Multiattribute Utility Theory
concepts
application
examples
Objectives
• ECONOMIC POLICY
•
•
maximize production
equalize distribution
• GOVERNMENT POLICY
•
reconcile many interest groups
• BUSINESS
•
•
reconcile short run/long run tradeoffs
utlize long range planning (maintenance, labor)
BUSINESS OBJECTIVES
• PROFIT
• short run cash flow, after tax profit, long run
• RISK
• diversify, hedge
• MARKET DEVELOPMENT
• new products, wider market, quality
• CAPITAL REPLENISHMENT
• LABOR RELATIONS
Multiobjective Problems
•
•
•
•
•
•
•
Energy Policy health, environment, self-determination
Administration budgeting, setting objectives
Government services, location, tax rates
Water Resources Management
NASA project selection
MIS system selection
POM vendor selection
Finnish Energy Policy
• Finland running out of energy in early 1980s
• alternatives: large nuclear
large coal
conservation & small plants
• 1984 2 companies applied for a nuclear plant
• hot issue
• Hamalainen built AHP DSS for interested users
Hierarchy
Finnish Energy Hierarchy
energy policy
national economy
cheap
sources
foreign
trade
health safety & environment
capital
resources
national
resources
pollution
reduction
accident
avoidance
political
independence centralization
alternatives of nuclear, coal, & conservation below each lower element
•Used by members of Parliament
•after Chernobyl, dropped nuclear
cooperation
Selection Techniques
many techniques exist to support
selection decisions
• multi-attribute utility theory (MAUT)
• simple multi-attribute rating technique
(SMART)
• analytic hierarchy process (AHP)
• French methods (outranking)
• Russian methods (ordinal)
MAUT concepts
rigorously measure value vj
• identify what is important (hierarchy)
• identify RELATIVE importance (weights wk)
• identify how well each alternative does on each
criterion (score sjk)
• can be linear
vj =  wk sjk
• or nonlinear
vj = {(1+Kkjsjk) - 1}/K
MAUT concepts
• basis: there is a single dimensional value
measure
– it is cardinal, can be used for ranking
• analyst’s job - find that function
– (measure accurately)
– scores
– weights
caveats
• people buy insurance (expected payoff < cost)
because they avoid risk
• people gamble (expected payoff << cost)
because they are entertained
• utility theory NORMATIVE (how we SHOULD act)
• utility not necessarily additive
[value of 8 eggs not always = 4x(value of 2 eggs)]
money CAN serve as utility measure
conclusions
• MAUT considered the “scientific” approach
• focuses:
– measure as accurately as possible
– identify utility function as accurately as
possible
– be as objective as possible
SMART
• MAUT is a little abstract
– difficult to accurately develop tradeoffs
• SMART based on the same theory
– simpler implementation
– linear form
– direct entry of relative scores & weights
SMART technique
1. identify person whose utilities are to be maximized
2. identify the issue or issues
3. identify the alternatives to be evaluated
4. identify the relevant dimensions of value for evaluating
alternatives (attribute scales)
5. rank the dimensions in order of importance
6. rate dimensions in importance, preserving ratios
7. sum the importance weights, & divide by total(wi)
8. measure how well each alternative does on each dimension(sij)
9. U =  wi sij
points
• in Step 4, limit criteria
– there are only so many things a human can keep
track of at one time
– 8 plenty
– if weight extremely low, drop
methodology
• Step 4: Jobs: Big 5 firm, dot.com, local bank
• Step 5: rank order criteria
–
–
–
–
–
Experience (no value to cutting edge);
Pay ($25k to $50k);
Location (unattractive to great);
Workload (40 hours/week to 80 hours/week)
Travel (very heavy to a little travel)
• Step 6: rate dimensions
– least important = 10:
location = 20
travel = 10
pay = 30
workload = 15
experience = 45
methodology
Step 7: Develop weights
Divide by total
check: 100 for best
Experience 45/120 = 0.375 100/260 = 0.385
Pay
30/120 = 0.250 70/260 = 0.269
Location
20/120 = 0.167 40/260 = 0.154
Workload
15/120 = 0.125 30/260 = 0.115
Travel
10/120 = 0.083 20/260 = 0.077
average
0.38
0.26
0.16
0.12
0.08
methodology
• purpose of swing weighting
– Consider difference in scales
