1. science
2. ecology
3. pollution

Università di Padova
SECOND CYCLE DEGREE PROGRAMME (MSC
LEVEL) IN ENVIRONMENTAL ENGINEERING
ENVIRONMENTAL
IMPACT ASSESSMENT
Multicriteria Analysis (MCA)
A.A. 2014-2015
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Introduction
MULTI CRITERIA METHODS
FROM SINGLE TO MANY GOALS
Classical methods of analysis (to solve managerial
decision problems) generally based on linear singlecriterion optimization
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Introduction
Example
evaluation of two different processes for electricity production, having as
limits emissions of pollutants and the availability of fuel
is expressed with:
•  A function to maximize:
Max f(x), where x is the energetic efficiency;
•  Constraints:
- QC<dC, where QC is the quantity of coal used and dC its availability;
- QM<dM where QM is the quantity of methane used and e dM its availability;
- Emissions < table values required by law.
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Introduction
IN A COMPLEX EVALUATION:
•  linear optimization may be too rigid function
•  not always possible to identify a single
objective
•  or is not quantifiable,
•  constraints are not always explicit,
•  in general the reality is not perfectly modeled.
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Introduction
Possible solutions:
•  use of non-linear programming models (complex and always
based on a perfect quantification of objectives),
•  Use of (optimization) models with several objectives.
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Multi Criteria Models
MULTI CRITERIA MODELS
"If something is considered valid at all, it definitely is
for several reasons" (Howard Raiffa).
Are based on the idea that in a complex decision problem
(EIA, SEA, etc.) there may be many aspects, not all
traceable to a single goal.
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Multi Criteria Models
ADVANTAGES:
• 
Takes into account different priorities and preferences
(participation)
• 
Highlights the different components of the problem and their
relationships, organizing and synthesizing these data in an
organic way (rationality)
• 
Makes explicit all the data processed (transparency)
• 
It reduces the arbitrariness of decisions (reproducibility)
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Multi Criteria Models
DISADVANTAGES:
•  Might “exagerate” any juxtapositions,
•  lends itself to manipulation (like all models)
•  simplifies reality (like all models)
•  Some techniques are very complex,
•  Sometimes the process is even "too" transparent (!).
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Multi Criteria Models
WHY IMPORTANT IN THE EIA ?
• 
allow to synthesize a lot of information
• 
take into account several objectives
• 
uses arrays of assessment (useful way to organize and
communicate information )
• 
decision closer to reality (compared for example to the
cost/benefit analysis)
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Multi Criteria Models
HOW DO THEY WORK ?
1. 
2. 
3. 
the object of analysis is broken down into simple factors, criteria,
which describe it exhaustively
These criteria are then analyzed separately
Several alternatives are then evaluated with respect to each single
criterion (of choice)
SCOPE OF
THE ANALYSIS
CRITERION C3
CRITERION C2
CRITERION C1
OPTION C
OPTION B
OPTION A
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Multi Criteria Models
HOW DO THEY WORK ?
Analyze OPTION A with respect to:
•  Criterion C1
•  Criterion C2
•  Criterion C3
Analyze OPTION B than .... Etc.
SCOPE OF
THE ANALYSIS
CRITERION C3
CRITERION C2
CRITERION C1
OPTION C
OPTION B
OPTION A
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Appendice: Multi Criteria Models
The criteria are the means by which the various alternatives are
compared to each other over the objective of the decision maker
Definition:
a criterion is a real function f such that it is meaningful to compare two
alternatives a and b of a set of alternatives A with respect to a particular
point of view, solely on the basis of the values of f(a) and f(b)
In practice, the criteria represent the environmental components,
the costs, the social aspects, etc..
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Multi Criteria Models
CONVENTION:
criteria and attributes are synonyms
Theory of Operational Research:
- multi-criteria analysis ! problem of choice among a finite number of alternatives
- multi-objectives analysis ! decision problem inherent infinite alternatives
in practice are also synonyms !
