K.Fedra ‘97 Spatial DSS environmental applications of spatial decision support systems

K.Fedra ‘97 Spatial Decisions Spatial decisions: Set of criteriaSet of criteria – objectives – constraints are functions of space are functions of space Spatial decisions: Set of criteriaSet of criteria – objectives – constraints are functions of space are functions of space

K.Fedra ‘97 Spatial Decisions Spatially distributed systems can be represented by spatially distributed models. Modeling is used to design a set of alternatives to choose from (simulation models)design a set of alternatives to choose from (simulation models) design an optimal alternative (optimisation models)design an optimal alternative (optimisation models) Spatially distributed systems can be represented by spatially distributed models. Modeling is used to design a set of alternatives to choose from (simulation models)design a set of alternatives to choose from (simulation models) design an optimal alternative (optimisation models)design an optimal alternative (optimisation models)

K.Fedra ‘97 Why Modeling: conceptualising, organisingconceptualising, organising communicatingcommunicating understanding, assessingunderstanding, assessing testing field measurementstesting field measurements forecasting, early warningforecasting, early warning optimising decision makingoptimising decision making conceptualising, organisingconceptualising, organising communicatingcommunicating understanding, assessingunderstanding, assessing testing field measurementstesting field measurements forecasting, early warningforecasting, early warning optimising decision makingoptimising decision making

K.Fedra ‘97 Modeling Domains Atmospheric systemsAtmospheric systems Hydrologic systemsHydrologic systems Land surface and subsurfaceLand surface and subsurface Biological and ecological systemsBiological and ecological systems Risks and hazardsRisks and hazards Technological systemsTechnological systems Management and policy modelsManagement and policy models Atmospheric systemsAtmospheric systems Hydrologic systemsHydrologic systems Land surface and subsurfaceLand surface and subsurface Biological and ecological systemsBiological and ecological systems Risks and hazardsRisks and hazards Technological systemsTechnological systems Management and policy modelsManagement and policy models

K.Fedra ‘97 Structuring the problem problem statement (description)problem statement (description) criteria (measurable attributes)criteria (measurable attributes) objectives (minimise, maximise)objectives (minimise, maximise) constraints (inequalities)constraints (inequalities) contextcontext problem statement (description)problem statement (description) criteria (measurable attributes)criteria (measurable attributes) objectives (minimise, maximise)objectives (minimise, maximise) constraints (inequalities)constraints (inequalities) contextcontext

K.Fedra ‘97 Modeling Domains Atmospheric systems weather forecastingweather forecasting climate modelsclimate models air pollution: industry, traffic, domestic sources, accidental releases (hazardous substances)air pollution: industry, traffic, domestic sources, accidental releases (hazardous substances) Atmospheric systems weather forecastingweather forecasting climate modelsclimate models air pollution: industry, traffic, domestic sources, accidental releases (hazardous substances)air pollution: industry, traffic, domestic sources, accidental releases (hazardous substances)

K.Fedra ‘97 Modeling Domains Air pollution control impacts and hazardsimpacts and hazards – human end environmental exposure – damage through explosion and fire – damage through chemical reactions (corrosion) (corrosion) Air pollution control impacts and hazardsimpacts and hazards – human end environmental exposure – damage through explosion and fire – damage through chemical reactions (corrosion) (corrosion)

K.Fedra ‘97 Modeling Domains Hydrologic systems hydrological cycle, rainfall-runoffhydrological cycle, rainfall-runoff river flow and floodingriver flow and flooding water distribution and allocationwater distribution and allocation reservoir operationsreservoir operations water quality, eutrophication,water quality, eutrophication, waste allocation waste allocation groundwater systemsgroundwater systems Hydrologic systems hydrological cycle, rainfall-runoffhydrological cycle, rainfall-runoff river flow and floodingriver flow and flooding water distribution and allocationwater distribution and allocation reservoir operationsreservoir operations water quality, eutrophication,water quality, eutrophication, waste allocation waste allocation groundwater systemsgroundwater systems

K.Fedra ‘97 Modeling Domains Coastal waters and oceans currents and energy balance (climate modeling)currents and energy balance (climate modeling) coastal water qualitycoastal water quality nutrient cycles, eutrophicationnutrient cycles, eutrophication fisheries (sustainable yield)fisheries (sustainable yield) Coastal waters and oceans currents and energy balance (climate modeling)currents and energy balance (climate modeling) coastal water qualitycoastal water quality nutrient cycles, eutrophicationnutrient cycles, eutrophication fisheries (sustainable yield)fisheries (sustainable yield)

