1PRIME Decisions - An Interactive Tool for Value Tree Analysis Helsinki University of Technology...

1PRIME Decisions - An Interactive Tool for Value Tree Analysis

Helsinki University of TechnologySystems Analysis Laboratory

PRIME Decisions - An Interactive ToolPRIME Decisions - An Interactive Tool

for Value Tree Analysisfor Value Tree Analysis

Janne Gustafsson, Tommi Gustafsson, and Ahti SaloSystems Analysis Laboratory

Helsinki University of TechnologyFinland


PRIME Decisions - An Interactive Tool for Value Tree Analysis 2

Outline 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



Value TreeValue Tree

Good

180 km/h 50 000 EUR

3 monthsCar XCar X

Comfort Performance Price Time

Quality Delivery terms

Car

N

ii

Nii xvwV

1

)()(x

v1N(x1) v2

N (x2) v3

N (x3) v4

N (x4)

w4w2w1 w3



MAVT - Preference ElicitationMAVT - 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

Consequence

Val

ue

Value function

v(x2)

v(x1)

x1 x2

5.2)(

)(

)()(

)()(1

2

01

02

xv

xv

xvxv

xvxv x0

0 = v(x0)

v(x*)

x*



MAVT - Preference ElicitationMAVT - 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

v1(x1*)

v1(x10)

1

0

v2(x2*)

v2(x20) v3(x3

0)

v3(x3*)

Val

ue

N

iii xv

1

1)()()( 0

iiiii xvxvw

1)(

)()(

1

1

0

11

N

iii

N

iii

N

iii

N

ii

xv

xvxvw

= 0



Incomplete Information in MAVT (1)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



Incomplete Information in MAVT (2)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



PRIME - Preference ElicitationPRIME - Preference Elicitation

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*

Uxvxv

xvxvL

íííí

ííj

íí

)()(

)()(0

0Price

Val

ue

v3(x31)

x31x3

*0 = v3(x3

0)

v3(x3*)

x30

Performance

Val

ue

v2(x31)

x21x2

0

0 = v2(x30)

v2(x2*)

x2*



PRIME - Preference ElicitationPRIME - 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

100100

U

w

wL

ref

i

100)()(

)()(

100 0

0 U

xvxv

xvxvL

refrefrefref

iiii



PRIME - SynthesisPRIME - 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

)()(max,)()(min 00iiiiiiiii xvxvxvxvw

N

iii

N

iii xvxvV

11

)(max,)(min)(x



PRIME - Dominance StructuresPRIME - 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

0)()(max0)()(max11

N

i

kii

N

i

jii xvxvVV kjjk xxxx

V(x1)1

0

Val

ue

V(x2)

V(x3)



PRIME - Decision RulesPRIME - Decision Rules

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

V(x1)1

0

Val

ue

V(x2)

V(x3)



PRIME Decisions (1)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/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




Four main tasks Construction of value tree Definition of alternatives Preference elicitation

» Score elicitation» Weight elicitation

Synthesis» Value intervals» Dominance structures» Decision rules



Score ElicitationScore Elicitation1. Ordinal Ranking 2. Cardinal Judgements



Weight ElicitationWeight Elicitation



Value IntervalsValue Intervals



DominanceDominance



Decision RulesDecision Rules



PerformancePerformance

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



Case Study: Valuation of Technology VentureCase 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




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




Infotainment M-Commerce UMSVoice / Video DataM-OfficeMachine-

to-Machine

VMS E-MailInformation Entertainment M-Banking M-Shopping M-Ticketing

WirelessServices




Table 1: Weights and scores of the PRIME model

Relative Service Market Size(SWING Weight)

Proportion requiring PKI %(Score)

Lower Bound Upper Bound Lower Bound Upper Bound

Voice/Video 100 100 0 0Data 10 30 3 15Infotainment 2 5- Information 60 140 0 5- Entertainment 100 100 0 0M-Commerce 2 5- M-Banking 40 120 100 100- M-Shopping 140 180 95 100- M-Ticketing 100 100 95 100UMS 4 20- VMS 5 20 0 0- E-Mail 100 100 0 4M-Office / VPN 2 8 100 100Machine-to-Machine 1 3 70 90




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 @ 12% discount rate– about 700 million EUR in neutral scenario– earlier estimates 6 billion EUR (Merrill Lynch) and 17 billion EUR (Merita)




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



Further Research 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



ReferencesReferences

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.



PRIME - Linear ConstraintsPRIME - Linear Constraints

Ratio statements yield two linear constraints

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lk

ji

)()(

)()(

0)()()()(

0)()()()(

dUvcUvbvav

dLvcLvbvav

lkji

lkji

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