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Decision Support Systems multiple objectives, multiple criteria and valuation in environmental DSS K.Fedra ‘97 DSS Definition A DSS is a computer based problem solving system that assists choice between alternatives in complex and controversial domains. K.Fedra ‘97 Decision making A choice between alternatives requires a ranking of alternatives by the decision makers preferences: the preferred alternative must • satisfy the constraints • maximise the decision makers utility function K.Fedra ‘97 Decision making ranking of alternatives is trivial with a single attribute (e.g., cost): select the alternative with the minimum cost provided the attribute can be measured without error. K.Fedra ‘97 Decision support paradigms Multiple attributes multiple objectives multiple criteria trade-off, compromise, satisfaction, acceptance K.Fedra ‘97 Multiple attributes Criteria: problem dimensions relevant for the decision Objectives: the goals to be furthered criteria to be maximized or minimized: max f(c) Constraints: bounds for acceptable solutions, limit values on criteria K.Fedra ‘97 Multicriteria decision example set of criteria individual criteria may be: • cardinal (numerical): distance to employment: 1,2,3,4 ...km • ordinal (symbolic but ordered) neighborhood: peaceful, active, noisy • nominal heating system: oil, gas, electric K.Fedra ‘97 Decision making ranking of alternatives with multiple attributes: • collapse attributes into a single attribute (e.g., monetization) • OR solve the multi-dimensional problem K.Fedra ‘97 Decision making the multi-dimensional problem Multi-objective optimisation min f(x) where X=(x1, x2, ….. ,xn) is the vector of decision variables. K.Fedra ‘97 Multi-objective optimisation The vector f(X) = (f1(x), f2(x), ….., f n(x)) represents the objective function. Decision X1 is considered preferable to X2 if f(X1) .GE. f(X2) and fi(x1) .GE. fi(x2) for all i K.Fedra ‘97 Multi-objective optimisation The Pareto optimal solution f(x*) to min f(x) requires that there is no attainable f(x) that scores better than f(x*) in at least one criterion i (fi(x) .LT. fi(x*)) without worsening all other components of f(x*) K.Fedra ‘97 Pareto optimal an alternative is Pareto optimal or non- dominated, if it is: • best in at least one criterion (better than any other alternative); • or equal to the best in at least one criterion without being worse in all other criteria. K.Fedra ‘97 Multi-objective optimisation Pareto solutions are efficient (non improvable), the implied ordering is incomplete, i.e., a partial ordering. This means that the problem has more than one solution which are not directly comparable with each other. K.Fedra ‘97 Multicriteria decisions A simple example: • statement of the problem (objectives) • set of alternatives • set of criteria • set of constraints (feasible sub-set) • evaluation of alternatives (trade-off) • decision rules, selection K.Fedra ‘97 Multicriteria decision example statement of the problem (objectives) • characterises the DM goals • allows identification of alternatives Buy a new car that is cost efficient Alternatives: different models K.Fedra ‘97 Multicriteria decision example set of alternatives • Rolls Royce • Porsche • Volvo • Volkswagen • Seat • Lada K.Fedra ‘97 Multicriteria decision example set of criteria • purchase price • operating costs – mileage – service, repairs – insurance, road tax • safety • prestige value K.Fedra ‘97 Multicriteria decision example set of criteria • is considered important with regard to the objectives of the decision makers • common for all feasible alternatives • necessary to describe the alternatives (decision utility), should be maximised or minimised • its elements are independent from each other K.Fedra ‘97 Multicriteria decision example set of constraints • maximum available budget (limit on one of the criteria) • repair shop within a 20 km radius (independent of criteria, implicit: distance to repair shop) • must fit into the garage (implicit: size, maneuverability) K.Fedra ‘97 Multicriteria decision example objectives and constraints can be reformulated: constraint: maximum cost objective: minimise cost K.Fedra ‘97 Multicriteria decision example set of constraints defines the feasible subset: 1 Roll Royce: exceeds budget limit does not fit into garage 2 Porsche: no repair shop within specified radius K.Fedra ‘97 Multicriteria decision example evaluation of alternatives (trade-off) price OMR S P 1 Rolls Royce 10 10 8 10 2 Porsche 6 8 6 8 3 Volvo 3 3 10 6 4 Volkswagen 2 2 5 4 5 Seat 1.5 2.1 3 2 6 Lada 1.0 3 1 1 K.Fedra ‘97 Multicriteria decision example decision rules, selection price only: select 6 (Lada) total cost (3y): select 5 (Seat) total cost (5y): select 4 (VW) safety only: select 3 (Volvo) total cost + safety: ?? all criteria: ?? K.Fedra ‘97 Multicriteria decision example cost plus safety: 1 utopia reference cost dominated point efficient point 3 nadir safety 10 K.Fedra ‘97 Pareto efficiency K.Fedra ‘97 Pareto efficiency Pareto frontier or surface represents the set of all non-dominated alternatives: an alternative is non-dominated, if it is better in at least one criterion than any other alternative; or equal to the best without being worse in all other criteria. K.Fedra ‘97 Multicriteria decision example cost plus safety: 1 utopia reference cost dominated point efficient point 3 nadir safety 10 K.Fedra ‘97 Multicriteria decision example axes normalized as % of possible achievement (utopia - nadir): 100% utopia reference cost dominated point efficient point 0% nadir safety 100% K.Fedra ‘97 Multicriteria decisions trade off: • indifference: a trade-off is the change in criterion C1 that is necessary to offset a given change in criterion C2 so that the new alternative A2 is indifferent to the original one (A1). K.Fedra ‘97 Multicriteria decisions trade off: • preferred proportions: a trade-off