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The procedure in detail
THE PROCEDURE IN DETAIL
Five main phases:
1.  Definition of evaluation matrix
2.  Standardization of data
3.  Assigning weights
4.  Calculation of sorting
5.  Sensitivity analysis
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The procedure in detail
THE EVALUATION MATRIX
(impact matrix, analysis matrix, evaluation matrix, score matrix, appraisal table)
nxm two-dimensional array, which crosses the n objectives (or criteria) with
the m option of choice.
presenting nxm indicators with different units of measurement (quantitative,
qualitative or mixed)
Crit. A
Crit. B
Crit. C
Alt. 1
0.4
60
++
Alt. 2
0.8
40
-
Alt. 3
0.6
65
+
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For example:
C1: land in hectares
C2: Cost in millions of euros
C3: impact on the landscape
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The procedure in detail
EVALUATION MATRIX
Not only serve to identify the impacts, but also to organize the
data possibly in a very complex way.
Evaluation matrices consist of two-dimensional checklists: a list of
"activities" (project, plan or program) is related with a list of
components (environmental, social, economic).
Two-dimensional representation of cause-effect relationships
between planning/programming activities and the social and
environmental factors potentially subject to change.
For each intersection between the elements of the two lists is
possible to verify the actual presence of the impact (reporting
matrix) and possibly already give an assessment (evaluation
matrix, impacts matrix, etc.).
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The procedure in detail
EVALUATION MATRICES
• 
Several methods for their construction
• 
Methods generally based on a hierarchical system: from generic
elements (environmental components, phases of plan, etc..)
descend in detail (breakdown, "forward")
• 
Sometimes is also used the reverse process ( "backward").
• 
is often based on scientific literature and case studies
Typically a matrix of impacts may be disaggregated by:
•  Temporal Horizons (stages)
•  Geographical areas
•  Typologies
•  Actors
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The procedure in detail
STANDARDIZATION
• needed to make data in the array homogeneous and operational.
• the data are transformed into dimensionless values (convention)
with one or more logical-mathematical function.
Two main types:
1. 
Linear standardization
2. 
Value function (utility)
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The procedure in detail
1. Linear standardization
Simple mathematical functions that operate on values in each column
of the matrix. Can vary from column to column of the matrix
Standardizzazione
Funzione
Row maximum
x
x max
Ideal value
( x − xmin .id . )
( xmax .id . − xmin .id . )
Average value
x
x mean
interval standardisation
( x − x min .row )
( x max .row − x min .row )
Additive constrain
x
∑ xrow
Vector normalisation
x
x2
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The procedure in detail
2. Value/utility function
•  Assign to each indicator value a corresponding score of merit/preference/utility
dimensionless, between 0 and 1.
•  Necessity to define a function for each indicator (e.g., function “dose-response”).
•  It is said "value" when the data are deterministic, "utility" when stochastic
•  The utility measures the satisfaction of the decision maker
1
a
1
b
1
0.8
Quality
0.6
0.4
0.2
0
0
0
Min.
Max
.
Min.
Max
.
0
0.05
0.10
0.15
0.20
0.25
Average annual concentration
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The procedure in detail
2. Value/utility function
• 
• 
• 
Certain functions are derived in an objective way by laboratory tests
(e.g. the "dose response");
others are necessarily subjective (aesthetic value, social tolerance,
etc..) and therefore subject to change depending on the evaluator.
Although subject to some ambiguity, these latter are widely used in
evaluations of sustainability.
The main difference between the two types of normalization is that in
the first case, the functions may (but need not) vary from column to
column of the matrix in the second case, you define a function for each
indicator.
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THE ASSIGNMENT OF WEIGHTS
• 
• 
• 
• 
are dimensionless numerical values;
measure the priorities of the various aspects of the problem (the criteria);
never have absolute but only relative value;
are the marginal rate of substitution between the various criteria.
