MULTI-ATTRIBUTE DECISION ANALYSIS: AN ILLUSTRATION • Overall focus: environmental impacts • Decision environment - Options (Coal, nuclear) - Impacts - Conflicting objectives - Uncertainty - Several decision makers - - EVALUATION OF STRATEGIES FOR ELECTRICAL ENERGY PRODUCTION IN WISCONSIN (Ref: Buehring, Foell and Keeney 1978; Watson and Beude 1987) MADAALTERNATIVE POLICIES FOR WISCONSIN ELECTRICAL GENERATION: 1970 TO 2000 Policy 1 • • • • Electrical generation increase at an average annual growth rate of 4.7%. Almost all new plants are fuelled with coal. SO2 emissions controlled by using stack gas removal systems and low-sulfur coal. 99% particular control. Policy 2 • • • • Electrical generation – same as Policy 1. Almost all new plants are fuelled with coal. No SO2 stack gas removal systems and same amount of low-sulfur coal as policy 1. 89% particulate control. Policy 3 • • • Electrical generation – same as Policy 1. Almost all new plants are nuclear. Emission controls for SO2 and particulate same as Policy 1. Policy 4 • • • • • Electrical generation – same as Policy 1. After 1975, all coal is low-sulfur from distant mines in Western states. New capacity after 1982 is 50% coal and 50 % nuclear. After 1975, all coal and uranium are obtained from surface mines. Emission controls for SO2 and particulate same as Policy 1. Policy 5 • • • Electrical generation increases at an average annual growth rate of 2.8%. Almost all new plants are fuelled with coal. Emission controls for SO2 and particulate same as Policy 1. Policy 6 • • • Electrical generation – same as Policy 5. Almost all new plants are nuclear. Emission controls for SO2 and particulate same as Policy 1.ATTRIBUTES FOR MULTIATTRIBUTE DECISION ANALYSIS ATTRIBUTE UNIT 1. Total quantified fatalities 2. Permanent land use 3. Temporary land use 4. Water evaporated 5. SO2 emissions 6. Particulate emissions 7. Thermal energy needed 8. Radioactive waste 9. Nuclear safeguards 10. Health effects of chronic air pollution 11. Electricity generated Deaths Acres Acres 10¹² Gallons 10⁶ Tons 10⁶ Tons 10¹² KWh (t) Metric tons Tons puf produced Tons lead emitted 10¹² Kwh (e)CUMULATIVE IMPACTS OF ALTERNATIVE PROLICIES ATTRIBUTES Policy 1 Policy 2 Policy 3 Policy 4 Policy 5 Policy 6 1. Fatalities (deaths) 380 380 240 680 280 210 2. Permanent Land Use (acres) 420 420 1,100 770 380 730 3. Temporary Land Use (acres) 140,000 137,000 85,000 43,000 99,000 71,000 4. Water Evaporated (10¹²gallons) 0.72 0.71 0.84 0.79 0.55 0.61 5. SO2 Pollution (10⁶tons) 12 23 8.0 8.6 9.5 7.4 6. Particulate Pollution (10⁶tons) 0.69 6.2 0.40 0.56 0.51 0.37 7. Energy Needed (10¹²kWh) 4.9 4.9 5.2 5.3 3.8 3.9 8. Radioactive Waste (MT fissile products) 61 61 160 110 54 105 9. Nuclear Safeguards (tons fissile plutonium) 11 11 30 21 10 19 10. Chronic Health Effects (tons lead emitted) 124 1,110 71 100 92 66 11. Electricity Generated (10¹²kWh nuclear) (10¹²kWh coal) (10¹²kWh coal + nuclear) 0.36 1.37 1.73 0.36 1.37 1.73 0.99 0.74 1.73 0.68 1.05 1.73 0.33 0.99 1.32 0.64 0.62 1.32 Polices 1. Mostly coal, SO2 removal, 99% particulate control. 