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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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