Regional development in Lithuania considering multiple objectives by the MOORA method/Lietuvos regionines pletros daugiaaspektis vertinimas MOORA metodu.
Brauers, Willem Karel M. ; Ginevicius, Romualdas ; Podvezko, Valentinas 等
1. Introduction
The economic relations between the regions of a country are usually
regulated by structural and automatic transfer payments from the richer
to the poorer regions, consequently a mono-objective relationship. This
automatic system is not a guaranty for success. Moreover a system of
transfer payments is not sufficient to measure the well being of a
regional population. In the well-being economy, each individual would
have to feel good concerning material wealth, health, education, all
kind of security and concerning the environment. With other words,
multiple objectives have to be fulfilled. However, Multi-Objectivity
poses many problems such as:
--the method to be followed;
--the normalization of the units of the different objectives;
--the importance of an objective compared to the other objectives;
--the final ranking of the objectives.
2. The Method to be followed
For the researcher in multi-objective decision support systems the
choice between many methods is not very easy. Indeed numerous theories
were developed since the forerunners: Condorcet [the Condorcet Paradox,
against binary comparisons, 1785, LVIII], Gossen (Law of decreasing
marginal utility 1853), Minkowski (Reference Point 1896, 1911) and
Pareto (Pareto Optimum and Indifference Curves analysis 1906, 1927) and
pioneers like Kendall (ordinal scales, since 1948), Roy et al. (ELECTRE,
since 1966), Miller and Starr (Multiplicative Form for multiple
objectives 1969), Hwang and Yoon (TOPSIS 1981) and Saaty (AHP, since
1987-1988).
We intend to assist the researcher with some guidelines for an
effective choice. In order to distinguish the different multi-objective
methods from each other we use the qualitative definition of robustness.
In 1969 the statistician Huber considered robustness as purely
cardinal as a compromise between a normal distribution and its light
deviations (1). Casella and Berger call a robust alternative the median
absolute deviation for a sample [x.sub.1], ..., [x.sub.n] (2002: 509).
Moreover, from the beginning Bayesian analysis could be characterized as
cardinal, nevertheless with a high grade of arbitrariness. This
arbitrariness could be softened by considerations on robustness (2).
By 1953, which is quite recent for statistics (3), robust became a
statistical term as "strong, healthy, sufficiently tough to
withstand life's adversities" (Stigler 1973: 872). Indeed, we
observe a move to a more vague and qualitative definition of robustness,
namely to the meaning of common language (4): from a cardinal towards a
qualitative scale: the most robust one, more robust than ..., as robust
as ..., robust, weak robust, less robust than ..., not robust etc.
3. Conditions of Robustness in Multi-Objective Methods
The most robust multi-objective method has to satisfy the following
conditions:
1. the method of multiple objectives in which all stakeholders are
involved is more robust than this one in which only one decision maker
or different decision makers defending only their limited number of
objectives are involved. All stakeholders mean everybody interested in a
certain issue (Brauers 2007: 454-455). Sooner or later, the method of
multiple objectives has to take full account of the consumer-stakeholder
(consumer sovereignty), either through private or through public
consumption. Consequently, the method taking into consideration consumer
sovereignty is more robust than this one which does not respect consumer
sovereignty. Consumer sovereignty is measured by community indifference
loci. Solutions have to deliver points inside the convex zone of the
highest possible community indifference locus;
2. the method of multiple objectives in which all non-correlated
objectives are considered is more robust than this one with a limited
number of objectives;
3. the method of multiple objectives in which all interrelations
between objectives and alternatives are taken into consideration at the
same time is more robust than this one in which the interrelations are
examined two by two (for the proof of this statement, see: Brauers 2004:
118-122);
4. the method of multiple objectives which is non-subjective is
more robust than this one which uses subjective estimations for the
choice and importance of the objectives and for normalization.
4.1. For the choice of the objectives
A complete set of representative and robust objectives is found
after Ameliorated Nominal Group Technique Sessions. The Ameliorated
Nominal Group Technique representing all the stakeholders consists of a
sequence of steps, each of which has been designed to achieve a specific
purpose, here to determine the objectives (Appendix A furnishes more
details).
4.2. For giving importance to an objective
Weights and scores mix importance of objectives with normalization.
On the contrary Delphi determines importance of objectives separately
from normalization. In addition, as all stakeholders concerned are
involved, the Delphi method is non-subjective.
The Delphi Method is a method for obtaining and processing
judgmental data. It consists of a sequenced program of interrogation (in
session or by mail) interspersed with feedback of persons interested in
the issue, while everything is conducted through a steering group
(Appendix B furnishes more details).
4.3. For Normalization
The method of multiple objectives which does not need external
normalization is more robust than this one which needs a subjective
external normalization (Brauers 2007: 445-460). Consequently, the method
of multiple objectives which uses non-subjective dimensionless measures
without normalization is more robust than this one which uses subjective
weights (weights were already introduced by Churchman et al. in 1954 and
1957) or subjective non-additive scores like in the traditional
reference point theory (Brauers 2004: 158-159);
5. the method of multiple objectives based on cardinal numbers is
more robust than this one based on ordinal numbers: "an ordinal
number is one that indicates order or position in a series, like first,
second, etc." (Kendall et al. 1990: 1). Robustness of cardinal
numbers is based first on the saying of Arrow (1974): "Obviously, a
cardinal utility implies an ordinal preference but not vice versa"
and second on the fact that the four essential operations of arithmetic:
adding, subtracting, multiplication and division are only reserved for
cardinal numbers;
6. the method of multiple objectives which uses the last recent
available data as a base is more robust than this one based on earlier
data;
7. once the previous six conditions fulfilled the use of two
different methods of multiobjective optimization is more robust than the
use of a single method; the use of three methods is more robust than the
use of two, etc.
The multi-objective optimization by ratio analysis method (MOORA)
satisfies the first six conditions. In addition, MOORA satisfies
partially the seventh condition by using two different methods of
multi-objective optimization. MOORA is the most robust method as no
other method satisfies the seven conditions better until now.
4. The MOORA Method
The method starts with a matrix of responses of all alternative
solutions on all objectives:
[[x.sub.ij]], (1)
with: [x.sub.ij] as the response of alternative j on objective or
attribute i, i = 1, 2, ..., n as the objective or the attributes, j = 1,
2, ..., m as the alternatives.
In order to define objectives better we have to focus on the notion
of attribute. Keeney and Raiffa (1993: 32) present the example of the
objective "reduce sulfur dioxide emissions" to be measured by
the attribute "tons of sulfur dioxide emitted per year". An
objective and a correspondent attribute always go together.
Consequently, when the text mentions "objective" the
correspondent attribute is meant as well.
The MOORA method consists of two parts: the ratio system and the
reference point approach.
4.1. The Ratio System as a Part of MOORA
We go for a ratio system in which each response of an alternative
on an objective is compared to a denominator, which is representative
for all alternatives concerning that objective (5):
[x.sup.*.sub.ij] = [x.sub.ij]/[square root of [m.summation over
(j=i)] [x.sup.2.sub.ij]] (2)
with: [x.sub.ij]--response of alternative j on objective i, j = 1,
2, ..., m; m the number of alternatives, i = 1, 2, ..., n; n the number
of objectives, [x.sup.*.sub.ij]--a dimensionless number representing the
normalized response of alternative j on objective i.
Dimensionless Numbers, having no specific unit of measurement, are
obtained for instance by multiplication or division. The normalized
responses of the alternatives on the objectives belong to the interval
[0; 1]. However, sometimes the interval could be [-1; 1]. Indeed, for
instance in the case of productivity growth some sectors, regions or
countries may show a decrease instead of an increase in productivity
i.e. a negative dimensionless number (6).
For optimization, these responses are added in case of maximization
and subtracted in case of minimization:
[y.sup.*.sub.j] [g.summation over (i=1)] [x.sup.*.sub.ij] -
[n.summation over (i=g+1)] [x.sup.*.sub.ij], (3)
with: i = 1, 2, ..., g as the objectives to be maximized; i = g +
1, g + 2, ..., n as the objectives to be minimized; [y.sup.*.sub.j]--the
normalized assessment of alternative j with respect to all objectives;
[y.sup.*.sub.j] can be positive or negative depending of the totals of
its maxima and minima.
An ordinal ranking of the [y.sup.*.sub.j] shows the final
preference. Indeed, cardinal scales can be compared in an ordinal
ranking after Arrow (1974): "Obviously, a cardinal utility implies
an ordinal preference but not vice versa".
4.2. The Reference Point Approach as a part of MOORA
Reference Point Theory will go out from the ratios found in formula
(2), whereby, a Maximal Objective Reference Point is also deduced. The
Maximal Objective Reference Point approach is called realistic and
non-subjective as the co-ordinates ([r.sub.i]), which are selected for
the reference point, are realized in one of the candidate alternatives.
In the example, A (10;100), B (100;20) and C (50;50), the maximal
objective reference point [R.sub.m] results in: (100;100). The Maximal
Objective Vector is self-evident, if the alternatives are well defined,
as for projects in Project Analysis and Project Planning.
