Helsinki University of Technology Systems Analysis Laboratory Portfolio

Helsinki University of Technology Systems Analysis Laboratory 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

Helsinki University of Technology Systems Analysis Laboratory Contents n Challenges in the evaluation of weapon systems n Multi-criteria portfolio model for weapon systems n Numerical example and future research n Conclusions 2

Helsinki University of Technology Systems Analysis Laboratory Challenges in the evaluation of weapon systems n Cost-efficiency of weapon systems depends on both impacts and costs n Several impact dimensions (i. e. criteria) must be accounted for – E. g. enemy and own casualties, mission success probability n Impacts depend on the context – Mission (attack/defence), weather conditions, enemy strategies etc. n Impacts are often very non-linear – 16 artillery guns may not be twice as effective as 8 guns n There are strong interactions among systems – How should joint impacts be attributed to constituent systems? – Earlier work mainly focused on individual systems 3

Helsinki University of Technology Systems Analysis Laboratory Impact assessment model 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 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 Own forces portfolio Enemy Scenario Criterion 1 Impact model Criterion 2 . . . Overall impact of the portfolio Criterion n 4

Helsinki University of Technology Systems Analysis Laboratory Modelling of weapon systems n 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. ) n Impact assessment criteria – Portfolios evaluated with regard to different impact criteria » Enemy casualties, own casualties etc. – Overall impacts captured by an additive value function 5

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

Helsinki University of Technology Systems Analysis Laboratory Cost-efficient portfolios n Feasible portfolios that are not dominated by any less or equally expensive portfolio 7

Helsinki University of Technology Systems Analysis Laboratory Numerical example based on realistic data n Three weapon systems – Only unit costs n Three impact criteria measuring different types of enemy casualties n Incomplete information on the value (i. e relevance) of the impacts n Analysis of different budget levels with a focus on cost-efficient portfolios 8

Helsinki University of Technology Systems Analysis Laboratory Simulated and interpolated impact functions 9

Helsinki University of Technology Systems Analysis Laboratory Impacts of weapon system portfolios 10

Helsinki University of Technology Systems Analysis Laboratory Composition of cost-efficient portfolios 11

Helsinki University of Technology Systems Analysis Laboratory Extensions and future research n Complementing simulation data with expert evaluations – Simulations can be augmented with judgmental expert evaluations of impacts – Experimental design of simulations and/or expert evaluations n 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 n 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 is cost-efficient? ” 12

Helsinki University of Technology Systems Analysis Laboratory Multiple battle scenarios 1 p 1 2 p 2 . . . Weapon system portfolio ps Overall expected value of the portfolio s 13

Helsinki University of Technology Systems Analysis Laboratory Cost-efficiency using core indices 1/2 14

Helsinki University of Technology Systems Analysis Laboratory Cost-efficiency using core indices 2/2 15

Helsinki University of Technology Systems Analysis Laboratory Conclusions n Portfolio approach is necessitated by strong interactions → Evaluation of individual weapon systems makes little sense n These interactions are captured by the 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 16

Helsinki University of Technology Systems Analysis Laboratory References n n n n 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. 13361350. 17

Helsinki University of Technology Systems Analysis Laboratory Questions and comments? 18