K.Fedra ‘97 Modeling Domains Land surface and subsurface erosion, soil processeserosion, soil processes vegetation, land covervegetation, land cover groundwater (unsaturated and saturated zones, links to the hydrological domain)groundwater (unsaturated and saturated zones, links to the hydrological domain) Land surface and subsurface erosion, soil processeserosion, soil processes vegetation, land covervegetation, land cover groundwater (unsaturated and saturated zones, links to the hydrological domain)groundwater (unsaturated and saturated zones, links to the hydrological domain)

K.Fedra ‘97 Modeling Domains Biological and ecological systems population models, predator-prey systems, food chainspopulation models, predator-prey systems, food chains ecosystem models (multi- compartment combining physical and biological elements)ecosystem models (multi- compartment combining physical and biological elements) Biological and ecological systems population models, predator-prey systems, food chainspopulation models, predator-prey systems, food chains ecosystem models (multi- compartment combining physical and biological elements)ecosystem models (multi- compartment combining physical and biological elements)

K.Fedra ‘97 Modeling Domains Agriculture and Forestry agricultural productionagricultural production livestock and grazing modelslivestock and grazing models forest models (stands, growth, yield, deforestation and reforestation)forest models (stands, growth, yield, deforestation and reforestation) Agriculture and Forestry agricultural productionagricultural production livestock and grazing modelslivestock and grazing models forest models (stands, growth, yield, deforestation and reforestation)forest models (stands, growth, yield, deforestation and reforestation)

K.Fedra ‘97 Modeling Domains Technological systems transportationtransportation energy systemsenergy systems industrial impactsindustrial impacts waste managementwaste management Technological systems transportationtransportation energy systemsenergy systems industrial impactsindustrial impacts waste managementwaste management

K.Fedra ‘97 Modeling Domains Risks and hazards floods and droughtsfloods and droughts erosion, desertificationerosion, desertification spills and accidental releasesspills and accidental releases epidemiological models (pests, infectious diseases)epidemiological models (pests, infectious diseases) Risks and hazards floods and droughtsfloods and droughts erosion, desertificationerosion, desertification spills and accidental releasesspills and accidental releases epidemiological models (pests, infectious diseases)epidemiological models (pests, infectious diseases)

K.Fedra ‘97 Spatial decisions Environmental decision are also spatial decisions: site selection, locationsite selection, location pollution controlpollution control natural resources managementnatural resources management environmental impact assessmentenvironmental impact assessment risk analysis and managementrisk analysis and management Environmental decision are also spatial decisions: site selection, locationsite selection, location pollution controlpollution control natural resources managementnatural resources management environmental impact assessmentenvironmental impact assessment risk analysis and managementrisk analysis and management

K.Fedra ‘97 Spatial decisions site selection, location site selection for special activities or installations (power plants, incinerators, hazardous waste facilities): NIMBYsite selection for special activities or installations (power plants, incinerators, hazardous waste facilities): NIMBY site suitability analysissite suitability analysis zoning, land use managementzoning, land use management site selection, location site selection for special activities or installations (power plants, incinerators, hazardous waste facilities): NIMBYsite selection for special activities or installations (power plants, incinerators, hazardous waste facilities): NIMBY site suitability analysissite suitability analysis zoning, land use managementzoning, land use management

K.Fedra ‘97 Spatial decisions pollution control commissioning of sourcescommissioning of sources resource allocation to source controlresource allocation to source control incentives and taxes for emission sourcesincentives and taxes for emission sources clean-up strategiesclean-up strategies pollution control commissioning of sourcescommissioning of sources resource allocation to source controlresource allocation to source control incentives and taxes for emission sourcesincentives and taxes for emission sources clean-up strategiesclean-up strategies

K.Fedra ‘97 Spatial decisions natural resources management harvest and management strategies (maximum sustainable yield) for forestry, fisheries, livestockharvest and management strategies (maximum sustainable yield) for forestry, fisheries, livestock land-use (crop) allocationland-use (crop) allocation commissioning (mining, extraction)commissioning (mining, extraction) land reclamation, site remediationland reclamation, site remediation water resources management, water allocationwater resources management, water allocation natural resources management harvest and management strategies (maximum sustainable yield) for forestry, fisheries, livestockharvest and management strategies (maximum sustainable yield) for forestry, fisheries, livestock land-use (crop) allocationland-use (crop) allocation commissioning (mining, extraction)commissioning (mining, extraction) land reclamation, site remediationland reclamation, site remediation water resources management, water allocationwater resources management, water allocation