Given the dimensionless number representing the normalized response
of alternative j on objective i, namely [x.sup.*.sub.ij] of formula (2)
and in this way arriving to:
([r.sub.i] - [x.sup.*.sub.ij], (4)
with: i = 1, 2, ..., n as the attributes, j = 1, 2, ..., m as the
alternatives, [r.sub.i] = the ith co-ordinate of the reference point,
[x.sup.*.sub.ij] = the normalized attribute i of alternative j, then
this matrix is subject to the Min-Max Metric of Tchebycheff (Karlin and
Studden 1966) (7):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
[absolute value of [r.sup.i] - [x.sup.*.sub.ij]] means the absolute
value if [x.sub.ij] is larger than [r.sub.i] for instance by
minimization.
Concerning the use of the maximal objective reference point
approach as a part of MOORA some reserves can be made in connection with
consumer sovereignty. Consumer sovereignty is measured with the
community indifference locus map of the consumers (Brauers 2008b:
92-94). Given its definition the maximal objective reference point can
be pushed in the non-allowed non-convex zone of the highest community
indifference locus and will try to pull the highest ranked alternatives
in the non-allowed non-convex zone too (Brauers, Zavadskas 2006:
460-461). Therefore an aspiration objective vector can be preferred,
which moderates the aspirations by choosing smaller co-ordinates than in
the maximal objective vector and consequently can be situated in the
convex zone of the highest community indifference locus. Indeed
stakeholders may be more moderate in their expectations. The
co-ordinates [q.sub.i] of an aspiration objective vector are formed as:
[q.sup.i] [less than or equal to] [r.sub.i],
([r.sub.i] - [q.sub.i]) being a subjective element we don't
like to introduce subjectivity in that way again. Instead, a test shows
that the min-max metric of Tchebycheff delivers points inside the convex
zone of the highest community indifference locus (Brauers 2008b:
98-103).
4.3. The Importance given to an Objective
The normalized responses of the alternatives on the objectives
belong to the interval [0; 1] (see formula 2). Nevertheless, it may turn
out to be necessary to stress that some objectives are more important
than other ones. In order to give more importance to an objective its
normalized responses on an alternative could be multiplied with a
Significance Coefficient:
[[??].sup.*.sub.j] = [summation over (i=1)]
[s.sub.i][x.sup.*.sub.j] - [summation over (i=g+1)]
[s.sub.i][x.sup.*.sub.ij], (6)
with: i = 1, 2, ..., g as the objectives to be maximized, i = g +
1, g + 2, ..., n as the objectives to be minimized, [s.sub.i] = the
significance coefficient of objective i, [[??].sup.*.sub.j] = the
normalized assessment of alternative j with respect to all objectives
with significance coefficients.
The Attribution of Sub-Objectives represents another solution. Take
the example of the purchase of fighter planes (Brauers 2002). For
economics, the objectives concerning the fighter planes are threefold:
price, employment and balance of payments, but there is also military
effectiveness. In order to give more importance to military defense,
effectiveness is broken down in, for instance, the maximum speed, the
power of the engines and the maximum range of the plane. Anyway, the
Attribution Method is more refined than that a significance coefficient
method could be as the attribution method succeeds in characterizing an
objective better. For instance, for employment two sub-objectives
replace a significance coefficient of two and in this way characterize
the direct and indirect side of employment.
Of course at that moment the problem is raised of the subjective
choice of objectives in general, or could we call it robustness of
choice? The Ameliorated Nominal Group Technique will gather all
stakeholders interested in the issue to determine the objectives in a
non-subjective and anonymous way (see: Appendix A) and Delphi Technique
will indicate their relative importance (for Delphi see Appendix B).
5. The Data on the Lithuanian Counties
Vilnius Gediminas Technical University creates a tradition in
studying multiple criteria, sustainable development or social indicators
in relation to the Lithuanian cities and counties. Let us illustrate
this statement with some examples. In 2007, Zavadskas. Viteikiene and
Saparauskas studied 22 indices defining the aspects of sustainability in
the different residential districts of the city of Vilnius. In the same
publication Zagorskas et al. evaluated the compactness of the Kaunas
city districts. In the International Journal of Environment and
Pollution Juskeviciius and Burinskiene studied quality factors of the
residential environment in urban planning in the municipality regions of
Lithuania. In the same publication Zavadskas et al. recommended how to
improve the situation for sustainability in Vilnius with special
emphasis on pollution (2007).
Another group of researchers at VGTU emphasized rather the
evaluation of the sustainable development of the Lithuanian counties
like Ginevicius et al. in Ekonomika (2004) and Ginevicius and Podvezko
in Environmental research, Engineering and Management in the same year.
Brauers and Ginevicius studied robustness in regional development
studies of Lithuania (2009). Already at that moment the subjectivity was
stressed for instance in the choice of the raw data connected with the
choice of the objectives, criteria or indicators.
Not only the method to handle the different objectives expressed in
different units had to be non-subjective but also the choice of the
objectives, starting with the data underlying the objectives. What is
meant with non-subjective?
In physical sciences, a natural law dictates non-subjectivity
without deviations. In human sciences, for instance in economics, an
economic law will state the attitude of men in general with very
exceptionally individual deviations. Outside these human laws in the
human sciences unanimity or at least a certain form of convergence in
opinion between all stakeholders, which means everybody concerned in a
certain issue, will lead to non-subjectivity (8). Consequently, the
choice of the data concerning the Lithuanian counties, leading to the
objectives, would mean bringing together the representatives of the
national government, of the counties, of the inhabitants, of the workers
and entrepreneurs and of the specialists from the academic world.
Instead of this considerable undertaking the authors themselves made a
broad choice of data in the different fields of interests. For instance,
for migrations of population the emigration is taken as negative and the
immigration as positive. Further are considered:
--the unemployment rate;
--for income and expenditure: the municipal budget and the monthly
earnings;
--for housing and other floor space: useful floor space and
completed dwellings;
--for education: number of pre-schools and of schools;
--for production and commerce: animal production, investments,
construction and retail trade;
--for justice: criminal offenses.
The number of physicians is considered for health care. On the
national level mostly the number of hospital beds is counted, which has
no sense on the regional level as many patients prefer treatment in
large towns sometimes outside the own district.
For pollution the following average emissions in kg per [km.sup.2]
are taken into account: solid emissions, S[O.sub.2], N[O.sub.x], CO,
volatile organic compounds (VOC) and some others.
We don't mention the greenhouse gas emission (C[O.sub.2]) as
Lithuania has still a reserve for 2020 of 15% above the 2005 figure (9).
Consequently, we suppose that also the Lithuanian districts have no
problem with the greenhouse effect (10).
Table 1 shows all the data.
6. The Geographical-Automatical-Structural System of Transfer
Payments
A note on terminology is needed to clarify the issue. Gross
Domestic Product (GDP) in a certain year is the value added created on
the national territory, being a territorial concept. On the contrary,
Gross National Product (GNP) is related to the civilians and the
permanent residents of a nation. Interpolated for a region, the Gross
Regional Domestic Product (GRDP) signifies the value added created on a
regional territory during a given year and the Gross Regional Product
(GRP) means the value added created by the permanent residents of a
region during that year. The Gross Regional Product is composed of the
Regional Private Income (also called Primary Incomes of the Households)
plus the cash flows of the regional companies before taxes but after
distribution of dividends and the indirect taxation on both groups. As
the last group is mostly not estimated the Gross Regional Product is
assumed to be equal to the Regional Private Income. Finally, the
Disposable Income per head equals the Private Income per head after
paying taxes and receiving or giving transfer payments.
Transfer Payments do not create Value Added but are a transfer of
value without counterpart like gifts or aid. Transfer payments are quite
common in daily life such as in all kind of insurances, but transfer
payments which are considered here are geographical. First of all
geographical transfer payments can be automatic through fiscal or
para-fiscal channels such as social security. They can also be seasonal,
cyclical or structural. Off season on the sea side in Klaipeda can ask
for additional but temporal transfer payments. Regions with a cyclical
economy could need additional transfer payments in recession times.
Structural transfer payments between regions are maintained under all
circumstances and form an essential and enduring financial instrument
for a state or a region, however becoming an element of stagnation for
that region or nation. This kind of transfer payments is very much
contested in Western Europe: "do not kill the goose that lays the
golden eggs". In Belgium it caused even an Income Paradox at least
until 1996: by the transfer payments the richer Flemish inhabitants came
worst off compared to the other Belgians as shown in Table 2.
For Lithuania the average gross monthly earnings for 2008 as
mentioned in table 1, sub 5 approaches more or less the notion of
Regional Income. Table 3 classifies the regions by this notion.
However, the computation of the Regional Income is not sufficient.
The RI per capita could be biased. Furthermore, regional income is a
typical exponent of the Economics of Welfare of Pigou (1920). The
well-being economy goes further. In the wellbeing economy each
individual would have to feel good concerning material wealth, health,
education, all kind of security and concerning the environment.
Therefore, multiple objectives have to be fulfilled. Multiple
objectives, realized simultaneously, will measure well being. The 16
data of Table 1 become attributes and when optimized, either as maxima
or minima, objectives. At that moment, the MOORA method will be
operational.