Example:
C1=30
C2=10
therefore C1= 3 C2
or C1/C2=3
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Three main classes of techniques for assignment:
1. 
2. 
3. 
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Direct assignment,
Comparison in pairs,
Methods based only on a ranking (even if incomplete).
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Direct assignment
is the easiest method (but more "ambiguous")
weights are assigned directly based on a predetermined
scale of scoring (1 to 100, 1000, etc.)
or redistributing this score among all the criteria (sum
equal to 100, 1000, etc...)
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Comparison in pairs:
• 
The criteria are compared in pairs and a relative score is assigned.
• 
This builds a matrix of paired comparisons square and symmetrical about
the main diagonal.
• 
The values of each row of the array are then aggregated into a final vector
using functions like: maximal eigenvector, least squares, etc..
Crit. A
Crit. B
Crit. C
Crit. A
1
1/2
7
0.6
Crit. B
2
1
3
0.2
Crit. C
1/7
1/3
1
0.2
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
By convention:
-  array elements are positive;
-  Aij=1/Aji;
-  The diagonal values are equal to unity..
Consequently, the number of comparisons required is:
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Crit. A
Crit. B
Crit. C
Crit. A
1
1/2
7
Crit. B
2
1
3
Crit. C
1/7
1/3
1
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[(n·(n-1)/2]
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Methods based only on a ranking (even if incomplete).
- 
- 
- 
Less common and very complex
No quantitative assessment only order of importance
It is assumed that the sum of the weights is equal to 1
- Three main approaches:
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1. 
Expected value
2. 
Extremal value
3. 
Random weights
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Expected value:
Given the premise, it assumes a distribution of values equally likely
Average values are those that approximate satisfactorily the vector
of weights sought.
NB
The weights do not depend on the nature of the criteria or the preference of the
decision maker, but only by their number and order.
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Extremal values:
Only the extreme weights are considered;
Calculate the resulting orders.
NB
All weights, and related rankings, included between these
extremes, comply with the order of priorities imposed.
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Random weights:
It is generated a large number of random rankings, and all the
possible combinations of weights satisfying the initial assumptions
are calculated
For each of these sets of weights it is calculated the resulting
ranking of alternatives and the probability for each ordering.
NB
The ordering is derived from a comparison of probabilities
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The procedure in detail
RANKING CALCULATION
The basic mechanism:
•  Combine weights and standardized indicators for any
alternative;
•  Compare alternatives to each other based on values
obtained.
Two main techniques:
1.  the weighted sum
2.  Indices of “concordance” and “discordance”
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Weighted sum:
• 
• 
• 
"prescriptive" technique (based on transitivity, completeness), extremely
common and simple
Sometimes it is "too" simple and can be unfaithful to the complex reality
Each indicator is multiplied by the respective weight and summed with
those of the same line
Aj=Σiwiaij
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
• 
“descriptive” techniques (depending on the assumption of
incomparability and intransitivity)
• 
Comparison in pairs of all the alternatives by evaluating two
different indices:
a.  Index of concordance
b.  Index of discordance
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
The concordance (Con) measures the satisfaction of choosing A1 than A2 (with
respect to the criteria c1, c2, etc.). Is equal to the sum of the corresponding
weights
Coni,j=Σnwn
The discordance (Dis) measures the regret in dismissing A2 compared to A1
and is (usually) measured as the maximum difference between the values of
the indicator of those criteria for which is expressed the regret of choosing the
second option than the first (usually but not necessarily, normalized to the
maximum difference of column)
Disi,j= max|ci-cj|
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
Construction of two matrices of pairwise comparisons (that of
discordance and that of concordance
and aggregate these values respectively into two vectors, whose
elements are the indices of concordance (Ic) and the indices of
discordance (Id), obtained according to the formulas:
Icj=ΣiConj,i - ΣiConi,j
Idj=ΣiDisj,i – ΣiDisi,j
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
The alternatives are then sorted into two lists:
1.  increasing index of concordance
2.  decreasing index of discordance.