K.Fedra ‘97 Spatial decisions environmental impact assessment scoping and screeningscoping and screening impact assessment for major development projectsimpact assessment for major development projects policy assessmentpolicy assessment environmental impact assessment scoping and screeningscoping and screening impact assessment for major development projectsimpact assessment for major development projects policy assessmentpolicy assessment

K.Fedra ‘97 Spatial decisions risk analysis and management siting and commissioning of hazardous installationssiting and commissioning of hazardous installations operational managementoperational management hazardous substances and waste managementhazardous substances and waste management emergency planningemergency planning emergency managementemergency management risk analysis and management siting and commissioning of hazardous installationssiting and commissioning of hazardous installations operational managementoperational management hazardous substances and waste managementhazardous substances and waste management emergency planningemergency planning emergency managementemergency management

K.Fedra ‘97 MC DSS Application Example Selecting Nuclear Power Plant Sites in the Pacific Northwest Using Decision Analysis Keeney and Nair, 1977 Keeney and Nair, 1977 Selecting Nuclear Power Plant Sites in the Pacific Northwest Using Decision Analysis Keeney and Nair, 1977 Keeney and Nair, 1977

K.Fedra ‘97 Site Selection Problem statement: identify and recommend potential new sites suitable for a nuclear 3,000 MWe thermal power station in the Pacific Northwest. 3,000 MWe thermal power station in the Pacific Northwest. Problem statement: identify and recommend potential new sites suitable for a nuclear 3,000 MWe thermal power station in the Pacific Northwest. 3,000 MWe thermal power station in the Pacific Northwest.

K.Fedra ‘97 Site Selection Objective: identify sites with a high probability for successful licensing; screen sites for detailed site specific studies Objective: identify sites with a high probability for successful licensing; screen sites for detailed site specific studies

K.Fedra ‘97 Site Selection Two step procedure: a screening process to identify candidate sitesa screening process to identify candidate sites a decision analysis to evaluate and rank the candidate sitesa decision analysis to evaluate and rank the candidate sites Two step procedure: a screening process to identify candidate sitesa screening process to identify candidate sites a decision analysis to evaluate and rank the candidate sitesa decision analysis to evaluate and rank the candidate sites

K.Fedra ‘97 Site Selection Study area: 250,000 km 2 including the State of Washington, major river basins in Oregon and Idaho, Oregon coast, excluding areas around existing TPS sites. Study area: 250,000 km 2 including the State of Washington, major river basins in Oregon and Idaho, Oregon coast, excluding areas around existing TPS sites.

K.Fedra ‘97 Site Selection Hierarchy of issues: safetysafety environmentalenvironmental socialsocial economiceconomic with criteria and required levels of achievements (constraints) Hierarchy of issues: safetysafety environmentalenvironmental socialsocial economiceconomic with criteria and required levels of achievements (constraints)

K.Fedra ‘97 Site Selection Safety: radiation exposure Distance from populated areas: more than 5 km from populated places > 2,500 inhabitants more than 2 km from populated places < 2,500 inhabitants Safety: radiation exposure Distance from populated areas: more than 5 km from populated places > 2,500 inhabitants more than 2 km from populated places < 2,500 inhabitants

K.Fedra ‘97 Site Selection Safety: Flooding Height above nearest water source: area must be above primary flood plain (100 year flood) Safety: Flooding Height above nearest water source: area must be above primary flood plain (100 year flood)

K.Fedra ‘97 Site Selection Safety: Surface faulting Distance from fault: area a must be more than 10 km from capable or > 15 km from unclassified faults Safety: Surface faulting Distance from fault: area a must be more than 10 km from capable or > 15 km from unclassified faults

K.Fedra ‘97 Site Selection Environment: Thermal pollution Average low flow: Cooling water source (river, reservoir) yielding 7 day average 10 year low-flow > 5 m 3 /sec Environment: Thermal pollution Average low flow: Cooling water source (river, reservoir) yielding 7 day average 10 year low-flow > 5 m 3 /sec

K.Fedra ‘97 Site Selection Environment: protected areas Relative location: Location must be outside designated or protected sensitive ecological areas Environment: protected areas Relative location: Location must be outside designated or protected sensitive ecological areas