7. Application of the MOORA Method on the data of the Lithuanian
Counties
7.1. The part of the Ratio System in MOORA
In order to apply the MOORA program the statistical data of Table 1
are rearranged in subTable 4a as objectives and alternative districts
under the form of the matrix:
[[x.sub.ij]]. (1)
Next, in sub Tables 4b and 4c formula (2) starts from this matrix:
[x.sup.*.sub.ij] = [x.sub.ij]/[square root of [m.summation over
(j=1)] [x.sup.2.sub.ij]] (2)
where by: [x.sub.ij] = response of alternative j on objective i, j
= 1, 2, ..., m; m the number of alternatives, i = 1, 2, ..., n; n the
number of objectives.
In addition, after formula (3) the objectives are then added in
case of maximization and subtracted in case of minimization (sub Table
4c):
[y.sup.*.sub.j] = [g.summation over (i=1)] [x.sup.*.sub.ij] -
[n.summation over (i=g+1)] [x.sup.*.sub.ij]. (3)
The last column of sub Table 4c gives the final ranking for the
ratio system in MOORA.
7.2. The part of the Reference Point Theory in MOORA
Reference Point Theory starting from the dimensionless numbers of
Table 4c is non-subjective, also by using the Maximal Objective
Reference Point, as expressed in formula (5):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
with: [r.sub.i] as the normalized Maximal Objective Reference
Point, i = 1, ..., n as the objectives, [x.sup.*.sub.ij] as the
dimensionless numbers of Table 4c.
The last column of sub Table 4e gives the final rank for the
Reference Point Theory in MOORA.
7.3. The Ranking of the Lithuanian Districts after their Well Being
Comparing sub Tables 4c and 4e the ranking is quite similar for the
head and tail of the last column. However, the remark could be made that
only the data for one year are observed. Therefore, having the figures
for 2002 (Ginevicius, Podvezko 2004) and for 2005 (Brauers, Ginevicius
2009) a comparison is made with these years. In that manner the 2002
pre-European Union year is compared to the European Union years, 2005
and 2008.
In Table 5 the income approach represents the measurement of the
average increase of material wealth of the inhabitants of a district but
not of their well-being. The well being is rather effectively measured
by MOORA using the multiple objectives concerning these inhabitants.
MOORA shows some differences between the ratio system and the reference
point versions. Nevertheless, a general tendency is present, even
compared with a pre-European Union year. Three well-being districts,
Vilnius, Klaipeda and Kaunas, are in sharp contrast with Telsiai,
Taurage and Siauliai, regions with a rather poor well being.
A reversed ranking will start with the most vulnerable regions
concerning their General Well-Being, the District of Telsiai on the
first place.
1) Telsiai
Telsiai is the last classified county concerning general
well-being. A slight deterioration seems even to be present since the
pre-European Union period. Nevertheless, Telsiai has one of the highest
average gross monthly earnings per capita of the country, probably
biased by the well known high salaries of the petroleum industry.
Indeed, the oil refinery of "Mazeikiu nafta", the only oil
refinery of the Baltic States, is located in the town of Mazeikiai
(Telsiai). On the other side the pollution in the district is the
highest in the country but mainly concentrated around the town of
Mazeikiai and it concerns mainly gaseous and liquid air pollutant
emissions. In 2005 the refinery started with the introduction of an
environment management system (web "Mazeikrq nafta" 2008), but
the situation remains stationary, as shown in next Table 6.
Strange enough the unemployment rate of 6.6% is the second worst in
the country. It is also the case with floor space per capita, whereas
investment in fixed assets, own construction work and completed
dwellings are also rather low rated. Health care is the third worst.
2) Taurage
Taurage is the second worst concerning general well-being. A
deterioration seems to be present since the pre-European Union period.
Anyway Taurage has the lowest income per capita of all the
Lithuanian counties over the period 2003-2008 (11). The second highest
emigration quota of the country is then an understandable outcome.
Taurage is also the worst in investment, in construction and in the
completion of dwellings and the second worst in health care.
Taurage has to attract more investments with more construction also
for private housing. The retail trade has to be developed, for instance
around an important highway, when trade with Russia could develop.
3) Siauliai
Siauliai is the third worst concerning general well-being. It is
also the worst in emigration, probably a result of being the third worst
in income over the period 2003-2008.
4) Alytus
Alytus is the sixth in ranking for income but is the third worst in
emigration and in investment.
5) Panevezys
Panevezys ranks only the seventh what income is concerned, is bad
in completed dwellings (2nd worst) and is the third worst in
construction.
6) Utena
General Well-Being classifies Utena more or less in the middle of
the ranking of the 10 counties. It is the fifth in ranking for income
but the worst of all counties for health care and the third worst for
completed dwellings, a slight amelioration compared to 2005 when it was
the second worst after Siauliai.
The existence of the atomic plant of Ignalina of the type of
Chernobyl presents a weak point for the Utena County. This nuclear power
plant was built by the Sovjets between 1978 and 1983. At a certain
moment the reactors now stopped produced 80% of Lithuania's
electricity. Presenting a potential danger the European Union ordered
the closing down of the plant. First it was planned for 2005 but it is
believed that the process will take another 25-30 years. Huge amounts
are allocated to the closure project. Nevertheless since 2005 pollution
emission is the lowest from of all Lithuanian Counties. Concerning
Income and General Well Being Utena is situated in the middle of the
classification of all Lithuanian Counties.
One day may be a later closed atomic plant, if safely protected,
can attract disaster tourists and industrial archeologists, industrial
archeology being the last modern branch of modern history. For the other
visitors one could think of a permanent exhibition on all sources of
energy for which Chernobyl was a bad example. A special place could be
given on an exhibition on renewables for energy a point so much
accentuated by the European Union.
7) Marijampole
Marijampole is the second worst in income over the period 2003-2008
and the second worst in investment and in construction.
8) Kaunas
Kaunas is the third best ranked in General Well-Being. It is also
the third ranked in income due to its industrial activity, which
nevertheless explains its third worst position in pollution emissions.
9) Klaipeda
Klaipeda is the second best ranked in General Well-Being. Although
Klaipeda has the second highest income of all districts it ranks the
worst in the unemployment level, the worst in floor space and the second
worst in criminal acts. Being the second worst in pollution, mainly
gaseous and liquid pollutant emissions, it could be influenced by the
neighborhood of the oil refinery of "Mazeikiu nafta" in
Telsiai.
10) Vilnius
Vilnius, the capital of the country, ranks first in General
Well-Being. It also ranks first in the income level, is a source of
immigration but ranks first in criminal acts. Strange enough it is
classified third worst in unemployment.
8. Project Management for the Lithuanian Counties
8.1. The Labor Drain
The labor drain to the county of Vilnius represents a serious
problem. In 2002 an immigration surplus still existed in the counties of
Alytus, Kaunas, Marijampole, Utena and Vilnius. In 2005 and 2008 only
the county of Vilnius remained with an immigration surplus. The capital
of a country or another main city as the only attraction pole is a
general world phenomenon, but has to be corrected. However some
fluctuations per county took place in that period, as shown in next
Table 7.
Thirty eight thousand persons emigrated abroad in 2005 and thirty
five thousand in 2008. All these important migration flows ask for
investment projects in industry, construction and commerce, which was
already clear from the analysis per county.
8.2. Projects for Industrialization and Construction
As was already suggested above structural transfer payments of an
automatic nature in order to solve the weaknesses of the counties have
to be avoided as much as possible. Instead some suggestions for Project
Management and Investments can be made.
1. The spin-offs of applied research of universities supported by
the government in research parks outside campus namely in the less
developed counties could lead to new products and applications. In this
way a kind of Lithuanian Silicon Valley could be created.
2. The European Commission foresees a 23% part of renewables in the
final energy demand of Lithuania by 2020. These renewables could come
from non-fossil energy sources: wind, solar, geothermal, wave, tidal,
hydropower, biomass, landfill gas, sewage treatment plant gas and
biogases. The European Commission remarks: "are related to the
promotion of local employment and opportunities for small and medium
sized enterprises, regional and rural development, stimulating economic
growth and increasing global European industry leadership" (12).
Anyway it would mean an opportunity for industrialization of the
Lithuanian counties.
3. The average useful floor space per capita is certainly
satisfactory in all counties, but may be that the quality of the
habitation can be ameliorated. Renovation and new construction is
perhaps necessary.
8.3. Projects for Commerce and Tourism
Development of tourism all over the Lithuanian territory would be
very good.
1. Following the Swedish and Finnish example fishing in the many
lakes and fitness centers around the lakes will certainly attract
foreign tourists.
2. The rocket base near Plateliai (Telsiai) can be an attraction
pole for all European and Turkish tourists as they were threatened by
the rockets one day.
9. Conclusion
The remark that significance of robustness depends on the context
is specified in different ways. First, robustness can be defined as
cardinal or qualitative.
