# Valuation

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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

Multiple attributes
multiple objectives
multiple criteria
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)
• 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
K.Fedra ‘97
Multicriteria decision example
set of criteria
• purchase price
• operating costs
– mileage
– service, repairs
• 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

K.Fedra ‘97
Multicriteria decision example
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

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
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
K.Fedra ‘97
Multicriteria decision example
axes normalized as % of possible
100%
utopia

reference
cost     dominated                 point
efficient
point

0%
K.Fedra ‘97
Multicriteria decisions
• 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
• 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:
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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