PRIME Decisions An Interactive Tool for Value Tree Analysis

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PRIME Decisions - An Interactive Toolfor Value
Tree Analysis

• Janne Gustafsson, Tommi Gustafsson, and Ahti Salo
• Systems Analysis Laboratory
• Helsinki University of Technology
• Finland

2
Outline

• Multi-Attribute Value Theory (MAVT)
• Incomplete information in MAVT
• Overview of PRIME
• PRIME Decisions
• Case Study Valuation of a New Technology Venture
• Research directions

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Value Tree
Car
Quality
Delivery terms
w4
w2
w1
w3
Comfort
Performance
Price
Time
v1N(x1)
v2N (x2)
v3N (x3)
v4N (x4)
Car X
Good
3 months
180 km/h
50 000 EUR
A02/ 99-08
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MAVT - Preference Elicitation

• 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

v(x)
Value function
v(x2)
Value
v(x1)
0 v(x0)
x1
x2
x0
x
Consequence
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MAVT - Preference Elicitation

• Weight elicitation
• several methods
• SWING, SMART, SMARTER, AHP
• ratio comparisons w1/w2
• widely used
• ratios to be understood in terms of value
  differences (Salo Hämäläinen, 1997)
• weights sum up to 1

0
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Incomplete Information in MAVT (1)

• Limitations of traditional analyses
• access to complete information
• may be costly, difficult or impossible
• intervals instead of point-estimates
• weight and score elicitation
• 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

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Incomplete Information in MAVT (2)

• Several methods
• 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
• Dedicated software needed
• computational requirements (i.e., solutions to
  linear programs)
• interaction between the user and the model
• ease of use

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PRIME - Preference Elicitation
v3(x3)

• Score elicitation
• upper and lower bounds for ratios
• e.g. interval direct rating
• xij rated with respect to best and
• worst achievement levels xi0 and xi

v3(x31)
Value
0 v3(x30)
x30
x31
x3
Price
v2(x2)
Value
v2(x31)
0 v2(x30)
x21
x2
x20
Performance
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PRIME - Preference Elicitation

• 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 attributeintervals to
  others

?
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PRIME - Synthesis

• 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
• Value interval of an alternative
• Weight interval of an attribute

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PRIME - Dominance Structures

• Absolute dominance
• value intervals do not overlap
• alternative with higher interval
• dominates the one with lower interval
• Pairwise dominance of alternative k over j
• value intervals overlap
• alternative x1 may be superior to alternative x2
  for all feasible parameter values

1
V(x1)
V(x3)
Value
V(x2)
0
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PRIME - Decision Rules

• Decision rules
• maximin greatest lower bound
• maximax greatest upper bound
• central values greatest midpoint
• minimax regret smallest possible loss of value

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PRIME Decisions (1)

• 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 http//www.sal.hut.fi/downloadable
  s/
• Features
• Guided elicitation tour to assist in preference
  elicitation
• Interval judgements in score and weight
  elicitation
• In-built simplex algorithm for solving PRIME
  models

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PRIME Decisions (2)

• Four main tasks
• Construction of value tree
• Definition of alternatives
• Preference elicitation
• Score elicitation
• Weight elicitation
• Synthesis
• Value intervals
• Dominance structures
• Decision rules

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PRIME Decisions (3)
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Score Elicitation
1. Ordinal Ranking
2. Cardinal Judgements
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Weight Elicitation
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Value Intervals
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Dominance
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Decision Rules
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Performance

• No a priori bounds for
• number of attributes
• number of alternatives
• levels of hierarchy in value tree
• Computational performance
• calculation time O(N2.5)
• 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
• time to complete 2 min 47 sec with Pentium II 350
  MHz
• 73 for value intervals of alternatives, weights,
  and dominance structures

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Case Study Valuation of Technology Venture

• Valuation of Sonera SmartTrust
• Sonera is a largest telecom operator in Finland
• 10 000 employees
• turnover more than 1.8 billion EUR
• SmartTrust is a provider of mobile security
  solutions
• PKI Public Key Infrastructure
• Joint study with Merita Securities (ArosMaizels)
• team of four members (2 from HUT, 1 from Merita,
  1 from Omnitele)
• Sales expected around 2003
• magnitude questionable
• several uncertainties
• advanced analysis needed

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Case Study Valuation of Technology Venture

• Valuation based on sales forecast of 2007
• 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
• Price estimated
• several pricing policies considered
• Market share estimated
• tough, estimate of 25 market share

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Case Study Valuation of Technology Venture
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Case Study Valuation of Technology Venture
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Case Study Valuation of Technology Venture

• 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
• 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)
• Valuation derived with NPV _at_ 12 discount rate
• about 700 million EUR in neutral scenario
• earlier estimates 6 billion EUR (Merrill Lynch)
  and 17 billion EUR (Merita)

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Case Study Valuation of Technology Venture

• PRIME Decisions was used to derive the estimate
  of relative PKI market size
• Size of PKI market
• about 3.5 - 13.4 of total wireless services
  markets
• One conculsion
• MCDM tools have practical applications in market
  analysis

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Further Research

• Empirical studies
• classify problems where PRIME is useful
• generate evidence to develop the method and the
  program
• Additional features
• definition of continuous value functions
• explicit definition of best and worst achievement
  levels
• enhancement of the elicitation tour
• sensitivity analysis

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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 25th 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.
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PRIME - Linear Constraints

• Ratio statements yield two linear constraints

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