Concerning the most robust method of multi-objective optimization
the following conditions are to be satisfied:
1. The method of multiple objectives in which all stakeholders are
involved is more robust than one in which only one decision maker or
different decision makers defending only a limited number of objectives
are involved. All stakeholders mean everybody interested in a certain
issue. All production will finally end in consumption. Consequently, the
method of multiple objectives which takes into consideration consumer
sovereignty is more robust than this one which does not respect consumer
sovereignty. Consumer sovereignty is measured with community
indifference loci. Solutions have to deliver points inside the convex
zone of the highest community indifference locus;
2. The method of multiple objectives in which all non-correlated
objectives are considered is more robust than this one in which only a
limited number of objectives is considered;
3. The method of multiple objectives in which all interrelations
between objectives and alternatives are taken into consideration at the
same time is more robust than this one in which the interrelations are
only examined two by two;
4. The method of multiple objectives which does not need separate
normalization is more robust than this one which needs a subjective
outside normalization. Consequently, a method of multiple objectives
which uses non-subjective dimensionless measures with inside
normalization is more robust than this one which for normalization uses
subjective weights or subjective non-additive scores like in the
traditional Reference Point Theory;
5. The method of multiple objectives based on cardinal numbers is
more robust than this one based on ordinal numbers: an ordinal number is
one that indicates order or position in a series, like first, second,
etc. The robustness of cardinality is based on the saying of Arrow:
"Obviously, a cardinal utility implies an ordinal preference but
not vice versa" and also on the fact that the four fundamental
operations of arithmetic: adding, subtracting, multiplication and
division are only reserved for cardinal numbers;
6. The method of multiple objectives which uses the last recent
available data as a base in the response matrix is more robust than this
one based on earlier data;
7. Once the previous six conditions are fulfilled the use of two
different methods of multiobjective optimization is more robust than the
use of a single method; the use of three methods is more robust than the
use of two, etc.
The Multi-Objective Optimization by Ratio Analysis Method (MOORA)
satisfies the first six conditions. In addition, MOORA satisfies
partially the seventh condition by using two different methods of
Multi-Objective Optimization. MOORA is the most robust method as no
other method satisfies the seven conditions better. For all these
reasons we selected MOORA.
In a country economic development can differ from region to region.
A policy of smoothing out the differences in economic development may
not result in a killing disadvantage for the richer regions. On the
contrary, any project of industrialization or commercialization has to
be a win-win-operation for all regions.
Next question is how to measure any redistribution. The computation
of the Regional Income, being an exponent of the welfare economy of
Pigou, is not sufficient for the measurement of the well being of the
regional population. A well-being economy goes further than a welfare
economy. In the wellbeing economy each individual would have to feel
good concerning material wealth, health, education, all kind of security
and concerning the environment. With other words, multiple objectives
have to be fulfilled. However, these different multiple objectives are
expressed in different units, which means that a problem of
normalization is posed. For this purpose the attribution of weights,
scores or exponents can be used, which means introduction of
subjectivity. Therefore, an internal mechanical procedure is operated in
order to escape from that subjective problem, namely Multi-Objective
Optimization by Ratio Analysis (MOORA). Dimensionless numbers obtained
in this manner will also form the basis for Reference Point Theory, the
second part of MOORA.
Given all the objectives MOORA measures finally the well being
differences between the ten districts of Lithuania. Three well being
districts are in sharp contrast with some districts with a rather poor
well being. In addition, the labor drain to the district of Vilnius from
all the other districts represents a serious problem.
An automatic redistribution of income has to be condemned, whereas
rather commercialization and industrialization of the regions has to
occur.
Does the regional application of Lithuania satisfy the seven
conditions of robustness?
1. First condition of robustness
The choice of the objectives and their respective importance has to
be made by all the stakeholders involved in the issue. As this procedure
is rather cost and time consuming the authors have taken the
responsibility to choose objectives for all the counties. Consequently,
this condition also respects consumer sovereignty.
2. Second condition of robustness
All objectives were taken into consideration as much as possible.
The choice of the objectives for all counties is representative for the
fields of migration of the population, unemployment rate, income and
expenditure, housing and other floor space problems, education,
production, commerce, justice and health care problems. For pollution
the following average emissions in kg and per [km.sup.2] are taken into
account: solid emissions, S[O.sub.2], N[O.sub.x], CO, and volatile
organic compounds. The greenhouse effect (C[O.sub.2]) is not included as
Lithuania may still exceed its actual emission level. On the contrary,
the production of renewable energy will form an opportunity for further
industrialization of Lithuania. Significance coefficients are too
subjective to characterize the importance of an objective. Instead,
sub-objectives, heightened to objectives, were introduced in order to
give importance to a certain objective.
3. Third condition of robustness
All interrelations between objectives and alternatives were
involved at the same time under the form of a matrix of responses
considered as a whole and as a starting point for the application of
MOORA.
4. Fourth condition of robustness
The use of dimensionless measures is a more robust method than
subjective methods of normalization. In the application MOORA's
dimensionless ratios satisfied this condition.
5. Fifth condition of robustness
The method of multiple objectives based on cardinal numbers is more
robust than this one based on ordinal numbers. The application was
entirely based on cardinal numbers.
6. Sixth condition of robustness
The last available data were used up until now.
7. Seventh condition of robustness
All the previous six conditions are fulfilled and also the seventh
condition as two different methods of Multi-Objective Optimization were
used. No other Multi-Objective Optimization Method exists which uses
more than two Multi-Objective Optimization Methods and fulfill the
previous six conditions.
In this way the regional research on Lithuania satisfies all
conditions on robustness. Is it possible to draw some conclusion for
policy making? Structural transfer payments of an automatic nature in
order to solve the weaknesses of the counties have to be avoided as much
as possible. Instead some suggestions for Project Management can be
made.
Further industrialization and commercialization will diminish the
labor drain to the Capital Vilnius and to abroad and would take away
many weak points in the well being of the inhabitants of the counties.
doi: 10.3846/tede.2010.38
Appendix A
The Ameliorated Nominal Group Technique as a source for objectives
A.1. The original Nominal Group Technique of Van de Ven and Delbecq
(1971)
A group of especially knowledgeable individuals (experts),
representing all stakeholders, is formed, which comes together in a
closed meeting. A steering panel or a panel leader leads the group.
The nominal group technique consists of a sequence of steps, each
of which has been designed to achieve a specific purpose.
1. The steering group or the panel leader carefully phrases as a
question the problem to be researched. Much of the success of the
technique hinges around a well-phrased question. Otherwise the exercise
can easily yield a collection of truisms and obvious statements. A
successful question is quite specific and refers to real problems. The
question has to have a singular meaning and a quantitative form as much
as possible.
2. The steering group or the panel leader explains the technique to
the audience. This group of participants is asked to generate and write
down ideas about the problem under examination. These ideas too have to
have a singular meaning and a quantitative form as much as possible.
Participants do not discuss their ideas with each other at this stage.
This stage lasts between five and twenty minutes.
3. Each person in round-robin fashion produces one idea from his
own list and eventually gives further details. Other rounds are
organized until all ideas are recorded.
4. The steering group or the panel leader will discuss with the
participants the overlapping of the ideas and the final wording of the
ideas.
5. The nominal voting consists of the selection of priorities,
rating by each participant separately, while the outcome is the totality
of the individual votes. A usual procedure consists of the choice by
each participant of the n best ideas from his point of view, with the
best idea receiving n points and the lowest one point. All the points of
the group are added up. A ranking is the democratic result for the whole
group.
A.2. The Ameliorated Nominal Group Technique of Brauers (1987)
6. Out of experience, one may say that there is still much wishful
thinking, even between experts. Therefore the group was also questioned
about the probability of occurrence of the event. In this way they
became more critical even about their own ideas. The probability of the
group is found as the median of the individual probabilities.
7. Finally, the group rating (R) is multiplied with the group
probability (P) in order to obtain the effectiveness rate of the event
(E):
R x P = E. (7)
Once again, the effectiveness rates of the group are ordered by
ranking. Experience proves that the introduction of probabilities
decreases significantly the total number of points.
A.3. An Application: Ameliorated Nominal Group Technique on the
business outlook of the facilities sector of Lithuania over the period
(2003-2012) (Brauers, Lepkova 2003)
The Facilities sector in Lithuania provides the following services:
--Acquisition, leasing and renting of existing buildings;
--Management of buildings, which is a multifunctional service. This
means that all supervision, maintenance and repairing is included in the
sector.
The Facilities Sector is only a very small sector in Lithuania,
composed of a small number of small firms, which even perform other
tasks outside facilities management, such as waste management. The
largest firm in the sector counts only 179 employees.
A group of especially knowledgeable people was composed of
delegates from the facilities sector, from the ministerial departments
concerned and from the academic world (15 participants). Were all
stakeholders interested in the issue represented? As neither
representative consumer organization nor a representative trade union
was present at that time it was assumed that the ministerial departments
and the academic world were representative for these groups.
First a Brainstorming Session toke place. Jantsch gave the
following basic rules for brainstorming sessions (1967: 136):
1. State the problem in basic terms, with only one focal point;
2. Do not find fault with, or stop to explore, any idea;
3. Reach for any kind of idea, even if its relevance may seem
remote at the time;
4. Provide the support and encouragement which are so necessary to
liberate participants from inhibiting attitudes".
In any case, an efficient reporting system is necessary to record
the ideas presented (stenography or recording).
For the nominal group technique each participant has chosen the
most important five events from his point of view, with the most
important event receiving five points and the less important event one
point Table A1 shows the results.
The introduction of probabilities of realization, introducing a
sense of reality and presenting a guaranty against wishful thinking,
produces quite some changes in the ranking.
The total 225 is a control figure for the group result. Indeed,
each participant could distribute maximum: 5+4+3+2+1 = 15 points. With
15 participants, the total has to be not more than 225. It could be
less, as each participant is not obliged to allot 15 points. The total
of the given points, here namely 225, means that each participant used
his rights completely. The reality check, however, diminishes the figure
to 145.21.