2. Mostly coal, SO2 removal, 89% particulate control. 3. Mostly nuclear. 4. Mostly western coal, more coal than nuclear. 5. Mostly coal, less energy. 6. Mostly nuclear, less energy.MADA: MAIN STEPS • Introducing terminology & ideas • Determining general preference structure - preference independence - utility independence • Assessing single attribute utility functions • Evaluating scaling constants • Evaluating alternativesDETERMINING GENERAL PREFERENCE STRUCTURE • Preferential independence Preferences for consequences involving any two attributes taken at a time do not depend on the levels at which the remaining attribute are fixed Decision maker’s trade-off between these two attributes do not depend on the levels at which other attributes are fixed (example: next page)• Utility independence DETERMINING GENERAL PREFERENCE STRUCTURE (CONTD.) UTILITY INDEPENDENCE FOR AN ATTRIBUTE Preference order for lotteries involving only changes in the level of that particular attribute does not depend on the levels at which other attributes are held.Selected Single-Attribute Utility Functions for Two Decision Makers A B A B A B A B A B Individuals and A B 1 U1 U 9 U 11 U 10 U 3 U 1 680 X 1 210 X 11 X X2 10 X 3 X 9 1,110 1.32 1,100 140 30 1.73 66 10 380 43 (Fatalities) (Tons Plutonium) (1012 KWH Electricity) (Acres) (Tons Lead) (103 Acres) 0 0 0 0 0 0 1 1 1 1 1Utility Function for Decision-Maker A Attribute Conditional Utility Function (Ui) X 1 (700 - X1)) / 600 X 2 (1- exp (- .004(2000-X2))) / 0.550 X 3 (1- exp (-3.5x 10 6 (200,000-X2))) / 0.486 X 4 (1- exp (- .825 (1.5-X4))) / 0.562 X 5 (1- exp (- .011 (80-X5))) / 0.562 X 6 (10 – X6) / 9.8 X 7 (10 – X7) / 3 X 8 (200– X8) / 199 X 9 (exp ( .12(50-X9)) – 1) / 357 X 10 (1- exp (- .0005(2000-X10))) / 0.632 X 11 (X11-0.5)0.2(1-(X11-1.5)2/2.5)/(1+(X11-1.5)2)0.5Utility Function for Decision-Maker B Attribute Conditional Utility Function (Ui) X 1 (700 - X1)) / 600 X 2 (2000-X2)/ 1999 X 3 (1- exp (-5.8x 10 6 (200,000-X2))) / 0.668 X 4 (1- exp (- .825 (1.5-X4))) / 0.562 X 5 (1- exp (- .011 (80-X5))) / 0.562 X 6 (10 – X6) / 9.8 X 7 (1- exp (- .1 (6-X7))) / 0.259 X 8 (200– X8) / 199 X 9 (1- exp ( -.035(50-X9))) / 0.820 X 10 (1- exp (- .0002(2000-X10))) / 0.330 X 11 (1- exp (- 1.31(X11 -0.5))) / 0.962EVALUATING SCALING CONSTANTS TWO STEP PROCESS a) Ranking in order of importance (for specified ranges) b) Quantifying each scaling constant - Develop relationship between various scaling constants - Determine value of a specific scaling constant - Calculate remaining scaling constants Decision maker is indifferent between the consequences represented by point A&DRelationship Between Various Scaling Constants: Decision-Maker B K i Relationship to K10 k 10 K 1 K1 = k10u10 (500) K 9 K9 = k10u10 (1,200) K 5 K5 = k10u10 (1,700) K 8 K8 = k5u5 (10) = k10u10 (1,110)u5 (10) K 11 K11= k5u5 (20) = k10u10 (1,700)u5 (20) K 3 K3= k5u5 (60) = k10u10 (1,700)u5 (60) K 2 K2= k3u3 (50) = k10u10 (1,700)u5 (60)u3 (50) K 4 K4= k3u3 (75) = k10u10 (1,700)u5 (60)u3 (75) K 7 K7= k3u3 (125) = k10u10 (1,700)u5 (60)u3 (125) K 6 K6= k3u3 (150) = k10u10 (1,700)u5 (60)ASSESSING THE INDIFFERENCE PROBABILITY FOR DECISION MAKER BSolving for Scaling Constants: DecisionMaker B K i Ki equals Value of Ki k 10 0.339 K 1 0.768 K10 0.266 K 9 0.449 K10 0.152 K 5 0.177 K10 0.060 K 8 0.169 K10 0.057 K 11 0.152 K10 0.051 K 3 0.062 K10 0.021 K 2 0.054 K10 0.018 K 4 0.048 K10 0.016 K 7 0.033 K10 0.011 K 6 0.023 K10 0.008 Σ= 2.953 K 10 Σ=1.0 Note: Solving Σ Ki = 2.953 k10 =1 yields k10 = 0.339, from which other kis are evaluated.Scaling Constants Attribute Individual A Individual B X 1 = total quantified fatalities 0.354 0.267 X 2 = permanent land use 0.004 0.018 X 3 = temporary land use 0.033 0.021 X 4 =water evaporated 0.083 0.016 X 5 = SO2 pollution 0.008 0.060 X 6 = particulate pollution 0.008 0.008 X 7 = thermal energy needed 0.017 0.011 X 8 = radioactive waste 0.132 0.057 X 9 = nuclear safeguards 0.177 0.052 X 10 = health effects of chronic air pollution exposure 0.118 0.339 X 11 = electricity generated 0.066 0.051 Σ=1.0 Σ=1.0Utilities for the Six Scenarios Individual A Individual B 1. Mostly coal, SO2 removal, 99% particulate control 0.616 0.798 2. Mostly coal, no SO2 removal, 89% particulate control 0.561 0.632 3. Mostly nuclear 0.588 0.793 4. More coal than nuclear, mostly western coal 0.379 0.638 5. Mostly coal, less energy 0.712 0.856 6. Mostly nuclear, less energy 0.680 0.857Relationship Between Various Scaling Constants: Decision-Maker B K i Relationship to K10 k 10 K 1 K1 = k10u10 (500) K 9 K9 = k10u10 (1,200) K 5 K5 = k10u10 (1,700) K 8 K8 = k5u5 (10) = k10u10 (1,110)u5 (10) K 11 K11= k5u5 (20) = k10u10 (1,700)u5 (20) K 3 K3= k5u5 (60) = k10u10 (1,700)u5 (60) K 2 K2= k3u3 (50) = k10u10 (1,700)u5 (60)u3 (50) K 4 K4= k3u3 (75) = k10u10 (1,700)u5 (60)u3 (75) K 7 K7= k3u3 (125) = k10u10 (1,700)u5 (60)u3 (125) K 6 K6= k3u3 (150) = k10u10 (1,700)u5 (60)CUMULATIVE IMPACTS OF ALTERNATIVE PROLICIES ATTRIBUTES Policy 1 Policy 2 Policy 3 Policy 4 Policy 5 Policy 6 1. Fatalities (deaths) 380 380 240 680 280 210 1. Permanent Land Use (acres) 420 420 1,100 770 380 730 1. Temporary Land Use (acres) 140,000 137,000 85,000 43,000 99,000 71,000 1. Water Evaporated (10¹²gallons) 0.72 0.71 0.84 0.79 0.55 0.61 1. SO2 Pollution (10⁶tons) 12 23 8.0 8.6 9.5 7.4 1. Particulate Pollution (10⁶tons) 0.69 6.2 0.40 0.56 0.51 0.37 1. Energy Needed (10¹²kWh) 4.9 4.9 5.2 5.3 3.8 3.9 1. Radioactive Waste (MT fissile products) 61 61 160 110 54 105 1. Nuclear Safeguards (tons fissile plutonium) 11 11 30 21 10 19 1. Chronic Health Effects (tons lead emitted) 124 1,110 71 100 92 66 1. Electricity Generated (10¹²kWh nuclear) (10¹²kWh coal) (10¹²kWh coal + nuclear) 0.36 1.37 1.73 0.36 1.37 1.73 0.99 0.74 1.73 0.68 1.05 1.73 0.33 0.99 1.32 0.64 0.62 1.32 Expected Utilities: Individual A 0.620 0.569 0.589 0.383 0.711 0.680 Individual B 0.789 0.624 0.785 0.631 0.846 0.849