K.Fedra ‘97 Site Selection Socio-economics: tourism, recreation Relative location: Location must be outside designated scenic and recreational areas Socio-economics: tourism, recreation Relative location: Location must be outside designated scenic and recreational areas

K.Fedra ‘97 Site Selection Costs: routine/emergency water supply Cost/reliability of water source: Cooling water source (river, reservoir) yielding 7 day average 10 year low-flow > 5 m 3 /sec Costs: routine/emergency water supply Cost/reliability of water source: Cooling water source (river, reservoir) yielding 7 day average 10 year low-flow > 5 m 3 /sec

K.Fedra ‘97 Site Selection Costs: routine/emergency water supply Cost of pumping water: Location within 15 km from nearest water supply, and less than 250 m above the water level Costs: routine/emergency water supply Cost of pumping water: Location within 15 km from nearest water supply, and less than 250 m above the water level

K.Fedra ‘97 Site Selection Cost: delivery of major components Cost of providing delivery access: Location must be within 50 km of navigable waterways Cost: delivery of major components Cost of providing delivery access: Location must be within 50 km of navigable waterways

K.Fedra ‘97 Site Selection Sensitivity: assume varying the cut-off values by a small percentage; how many potential sites are included or excluded ? Sensitivity:

K.Fedra ‘97 Site Selection Site information: (approx. 30 attributes) area, location, present use, ownershiparea, location, present use, ownership quality, quantity, location of waterquality, quantity, location of water geology, topography, flooding potentialgeology, topography, flooding potential population, vegetation, wildlifepopulation, vegetation, wildlife access to transportation networksaccess to transportation networks local workforce, potential socio- economic problems during construction phase, …….local workforce, potential socio- economic problems during construction phase, ……. Site information: (approx. 30 attributes) area, location, present use, ownershiparea, location, present use, ownership quality, quantity, location of waterquality, quantity, location of water geology, topography, flooding potentialgeology, topography, flooding potential population, vegetation, wildlifepopulation, vegetation, wildlife access to transportation networksaccess to transportation networks local workforce, potential socio- economic problems during construction phase, …….local workforce, potential socio- economic problems during construction phase, …….

K.Fedra ‘97 Site Selection Screening of attributes: relative importancerelative importance annualised capital cost of the TPS is around MUS$; annual revenue loss from adverse effects on fisheries is around 0-50,000 US$  ignore the fish Screening of attributes: relative importancerelative importance annualised capital cost of the TPS is around MUS$; annual revenue loss from adverse effects on fisheries is around 0-50,000 US$  ignore the fish

K.Fedra ‘97 Site Selection Screening of attributes: site-dependent variationsite-dependent variation even though manpower costs for operations are important, they don’t vary significantly between sites þ ignore labor costs Screening of attributes: site-dependent variationsite-dependent variation even though manpower costs for operations are important, they don’t vary significantly between sites þ ignore labor costs

K.Fedra ‘97 Site Selection Screening of attributes: likelihood of occurrencelikelihood of occurrence adverse effects on crops could amount to several million US$; the probability of such extreme losses is near zero þ ignore crop losses Screening of attributes: likelihood of occurrencelikelihood of occurrence adverse effects on crops could amount to several million US$; the probability of such extreme losses is near zero þ ignore crop losses

K.Fedra ‘97 Site Selection Final Objectives and Criteria: Health and Safety X 1 = site population factor best: 0 best: 0 worst: 0.20 worst: 0.20 Final Objectives and Criteria: Health and Safety X 1 = site population factor best: 0 best: 0 worst: 0.20 worst: 0.20

K.Fedra ‘97 Site Selection Site Population Factor (US Atomic Energy Commission) SUM ((d=1,50) P(d)d -2 ) SUM ((d=1,50) P(d)d -2 ) SPF(L) = SPF(L) = SUM ((d=1,50) Q(d) -2 ) SUM ((d=1,50) Q(d) -2 ) where d is distance in miles, P is the population within this radius, Q is the population in this radius at a density of 1,000 people per square mile Site Population Factor (US Atomic Energy Commission) SUM ((d=1,50) P(d)d -2 ) SUM ((d=1,50) P(d)d -2 ) SPF(L) = SPF(L) = SUM ((d=1,50) Q(d) -2 ) SUM ((d=1,50) Q(d) -2 ) where d is distance in miles, P is the population within this radius, Q is the population in this radius at a density of 1,000 people per square mile