Table A1. Important Events influencing the Business Outlook of
the Facilities Sector of Lithuania over the period 2003-2012
Given Median
Events 2003-2012 Points R Rank Probabilities P
1 Member of European Union (a) 37 1 0.75
2 Large increase in foreign 20 2 0.75
capital
3 More competition between 16 3 0.88
facilities management
companies
4 Large increase in GDP 16 3 0.75
5 New materials and technologies 12 6 0.75
6 Stability in international 14 5 0.50
security
7 Higher quality in building 8 11 0.75
construction
8 Application of new information 9 9 0.63
technologies to facilities
management
9 More relations with foreign 9 9 0.63
companies having more
experience in facilities
management
10 Better legislation in 11 7 0.50
supervision sector
11 Optimal quality-price relation 7 13 0.75
for services
12 Better public estimation for 8 11 0.63
facilities management 13 till
21
22 Increase of individual 1 22 0.25
property of housing
Total Points 225
Final
Events 2003-2012 E = RxP rank
1 Member of European Union (a) 27.75 1
2 Large increase in foreign 15 2
capital
3 More competition between 14.08 33
facilities management
companies
4 Large increase in GDP 12 4
5 New materials and technologies 9 5
6 Stability in international 7 6
security
7 Higher quality in building 6 7
construction
8 Application of new information 5.67 8
technologies to facilities
management
9 More relations with foreign 5.67 8
companies having more
experience in facilities
management
10 Better legislation in 5.5 10
supervision sector
11 Optimal quality-price relation 5.25 11
for services
12 Better public estimation for 5.04 12
facilities management 13 till
21
22 Increase of individual 0.25 22
property of housing
Total Points 145.21
(a) In 2003 Lithuania was not yet member of the European Union.
Appendix B
The Delphi Technique to determine the importance of an objective
Delphi, so named after the Greek oracle, was first thought of as a
tool for better forecasting. In this sense, it seems that the first
experiments took place around 1948 (Quade, Boucher 1968: 334). Today
Delphi is no longer limited to forecasting alone. Dalkey and Helmer at
RAND Corporation first used Delphi in its present form around 1953
(Dalkey, Helmer 1963).
The Delphi Method is a method for obtaining and processing
judgmental data. It consists of a sequenced program of interrogation (in
session or by mail) interspersed with feedback of persons interested in
the issue, while everything is conducted through a steering group.
The essential features of Delphi are the following:
1. the rather vague notion "persons interested in the
issue" is interpreted by Quade as follows: "In practice, the
group would consist of experts or especially knowledgeable individuals,
possibly including responsible decision makers" (Quade 1970: 9-10);
2. the steering group treats anonymously the sources of each input;
3. inputs must as much as possible possess a single meaning and a
quantitative form. Te inputs with these characteristics are elicited
with feedback in a series of rounds;
4. opinions about the inputs are evaluated with statistical indexes
such as median and quartiles;
5. there is also a feedback of the statistical indexes with a
request for re-estimation after consideration of reasons for extreme
positions. The practice of Delphi reveals that after several rounds
convergence is shown between the various opinions (one of the main
advantages of the Delphi method);
6. there are two developments of Delphi: one is based on a meeting,
the other on the sending of questionnaires. The organization of a
meeting produces quicker results; the meeting, however, has to be
organized in such a way that communication between the panel members is
impossible. In order to increase even further the speed of the outcome
of a meeting, an on-line computer could be installed. Everybody involved
in the Delphi teamwork would have a desk terminal linked to a computer
and would be able to look at a television screen giving the results
calculated by the computer.
Convergence in opinion between all stakeholders to give more
importance to an objective results from a Delphi exercise, which could
provide the given objective with a Significance Coefficient. For
instance, giving a significance coefficient to pollution abatement, the
stakeholders are asked to give the following importance to pollution
abatement:
0, 1, 2 or 3
Suppose that after several rounds convergence is reached on 3 (for
an example concerning voting by a jury, see Brauers 2008a).
References
Arrow, K. J. 1974. General economic equilibrium: purpose, analytic
techniques, collective choice, American Economic Review June: 256.
Brauers, W. K. M.; Ginevicius, R. 2009. Robustness in regional
development studies. The case of Lithuania, Journal of Business
Economics and Management 10(2): 121-140.
doi:10.3846/1611-1699.2009.10.121-140
Brauers, W. K. 2008a. Group decision making with Multi-Objective
optimization, Foundations of Computing and Decision Sciences 33(2):
167-179.
Brauers, W. K. 2008b. Multi-Objective decision making by reference
point theory for a wellbeing economy, Operations Research International
Journal 8: 89-104.
Brauers, W. K. 2007. What is meant by normalization in decision
making?, International Journal of Management and Decision Making 8(5/6):
445-460. ISSN 1462-4621
Brauers, W. K. M.; Zavadskas, E. K. 2006. The MOORA Method and its
application to privatization in a transition economy, Control and
Cybernetics 35(2): 445-469. Systems Research Institute of the Polish
Academy of Sciences. ISSN 0324-8569
Brauers, W. K. 2004. Optimization Methods for a Stakeholder
Society. A Revolution in Economic Thinking by Multiobjective
Optimization. Kluwer Academic Publishers and Springer, Boston. ISBN
1-4020-7681-9
Brauers, W. K.; Lepkova, N. 2003. The application of the nominal
group technique to the business outlook of the facilities sector of
Lithuania over the period 2003-2012, International Journal of Strategic
Property Management 7(1): 1-9. ISSN 1648-715x
Brauers, W. K. 2002. The multiplicative representation for multiple
objective optimization with an Application for arms procurement, Naval
Research Logistics 49: 327-340. doi:10.1002/nav.10014
Brauers, W. K. 1999. Het Bruto Regionale Product van Vlaanderen,
Wallonie en Brussel (the GRP of Flanders, Wallonia and Brussels).
Working Paper 99/2, University of Antwerp (RUCA), Antwerpen.
Brauers, W. K. 1987. Nominal Methods in Group Multiple Decision
Making. Research Paper No3, Institute for Developing Countries,
University of Antwerp, RUCA, Antwerpen.
Casella, G.; Berger, R. L. 2002. Statistical Inference. Second
Edition. Pacific Grove, Cal., US, Duxbury, Thomson Learning.
Churchman, C. W; Ackoff, R. L.; Arnoff, E. L. 1957. Introduction to
Operations Research. New York, US, Wiley.
Churchman, C. W.; Ackoff, R. L. 1954. An Approximate Measure of
Value, Operations Research 2: 172-180. doi:10.1287/opre.2.2.172
Commission of the European Communities 2008. Proposal for a
decision of the European Parliament and the Council on the effort of the
Member States to reduce their greenhouse gas emissions. Brussels,
COM(2008) SEC (2008).
Commission of the European Communities 2008. Proposal for a
Directive of the European Parliament and the Council on the promotion of
energy from renewable sources. Brussels, COM (2008) version 15.4
Condorcet, Marquis de. 1785. Essai sur lapplication de
l'analyse a la probability des decisions rendues a l a pluralite
des voix (Proposal on the application of the probability analysis of the
decisions taken by majority vote). Paris, l'Imprimerie royale..
Dalkey, N.; Helmer, O. 1963. An experimental application of the
delphi method to the use of experts, Management Science: 458-487.
doi:10.1287/mnsc.9.3.458
Ginevicius, R.; Podvezko, V.; Mikelis, D. 2004. Quantitative
evaluation of economic and social development of Lithuanian regions,
Ekonomika 65: 1-13.
Ginevicius, R.; Podvezko, V. 2004. Quantitative assessment of
regional development, Environmental Research, Engineering and Management
1(27): 10-14.
Gossen, H. H. 1853. Entwicklung der Gesetze des menschlichen
Verkehrs und der daraus Flieszenden Regeln fur menschliches Handeln
(Development of the law of human relations and the therefrom derived
rules of human behavior). 3 Auflage, Prager, Berlin (1927).
Huber, P. J. 1981. Robust Statistics. New York, US, Wiley.
doi:10.1002/0471725250
Huber, P. J. 1969. Theorie de l'Inference Statistique Robuste
(Theory of Robust Statistical Inference). Montreal, Canada, Les Presses
de l'Universite de Montreal.
Hwang, C-L.; Yoon, K. 1981. Multiple Attribute Decision Making,
Methods and Applications. Lecture Notes in Economics and Mathematical
Systems. Springer, Berlin.
Jantsch, E. 1967. Technological Forecasting in Perspective. Paris,
OECD.
Karlin, S.; Studden, W. J. 1966. Tchebycheff Systems: with
Applications in Analysis and Statistics, Interscience Publishers, New
York, 278-280.
Keeney, R. L.; Raiffa, H. 1993. Decisions with Multiple Objectives,
Preferences and Value Tradeoffs. Cambridge U.S., University Press.
Kendall, M. G.; Gibbons, J. D. 1990. Rank Correlation Methods.
Edward Arnold, London.
Kendall, M. G. 1948. Rank Correlation Methods. Griffin London.
"Mazeikiu nafta". Available from Internet:
<www.nafta.lt/en/content.php?pid=34>.
