Decision Support Systems

1
Decision Support Systems

• multiple objectives, multiple criteria and
  valuation in environmental DSS

2
DSS Definition

• A DSS is a computer based problem solving system
  that assists choice between alternatives in
  complex and controversial domains.

3
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

4
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.

5
Decision support paradigms

• Multiple attributes
• multiple objectives
• multiple criteria
• trade-off, compromise,
• satisfaction, acceptance

6
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

7
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

8
Decision making

• ranking of alternatives with multiple attributes
• collapse attributes into a single attribute
  (e.g., monetization)
• OR solve the multi-dimensional problem

9
Decision making

• the multi-dimensional problem
• Multi-objective optimisation
• min f(x)
• where X(x1, x2, .. ,xn)
• is the vector of decision variables.

10
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

11
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)

12
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.

13
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.

14
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

15
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

16
Multicriteria decision example

• set of alternatives
• Rolls Royce
• Porsche
• Volvo
• Volkswagen
• Seat
• Lada

17
Multicriteria decision example

• set of criteria
• purchase price
• operating costs
• mileage
• service, repairs
• insurance, road tax
• safety
• prestige value

18
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

19
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)

20
Multicriteria decision example

• objectives and constraints
• can be reformulated
• constraint maximum cost
• objective minimise cost

21
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

22
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

23
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 ??

24
Multicriteria decision example

• cost plus safety

1
utopia
reference point
cost
dominated
efficient point
3
safety
10
nadir
25
Pareto efficiency

26
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.

27
Multicriteria decision example

• cost plus safety

1
utopia
reference point
cost
dominated
efficient point
3
safety
10
nadir
28
Multicriteria decision example

• axes normalized as of possible achievement
  (utopia - nadir)

100
utopia
reference point
cost
dominated
efficient point
0
safety
100
nadir
29
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).

30
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).

31
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.

32
Multicriteria decisions

• trade-off between price and location of
• a
  house
• 
  (distance
• to
  work)

dominated
33
Multicriteria decisions

• indifference and preference curves for
• 
  cost vs
• 
  distance

34
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.

35
Multicriteria decisions

• 3 criteria (3D) extension of the indifference
  curves

36
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

37
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

38
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.

39
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)

40
Valuation

• of environmental goods and services
• can be grouped in
• use and non-use values.
• How to measure
• non-use values ?

41
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 ?)

42
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)

43
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.

44
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.

45
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.

46
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).

47
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

48
Valuation

• Simple example
• use scores, points, indices, or similar
  subjective measurements to make non-commensurate
  attributes comparable

49
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

50
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

51
Valuation

• Hypothetical water project
• TOTAL score for benefits
  104
• TOTAL score for losses
  155
• Public welfare contribution -49
• Conclusion dont build !

52
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

53
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

54
Valuation

• Hypothetical water project
• TOTAL score for benefits
  145
• TOTAL score for losses
  120
• Public welfare contribution
  25
• Conclusion build !

55
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

56
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

57
Travel cost method

• Create a hypothetical simple but complete
  example from your local setting, use realistic
  estimates for number and prices.
• How can you treat time ?
• How could you use GIS data ?