Multiattribute Utility Theory

conceptsapplicationexamples

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 coalconservation & small plants

• 1984 2 companies applied for a nuclear plant• hot issue• Hamalainen built AHP DSS for interested users

HierarchyF in n ish E n e rg y H ie ra rchy

ch eapso u rc es

fo re igntra de

ca p ita lre so u rces

n a tion a l e co no m y

n a tion a lre so u rces

p o llu t ionre d uc tion

a cc id e n ta vo id an ce

h e a lth sa fe ty & en v iro n m e nt

in de pe nd en ce ce n tra liza tion co op e ra tion

p o lit ica l

e n e rg y p o licy

alternatives of nuclear, coal, & conservation below each lower element

•Used by members of Parliament

•after Chernobyl, dropped nuclear

Selection Techniquesmany 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 conceptsrigorously 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 technique1. identify person whose utilities are to be maximized2. identify the issue or issues3. identify the alternatives to be evaluated4. identify the relevant dimensions of value for evaluating

alternatives (attribute scales)5. rank the dimensions in order of importance6. rate dimensions in importance, preserving ratios7. 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: travel = 10 workload = 15

location = 20 pay = 30 experience = 45

methodologyStep 7: Develop weights

Divide by total check: 100 for bestaverage

Experience 45/120 = 0.375 100/260 = 0.385 0.38Pay 30/120 = 0.250 70/260 = 0.269 0.26Location 20/120 = 0.167 40/260 = 0.154 0.16Workload15/120 = 0.125 30/260 = 0.115 0.12Travel 10/120 = 0.083 20/260 = 0.077 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 1.0Experience 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 valueStep 9:

U = wi sijEXP PAY LOC WOR TRA

weights 0.38 0.26 0.16 0.12 0.08scores: TOTALSBig 5 0.9 0.8 0.7 0.2 0.3 0.710Dot.com 1.0 0.7 0.9 0.8 1.0 0.826Local bank 0.3 0.5 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 criteriaidentify alternatives available, measure scores

simple calculation

selecting nuclear depositoryKeeney, 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, WANAS criticized selection method - said use MAUTIDENTIFY OBJECTIVE HIERARCHY

objectives attributes measuresDETERMINE RELATIVE IMPORTANCE

lottery tradeoffsRANK by value = weights x scores

DOE objectives• at depository worker health effects worker fatalities

public health effects public fatalities

• in transit 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 26.4% Belgium 4.1%France 20.5% Denmark 2.2%Italy 15.4% Greece 1.2%Great Britain 14.8% Portugal 1.1%Spain 7.4% Ireland 0.8%Netherlands 6.0% Luxemburg 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 SetsScen 1 Scen 2 Scen 3 Scen 4 Scen 5

GDP/POP.25 .4 .53 .53 1.0POL .25 .4 .27 .13 -EX/GDP .25 .05 .07 .07 -BEN/POP.25 .15 .13 .27 -

Proportional Contributions1989 Scen 1 Scen 2 Scen 3 Scen 4 Scen 5

Germany 26.36 26.11 26.10 26.39 26.33 26.22France 20.49 21.59 21.79 21.60 21.45 21.09Italy 15.43 17.23 17.50 17.22 17.07 17.30Great Britain 14.77 14.51 14.51 14.87 15.16 15.74Spain 7.36 6.25 6.37 6.28 6.27 6.27Netherlands 5.97 5.60 5.37 5.29 5.26 5.09Belgium 4.12 3.48 3.31 3.25 3.24 3.23Denmark 2.19 2.48 2.40 2.45 2.51 2.43Greece 1.23 1.09 1.06 1.06 1.09 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 wardesire for disarmament

want to get rid of plutonium

Clinton DirectiveSeptember 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 warheadsat 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 X: retrievable, time– deep borehole (immobilized) reasonable– deep borehole (direct emplacement) reasonable– discard to WIPP X: capacity– hydraulic fracturing X: technical viability– deep well injection X: ES&H– injection into continental magma X: technical viability, ES&H– melting in crystalline rock X: technical viability, ES&H– disposal under ice caps X: technical viability, ES&H– seabed (placement on ocean floor) X: technical viability– ocean dilution X: ES&H, treaty– deep space launch X: retrievability, ES&H

Disposition Options• Reactor & Accelerator Options

– Euratom MOX fabrication/reactor burning reasonable– existing light water reactors (LWRs) reasonable– partially completed LWRS reasonable– evolutionary or advanced LWRS reasonable– naval propulsion reactors X: transparency– modular helium reactors (MHRS) X: technical maturity– CANDU heavy water reactors reasonable– ALMRS with pyroprocessing X: technical maturity, ES&H– accelerator conversion X: technical maturity– LWRS with reprocessing X:theft diversion, policy– ALMRS with recycle X: technical maturity, policy– particle bed, molten salt reactors 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 Objectivesevolutionary - this was the initial set• non-proliferation max resistance to theft from unauthorized parties

max resistance to diversion by host nationmax international cooperation & compliance

• operational effective max technical viabilitymax cost effectivenessmax timelinessmax additional benefits

• env, saf, & health protect human health & safetyprotect the natural environmentprotect the human environment

• public & institutional acceptance

Phase 2 ObjectivesNonProliferation Theft material characteristics

environmentsafeguards & security

Diversion material characteristicsenvironmentsafeguards & security

Irreversibility formlocation

International Cooperation Russiancivil use of plutonium

Timeliness start yeartime to complete

Phase 2 ObjectivesOperational Effectiveness Technical Maturity

CostInvestment CostLife Cycle Cost

Environment, Safety, & HealthHuman Health & SafetyNatural EnvironmentSocio-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 ratiosprofitability ratiosmanagement 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 18these prioritized by PROMETHEE II study

• groundwater quality, quantity, extractionsconservation, 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