Miller, D. W; Starr, M. K. 1969. Executive Decisions and Operations
Research. 2nd Edition. Prentice-Hall Inc. Englewood Cliffs (N.J.).
Minkowsky, H. 1896. Geometrie der Zahlen (Geometry of Numbers).
Teubner, Leipzig.
Minkowsky, H. 1911. Gesammelte Abhandlungen (Collected Papers).
Teubner, Leipzig.
Pareto, V. 1906. Manuale di Economia Politica (Handbook of
Political Economy). Translation revised by Pareto himself: Manuel
d'economie politique, Second Ed., Paris, 1927.
Pigou, A. C. 1920. (Ed.). Economics of Welfare. London.
Quade, E. S. 1970. Cost-Effectiveness: Some Trends in Analysis.
Rand Corporation, P-3529-1, Santa Monica (CAL).
Quade, E. S.; Boucher, W. I. 1968. Systems Analysis and Policy
Planning: Applications in Defense. Elsevier, New York.
Rieder, H. (Ed.). 1996. Robust Statistics, Data Analysis and
Computer Intensive Methods. New York, Springer.
Roy, B.; Benayoun, R.; Sussman, B. 1966. ELECTRE, Societe
d'Economie et de Mathematique appliques. Paris.
Ruggeri, F. 2008. Bayesian Robustness, European Working Group,
Multiple Criteria Decision Aiding, Series 3, No17: 6-10.
Saaty, T. L. 1987. What is the Analytic Hierarchy process?, in
Mathematical Models for Decision Support. Nato Advanced Study Institute,
Val d'Isere (f), July 26,1987, Mon 82.
Saaty, T. L. 1988. The Analytic Hierarchy Process. Mcgraw-Hill, New
York.
Stigler, S. 1973. Simon Newcomb, Percy Daniell and the history of
Robust estimation 1885-1920, Journal of the American Statistical
Association 68: 872-9. doi:10.2307/2284515
The Journal of Economic Perspectives, Spring 2009, Symposium on
Climate Change 23(2): 5-76.
Van De Ven, A. H.; Delbecq, A. L. 1971. Nominal Versus interacting
group processes for committee decision making effectiveness, Academy of
Management Journal 14(2): 203 and fol.
Zagorskas, J.; Burinskiene, M.; Zavadskas, E. K.; Turskis, Z.
2007.Urbanistic assessment of city compactness on the basis of GIS
applying the COPRAS method, Ekologija 53: 55-63.
Zavadskas, E. K.; Viteikiene, M.; Saparauskas, J. 2007. Sustainable
development assessment of cities and their residential districts,
Ekologija 53: 49-54.
Zavadskas, E. K.; Kaklauskas, A.; Kaklauskiene, J. 2007. Modelling
and forecasting of a rational and sustainable development of Vilnius:
emphasis on pollution, International Journal of Environment and
Pollution 30(3-4): 485-500. doi:10.1504/IJEP.2007.014824
Zavadskas, E. K.; Burinskiene, M. (Guest Editors). 2007. Internal
and External Housing Environments, International Journal of Environment
and Pollution, Inderscience Enterprises 30(3-4): 359-528.
Willem Karel M. Brauers [1], Romualdas Ginevicius [2], Valentinas
Podvezko [3]
[1,2,3] Vilnius Gediminas Technical University, Sauletekio al. 11,
LT-10223 Vilnius, Lithuania
E-mails: [1]
[email protected]; [2]
[email protected]; [3]
[email protected]
Received 16 April 2010; accepted 20 October 2010
(1) At a later time, namely in 1981, Huber wrote a more complete
book on Robust Statistics. In 1994 at the occasion of Huber's
birthday his colleagues edited a book on Robust Statistics (editor:
Rieder 1996).
(2) A good overview of this problem of robustness and Bayesian
Analysis is brought by Ruggeri 2008.
(3) As well known, statistics already existed in Roman times with
the census of population.
(4) Webster's new Universal Unabridged Dictionary: robust:
strong; stronger, strongest.
(5) Brauers and Zavadskas, 2006, prove that the most robust choice
for this denominator is the square root of the sum of squares of each
alternative per objective.
(6) Instead of a normal increase in productivity growth a decrease
remains possible. At that moment the interval becomes [-1, 1]. Take the
example of productivity, which has to increase (positive). Consequently,
we look for a maximization of productivity e.g. in European and American
countries. What if the opposite does occur? For instance, take the
original transition from the USSR to Russia. Contrary to the other
European countries productivity decreased. It means that in formula (2)
the numerator for Russia was negative with the whole ratio becoming
negative. Consequently, the interval changes to: [-1, +1] instead of [0,
1].
(7) Brauers 2008b proves that the Min-Max metric is the most robust
choice between all the possible metrics of reference point theory.
(8) This convergence of opinion has to be brought not by face to
face methods but rather by nominal methods such as the Ameliorated
Nominal Group Technique or by the Delphi Method (See Appendices A and
B).
(9) Lithuania greenhouse gas emission limited by 2020 compared to
2005: 18,429,024 tons of CO2 equivalent or 15% above the 2005 emission;
cf. other Baltic States: Latvia 17%, Estonia 11% (Commission of the
European Communities, decision to reduce emissions, SEC 2008).
(10) A huge literature exists on pollution and climate change. A
number of the Journal of Economic Perspectives (Spring 2009, Symposium
on Climate Change) presents a large uptodate literature on pollution and
climate change. In addition we have to mention the International Journal
of Environment and Pollution, especially volume 30 with as guest editors
Zavadskas and Burinskiene.
(11) Economic and Social Development in Lithuania 2003, Statistics
Lithuania. Vilnius, 2004. Counties of Lithuania 2004. Statistics
Lithuania, Vilnius, 2005. Counties of Lithuania 2005. Statistics
Lithuania, Vilnius, 2006. Counties of Lithuania 2006. Statistics
Lithuania, Vilnius, 2007. Counties of Lithuania 2007. Statistics
Lithuania, Vilnius, 2008.
(12) Commission of the European Communities, COM 2008, version
15.4.
Willem K. M. BRAUERS was graduated as: Ph.D in economics (Un. of
Leuven), Master of Arts (in economics) of Columbia Un. (New York),
Master in Management and Financial Sciences, in Political and Diplomatic
Sciences and Bachelor in Philosophy (Un. of Leuven). He is professor at
the Faculty of Applied Economics and at the Institute for Development
Policy and Management of the University of Antwerp. Previously, he was
professor at the University of Leuven, the Belgian War College, the
School of Military Administrators, and the Antwerp Business School. He
was a research fellow in several American institutions like Rand
Corporation, the Pentagon, the Institute for the Future, the Futures
Group and extraordinary advisor to the Center for Economic Studies of
the University of Leuven. He was consultant in the public sector, such
as the Belgian Department of National Defense, the Department of
Industry in Thailand, the project for the construction of a new port in
Algeria (the port of Arzew) and in the private sector such as the
international seaport of Antwerp and in electrical works. He was
Chairman of the Board of Directors of SORCA Ltd. Brussels, Management
Consultants for Developing Countries, linked to the world-wide group of
ARCADIS and Chairman of the Board of Directors of MARESCO Ltd. Antwerp,
Marketing Consultants. At the moment he is General Manager of
CONSULTING, Systems Engineering Consultants. Brauers is member of many
international scientific organizations. His specialization covers:
Optimizing Techniques with Several Objectives, Forecasting Techniques
and Public Sector Economics such as for National Defense and for
Regional Sub-optimization and Input-Output Techniques. His scientific
publications consist of twelve books and hundreds of articles and
reports.
Romualdas GINEVICIUS. Professor, Dr Habil, Head of the Department
of Enterprise Economics and Management, Vilnius Gediminas Technical
University construction engineer and economist. The author of more than
350 research papers and over 20 scientific books; editor-in-chief of the
'Journal of Business Economics and Management' (located in ISI
database 'Web of Science') and the journal 'Business:
Theory and Practice. Research interests: organization theory, complex
quantitative evaluation of social processes and phenomena.
Valentinas PODVEZKO. Professor, Doctor, Department of Mathematical
Statistics. Vilnius Gediminas Technical University. MSc Dept. of
Mechanics and Mathematics (now Dept. of Applied Mathematics and
Cybernetics) Lomonosov Moscow University (1966), Doctor (1984)
(Scientific Institute for System Research of the Academy of Sciences of
the USSR, Moscow), procedure of Habilitation, professor (2006). Author
of over 150 publications. Research interests: decision-making theory,
expert systems, sampling models in economics and technology.