K.Fedra ‘97 Site Selection Final Objectives and Criteria: Environmental Effects X 2 = loss of salmonides best: 0 best: 0 worst: 100 % of fish population worst: 100 % of fish population Final Objectives and Criteria: Environmental Effects X 2 = loss of salmonides best: 0 best: 0 worst: 100 % of fish population worst: 100 % of fish population

K.Fedra ‘97 Site Selection Final Objectives and Criteria: Environmental Effects X 3 = ecological impacts best: 0 best: 0 worst: 8 (subjective ordinal scale) worst: 8 (subjective ordinal scale) Final Objectives and Criteria: Environmental Effects X 3 = ecological impacts best: 0 best: 0 worst: 8 (subjective ordinal scale) worst: 8 (subjective ordinal scale)

K.Fedra ‘97 Site Selection ecological impacts: loss per mi 2 for site 0 agricultural or urban land, no native ecological communities affected ecological communities affected 1 primarily agricultural land, no wetlands ……... 7 mature community or 90% loss of wetlands and endangered species habitat and endangered species habitat 8 100% mature forest, virgin wetlands, or endangered species habitats endangered species habitats ecological impacts: loss per mi 2 for site 0 agricultural or urban land, no native ecological communities affected ecological communities affected 1 primarily agricultural land, no wetlands ……... 7 mature community or 90% loss of wetlands and endangered species habitat and endangered species habitat 8 100% mature forest, virgin wetlands, or endangered species habitats endangered species habitats

K.Fedra ‘97 Site Selection Final Objectives and Criteria: Environmental Effects X 4 = length of 500 kV intertie best: 0 best: 0 worst: 50 miles worst: 50 miles Final Objectives and Criteria: Environmental Effects X 4 = length of 500 kV intertie best: 0 best: 0 worst: 50 miles worst: 50 miles

K.Fedra ‘97 Site Selection Final Objectives and Criteria: Socio-Economic Effects X 5 = socio-economic impacts best: 0 best: 0 worst: 7 (subjective ordinal scale) worst: 7 (subjective ordinal scale) Final Objectives and Criteria: Socio-Economic Effects X 5 = socio-economic impacts best: 0 best: 0 worst: 7 (subjective ordinal scale) worst: 7 (subjective ordinal scale)

K.Fedra ‘97 Site Selection Final Objectives and Criteria: System Cost X 6 = annual differential cost (30 yr) best: 0 best: 0 worst: 40,000,000 US$ (1985) worst: 40,000,000 US$ (1985) Final Objectives and Criteria: System Cost X 6 = annual differential cost (30 yr) best: 0 best: 0 worst: 40,000,000 US$ (1985) worst: 40,000,000 US$ (1985)

K.Fedra ‘97 Site Selection Preference Structure determine the general preferencedetermine the general preference structure structure assess the single-attribute utilityassess the single-attribute utility functions functions evaluate the scaling constantsevaluate the scaling constants specify the combined utility functionspecify the combined utility function Preference Structure determine the general preferencedetermine the general preference structure structure assess the single-attribute utilityassess the single-attribute utility functions functions evaluate the scaling constantsevaluate the scaling constants specify the combined utility functionspecify the combined utility function

K.Fedra ‘97 Site Selection General Preference Structure Independence of attributes: {X i, X j } are preferentially independent {X i, X j } are preferentially independent if the preference order for (x i, x j ) does not depend on the levels of other attributes. General Preference Structure Independence of attributes: {X i, X j } are preferentially independent {X i, X j } are preferentially independent if the preference order for (x i, x j ) does not depend on the levels of other attributes.

K.Fedra ‘97 Site Selection Multiattribute utility function attribute independence  suggests an additive utility function: u(x) = SUM (1,6) ( k i u i (x i ) ) u(x) = SUM (1,6) ( k i u i (x i ) ) where u is scaled 0 to 1, u i are the single attribute utility functions, and k i are scaling constants with 0<k i <1 Multiattribute utility function attribute independence  suggests an additive utility function: u(x) = SUM (1,6) ( k i u i (x i ) ) u(x) = SUM (1,6) ( k i u i (x i ) ) where u is scaled 0 to 1, u i are the single attribute utility functions, and k i are scaling constants with 0<k i <1

