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Please cite this article SELECTION OF THE OPTIMAL MEDICAL WASTE
INCINERATION FACILITY LOCATION: A CHALLENGE OF MEDICAL WASTE RISK
MANAGEMENT
IZBOR OPTIMALNE LOKACIJE POSTROJENJA ZA SPALJIVANJE MEDICINSKOG
OTPADA: IZAZOV U UPRAVLJANJU RIZIKOM OD MEDICINSKOG OTPADA
Authors: Kristina Stanojević, Goran Radovanović, Dragana Makajić-Nikolić, Gordana Savić,
Barbara Simeunović, Nataša Petrović, Vojnosanitetski pregled (2020); Online First Jule, 2020.
UDC:
DOI: https://doi.org/10.2298/VSP200521072S
When the final article is assigned to volumes/issues of the Journal, the Article in Press version will
be removed and the final version appear in the associated published volumes/issues of the Journal.
The date the article was made available online first will be carried over.
Selection of the optimal medical waste incineration facility location: A challenge of medical
waste risk management
Izbor optimalne lokacije postrojenja za spaljivanje medicinskog otpada: Izazov u upravljanju
rizikom od medicinskog otpada
Kristina Stanojević*, Goran Radovanović†, Dragana Makajić-Nikolić*, Gordana Savić*,
Barbara Simeunović*, Nataša Petrović*
* Faculty of Organizational Sciences - University of Belgrade, Belgrade, Serbia
†Rectorate - University of Defence, Belgrade, Serbia
Correspondence to:
Prof. dr Nataša Petrović
Faculty of Organizational Sciences - University of Belgrade
Jove Ilića 154, Serbia
T: +381 11 3950 800
M: +381 69 8893 292
F: +381 11 2461 221
E: natasa.petrovic@fon.bg.ac.rs
KS - conception; study design, methods used; acquisition and collation of data; analysis,
interpretation of data; writing the manuscript
GR – conception, study design, methods used; analysis, interpretation of data; writing the
manuscript
DMN - conception; study design, methods used; analysis, interpretation of data; writing the
manuscript
GS – conception; study design, methods used; analysis, interpretation of data; writing the
manuscript
BS – acquisition and collation of data; analysis, interpretation of data; writing the manuscript
NP – analysis, interpretation of data; writing the manuscript; critical revision of the paper
Medical waste incineration facility
Selection of the optimal medical waste incineration facility location: A challenge of medical
waste risk management
Abstract
Background/Aim. Among the other challenges of the 21st century, medical waste has become an
arising problem for both the environment and people because of its increasing amount, variety, and
complexity. With this, medical waste management started to present a highly important
environmental issue. Serbia with no potential for appropriate disposal of all medical waste is forced
to export medical waste to countries with medical waste incineration facilities. The reason lies in
the fact that the incinerator facility represents an adequate way and a priority in handling medical
waste in its end-of-life phase. It must be noted that incineration lowers the possible risks of
inappropriate disposal and the emission of environmental pollutants, which leads to the need for a
“clever” choice of the incinerator facility location which needs to meet diverse environmental,
economic and technical criteria to manage successful processing of medical waste. Methods. In the
paper, we applied the criteria for the choice of optimal locations for a medical waste incinerator
facility as follows: the amount of waste that needs to be transported, the transport time from other
locations, the current pollution of the location, the unemployment rate and the location safety in
terms of natural disasters and accidents. By using the obtained results for seven efficient locations
gained by Data Envelopment Analysis, we used a goal programming for the analysis of the most
suitable location for a medical waste incineration facility. Results. After applying the proposed
methodology on the chosen scenario and analysing the criteria relevant for selecting the most
suitable location, optimal location is determined for a medical waste incineration facility.
Conclusion. Based on the obtained results, we demonstrated that it is possible to develop a
methodology that can used goal programming in optimal location selection for a medical waste
incineration facility in risk and medical waste management.
Keywords:
medical waste; risk management; Data envelopment analysis (DEA); incineration facility;
efficient locations; goal programming; optimal location.