Table 1. The statistical data on economic-social
development of Lithuanian Counties for 2008
Units Alytus Kaunas
1. Population migration (net 1000 p. -5.345 -2.550
migration) per 1000 inhabitants
2. Municipal budget's revenue 1000 2.221 2.175
(average amount per capita) LTL
3. Municipal budget's LTL 189.39 185.18
expenditure (average amount,
social security)
4. Unemployment rate % 4.1 5.9
5. Average gross monthly LTL 1874 2062
earnings
6. Average useful floor space [m.sup.2] 27.1 24.0
per capita
7. Number of pre--school number 109 94
establishments (places per 100
children)
8. Number of schools number 3.11 2.52
(per 1000 of students)
9. Animal products recalculated 100 kg 674 683
in terms of milk (100 kg per 100
ha of agricultural land)
10. Indicators of activity of LTL 4954 5857
retail trade enterprises (per
capita)
11. Investment in tangible fixed LTL 4560 6265
assets (per capita)
12. Own-account construction LTL 2687.2 3036.0
work carried out within the
country (per capita)
13. Dwellings completed (per [m.sup.2] 0.243 0.354
capita)
14. Registered criminal offences number 112 164
(misdemeanors per 100000
inhabitants)
15. Physicians per 10000 number 24.3 51.3
population
16. Average pollutant emissions kg 244.1 1374.9
per [km.sup.2]
Klaipeda Marijampole Panevezys
1. Population migration (net -0.812 -0.369 -4.996
migration) per 1000 inhabitants
2. Municipal budget's revenue 2.111 2.116 2.109
(average amount per capita)
3. Municipal budget's 180.36 193.31 190.04
expenditure (average amount,
social security)
4. Unemployment rate 7.2 2.8 5.6
5. Average gross monthly 2114 1738 1835
earnings
6. Average useful floor space 22.7 23.6 26.9
per capita
7. Number of pre--school 96 97 108
establishments (places per 100
children)
8. Number of schools 2.82 3.45 3.21
(per 1000 of students)
9. Animal products recalculated 788 832 658
in terms of milk (100 kg per 100
ha of agricultural land)
10. Indicators of activity of 6982 4408 5129
retail trade enterprises (per
capita)
11. Investment in tangible fixed 7761 3527 5308
assets (per capita)
12. Own-account construction 4434.8 2074.7 2354.2
work carried out within the
country (per capita)
13. Dwellings completed (per 0.335 0.142 0.077
capita)
14. Registered criminal offences 173 130 130
(misdemeanors per 100000
inhabitants)
15. Physicians per 10000 33.1 20.7 28.1
population
16. Average pollutant emissions 1552.5 380.6 346.1
per [km.sup.2]
Siauliai Taurage Telsiai
1. Population migration (net -7.379 -6.894 -4.941
migration) per 1000 inhabitants
2. Municipal budget's revenue 2.190 2.294 2.142
(average amount per capita)
3. Municipal budget's 230.21 254.38 198.20
expenditure (average amount,
social security)
4. Unemployment rate 5.5 5.7 6.6
5. Average gross monthly 1821 1637 2004
earnings
6. Average useful floor space 24.1 24.0 23.1
per capita
7. Number of pre--school 92 96 86
establishments (places per 100
children)
8. Number of schools 3.33 3.53 3.37
(per 1000 of students)
9. Animal products recalculated 661 891 722
in terms of milk (100 kg per 100
ha of agricultural land)
10. Indicators of activity of 5065 4207 4492
retail trade enterprises (per
capita)
11. Investment in tangible fixed 4752 2887 9115
assets (per capita)
12. Own-account construction 2846.5 1878.0 2477.2
work carried out within the
country (per capita)
13. Dwellings completed (per 0.123 0.057 0.097
capita)
14. Registered criminal offences 144 169 98
(misdemeanors per 100000
inhabitants)
15. Physicians per 10000 23.2 13.3 17.6
population
16. Average pollutant emissions 681.1 278.3 7204.7
per [km.sup.2]
Utena Vilnius
1. Population migration (net -4.941 3.003
migration) per 1000 inhabitants
2. Municipal budget's revenue 2.889 1.956
(average amount per capita)
3. Municipal budget's 206.22 203.48
expenditure (average amount,
social security)
4. Unemployment rate 5.4 6.3
5. Average gross monthly 1946 2450
earnings
6. Average useful floor space 30.1 25.4
per capita
7. Number of pre--school 99 98
establishments (places per 100
children)
8. Number of schools 3.74 2.99
(per 1000 of students)
9. Animal products recalculated 621 603
in terms of milk (100 kg per 100
ha of agricultural land)
10. Indicators of activity of 4743 9859
retail trade enterprises (per
capita)
11. Investment in tangible fixed 4824 10729
assets (per capita)
12. Own-account construction 2848.6 5337.6
work carried out within the
country (per capita)
13. Dwellings completed (per 0.090 0.739
capita)
14. Registered criminal offences 122 287
(misdemeanors per 100000
inhabitants)
15. Physicians per 10000 13.0 48.4
population
16. Average pollutant emissions 189.6 664.8
per [km.sup.2]
Source: Department of Statistics to the Government
of the Republic of Lithuania (Statistics Lithuania).
Table 2. Income Paradox in Belgium (1996)
in BEF * GRP per head Disposable Income per head
Flanders 869, 976 676, 743
Wallonia 752, 452 692, 883
Brussels 839, 913 698, 809
Belgium (total) 828, 693 684, 076
* 1 [euro] equaled 40.3399 BEF
Calculations in: W K. Brauers: het Bruto Regionale Product van
Vlaanderen. Wallonie en Brussel (the GRP of Flanders, Wallonia
and Brussels) Working Paper 99-2, RUCA, Faculty Applied
Economics, University of Antwerp, 8-18.
Table 3. Classification of the Lithuanian Counties by the average
gross monthly earnings per capita for 2008 (in Litas)
1 Vilnius 2450
2 Klaipeda 2114
3 Kaunas 2062
4 Telsiai 2004
5 Utena 1946
6 Alytus 1874
7 Panevezys 1835
8 Siauliai 1821
9 Marijampole 1738
10 Taurage 1637
Table 4. MOORA applied on 16 objectives for the 10 Lithuanian
Counties for 2008
4a. Matrix of Responses of Counties on Objectives: ([x.sub.ij])
1 2 3 4
migration revenue expenditure unemploym.
MAX MAX MAX MIN
Alytus -5.345 2.221 189.39 4.1
Kaunas -2.55 2.175 185.18 5.9
Klaipeda -0.812 2.111 180.36 7.2
Marijampole -0.369 2.116 193.31 2.8
Panevezys -4.996 2.109 190.04 5.6
Siauliai -7.379 2.19 230.21 5.5
Taurage -6.894 2.294 254.38 5.7
Telsiai -4.941 2.142 198.2 6.6
Utena -4.941 2.889 206.22 5.4
Vilnius 3.003 1.956 203.48 6.3
5 6 7 8
earnings floor-space pre-schools schools
MAX MAX MAX MAX
Alytus 1874 27.1 109 3.11
Kaunas 2062 24 94 2.52
Klaipeda 2114 22.7 96 2.82
Marijampole 1738 23.6 97 3.45
Panevezys 1835 26.9 108 3.21
Siauliai 1821 24.1 92 3.33
Taurage 1637 24 96 3.53
Telsiai 2004 23.1 86 3.37
Utena 1946 30.1 99 3.74
Vilnius 2450 25.4 98 2.99
9 10 11 12
animal
products retail trade Investment construction
MAX MAX MAX MAX
Alytus 674 4954 4560 2687.2
Kaunas 683 5857 6265 3036
Klaipeda 788 6982 7761 4434.8
Marijampole 832 4408 3527 2074.7
Panevezys 658 5129 5308 2354.2
Siauliai 661 5065 4752 2846.5
Taurage 891 4207 2887 1878
Telsiai 722 4492 9115 2477.2
Utena 621 4743 4824 2848.6
Vilnius 603 9859 10729 5337.6
13 14 15 16
criminal total
dwellings acts Physicians pollution
MAX MIN MAX MIN
Alytus 0.243 112 24.3 244.1
Kaunas 0.354 164 51.3 1374.9
Klaipeda 0.335 173 33.1 1552.5
Marijampole 0.142 130 20.7 380.6
Panevezys 0.077 130 28.1 346.1
Siauliai 0.123 144 23.2 681.1
Taurage 0.057 169 13.3 278.3
Telsiai 0.097 98 17.6 7204.7
