1PRIME Decisions - An Interactive Tool for Value Tree Analysis Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis Janne Gustafsson, Tommi Gustafsson, and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology Finland

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 2 Outline n Multi-Attribute Value Theory (MAVT) n Incomplete information in MAVT n Overview of PRIME n PRIME Decisions n Case Study: Valuation of a New Technology Venture n Research directions

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 3 Value Tree A02/ Good 180 km/h EUR 3 months Car X ComfortPerformancePriceTime QualityDelivery terms Car v1N(x1)v1N(x1)v2N (x2)v2N (x2)v3N (x3)v3N (x3)v4N (x4)v4N (x4) w4w4 w2w2 w1w1 w3w3

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 4 MAVT - Preference Elicitation n Score elicitation –Two equivalent apporaches  explicit value functions  ratio comparisons of value differences »e.g. direct rating »implicit value functions: »value functions are defined pointwise Consequence Value Value function v(x2)v(x2) v(x1)v(x1) x1x1 x2x2 x0x0 0 = v(x 0 ) v(x*)v(x*) x*x*

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 5 MAVT - Preference Elicitation n Weight elicitation –several methods »SWING, SMART, SMARTER, AHP –ratio comparisons: w 1 /w 2 »widely used »ratios to be understood in terms of value differences (Salo & Hämäläinen, 1997) –weights sum up to 1 v 1 (x 1 *) v1(x10)v1(x10) 1 0 v 2 (x 2 *) v2(x20)v2(x20)v3(x30)v3(x30) v 3 (x 3 *) Value = 0

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 6 Incomplete Information in MAVT (1) n Limitations of traditional analyses –access to complete information »may be costly, difficult or impossible –intervals instead of point-estimates »weight and score elicitation n Intervals can be used to  model uncertainty –interval as a confidence interval  model group preferences –interval captures variation of preferences within the group  carry out multi-way sensitivity analyses –intervals describe confidence intervals around parameter estimates

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 7 Incomplete Information in MAVT (2) n Several methods –PRIME (Salo & Hämäläinen, 1999) –PAIRS (Salo & Hämäläinen, 1992) –ARIADNE (White et al., 1984) –HOPIE (Weber, 1985) n Few empirical studies –Hämäläinen and Pöyhönen (1996) –Hämäläinen and Leikola (1995) »promising approach - further work called for n Dedicated software needed –computational requirements (i.e., solutions to linear programs) –interaction between the user and the model –ease of use

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 8 PRIME - Preference Elicitation n Score elicitation –upper and lower bounds for ratios –e.g. interval direct rating »x i j rated with respect to best and worst achievement levels x i 0 and x i * Price Value v3(x31)v3(x31) x31x31 x3*x3* 0 = v 3 (x 3 0 ) v3(x3*)v3(x3*) x30x30 Performance Value v2(x31)v2(x31) x21x21 x20x20 0 = v 2 (x 3 0 ) v2(x2*)v2(x2*) x2*x2*

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 9 PRIME - Preference Elicitation n Weight elicitation –upper and lower bounds for weight ratios –cf. AHP »to be understood as value differences –e.g. interval SWING »100 points to reference attribute intervals to others 

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 10 PRIME - Synthesis n Value and weight intervals –acquired from optimization problems »scores subjected to linear constraints from preference statements –objective functions vary –lower bound from minimization, upper bound from maximization n Value interval of an alternative n Weight interval of an attribute

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 11 PRIME - Dominance Structures n Absolute dominance –value intervals do not overlap –alternative with higher interval dominates the one with lower interval n Pairwise dominance of alternative k over j: –value intervals overlap –alternative x 1 may be superior to alternative x 2 for all feasible parameter values V(x1)V(x1) 1 0 Value V(x2)V(x2) V(x3)V(x3)

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 12 PRIME - Decision Rules n Decision rules –maximin: greatest lower bound –maximax: greatest upper bound –central values: greatest midpoint –minimax regret: smallest possible loss of value V(x1)V(x1) 1 0 Value V(x2)V(x2) V(x3)V(x3)

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 13 PRIME Decisions (1) n Tool for value tree analysis with incomplete information –first tool to implement PRIME and related methods –Windows 95, 98, NT and 2000 –programmed with C++ and Windows SDK –beta version 1.00 released in spring of 1999 –downloadable at n Features  Guided elicitation tour to assist in preference elicitation  Interval judgements in score and weight elicitation  In-built simplex algorithm for solving PRIME models

