Bulgarian Academy of Sciences. 22 July, 2008 1 Index Introduction Outline of the scheme Step 1. Individual weights Step 2. Preference aggregation Step

1

Bulgarian Academy of Sciences. 22 July, 2008

Index

• Introduction

• Outline of the scheme

• Step 1. Individual weights

• Step 2. Preference aggregation

• Step 3. Determination of the indicators

• Step 4. Final aggregation

• Conclusions

End

2


Introduction

• Sustainable development (Brundtland Commision, 1987): development that meets the needs of the present without compromising the ability of future generations to meet their own needs.

• This is, by nature, a multicriteria concept.

3


Introduction

Sustainability

Social

Economic Environmental

4


Introduction

Natural capital vs. Man-made capital.• Weak sustainability. Total capital

constant. Substitutability paradigm.• Strong sustainability. Natural capital and

man-made capital are (at the most) complementary. Non substitutability paradigm.

5


Introduction

• Life cycle assesment. Environmental performance of production and services through all phases of their life cycle (from craddle to tomb): Extracting and processing raw materials; manufacturing; transportation and distribution; use, reuse and maintainance; recycling; final disposal.

How to measure sustainability?

6


Introduction

• Ecological footprint. Estimate of the ammount of land area a human population, given prevailing technology, would need if the current resource consumption and pollution by the population is matched by the sustainable (renewable) resource production and waste asimilation by such a land area.


7


Introduction

• (Urban) Indicators. A set of magnitudes measuring different concrete aspects of sustainability. Over 200 indicators are presently used.

• Still to be done:– To define a full common framework (meningful and

comparable),– To actually measure them,– To develop synthetic urban sustainability indicators.


8


Introduction

• ... define a methodology, based on the reference point approach, to develop a pair of urban synthetic sustainability indicators (weak and strong) for a set of municipalities of Andalucía, based on a pre-defined set of indicators.

In this work, we...

9


Outline of the scheme

Data selection0

Determination of individual weights1

Preference aggregation2

Synthetic indicators within each class3

Final aggregation4

-Municipalities-Indicators-Criteria-Experts

Haldi (1995)

Meta-Goal ProgrammingRodríguez et al. (2000)

Reference PointWierzbicki (1986)

Strong and Weak Indicator

10


• Municipalities. 18 (M) Andalusian municipalities, over 55,000 inhabitants.

• Indicators. 4 classes:– Environmental (13)– Urban development (12)– Demographic (16)– Economic (22)

(I - number of indicators in a given class)


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ENVIRONMENTAL CLASS

WATER CYCLE

% of water losses in the pipe line

Water consumption (per inhabitant)

Km of water supply line

Km of drainage line

ENERGY Electricity consumption (per inhabitant)

MATERIALS CYCLE

Volume of waste (per inhabitant)

Paper containers (per inhabitant)

Volume of glass recycled (per inhabitant)

NOISEDay noise

Night noise

ATMOSPHERE

Atmospheric inmissions

Greenhouse efect emissions

Global emissions

12


• Criteria. The indicators are to be maximized or minimized– Some are clear (e.g. % of water loss)– Others are not so clear (e.g. Paper

containers/inhabitant, electricity consumption)

• Panel of experts. 6 experts (ND):– 2 Environmental – 2 Social– 2 Economic


13


1. Individual Weights

Each expert k (k = 1, ..., ND) assigns weights to the indicators in the following way:

• Assume a class of indicators is chosen, which contains I indicators.

• The expert classifies the indicators into L sets (VI, CI, I, NVI, NI is suggested)

14



• For each l = 2,..., L-1, the expert is asked to place set l between sets l-1 and l+1.

l - 1

l + 1

0

0.25

0.5

0.75

1

set lalk

15



• The following system of equations is solved:

0

1,,2,0)1(

100

11

1

kL

kl

kl

kl

kl

kl

k

Llaa

• The weights are assigned:

),,1(

set tobelongs indicator

Ii

likl

ki

16



ENVIRONMENTAL CLASS

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13

DM1 30.00100.0

010.00 0.00

100.00

30.00 30.00 60.00 30.00 60.00 60.00 60.00 60.00

DM2 50.00 75.00 50.00 75.00100.0

050.00 50.00 50.00 50.00 75.00 75.00

100.00

100.00

DM3 100.00 50.00 25.00 50.00 50.00 50.00 50.00 50.00 50.00 100.00 50.00 50.00 50.00

DM4 100.00 25.00 25.00 50.00 50.00 50.00 50.00 50.00 50.00 100.00100.0

050.00

100.00

DM5 100.00100.0

0100.0

0100.0

0100.0

075.00 75.00 75.00 25.00 50.00 50.00 25.00 25.00

DM6 50.00100.0

00.00 25.00

100.00

25.00 75.00 75.00 75.00 100.00100.0

0100.0

075.00

• Weights for the environmental class:

17


2. Preference Aggregation

• We establish the following set of goals:

NDkIipn ki

ki

kii ,,1,,,1,

• The achievement function takes the form:

)( ki

ki pnh

18


• Best maximum deviation:

NDkIipn

Ii

NDkIipn

NDkdpn

d

P

ki

ki

i

ki

ki

kii

I

i

ki

ki

,,1,,,1,0,

,,1,1000

,,1,,,1,

,,10)(s.t.

min

)1(1


(AP1) d*, smax

19


• Best total deviation:

NDkIipn

Ii

NDkIipn

pn

P

ki

ki

i

ki

ki

kii

ND

k

I

i

ki

ki

,,1,,,1,0,

,,1,1000

,,1,,,1,s.t.

)(min

)2(1 1


(AP2) s*, dmax

20


• Pay-off matrix:


Best Worst

Max. dev. d* dmax

Agg. dev. s* smax

• Meta-Goals: we choose values

max

max

sss

ddd

*,~*,

~

21


• Meta-Goal Programming Problem:

0,,,

~)(

~,,1,,,1,0,

,,1,1000

,,1,,,1,

,,10)(s.t.

*

1

*

1min

)3(

2121

221 1

11

1

21

spn

dd

NDkIipn

Ii

NDkIipn

NDkdpn

ssdd

P

ND

k

I

i

ki

ki

ki

ki

i

ki

ki

kii

I

i

ki

ki

maxmax


22


• An auxiliary problem is solved.

• The process can continue until we achieve a satisfactory solution.

• The final result gives the group weights for each class of indicators.


23



Best Worst

Max. dev. 275.00 310.00

Agg. dev. 1470.00 1540.00

00.1505~

50.292~

s

d

• Group weights for the environmental class:

24



ENVIRONMENTAL CLASS

I1 I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13

DM1 30.00100.0

010.00 0.00

100.00

30.00 30.00 60.00 30.00 60.00 60.00 60.00 60.00

DM2 50.00 75.00 50.00 75.00100.0

050.00 50.00 50.00 50.00 75.00 75.00

100.00

100.00

DM3 100.00 50.00 25.00 50.00 50.00 50.00 50.00 50.00 50.00 100.00 50.00 50.00 50.00

DM4 100.00 25.00 25.00 50.00 50.00 50.00 50.00 50.00 50.00 100.00100.0

050.00

100.00

DM5 100.00100.0

0100.0

0100.0

0100.0

075.00 75.00 75.00 25.00 50.00 50.00 25.00 25.00

DM6 50.00100.0

00.00 25.00

100.00

25.00 75.00 75.00 75.00 100.00100.0

0100.0

075.00

Group 100.00100.0

025.00 50.00

100.00

65.00 75.00 75.00 32.50 75.00 75.00 75.00 75.00

• Group weights for the environmental class:

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3. Determination of Indicators

• For a given class of indicators, ijq

is the value of indicator i for municipality j

ijMj

miniij

Mj

maxi qqqq

,,1,,1min,max

100100:min

100:max

mini

maxi

miniij

ij

mini

maxi

miniij

ij

qq

qqq

qq

qqq

26


• Aspiration and reservation levels:

2

2

100

),,1(1

1

aviav

iri

aviav

iai

M

jij

avi

qqq

qqq

IiqM

q


0 100aviq

aiq

riq

27


• Individual achievement functions:

),,1(),,1(

0if

if

100if100

1

),,(

MjIi

qqq

qq

qqqqq

qq

qqq

qq

qqq

riijr

i

riij

aiij

rir

iai

riij

ijaia

i

aiij

ri

aiiji


-1

0

1

2

aviq

aiq

riq 100

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3. Determination of IndicatorsMun