K.Fedra ‘97 Site Selection Single attribute utility functions lottery method (Keeney and Raiffa, 1976)50-50 lottery method (Keeney and Raiffa, 1976) X 6 (cost, 0-40 M) offer various values of X 6 against a 50/50 “lottery” of 0 or 40 M. Point of indifference: 22 M u(0) = 1, and u(40) = 0 u(22) = 0.5 Single attribute utility functions lottery method (Keeney and Raiffa, 1976)50-50 lottery method (Keeney and Raiffa, 1976) X 6 (cost, 0-40 M) offer various values of X 6 against a 50/50 “lottery” of 0 or 40 M. Point of indifference: 22 M u(0) = 1, and u(40) = 0 u(22) = 0.5

K.Fedra ‘97 Site Selection Single attribute utility functions X 6 cost u(40) = 0.0 u(26) = 0.5 u(0) = 1.0 Single attribute utility functions X 6 cost u(40) = 0.0 u(26) = 0.5 u(0) = 1.0

K.Fedra ‘97 Site Selection Single attribute utility functions X 3 ecology u(8) = 0.0 u(5) = 0.5 u(0) = 1.0 Single attribute utility functions X 3 ecology u(8) = 0.0 u(5) = 0.5 u(0) = 1.0

K.Fedra ‘97 Site Selection Scaling constants ranking of attribute (importance)ranking of attribute (importance) quantifying the k iquantifying the k i Ranking: everything else being equal, which attribute would you prefer to be at its best value ? k 6 > k 1 > k 2 > k 4 > k 5 > k 3 k 6 > k 1 > k 2 > k 4 > k 5 > k 3 Scaling constants ranking of attribute (importance)ranking of attribute (importance) quantifying the k iquantifying the k i Ranking: everything else being equal, which attribute would you prefer to be at its best value ? k 6 > k 1 > k 2 > k 4 > k 5 > k 3 k 6 > k 1 > k 2 > k 4 > k 5 > k 3

K.Fedra ‘97 Site Selection Scaling constants quantifying the k iquantifying the k i trade-off between attributes: trade-off between attributes: Site A: SPF = 0.0 cost = 40 Site B: SPF = 0.2 cost = ? At which cost are A and B considered equivalent (indifference) ? Scaling constants quantifying the k iquantifying the k i trade-off between attributes: trade-off between attributes: Site A: SPF = 0.0 cost = 40 Site B: SPF = 0.2 cost = ? At which cost are A and B considered equivalent (indifference) ?

K.Fedra ‘97 Site Selection Scaling constants trade-off between attributes: attributes: cost versus cost versus site factor site factor 40 M ~ M ~ M ~ M ~ 0.2 Scaling constants trade-off between attributes: attributes: cost versus cost versus site factor site factor 40 M ~ M ~ M ~ M ~ 0.2

K.Fedra ‘97 Site Selection Utility function establish probability (weight) p establish probability (weight) p such that such that option A: cost = 0, everything else at the worst level is indifferent to option A: cost = 0, everything else at the worst level is indifferent to option B: option B: all attributes at best level (p) all attributes at best level (p) all attributes at worst level (1-p) all attributes at worst level (1-p) Utility function establish probability (weight) p establish probability (weight) p such that such that option A: cost = 0, everything else at the worst level is indifferent to option A: cost = 0, everything else at the worst level is indifferent to option B: option B: all attributes at best level (p) all attributes at best level (p) all attributes at worst level (1-p) all attributes at worst level (1-p)

K.Fedra ‘97 Site Selection Utility function p = 0.4 p = 0.4 utility of option A: utility of option A: p(1.0)+(1-p)(0.0) = p p(1.0)+(1-p)(0.0) = p k 6 = p = 0.4 k 6 = p = 0.4 from trade-offs against k 6, all other k i can be determined Utility function p = 0.4 p = 0.4 utility of option A: utility of option A: p(1.0)+(1-p)(0.0) = p p(1.0)+(1-p)(0.0) = p k 6 = p = 0.4 k 6 = p = 0.4 from trade-offs against k 6, all other k i can be determined

K.Fedra ‘97 Site Selection Utility function given all k i, the multiattribute utility function can now be determined: given all k i, the multiattribute utility function can now be determined: u(x) = SUM (1,6) ( k i u i (x i ) ) u(x) = SUM (1,6) ( k i u i (x i ) ) which leads to a ranking of the candidate sites. Utility function given all k i, the multiattribute utility function can now be determined: given all k i, the multiattribute utility function can now be determined: u(x) = SUM (1,6) ( k i u i (x i ) ) u(x) = SUM (1,6) ( k i u i (x i ) ) which leads to a ranking of the candidate sites.