– The input is admittedly an approximation
– Giving values based on a different perspective
• additional check
• should yield greater accuracy
scores
• Step 8: score each alternative on each criterion
• need as objective a scale as you can get
• doesn’t have to be linear
0 worst
ideal 1.0
Experience none (0) focused (0.3) general (0.9) cutting edge (1.0)
Pay
$25k (0) $30k (0.5) $35k (0.7) $40k (0.8) $50k (1.0)
Location bad (0)
Dallas (0.7) Austin (0.9) Bryan (1.0)
Workload 80 hr (0) 70 hr (0.2)
50 hr (0.8)
40 hr (1.0)
Travel
excessive (0) lots (0.3) none (0.4)
a little (1.0)
Scores
Big 5
Dot.com
Local bank
Experience General 0.9 CutEdge1.0 Focused 0.3
Pay
$40k
0.8 $35k
0.7 $30k
0.5
Location
Dallas 0.7 Austin 0.9 Bryan
1.0
Workload
70 hr
0.2 50 hr
0.8 $40k
1.0
Travel
Lots
0.3 10%
1.0 None
0.4
calculation of value
Step 9:
U =  wi sij
weights
scores:
Big 5
Dot.com
Local bank
EXP
0.38
PAY
0.26
0.9
1.0
0.3
0.8
0.7
0.5
LOC WOR TRA
0.16 0.12 0.08
TOTALS
0.7 0.2
0.3
0.710
0.9 0.8
1.0
0.826
0.1 0.1
0.4
0.304
recommends the Dot.com
SMART
• provides a very workable means to implement the
principles of MAUT
• in fact, it can be MORE accurate than MAUT
(more realistic scores, tradeoffs)
identify criteria
develop scores over criteria
identify alternatives available, measure scores
simple calculation
selecting nuclear depository
Keeney, An analysis of the portfolio of sites to characterize for selecting a nuclear
repository, Risk Analysis 7:2 [1987]
DOE - dump nuclear waste - selected Hanford, WA
NAS criticized selection method - said use MAUT
IDENTIFY OBJECTIVE HIERARCHY
objectives attributes
measures
DETERMINE RELATIVE IMPORTANCE
lottery tradeoffs
RANK by value =  weights x scores
DOE objectives
• at depository
• in transit
worker health effects
worker fatalities
public health effects
public fatalities
worker health effects
worker fatalities
public health effects
public fatalities
• environmental aesthetic degradation
biological
degradation of archaeological, historical & cultural properties
• socioeconomic
• cost
repository costs
waste transportation costs
Nuclear Depository
• MAUT separated facts from values
• explicit professional judgments identified
• 14 criteria
• each alternative’s value on each criterion measured
with metric making sense relative to the decision
(radiation - expected deaths rather than rads)
• interviewed policy makers for tradeoffs
Nuclear Depository
• Keeney comments:
– the four policy makers tended to share
values
– “public utility probably should be linear”
• ended up digging at Yucca Mountain, Carlsbad
• catch - can’t use either
Hens Pastijn & Struys, “Multicriteria Analysis of the Burden Sharing
in the European Community,” EJOR 59 1992 248-261
• European Community
– 1958 to 1974 financed by direct contributions
by member states
– Treaty of Rome fixed proportional
contributions reflecting ability, advantage
– disputes about distribution of funds since early
1970s
• Study of equity of present system
European Community
revenues
•
•
•
•
External tariff - 20.1% in 1989
agricultural import levies - 2.9%
sugar storage levies - 2.9%
VAT contributions - 56.8%
– on goods and services
– 1988 added element based on GNP
• GDP-based contributions - 17.2%
European Community
Financing - 1989
Percent of EC Funding Contributed
Germany
France
Italy
Great Britain
Spain
Netherlands
26.4%
20.5%
15.4%
14.8%
7.4%
6.0%
Belgium
Denmark
Greece
Portugal
Ireland
Luxemburg
4.1%
2.2%
1.2%
1.1%
0.8%
0.2%
European Community
Financing
• Problems:
– country of port of entry may not be
destination (Rotterdam effect) but customs
collected in the Netherlands
– Belgium, Denmark, Germany, Ireland,
Luxembourg & the Netherlands paid more
than their relative share of GDP
– BENEFIT PRINCIPLE - those who benefit
should pay the tax
Reform Proposals
• 1976 Financial Mechanism: refund
payable if contribution significantly
higher than proportionate share of GNP
– didn’t work as planned
• 1984 corrective mechanism: rebate of
66% of difference between VAT
payment & budget expenditure share
criteria
•
•
•
•
GDP/population
POL - political willingness to cooperate
EX/GDP - exports per GDP
BEN/POP - EC payments/population
– USED AHP TO GET WEIGHTS!