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
EXAMPLE: Indices of “concordance” and “discordance”
three alternatives [A1, A2, A3] and three criteria [C1, C2, C3] whose weights are
respectively [0.2, 0.3, 0.5] (direct assignment).
M = Con i,k = mi,k = ∑ w j
j
C1
A1 80
A=
A2 40
A3 60
C2
0.6
€
0.8
0.1
Impact matrix
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C3
A1 A2 A3
10
A1 − 0,2 0,5
M =
€
40
A2 0,8 − 0,8
35
A3 0,5 0,2 −
Concordance matrix (M)
N = Disi,k = n i,k = max akj − aij
A1
A1 −
N=
A2 1
A3 0,7
A2 A3
1 0,8
− 0,5
1
−
Discordance matrix (N)
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C1
0,2
80
40
60
weights
A1
A2
A3
C2
0,3
0,6
0,8
0,1
180
normalized
by1column
sum
normalized
by1column
maximum
0,4
0,2
0,3
1
0,5
0,75
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C3
0,5
10
40
35
1,5
0,4
0,5
0,1
0,75
1
0,125
A1
A2
A3
85
Weighted(sum
0,1
0,3
0,5
0,4
0,4
0,3
0,25
1
0,875
0,6
0,9
0,6
A1
A2
A3
A1
A2
A3
%
0,8
0,5
1,3
0,2
%
0,2
0,4
0,5
0,7
0,8
1,6
%
0,7
1,3
Concordance
A1 !0,6
A2 1,2
A3 !0,6
%
1
0,7
1,7
1
%
1
2
0,8
1,8
0,5
1,5
%
1,7
1,3
Discordance
0,1
$0,5
0,4
0,7
C2
0,29
8
8
8
0,71
0,13
30
C3
1,00
0,83
8
8
8
Maximum'difference
cfr
A1''A2
A1''A3
A2''A1
A2''A3
A3''A1
A3''A2
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40
C1
8
8
1
0,5
0,5
1
MAX
1,0
0,8
1,0
0,5
0,7
1,0
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
EXAMPLE: Indices of “concordance” and “discordance”
three alternatives [A1, A2, A3] and three criteria [C1, C2, C3] whose weights are
respectively [0.2, 0.3, 0.5] (direct assignment).
For the discordance
It is normalized the difference of the values of the
indicator with the maximum difference of the criteria
indicator (for those criteria that “lose”) and then it is
choosen the maximum
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
EXAMPLE
Coni ,k = mi ,k = ∑ w j
j
M =
A1
A1 A2 A3
− 0,2 0,5
A2 0,8 − 0,8
A3 0,5 0,2 −
Concordance matrix (M)
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
EXAMPLE
Disi ,k = ni ,k = max a kj − aij
A1
A1 −
N=
A2 1
A3 0,7
A2 A3
1 0,8
− 0,5
1
−
Discordance matrix (N)
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
Indices of “concordance” and “discordance”
EXAMPLE
Ic(i ) = ∑ mi , j − ∑ m j ,i Id (i ) = ∑ ni , j − ∑ n j ,i
j
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j
j
A1 − 0,6
A2 1,2
A3 − 0,6
A1 0,1
A2 − 0,5
A3 0,4
Concordance
Discordance
vector
vector
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j
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
EXAMPLE (the same): weighted sum
(0,2) (0,3) (0,5)
C1
A1 80
A=
A2 40
A3 60
C2
0.6
0.8
0.1
C3
10
40
35
(0,2) (0,3) (0,5)
C1 C2 C3
0.4 0.4 0.1 (0,4X0,2)+(0,4X0,3)+(0,1X0,5)=0,3
0.2 0.5 0.5 (0,2X0,2)+(0,5X0,3)+(0,5X0,5)=0,4
0.3 0.1 0.4 (0,3X0,2)+(0,1X0,3)+(0,4X0,5)=0,3
A3
Results standardized
only on the criteria
(column or row sum)
A2
A1
0
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0,2
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0,4
0,6
0,8
1
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The procedure in detail
THE ASSIGNMENT OF WEIGHTS
ESEMPIO (the same): weighted sum
(0,2) (0,3) (0,5)
1 0,75 0,25 (1X0,2)+(0,75X0,3)+(0,25X0,5)=0,6 (0,55)
0,5
1
1 (0,5X0,2)+(1X0,3)+(1X0,5)=0,9
0,75 0,13 0,88 (0,75X0,2)+(0,13X0,3)+(0,88X0,5)=0,6 (0,63)
Results standardized
by column maximum
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The procedure in detail
SENSITIVITY ANALISYS
is particularly indicated in cases of uncertainty and ensure a proper
evaluation of all possible points of view of the problem.
