Helsinki University of Technology Systems Analysis Laboratory PRIME
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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 1
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 2
Helsinki University of Technology Systems Analysis Laboratory Value Tree Car Quality w 1 Delivery terms w 2 Comfort w 3 Performance v 1 N(x 1) w 4 Price v 2 N (x 2) Time v 3 N (x 3) Car X Good 180 km/h v 4 N (x 4) 3 months 50 000 EUR PRIME Decisions - An Interactive Tool for Value Tree Analysis 3
Helsinki University of Technology Systems Analysis Laboratory MAVT - Preference Elicitation Score elicitation v(x*) – Two equivalent apporaches explicit value functions ratio comparisons of value differences v(x 2) » e. g. direct rating v(x 1) » implicit value functions: » value functions are defined pointwise 0 = v(x 0) Value function Value n x 0 x 1 x 2 x* Consequence PRIME Decisions - An Interactive Tool for Value Tree Analysis 4
Helsinki University of Technology Systems Analysis Laboratory MAVT - Preference Elicitation Weight elicitation – several methods » SWING, SMARTER, AHP – ratio comparisons: w 1/w 2 » widely used » ratios to be understood in terms of value differences (Salo & Hämäläinen, 1997) 1 – weights sum up to 1 Value n =0 0 v 1(x 1*) v 2(x 2*) v 3(x 3*) v 1(x 10) v 2(x 20) v 3(x 30) PRIME Decisions - An Interactive Tool for Value Tree Analysis 5
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 6
Helsinki University of Technology Systems Analysis Laboratory Incomplete Information in MAVT (2) n Several methods – – n PRIME (Salo & Hämäläinen, 1999) PAIRS (Salo & Hämäläinen, 1992) ARIADNE (White et al. , 1984) HOPIE (Weber, 1985) 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 7
Helsinki University of Technology Systems Analysis Laboratory PRIME - Preference Elicitation – upper and lower bounds for ratios – e. g. interval direct rating » xij rated with respect to best and worst achievement levels xi 0 and xi* Value Score elicitation 0 = v 3(x 30) x 3* x 31 Price x 30 v 2(x 2*) Value n v 3(x 3*) v 3(x 31) v 2(x 31) 0 = v 2(x 30) x 20 x 21 x 2* Performance PRIME Decisions - An Interactive Tool for Value Tree Analysis 8
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 9
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 10
Helsinki University of Technology Systems Analysis Laboratory PRIME - Dominance Structures Absolute dominance 1 – value intervals do not overlap – alternative with higher interval dominates the one with lower interval Value n V(x 1) V(x 3) V(x 2) 0 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 11
Helsinki University of Technology Systems Analysis Laboratory PRIME - Decision Rules Decision rules – – maximin: greatest lower bound maximax: greatest upper bound central values: greatest midpoint minimax regret: smallest possible loss of value 1 Value n V(x 1) V(x 3) V(x 2) 0 PRIME Decisions - An Interactive Tool for Value Tree Analysis 12
Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions (1) n Tool for value tree analysis with incomplete information – – – n 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 http: //www. sal. hut. fi/downloadables/ Features Guided elicitation tour to assist in preference elicitation Interval judgements in score and weight elicitation In-built simplex algorithm for solving PRIME models PRIME Decisions - An Interactive Tool for Value Tree Analysis 13
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 14
Helsinki University of Technology Systems Analysis Laboratory PRIME Decisions (3) PRIME Decisions - An Interactive Tool for Value Tree Analysis 15
Helsinki University of Technology Systems Analysis Laboratory Score Elicitation 1. Ordinal Ranking 2. Cardinal Judgements PRIME Decisions - An Interactive Tool for Value Tree Analysis 16
Helsinki University of Technology Systems Analysis Laboratory Weight Elicitation PRIME Decisions - An Interactive Tool for Value Tree Analysis 17
Helsinki University of Technology Systems Analysis Laboratory Value Intervals PRIME Decisions - An Interactive Tool for Value Tree Analysis 18
Helsinki University of Technology Systems Analysis Laboratory Dominance PRIME Decisions - An Interactive Tool for Value Tree Analysis 19
Helsinki University of Technology Systems Analysis Laboratory Decision Rules PRIME Decisions - An Interactive Tool for Value Tree Analysis 20
Helsinki University of Technology Systems Analysis Laboratory 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 100 -1000 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 21
Helsinki University of Technology Systems Analysis Laboratory Case Study: Valuation of Technology Venture n Valuation of Sonera Smart. Trust – Sonera is a largest telecom operator in Finland » 10 000 employees » turnover more than 1. 8 billion EUR – Smart. Trust is a provider of mobile security solutions » PKI = Public Key Infrastructure n Joint study with Merita Securities (Aros. Maizels) – 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 22
Helsinki University of Technology Systems Analysis Laboratory Case Study: Valuation of Technology Venture n Valuation based on sales forecast of 2007 n Markets segmented – – n 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 Price estimated – several pricing policies considered n Market share estimated – tough, estimate of 25% market share PRIME Decisions - An Interactive Tool for Value Tree Analysis 23
Helsinki University of Technology Systems Analysis Laboratory Case Study: Valuation of Technology Venture PRIME Decisions - An Interactive Tool for Value Tree Analysis 24
Helsinki University of Technology Systems Analysis Laboratory Case Study: Valuation of Technology Venture PRIME Decisions - An Interactive Tool for Value Tree Analysis 25
Helsinki University of Technology Systems Analysis Laboratory 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 NPV @ 12% discount rate – about 700 million EUR in neutral scenario – earlier estimates 6 billion EUR (Merrill Lynch) and 17 billion EUR (Merita) PRIME Decisions - An Interactive Tool for Value Tree Analysis 26
Helsinki University of Technology Systems Analysis Laboratory 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 3. 5 - 13. 4 % of total wireless services markets n One conculsion: – MCDM tools have practical applications in market analysis PRIME Decisions - An Interactive Tool for Value Tree Analysis 27
Helsinki University of Technology Systems Analysis Laboratory 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 PRIME Decisions - An Interactive Tool for Value Tree Analysis 28
Helsinki University of Technology Systems Analysis Laboratory References Hämäläinen, R. P. and M. Pöyhönen (1996), “On-Line Group Decision Support by Preference Programming in Traffic Planning, ” Group Decision and Negotiation 5, 485 -500. Hämäläinen, R. P. , A. A. Salo and Pöysti, K. (1992), “Observations about Consensus Seeking in a Multiple Criteria Environment, ” in Proceedings of the 25 th Hawaii In-ternational Conference on System Sciences, Vol. IV, January 1992, 190 -198. Salo, A. A. and R. P. Hämäläinen (1992), “Preference Assessment by Imprecise Ratio Statements”, Operations Research 40, 1053 -1061. Salo, A. A. (1995), “Interactive Decision Aiding for Group Decision Support”, European Journal of Operational Research 84, 134 -149. 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), 309 -319 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), 223 -229. Weber, M. (1987), “Decision Making with Incomplete Information”, European Journal of Operational Research 28, 44 -57. PRIME Decisions - An Interactive Tool for Value Tree Analysis 29
Helsinki University of Technology Systems Analysis Laboratory PRIME - Linear Constraints n Ratio statements yield two linear constraints PRIME Decisions - An Interactive Tool for Value Tree Analysis 30
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