Weight Sets
Scen 1 Scen 2 Scen 3 Scen 4 Scen 5
GDP/POP
POL
EX/GDP
BEN/POP
.25
.25
.25
.25
.4
.4
.05
.15
.53
.27
.07
.13
.53
.13
.07
.27
1.0
-
Proportional Contributions
Germany
France
Italy
Great Britain
Spain
Netherlands
Belgium
Denmark
Greece
1989
26.36
20.49
15.43
14.77
7.36
5.97
4.12
2.19
1.23
Scen 1
26.11
21.59
17.23
14.51
6.25
5.60
3.48
2.48
1.09
Scen 2
26.10
21.79
17.50
14.51
6.37
5.37
3.31
2.40
1.06
Scen 3
26.39
21.60
17.22
14.87
6.28
5.29
3.25
2.45
1.06
Scen 4
26.33
21.45
17.07
15.16
6.27
5.26
3.24
2.51
1.09
Scen 5
26.22
21.09
17.30
15.74
6.27
5.09
3.23
2.43
1.06
conclusions
• Great Britain should pay more if weight
higher for progressivity
• Italy should pay less than GDP, but more
than they currently do
• France & Denmark should pay more
• smaller countries should pay less
Disposition of Weapons
Grade Plutonium
end of cold war
desire for disarmament
want to get rid of plutonium
Clinton Directive
September 1993
• Where possible, eliminate stockpiles of HEU & Pu,
ensure they are subject to highest standards of safety,
security, international accountability
• Try to purchase HEU from former USSR & other
countries and convert to reactor fuel
• Start comprehensive review of long-term options for Pu
disposition, considering technical, nonproliferation,
environmental, budgetary, & economic factors; invite
international participation
Problem Scope
• about 50,000 tons of Pu is surplus in US
• about twice that amount surplus in
former USSR
• form is pits (warheads)
at plants ready to make warheads
at breeder reactors (Pu production facilities)
contaminated waste (gloves, etc.)
Plutonium Characteristics
•
•
•
•
artificial
EXTREMELY toxic
very long half-life (centuries)
NOT a particularly efficient reactor fuel,
but can be used
– if used in reactors, there still would be about 92% of Pu
left over (but it would not be suitable for weapons)
– lots of other spent fuel Pu, but has natural barrier
(you die if you pick it up)
Disposition Process
• transport warhead Pu to oxidation site
• oxidize Pu to PuOx
• Process
– vitrify: apply radionuclide, encase in matrix
– borehole: vitrify (or none)
– reactor: burn
• permanent storage
Decision Process
• Notice of Intent for Programmatic
Environmental Impact Statement 21 Jun 1994
• Department of Energy
– Office of Fissile Materials Disposition
• want Documented Record of Decision
– phase 1: SCREENING 17 Mar 95 41 options down to 11
– phase 2: multiattribute analysis
down to 1 - 3
– phase 3: final decision
Screening Criteria
• disposition
–
–
–
–
–
–
–
–
–
long term storage
resistance to theft & diversion by unauthorized parties
resistance to retrieval, extraction, & reuse by host nation
technical viability
environmental, safety, & health
cost effectiveness
timeliness
foster progress & cooperation with Russia and others
public & institutional acceptance
additional benefits
*
*
*
*
*
*
*
Disposition Options
• storage options
– no disposal action
baseline
– radiation barrier alloy
X:open-ended, ES&H
• immobilization with radionuclides
–
–
–
–
–
–
underground nuclear detonation
X: ES&H, licensing/regulatory
borosilicate glass immobilization (DWPF) X: ES&H, cost
borosilicate glass immobilization (new)
reasonable
ceramic immobilization
reasonable
electrometallurgical treatment
reasonable
borosilicate glass oxidation/dissolution
reasonable
Disposition Options
• direct disposal options
–
–
–
–
–
–
–
–
–
–
–
–
direct emplacement in HLW repository
deep borehole (immobilized)
deep borehole (direct emplacement)
discard to WIPP
hydraulic fracturing
deep well injection
injection into continental magma
melting in crystalline rock
disposal under ice caps
seabed (placement on ocean floor)
ocean dilution
deep space launch
X: retrievable, time
reasonable
reasonable
X: capacity
X: technical viability
X: ES&H
X: technical viability, ES&H
