Locating and Classification of Facilities
with Possible Undesirable Effects on Environment
Ing.
Stanislav Machalík[1],
RNDr. František Machalík[2]
Abstract: The paper
presents a way of solving the problem of locating facilities with possible
undesirable effects on environment. Various types of this problem are
introduced and classified. The problem is transformed into a task of looking
for solutions that are minimum based on three points of view: total costs,
opposition of inhabitants, maximum individual disutility (equity). A model was created
in order to achieve this. The description is presented in this paper.
Keywords: locating facilities with possible undesirable
effects on environment, classification and solving of locating problems
Solutions of locating problems of one
or more facilities working on the basis of traditional mathematical models,
assume in most cases that the facilities provide a desirable service for
population. This can be, for example, the case of public service centres, like firehouses,
hospitals or police stations, or the case of banks or warehouses for a
business. In such cases the interaction between customers and service centre generates
the travel problem. Future travelling costs are directly connected to the distance
between customer and facility. The solution consists in the problem to find such
location for a new facility (or new facilities), that functions of the distance
(and also the costs of the offered service) are minimised.
But a minimal distance is not always the
most important factor. There are a lot of other types of facilities where, on
the second side, a minimal distance is not acceptable. This can be a problem e.
g. in the case of landfills, waste incinerators or chemical factories, or in
many other cases, where the minimisation of distance between customers and the
facility is not desirable. One of the reasons can be a harmful influence on the
surroundings of the facility. Such facilities we denote as
"undesirable". A facility can be defined as "undesirable"
when, although it is useful or necessary for the society, it brings some
disadvantages for the population living nearby. Such disadvantage is, for
example, production of frequent or traffic noise, like in case of an airport, or
emissions of smoke from factory. Other facilities, although normally safe, can
be dangerous for the surroundings because they work with some hazardous
materials.
Beside this, public has become more sensitive
to environmental problems, and population is often in the strong opposition to
every project for the installation of a new facility that might be defined as
"undesirable". This is one of the main problems related to location
of undesirable facilities, why is needed do find some solution that will be
acceptable for life quality as well as for industry and economy.
However, a location problem for an
undesirable facility usually involves more objectives often with contending
claims. So the latest analytical models solving these problems are mostly
multiobjective models that try to work with different aspects of the problem.
The most prominent objectives seem to
be minimisation of costs, minimisation of risks (real risks or perceived risks,
which reflect opposition of people), and maximisation of equity (intended as
equity in the risk distribution).
2 Model for locating undesirable
facilities
We assume that each region requires some specified services and this
need is realized by installing the facilities of different sizes. Next we
assume that a number of candidate sites has already been selected because of
the fact that not everywhere can be any facility placed, e. g. because of natural
barriers as lakes or forests, as well as protected zones and so on.
We
assume that for each population centre the common demand of each service is
known and that the population is considered to be concentrated in the centre of
the populated area. For facility sizes (which means their capacity to provide
the service), we assume only a small number of different sizes can be considered.
The
first objective of the model is minimisation of total costs consisting of total
costs of the facility plus the transportation costs. We know the total costs of
the facility in each candidate site for every alternative size. These total
costs include common operating costs and investment costs. Investment costs can
include purchase money for the land and building-up costs, as well as possible
compensation for the people living nearby or cleaning costs after the activity
is finished.
The
second objective is minimisation of total opposition of people which is
considered the same as the risk perception of people. This objective is based
on the definition of the “disutility” function, by means of which we can
express the risk perception for a citizen living in the population centre due
to the facility size, with the Euclidean distance from population centre. We
assume that disutility is a decreasing function of the Euclidean distance
between a population centre and a facility, and an increasing function of the
facility size. We also have to work with the influence of empirical study
results, they depend especially on the nature of the facility and on position
of residents of the region towards the facility.
Total
disutility for a single citizen is calculated as the sum of the disutilities
due to all the facilities of the proposed system. Opposition of a population
centre is calculated as a sum of all individual disutilities of the residents,
and total opposition towards the proposed system is calculated as a sum of oppositions
of all population centres.
The
last objective is maximisation of equity. A suitable measure for equity has to
assure that smaller population centres are not disadvantaged against the bigger
ones. As a measure of equity (or unequity) we take the maximum individual
disutility calculated as explained above. The third objective is hence
minimising maximum individual disutility associated with the proposed system of
facilities.
2.1 Conflicts among defined objectives
In
defined model we can identify some conflicts that come out of definitions of
basic considered objectives.
Total
costs are given by sum of the facility costs (investment and operating costs)
and transportation costs. These two components collides with each other: few
big facilities will be needed in order to reduce investment costs, but it would
be necessary to have many facilities in order to reduce transportation costs
and they should be consequently smaller in order to distribute the service over
the region in a better way.
The
opposition objective collides with the reduction of transportation costs: in
order to minimise them, we should in fact locate the facilities as close as
possible to the demand centres, but in order to minimise the opposition of
people, the contrary should be done.
The
equity objective is in conflict with the investment costs reduction, because
these costs can be reduced by locating less facilities, and to maximise the
equity the highest possible number of facilities must be located.
Finally,
there’s a conflict between equity and opposition objectives: high number of
small facilities can increase equity, but at the same time the opposition will increase.
3 Suggestions for further work
Further
development of the model could consider pre-existing undesirable facilities
that are not related to the service demanded by the region, for example when
evaluating maximum individual disutility (i. e. considering chemical facilities
when planning waste incinerators). It could be interesting to follow e. g. effect
of building an incinerator near the same population centre that bears the
presence of a nuclear power facility. Of course, these pre-existing facilities
would contribute to the demand satisfaction in any way and the number of fit
solutions would not change, hence the number of efficient solutions would not
be affected. The only inconvenience would be the growth of the number
difficulties in data collecting and input.
4 Conclusion
In
connection with an increasing pressure of specialists as well as the lay public
on efficient solving of various types of environmental problems will number of
facilities (with any undesirable effects on surroundings) quickly grows up. In
this fact the locating problem applications are very actual. But there is
needed to know that no mathematic or other model will locate undesirable
facilities fully optimally. The main reason is especially in the fact that the
problematics of locating undesirable facilities is a set of complex problems
where is necessary to look at many aspects (economic, power, material,
hygienic, but also social, political, aesthetic), that must be often solved
individually. Current mathematical models works only with bigger or smaller
part of these aspects; in spite of this fact but solutions of locating problems
by the help of location models can help in the process of decision making. Even
if these models cannot, of course, replace this process completely, they may be
very useful for decreasing the number of assessed variants and thereby can help
and objectify the process of decision making.
Next
partial expansion of this problematics can be in inclusion of risks rising
during service activities. Although the mentioned model includes travelling
costs, model doesn't work with undesirable effects connected with transport during
service activities (transport of dangerous wastes or other dangerous goods). It
would be fit to complete the model to contain except criteria for facility
locating also selection of fit transport tracks, to minimize the risks
connected with transport. This problem is out of range of this paper and will
be discussed further.
[1] University of Pardubice, Jan Perner Transport Faculty, Department of Informatics in Transport, Studentská 95, 532 10 Pardubice, Czech Republic, tel.: (+420) 466 036 181, e-mail: stanislav.machalik@upce.cz
[2] University of Pardubice, Jan Perner Transport Faculty, Department of Informatics in Transport, Studentská 95, 532 10 Pardubice, Czech Republic, tel.: (+420) 466 036 181, e-mail: frantisek.machalik@upce.cz