Operated on the results to see what changes in the model of
analysis can generate substantial differences in performance of the
alternatives.
"Point of inversion": for what values of criteria and indicators, there
is a reversal of the order of alternatives in the rankings.
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SENSITIVITY ANALISYS
Purpose:
identify the most sensitive components of the
model
e.g. parameters, weights, criteria
⇓
that make rankings vary
Sensitivity: (condition number): S x =
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∂x
∂P
x
P
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The procedure in detail
SENSITIVITY ANALISYS
Three main types of sensitivity analysis:
1)  on the method: apply a different method of data standardization
and (when possible) of computation of final scores. Is used to
control the dependence of the results from the method of
calculation.
2)  on the criteria: add or delete some decision criteria. Is used to
check if basic criteria are missing
3)  on the weights (most used): change the ratings on certain criteria.
Allows to notice the degree of influence of each factor on the final
decision.
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The procedure in detail
SENSITIVITY ANALISYS
Sx measures the sensitivisty of alternative x to criteria P
!  Investigate at least 2 levels of variation, e.g. ± 30%, ± 60%
!  Determine more accurately the values of the more sensitive
criteria
!  Further levels of variation for more sensitive criteria
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DO
2
CBOD
NH3
CN
NO3
ON
1
PARAMETRI
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CARICHI
E_ON
E_NO3
E_NH3
E_DO
E_CBOD
Fl_ON
Fl_NH3
Fl_CBOD
td
kd
t71
k71
k2
t1R
K1R
t1C
k1C
t12
k12
tS
SOD
0
CONDIZIONI
AL CONTORNO
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Practical aspects
IN PRACTICE
SOME MODELS
PRESCRIPTIVE
SMART (Simple Multi Attribute Rating Technique) – SMARTS – SMARTER
AHP (Analytic Hierarchy Process) – ANP (Analytic Network Process)
etc. (based on weighted sum, value function, utility functions, direct assignment,
pairwise comparisons)
(IDEAL VALUE METHOD)
DESCRIPTIVE
ELECTRE (I, II, III IV V)
Regime
EvaMIX
etc. (based on concordance and discordance indices, random assignment,
expected value, etc.)
Università di Padova
LASA - DII
Environmental Impact Assessment
Environmental Engineering
a.a. 2014/2015
Practical aspects
IN PRACTICE
PRODUCTS
SOFTWARE
Infoharvest (SMART)
EC Pro (Expertchoice) (AHP)
Macbeth
Etc.
DSS
Definite
Vispa
GIS
Etc
Università di Padova
LASA - DII
Environmental Impact Assessment
Environmental Engineering
a.a. 2014/2015
Conclusions
References
• 
Bana e Costa C. A. (ed.) (1990), Reading in Multiple Criteria
Decision Aid, Spring-Verlag, Germany.
• 
Luria P ., Morara M. (2002), Analisi A Multi Criteri.
Documento Informativo, Padova: documento interno ARPA.
• 
Voogd H. (1983), Multicriteria Evaluation for Urban and
Regional Planning. London, UK: Pion Limited,
Università di Padova
LASA - DII
Environmental Impact Assessment
Environmental Engineering
a.a. 2014/2015