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Determining cost-effective portfolios of weapon systems : 

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, 02015 TKK, Finland http://www.sal.tkk.fi firstname.lastname@tkk.fi

Contents: 

Contents Finnish Defense Forces Challenges in the cost-efficiency analysis of weapon systems Multi-criteria portfolio model for weapon systems A realistic example Conclusions

Finnish Defense Forces: 

Finnish Defense Forces 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 Tasks Territorial surveillance Safeguarding territorial integrity Defending national sovereignty in all situations

Cost efficiency analysis of weapon systems: 

Cost efficiency analysis of weapon systems 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. Earlier work based on expert evaluations Air Force 2025 (Parnell et al. 1998) Systems for counterproliferation role (Stafira et al. 1997)

 Multi-criteria portfolio model: 

Multi-criteria portfolio model Weapon system portfolio m: number of different kinds of weapon systems xj: number of pieces of equipment of the jth 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.) Impact assessment criteria Impact functions map portfolios to criterion-specific performances Overall impacts modeled with an additive value function

Incomplete information and dominance: 

Instead of point-estimate criterion weights, a set of feasible weights 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 dominance w1=1 w2=0 w1=0 w2=1 w1=.5 w2=.5 V2 V1 two criteria; w1≥w2 V(x’) V(x)

Cost-efficient portfolios: 

Cost-efficient portfolios Feasible portfolios which are not dominated by any less or equally expensive portfolio Cost-efficient portfolios w1=1 w2=0 w1=0 w2=1 w1=.5 w2=.5 V2 V1 two criteria; w1≥w2 three portfolios C(x’’)<C(x’)=C(x) V(x’) V(x) V(x’’)

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 Numerous simulation runs with different portfolios of selected weapon systems Simulation results extended by interpolation Impact assessment model Criterion 1 V1(x) Criterion 2 V2(x) Criterion n V2(x) Overall impact of the portfolio Impact model V(.)=[V1(.),...,Vn(.)]T Scenario friendly portfolio x ... Battle simulator enemy

Realistic example: 

Realistic example Analysis of three weapon systems based on real data Defense Forces interested informing upcoming purchase decisions Results classified 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

Impact functions : 

Impact functions x3=0 x3=1

Impacts of weapon system portfolios: 

Impacts of weapon system portfolios

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

Composition of cost-efficient portfolios (1/2)

Composition of efficient portfolios (2/2): 

Composition of efficient portfolios (2/2) x3=0 x3=1

Conclusions: 

Conclusions Portfolio approach is necessitated by strong interactions Evaluation of individual systems makes little sense Weapon system interactions captured in 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

Extensions and future research: 

Extensions and future research 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 Systematic experimental design of simulation runs and/or expert evaluations Considering multiple scenarios in efficiency evaluation Cost-efficiency is highly context dependent Risk and/or robustness measures for portfolios are therefore needed

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.

Non-dominated and cost-efficient portfolios: 

Non-dominated portfolios Feasible portfolios for which no other feasible portfolio has greater overall impact for all feasible weights Cost-efficient portfolios Feasible portfolios which are not dominated by any less expensive portfolio Non-dominated and cost-efficient portfolios w1=1 w2=0 w1=0 w2=1 w1=.5 w2=.5 V2(x) V1(x) two criteria; w1≥w2