is the proportion of change in criteria C1 and C2 that the DM would prefer if he could move away from the initial alternative in some specific way. (implicit relative weights of attributes). K.Fedra ‘97 Multicriteria decisions weights (relative importance) of criteria are not constant over the range of alternatives: trade-off between criteria and the relative weights of criteria are context dependent. K.Fedra ‘97 Multicriteria decisions trade-off between price and location of a house (distance dominated to work) K.Fedra ‘97 Multicriteria decisions indifference and preference curves for cost vs distance K.Fedra ‘97 Multicriteria decisions indifference: moving from the initial alternative A0(18,50) to the closer alternative A1 at (10,.) the DM is willing to pay 85. A1(10,85) is considered equivalent to A0(18,50) , DM has no preference, he is indifferent. K.Fedra ‘97 Multicriteria decisions 3 criteria (3D) extension of the indifference curves K.Fedra ‘97 Multicriteria decisions complicated by high dimensionality of the problem difficulty to elicit meaningful and consistent preferences from DM – explicit weights – elicitation (pairwise comparison, etc.) – reference point K.Fedra ‘97 Multicriteria decision making Valuation: expressing the value of ALL criteria in the same (monetary) units, so that a simple ordering is possible. How to value: safety cost of insurance prestige value cost of an alternative way to achieve the same goals K.Fedra ‘97 Multicriteria decision making Valuation: monetization (assigning monetary values) depends on the existence of some form of market. There is no market for most environmental goods and services. K.Fedra ‘97 Valuation of environmental goods and services • commercial use of a resource • functional value (service) • on-site recreational use • option for maintaining the potential for future use (visit) • existence value (knowing it is there) • bequest value (for future generations) K.Fedra ‘97 Valuation of environmental goods and services can be grouped in use and non-use values. How to measure non-use values ? K.Fedra ‘97 Valuation How to measure non-use values ? willingness to pay (or compensation demanded) - contingent valuation - travel cost restoration cost (what is the restoration cost for an extinct species ?) K.Fedra ‘97 Valuation Willingness to pay measures the value of goods or services that do not have a market to establish prices. Basic methods: contingent valuation (hypothetical) observed behavior (travel cost) K.Fedra ‘97 Valuation Travel cost method: uses the average expenditures (travel cost) and number of visitors to determine the value of a recreational resource like a park, lake, etc. K.Fedra ‘97 Valuation Contingent valuation: uses survey data on hypothetical transactions (willingness to pay, compensation demanded) contingent upon the creation of a market to establish the value of a non-market good. K.Fedra ‘97 Valuation Restoration costs or opportunity costs: estimates the costs of restoring an environmental good or service, or providing it in an alternative way: Estimate the value of an aquifer by the cost of restoring it, or the cost of alternative water supply. K.Fedra ‘97 Valuation Restoration costs or opportunity costs: fails for irreversible damage (extinction of a species) or the existence value of an environmental good (irreplaceable by definition). K.Fedra ‘97 Valuation The basic problems: • Intangibles: difficult to measure and express in quantitative terms • Qualitative character of values: including ethical, moral, religious ….. aspects • Time dependency: discounting versus sustainability, intergenerational equity K.Fedra ‘97 Valuation Simple example: use scores, points, indices, or similar subjective measurements to make non-commensurate attributes comparable K.Fedra ‘97 Valuation Hypothetical water project: score Water supply 50 M m3/day 40 Flood control: damage 200,000 $/year 20 Flood control: lives 1/year 20 Electricity supply: 3 MKWh 20 Recreation: reservoir 40,000 visitor days 3 Aquatic habitat: increase 100,000 fish 1 TOTAL score for benefits 104 K.Fedra ‘97 Valuation Hypothetical water project: score Construction cost 10 M$ 120 Operating costs 100,000 $/year 10 Nutrient losses: farming 100 tons/year 5 Beach nourishment: 20 tons/year 5 Loss of Recreation: 1,000 visitor days 5 Terrestrial habitat: losses 1 bear, 50 deer 10 TOTAL score for losses 155 K.Fedra ‘97 Valuation Hypothetical water project: TOTAL score for benefits 104 TOTAL score for losses 155 Public welfare contribution -49 Conclusion: don’t build ! K.Fedra ‘97 Valuation Hypothetical water project: score Water supply 50 M m3/day 60 Flood control: damage 200,000 $/year 20 Flood control: lives 1/year 30 Electricity supply: 3 MKWh 25 Recreation: reservoir 40,000 visitor days 5 Aquatic habitat: increase 100,000 fish 5 TOTAL score for benefits 145 K.Fedra ‘97 Valuation Hypothetical water project: score Construction cost 10 M$ 100 Operating costs 100,000 $/year 10 Nutrient losses: farming 100 tons/year 3 Beach nourishment: 20 tons/year 2 Loss of Recreation: 1,000 visitor days 1 Terrestrial habitat: losses 1 bear, 50 deer 4 TOTAL score for losses 120 K.Fedra ‘97 Valuation Hypothetical water project: TOTAL score for benefits 145 TOTAL score for losses 120 Public welfare contribution 25 Conclusion: build ! K.Fedra ‘97 Valuation Hypothetical water project: to improve the estimate for recreational benefits, use the travel cost method: since the reservoir (lake) does not yet exist, use: • a similar lake or reservoir • hypothetical questions K.Fedra ‘97 Valuation Travel cost method: • count visitors • determine distance traveled (travel cost based on mileage) • determine other expenditures • estimate total expenditures from recreational users == value of the resource K.Fedra ‘97

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posted: | 9/28/2012 |

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