helsinki University of Technology Systems Analysis Laboratory 5 Multi-criteria portfolio model Multi-criteria portfolio model n Weapon system portfolio –m: number of different kinds of weapon systems –x j : number of pieces of equipment of the j th type –C(x): cost of weapon system portfolio x –Feasible portfolios satisfy relevant constraints »E.g., budget constraints (C(x)≤B), logical constraints (incompatibilities etc.) n Impact assessment criteria –Impact functions map portfolios to criterion-specific performances –Overall impacts modeled with an additive value function

Helsinki University of Technology Systems Analysis Laboratory 6 n Instead of point-estimate criterion weights, a set of feasible weights –E.g. rank-ordering for criterion importance n Portfolio x’ dominates x if it has greater or equal overall impact for all feasible weights: Incomplete information and dominance w 1 =1 w 2 =0 w 1 =0 w 2 =1 w 1 =.5 w 2 =.5 V2V2 V1V1 two criteria; w 1 ≥w 2 V(x’) V(x)

Helsinki University of Technology Systems Analysis Laboratory 7 n Cost-efficient portfolios –Feasible portfolios which are not dominated by any less or equally expensive portfolio Cost-efficient portfolios w 1 =1 w 2 =0 w 1 =0 w 2 =1 w 1 =.5 w 2 =.5 V2V2 V1V1 two criteria; w 1 ≥w 2 three portfolios C(x’’)<C(x’)=C(x) V(x’) V(x) V(x’’)

Helsinki University of Technology Systems Analysis Laboratory 8 n 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 –Numerous simulation runs with different portfolios of selected weapon systems –Simulation results extended by interpolation Impact assessment model Criterion 1 V 1 (x) Criterion 2 V 2 (x) Criterion n V 2 (x) Overall impact of the portfolio Impact model V(.)=[V 1 (.),...,V n (.)] T Scenario friendly portfolio x... Battle simulator enemy

Helsinki University of Technology Systems Analysis Laboratory 9 Realistic example n Analysis of three weapon systems based on real data –Defense Forces interested informing upcoming purchase decisions –Results classified n Similar but imaginary setting –Three weapon systems –Three impact criteria measuring different types of enemy losses –Incomplete information on the value (i.e relevance) of the impacts –Linear portfolio cost –Analysis of different budget levels with a focus on cost-efficient portfolios

Helsinki University of Technology Systems Analysis Laboratory 10 Impact functions x 3 =0 x 3 =1

Helsinki University of Technology Systems Analysis Laboratory 11 Impacts of weapon system portfolios Efficient portfolio Inefficient portfolio

Helsinki University of Technology Systems Analysis Laboratory 12 Composition of cost-efficient portfolios (1/2) Efficient portfolio

Helsinki University of Technology Systems Analysis Laboratory 13 Composition of efficient portfolios (2/2) Efficient portfolio Inefficient portfolio x 3 =0 x 3 =1

Helsinki University of Technology Systems Analysis Laboratory 14 Conclusions n Portfolio approach is necessitated by strong interactions → Evaluation of individual systems makes little sense n Weapon system interactions captured in battle simulator results n Multi-criteria model aggregates several impact dimensions –Contextual importance of impacts captured through incomplete information n Cost-efficiency depends on both impacts and costs → Focus on the computation of cost-efficient portfolios

Helsinki University of Technology Systems Analysis Laboratory 15 Extensions and future research n Combining simulation data and expert evaluations –Helps overcome ”curse of dimensionality” with a growing number of systems –Simulations can be augmented with judgmental expert evaluations of impacts n Systematic experimental design of simulation runs and/or expert evaluations n Considering multiple scenarios in efficiency evaluation –Cost-efficiency is highly context dependent –Risk and/or robustness measures for portfolios are therefore needed

Helsinki University of Technology Systems Analysis Laboratory 16 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 »Parnell, G., et. al. (1998). Foundations 2025: A Value Model for Evaluating Future Air and Space Forces, Management Science, Vol. 44, No. 10, pp

Helsinki University of Technology Systems Analysis Laboratory 17 n Non-dominated portfolios –Feasible portfolios for which no other feasible portfolio has greater overall impact for all feasible weights n Cost-efficient portfolios –Feasible portfolios which are not dominated by any less expensive portfolio Non-dominated and cost-efficient portfolios w 1 =1 w 2 =0 w 1 =0 w 2 =1 w 1 =.5 w 2 =.5 V 2 (x) V 1 (x) two criteria; w 1 ≥w 2