X: technical viability, ES&H
X: technical viability, ES&H
X: technical viability
X: ES&H, treaty
X: retrievability, ES&H
Disposition Options
• Reactor & Accelerator Options
–
–
–
–
–
–
–
–
–
–
–
–
Euratom MOX fabrication/reactor burning
existing light water reactors (LWRs)
partially completed LWRS
evolutionary or advanced LWRS
naval propulsion reactors
modular helium reactors (MHRS)
CANDU heavy water reactors
ALMRS with pyroprocessing
accelerator conversion
LWRS with reprocessing
ALMRS with recycle
particle bed, molten salt reactors
reasonable
reasonable
reasonable
reasonable
X: transparency
X: technical maturity
reasonable
X: technical maturity, ES&H
X: technical maturity
X:theft diversion, policy
X: technical maturity, policy
X: technical maturity
Phase 2: MAUT Analysis
• Decision maker - Secretary of Energy
• Project manager - Office of Fissile
Materials Disposition
• Technical Analysis - National
Laboratories
– Livermore, Oak Ridge, Sandia
• MAUT Framework - Pantex
– UT, Texas A&M
Phase 2 Purpose
• to generate a multiattribute utility model
option score=sum(weights*obj scores)
• National Laboratories - give accurate
estimates of each option’s score on
each objective
• OFMD - source of relative weights
Phase 2 Objectives
evolutionary - this was the initial set
max resistance to theft from unauthorized parties
max resistance to diversion by host nation
max international cooperation & compliance
• operational effective max technical viability
max cost effectiveness
max timeliness
max additional benefits
• env, saf, & health
protect human health & safety
protect the natural environment
protect the human environment
• public & institutional acceptance
• non-proliferation
Phase 2 Objectives
NonProliferation
Theft
material characteristics
environment
safeguards & security
Diversion
material characteristics
environment
safeguards & security
Irreversibility
form
location
International Cooperation Russian
civil use of plutonium
Timeliness
start year
time to complete
Phase 2 Objectives
Operational Effectiveness
Technical Maturity
Cost
Investment Cost
Life Cycle Cost
Environment, Safety, & Health
Human Health & Safety
Natural Environment
Socio-Economic
(last 3 measures had many sub-measures)
BANKADVISOR
• Mareschal & Brans, EJOR [1991]
•
•
•
•
use PROMETHEE as a bank DSS
evaluate firms relative to their competitors
input balance sheets, income statements (4 yr)
identify ratios
– management
• commercial
• industrial
• financial
BANKADVISOR
• PHASE I: display firm financial data
firm specific
• PHASE II: industrial evaluation
comparative
• each firm an alternative
• criteria types:
solvency rations
liquidity ratios
profitability ratios
management ratios
Croatian Highways
• Mladineo, Lozic, Stosic, Mlinaric & Radica, EJOR [1992]
• pick highway route
• 4 alternatives (2 coastal, 2 inland)
• interdisciplinary
local interests
social interests
Croatian Highways
•
•
•
•
•
•
•
27 criteria
TRAFFIC
ENGINEERING/TECHNICAL
CIVIL ENGINEERING
DEMOGRAPHIC
ENVIRONMENTAL
SOCIO-ECONOMIC
Jordanian Water
• Abu-Taleb & Mareschal EJOR [1995]
• 18 CRITERIA:
over time, government had developed 18
these prioritized by PROMETHEE II study
• groundwater quality, quantity, extractions
conservation, cost, supply, efficiency
• sanitation, output value, surface quality& quantity
• irrigated area, energy, land quality, sedimentation, recreation, air
quality, foreign labor
Jordanian Water
• Constraints
–
–
–
–
capital budget
operating budget
geographical dispersion
incompatability (bar overlapping combinations)
• PROMETHEE V gives optimal portfolio with net
flows as objective function coefficients
Conclusions
• Multiple attributes can be important in
many categories of decision making
• A number of techniques exist
• Systematic
– As objective as possible
– Preference of decision maker inherently
subjective