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 14 PRIME Decisions (2) n Four main tasks  Construction of value tree  Definition of alternatives  Preference elicitation »Score elicitation »Weight elicitation  Synthesis »Value intervals »Dominance structures »Decision rules

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 15 PRIME Decisions (3)

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 16 Score Elicitation 1. Ordinal Ranking2. Cardinal Judgements

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 17 Weight Elicitation

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 18 Value Intervals

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 19 Dominance

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 20 Decision Rules

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 21 Performance n No a priori bounds for –number of attributes –number of alternatives –levels of hierarchy in value tree n Computational performance –calculation time ~O(N 2.5 ) »N = number of linear programs –usually linear programs to be solved »depends on the number of alternatives and attributes »approximately alternatives x attributes decision variables and constraints –19 attributes, 5 alternatives »total of 491 linear programs to solve all aspects of the model n time to complete 2 min 47 sec with Pentium II 350 MHz »73 for value intervals of alternatives, weights, and dominance structures

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 22 Case Study: Valuation of Technology Venture n Valuation of Sonera SmartTrust –Sonera is a largest telecom operator in Finland » employees »turnover more than 1.8 billion EUR –SmartTrust is a provider of mobile security solutions »PKI = Public Key Infrastructure n Joint study with Merita Securities (ArosMaizels) –team of four members (2 from HUT, 1 from Merita, 1 from Omnitele) n Sales expected around 2003 –magnitude questionable –several uncertainties –advanced analysis needed

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 23 Case Study: Valuation of Technology Venture n Valuation based on sales forecast of 2007 n Markets segmented –relative sizes estimated (weights) –need for PKI estimated (scores) –due to uncertainties intervals appeared appealing choice –PRIME selected for deriving estimate for overall market size n Price estimated –several pricing policies considered n Market share estimated –tough, estimate of 25% market share

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 24 Case Study: Valuation of Technology Venture

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 25 Case Study: Valuation of Technology Venture

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 26 Case Study: Valuation of Technology Venture n Growth curves and penetration rates estimated –temporal development of key figures estimated –based on temporally stabile figures »average revenue per user (ARPU) »spreading of mobile phones n Three scenarios for cash flows –pessimistic (market size 3.5% of wireless services) –neutral (market size 8.5% of wireless services) –optimistic (market size 13.4% of wireless services) n Valuation derived with 12% discount rate –about 700 million EUR in neutral scenario –earlier estimates 6 billion EUR (Merrill Lynch) and 17 billion EUR (Merita)

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 27 Case Study: Valuation of Technology Venture n PRIME Decisions was used to derive the estimate of relative PKI market size n Size of PKI market –about % of total wireless services markets n One conculsion: –MCDM tools have practical applications in market analysis

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 28 Further Research n Empirical studies –classify problems where PRIME is useful –generate evidence to develop the method and the program n Additional features –definition of continuous value functions –explicit definition of best and worst achievement levels –enhancement of the elicitation tour –sensitivity analysis

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 29 References Hämäläinen, R.P. and M. Pöyhönen (1996), “On-Line Group Decision Support by Preference Programming in Traffic Planning,” Group Decision and Negotiation 5, Hämäläinen, R.P., A.A. Salo and Pöysti, K. (1992), “Observations about Consensus Seeking in a Multiple Criteria Environment,” in Proceedings of the 25th Hawaii In-ternational Conference on System Sciences, Vol. IV, January 1992, Salo, A.A. and R.P. Hämäläinen (1992), “Preference Assessment by Imprecise Ratio Statements”, Operations Research 40, Salo, A.A. (1995), “Interactive Decision Aiding for Group Decision Support”, European Journal of Operational Research 84, Salo, A.A. and Hämäläinen, R.P. (1997), “On the Measurement of Preferences in the Analytic Hierarchy Process”, Journal of Multi-Criteria Decision Analysis 6(6), Salo, A. A., Hämäläinen, R. P. (1997). PRIME – Preference Ratios In Multiattribute Evaluation, Helsinki University of Technology, Systems Analysis Laboratory. White III, C.C., A.P. Sage and S. Dozono (1984), “A Model of Multiattribute Decision Making and Trade-Off Determination Under Uncertainty”, IEEE Transactions on Sys-tems, Man, and Cybernetics 14(2), Weber, M. (1987), “Decision Making with Incomplete Information”, European Journal of Operational Research 28,

Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions - An Interactive Tool for Value Tree Analysis 30 PRIME - Linear Constraints n Ratio statements yield two linear constraints 