Utena 0.09 122 13 189.6
Vilnius 0.739 287 48.4 664.8
Sub-Tables 4b and 4c: the part of the MOORA Ratio
System for the 10 Lithuanian Counties (2008)
4b. Sum of squares and their square roots
1 2 3 4
Alytus 28.569 4.9328 35869 16.81
Kaunas 6.5025 4.7306 34292 34.81
Klapeda 0.6593 4.4563 32530 51.84
Marijampole 0.1362 4.4775 37369 7.84
Panevezys 24.96 4.4479 36115 31.36
Siauliai 54.45 4.7961 52997 30.25
Taurage 47.527 5.2624 64709 32.49
Telsiai 24.413 4.5882 39283 43.56
Utena 24.413 8.3463 42527 29.16
Vilnius 9.018 3.8259 41404 39.69
[SIGMA] 220.65 49.86 417094 318
root 14.854 7.0615 645.83 17.827
5 6 7 8
Alytus 3511876 4.448 36115 31.36
Kaunas 4251844 576 8836 9.6721
Klapeda 4468996 515.3 9216 6.3504
Marijampole 3020644 557 9409 7.9524
Panevezys 3367225 723.6 11664 11.903
Siauliai 3316041 580.8 8464 10.304
Taurage 2679769 576 9216 11.089
Telsiai 4016016 533.6 7396 12.461
Utena 3786916 906 9801 11.357
Vilnius 6002500 645.2 9604 13.988
[SIGMA] 38421827 5618 119721 126
root 6198.534 74.95 346.01 11.244
9 10 11 12
Alytus 454276 24542116 20793600 7221043.8
Kaunas 466489 34304449 39250225 9217296
Klapeda 620944 48748324 60233121 19667451
Marijampole 692224 19430464 12439729 4304380.1
Panevezys 432964 26306641 28174864 5542257.6
Siauliai 436921 25654225 22581504 8102562.3
Taurage 793881 17698849 8334769 3526884
Telsiai 521284 20178064 83083225 6136519.8
Utena 385641 22496049 23270976 8114522
Vilnius 363609 97199881 115111441 28489974
[SIGMA] 5168233 33655906 41327345 10032289
root 2273.375 18345.546 20329.128 10016.132
13 14 15 16
Alytus 0.05905 12544 590.49 59584.81
Kaunas 0.12532 26896 2631.69 1890350
Klapeda 0.11223 29929 1095.61 2410256
Marijampole 0.02016 16900 428.49 144856.4
Panevezys 0.00593 16900 789.61 119785.2
Siauliai 0.01513 20736 538.24 463897.2
Taurage 0.00325 28561 176.89 77450.89
Telsiai 0.00941 9604 309.76 5190770
Utena 0.0081 14884 169 35948.16
Vilnius 0.54612 82369 2342.56 441959
[SIGMA] 0.90469 259323 9072.34 5755179
root 0.95115 509.238 95.2488 7586.29
4c. Objectives divided by their square roots and MOORA
1 2 3 4
Alytus -0.36 0.3145 0.2933 0.23
Kaunas -0.172 0.308 0.2867 0.331
Klapeda -0.055 0.2989 0.2793 0.4039
Marijampole -0.025 0.2997 0.2993 0.1571
Panevezys -0.336 0.2987 0.2943 0.3141
Siauliai -0.497 0.3101 0.3565 0.3085
Taurage -0.464 0.3249 0.3939 0.3197
Telsiai -0.333 0.3033 0.3069 0.3702
Utena -0.333 0.4091 0.3193 0.3029
Vilnius 0.2022 0.277 0.3151 0.3534
5 6 7 8
Alytus 0.30233 0.362 0.315 0.277
Kaunas 0.332659 0.32 0.2717 0.2241
Klapeda 0.341048 0.303 0.2775 0.2508
Marijampole 0.280389 0.315 0.2803 0.3068
Panevezys 0.296038 0.359 0.3121 0.2855
Siauliai 0.293779 0.322 0.2659 0.2961
Taurage 0.264095 0.32 0.2775 0.3139
Telsiai 0.323302 0.308 0.2485 0.2997
Utena 0.313945 0.402 0.2861 0.3326
Vilnius 0.395255 0.339 0.2832 0.2659
9 10 11 12
Alytus 0.296 0.270 0.224 0.268
Kaunas 0.300434 0.3192601 0.3081785 0.303111
Klapeda 0.346621 0.3805828 0.3817675 0.4427658
Marijampole 0.365976 0.2402763 0.1734949 0.2071359
Panevezys 0.289438 0.2795774 0.2611032 0.2350408
Siauliai 0.290757 0.2760888 0.2337533 0.2841916
Taurage 0.391928 0.22932 0.142013 0.1874975
Telsiai 0.31759 0.2448551 0.4483714 0.247321
Utena 0.273162 0.2585369 0.237295 0.2844012
Vilnius 0.265244 0.5374056 0.5277649 0.5329004
13 14 15
Alytus 0.255 0.220 0.25512
Kaunas 0.37218 0.32205 0.53859
Klapeda 0.3522 0.33972 0.34751
Marijampole 0.14929 0.25528 0.21733
Panevezys 0.08095 0.25528 0.29502
Siauliai 0.12932 0.28278 0.24357
Taurage 0.05993 0.33187 0.13963
Telsiai 0.10198 0.19244 0.18478
Utena 0.09462 0.23957 0.13648
Vilnius 0.77695 0.56359 0.5081
16 sum rank
Alytus 0.032176 2.3228 7
Kaunas 0.181235 2.8792 3
Klapeda 0.204645 2.9999 2
Marijampole 0.050169 2.6475 4
Panevezys 0.045622 2.3352 6
Siauliai 0.08978 2.1238 8
Taurage 0.036685 1.8924 9
Telsiai 0.9497 1.4900 10
Utena 0.024992 2.4471 5
Vilnius 0.087632 4.2213 1
Sub-Tables 4d and 4e: the part of the MOORA Reference
Point Theory for the 10 Lithuanian Counties (2008)
4d. Reference Point Theory with Ratios: co-ordinates of
the reference point equal to the maximal objective values
1 2 3 4
[r.sub.i] 0.2022 0.4091 0.3939 0.1571
5 6 7 8
[r.sub.i] 0.395255 0.402 0.315 0.333
9 10 11 12
[r.sub.i] 0.391928 0.537406 0.527765 0.5329
13 14 15 16
[r.sub.i] 0.77695 0.1924 0.53859 0.024992
4e. Reference Point Theory: Deviations from the reference point
1 2 3 4
Alytus 0.562 0.095 0.1006 0.0729
Kaunas 0.3738 0.1011 0.1071 0.1739
Klaipeda 0.2568 0.1102 0.1146 0.2468
Marijampole 0.227 0.1095 0.0946 0.000
Panevezys 0.5385 0.1105 0.0996 0.1571
Siauliai 0.6989 0.099 0.037 0.1515
Taurage 0.6663 0.0843 0 0.1627
Telsiai 0.5348 0.1058 0.087 0.213
Utena 0.5348 0 0.0746 0.1458
Vilnius 0 0.1321 0.0788 0.1963
5 6 7 8
Alytus 0.092925 0.04 0 0.0560
Kaunas 0.062595 0.081 0.0434 0.1085
Klaipeda 0.054206 0.099 0.0376 0.0818
Marijampole 0.114866 0.087 0.0347 0.026
Panevezys 0.099217 0.043 0.0029 0.047
Siauliai 0.101476 0.08 0.0491 0.036
Taurage 0.13116 0.081 0.0376 0.019
Telsiai 0.071952 0.093 0.0665 0.033
Utena 0.08131 0 0.0289 0.0329
Vilnius 0 0.063 0.0318 0
9 10 11 12
Alytus 0.0955 0.2674 0.3035 0.2646
Kaunas 0.0915 0.2181 0.2196 0.2298
Klaipeda 0.0453 0.1568 0.1460 0.0901
Marijampole 0.025953 0.2971293 0.35427 0.3257645
Panevezys 0.102491 0.2578282 0.2666617 0.2978595
Siauliai 0.101171 0.2613168 0.2940116 0.2487088
Taurage 0 0.3080857 0.3857519 0.3454028
Telsiai 0.074339 0.2925506 0.0793935 0.2855793
Utena 0.118766 0.2788688 0.2904699 0.2484991
Vilnius 0.126684 0 0 0
13 14 15
Alytus 0.5215 0.0275 0.28347
Kaunas 0.4048 0.1296 0
Klaipeda 0.4247 0.1473 0.19108
Marijampole 0.62766 0.063 0.32126
Panevezys 0.696 0.0628 0.2436
Siauliai 0.64764 0.0903 0.29502
Taurage 0.71702 0.1394 0.39896
Telsiai 0.67497 0.000 0.35381
Utena 0.68233 0.0471 0.4021
Vilnius 0 0.3711 0.03045
16 rank
max min
Alytus 0.007184 0.561994 4
Kaunas 0.156242 0.404772 2
Klaipeda 0.179653 0.42475 3
Marijampole 0.025177 0.62766 5
Panevezys 0.020629 0.69600 7
Siauliai 0.064788 0.69892 8
Taurage 0.011692 0.71702 9
Telsiai 0.924708 0.92471 10
Utena 0 0.68233 6
Vilnius 0.062639 0.37114 1
Table 5. Ranking of the Lithuanian Counties
after their general Well-Being
MOORA MOORA MOORA
Ratio System Reference Ratio
Regions Income 2008 2008 Point 2008 System 2005
Vilnius 1 1 1 1
Klaipeda 2 2 3 2
Kaunas 3 3 2 3
Marijampole 9 4 5 4
Utena 5 5 6 5
Panevezys 7 6 7 6
Alytus 6 7 4 7
Siauliai 8 8 8 8
Taurage 10 9 9 9
Telsiai 4 10 10 10
MOORA MOORA MOORA
Reference Ratio Reference
Regions Point 2005 System 2002 Point 2002
Vilnius 1 1 1
Klaipeda 2 4 6
Kaunas 3 2 2
Marijampole 8 3 3
Utena 6 5 5
Panevezys 5 7 8
Alytus 4 6 4
Siauliai 7 10 10
Taurage 9 8 7
Telsiai 10 9 9
Table 6. Average Pollutant Emission in kilograms
per [km.sup.2] in the County of Telsiai
year pollution
2002 7716
2005 7803
2008 7205
Table 7. Migration flows per Lithuanian County
2005 2008
Alytus -5277 -5345
Kaunas -3636 -2550
Klaipeda -1435 -812
Marijampole -3791 -369
Panevezys -4627 -4996
Siauliai -5748 -7379
Taurage -5986 -6894
Telsiai -5522 -4941
Utena -4663 -4941
Vilnius 2238 3003