Individual Achievement Functions

1 2 3 4 5 6 7 8 9 10 11 12 13

1 0.05 0.09 2.00 2.00 0.93 -1.00 0.79 0.79 0.39 -0.12 1.52 1.36 1.86

2 2.00 1.49 -0.17 1.17 0.99 0.8 1.58 0.21 0.7 0.38 1.07 0.9 1.01

3 0.54 0.79 -0.57 0.45 0.87 0.26 0.68 1.46 0.21 -0.35 0.1 0.76 0.86

4 0.59 1.55 0.44 0.68 0.98 0.6 1.55 2.00 0.01 -0.42 0.6 1.34 1.72

5 0.77 0.96 -0.72 0.13 0.97 0.52 0.94 0.47 0.78 1.12 0.06 0.46 0.51

6 -0.28 1.52 -0.34 -0.19 1.42 2.00 0.52 0.34 0.25 0.5 1.11 1.1 1.43

7 1.09 0.15 0.02 0.09 0.36 0.4 -1.00 0.22 0.65 0.57 0.72 -1.00 -1.00

8 0.61 0.78 0.82 0.11 1.22 0.55 0.26 0.63 0.31 -0.19 0.65 0.83 0.86

9 0.11 0.67 -0.64 0.02 0.95 1.56 0.95 0.58 0.52 0.65 -1.00 1.02 1.15

10 1.73 0.68 -0.99 -0.29 0.91 -0.66 -0.83 0.44 1.41 1.03 2.00 0.99 1.15

11 0.65 -1.00 0.14 0.01 1.11 -0.16 -0.32 -0.16 0.35 0.04 0.94 -0.12 -0.11

12 1.39 0.56 -0.26 -0.18 0.97 -0.81 -0.48 -1.00 1.11 0.48 1.31 0.96 0.97

13 0.64 0.82 -1.00 -0.54 1.29 0.82 -0.59 0.63 -1.00 -1.00 1.31 1.46 1.43

14 0.4 1.00 -0.43 -0.52 1.8 -0.04 -0.47 0.15 0.97 2.00 1.31 1.62 1.57

15 1.26 0.9 0.44 -0.46 2.00 -0.25 -0.32 -0.06 -0.31 -1.00 1.16 2.00 2.00

16 -1.00 0.12 -0.26 -0.85 0.65 0.85 2.00 0.14 1.14 1.53 0.52 0.98 0.93

17 1.4 0.37 -0.41 -0.45 0.89 1.55 0.22 0.09 2.00 1.48 -0.19 0.86 0.83

18 1.62 2.00 -0.52 -1.00 -1.00 -0.83 0.08 0.41 0.28 0.01 0.4 -0.73 -0.86

Weight 100.00 100.00 25.00 50.00 100.00 65.00 75.00 75.00 32.50 75.00 75.00 75.00 75.00

Norm 0.11 0.11 0.03 0.05 0.11 0.07 0.08 0.08 0.04 0.08 0.08 0.08 0.08

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• Construction of the synthetic indicators

(i are the normalized group weigths)

),,1(

),,(:weak

),,(min:strong

1

,,1

Mj

qqq

qqq

I

i

ri

aiijii

wj

ri

aiijii

Ii

sj


30


• Graphical representation:


M1

M4

M7M11

M16

M18

M2

M3M5

M6

M8M9M10

M12 M13

M14

M15

M17

0,00

0,20

0,40

0,60

0,80

1,00

1,20

-0,14 -0,12 -0,10 -0,08 -0,06 -0,04 -0,02 0,00

Strong Indicator

Wea

k In

dic

ato

r

31


4. Final aggregation

• Let us denote by

the strong and weak indicators corresponding to municipality j and to the indicator class h (h = 1, 2, 3, 4)

wjh

sjh ,

• Let us assume that the weights

4321 ,,,

are assigned to the four classes of indicators

32


• Global indicators:


),,1(

:weak

min:strong

4

1

4,,1

Mjh

wjhh

wj

sjhh

h

sj

• Weights:– Environmental: 0.4– Economic: 0.3– Urban development: 0.15– Demographic: 0.15

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• Graphical representation:


M1 M3

M4

M7

M11

M12

M13

M15

M16

M18

M2

M5M6

M8

M9

M10 M14

M17

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

-0,06 -0,05 -0,04 -0,03 -0,02 -0,01 0

Strong Indicator

Weak In

dic

ato

r

34


• Weights: two options– Give the weights ourselves and carry out a

sensitivity analysis.– Determine the weights in a group decision making

process like the one carried out in step 2


35


Conclusions

• Urban indicators have been designed to measure concrete aspects of sustainability, but there is a lack of a unified measure.

• We have developed a full methodology to build synthetic urban indicators.

• Both strong and weak sustainability indicators are built and taken into account.

• The pair of indicators and their graphical representation allows a more in depth analysis of the data.

36


Conclusions

• The methodology developed comprises several different schemes, among which we can point out:– Meta-Goal Programming, for the

determination of the group weights.– Reference point technique (objective ranking)

for the construction of the indicators.

• The scheme can be adapted to any number of indicators and/or municipalities.

37


Conclusions

• Future Research Lines:– To carry out a wider study:

• Broader range (national?), higher number of municipalities.

• Refine the panel of experts.• More reliable data.

– Final aggregation:• Full systematic sensitivity analysis.• Classification scheme.

38


Conclusions

• Future Research Lines:– Group weights:

• Full group decision making process.• Different penalizations for n and p.

– Reference point scheme:• Interval criteria.• Different slopes for the branches of the

achievement functions.• Different aspiration and reservation values.

Documents

Bulgarian Academy of Sciences. 22 July, 2008 1 Index Introduction Outline of the scheme Step 1. Individual weights Step 2. Preference aggregation Step