Apstrakt
Uvod/Cilj. Između drugih izazova 21. veka, medicinski otpad je postao rastući problem kako za
životnu sredinu, tako i za ljude imajući u vidu povećanje njegove količine, raznovrsnost i
kompleksnost. Sa ovim, upravljanje medicinskim otpadom je počelo da predstavlja veoma bitan
ekološki problem. Srbija nema potencijala za adekvatno odlaganje celokupnog medicinskog otpada
i stoga je primorana da ga izvozi u zemlje koje imaju postrojenja za insineraciju medicinskog
otpada. Razlog ovoga je činjenica da upotreba postrojenja za insineraciju predstavlja odgovarajući
način i prioritet u rukovanju medicinskim otpadom u njegovoj završnoj fazi životnog ciklusa. Mora
se naglasiti da insineracija smanjuje moguće rizike prouzrokovane neodgovarajućim odlaganjem
medicinskog otpada kao i emisije zagađivača životne sredine, što rezultira i potrebom za
“pametnijim” izborom lokacije postrojenja za insineraciju koje mora da zadovolji različite ekološke,
ekonomske i tehničke kriterijume, kako bi se uspešno upravljalo ovom obradom medicinskog
otpada. Metode. U radu smo koristili sledeće kriterijume za izbor optimalne lokacije postrojenja za
insineraciju medicinskog otpada: količina otpada koja mora da se transportuje, vreme transporta
između lokacija, trenutno zagađenje lokacija, stopa nezaposlenosti i bezbednost lokacije u odnosu
na njenu izloženost prirodnim nepogodama i nesrećama. Korišćenjem rezultata za sedam efikasnih
lokacija dobijenih metodom Analize obavijanja podataka, u ovom istraživanju je korišćen model
ciljnog programiranja za dalju analizu izbora najpogodnije lokacije postrojenja za insineraciju
medicinskog otpada. Rezultati. Nakon primene predložene metodologije za izabrani scenario i
analize kriterijuma relevantnih za izbor najpogodnije lokacije, dobijena je optimalna lokacija za
postrojenje za insineraciju medicinskog otpada. Zaključak. Na osnovu dobijenih rezultata
izabranog scenarija pokazali smo da je moguće razviti metodologiju primenom ciljnog
programiranja za selekciju optimalne lokacije postrojenja za spaljivanje medicinskog otpada u
upravljanju rizikom i medicinskim otpadom.
Ključne reči:
medicinski otpad; upravljanje rizikom; Analiza obavijanja podataka (DEA); postrojenje za
spaljivanje; efikasne lokacije; ciljno programiranje; optimalna lokacija.
Introduction
Over the past two decades, medical waste (MW) has become one of the most important topics,
having in mind its negative impact on the health of the population and the environment 1-4. Several
terms are used for MW both in literature as well as practice: “hospital waste”, “health care waste”,
“infectious waste” or “pharmaceutical waste” 2. Since there is no single universal term for this type
of waste, there is also no universally accepted definition of MW. The reason for this lies in the fact
that MW is determined by various laws and regulations, resulting in the evidence that different
countries, even different regions of the same country, imply different types of waste as MW 2, 5, 6.
Knowing this MW can be defined as:
“waste resulting in the provision of health care services, which includes a variety of materials,
of used needles and syringes, body parts, diagnostic samples, blood, chemicals,
pharmaceuticals, medical devices and radioactive materials” 7.
“all medical, liquid or gaseous wastes which are generated from healthcare facilities, medical
laboratories, research centers, pharmaceutical and veterinary factories, veterinary clinics, home
nursing institutions; human and animal remnants, body fluids; blood and derivatives, human
excreta, contaminated clothing, wipes, injectors, contaminated sharp tools, expired medicines
and chemicals” 8.
“heterogenous mixture of communal waste, infectious, pathoanatomical, pharmaceutical and
laboratory waste, disinfectants and packages, as well as chemical waste from health care
institutions and veterinary organizations” 9.
Having in mind that all of the various types of MW can imply different negative impacts, special
attention has been given to appropriate treatment and disposal of MW, as well as necessary medical
waste management (MWM) 10, 11. Consequently, all types of health care institutions must be “in
standby mode” in situations that include the possible creation of MW 12, especially when the
generated MW can cause potential injuries to medical staff and the general public (directly in contact
with MW or indirectly) 5, 12, 13. This is especially important given that according to the World Health
Organization and the USA Environmental Protection Agency, 10-25% of MW falls into the category
of hazardous MW 14, and that “the global trend in rising healthcare usage will result in more medical
waste” 15. Besides, inadequate MWM can lead to the risk of this waste, too 16-20. That is why research
in the field of risks related to MW began in the 1990s. These MW risks include: “environmental
pollution, such as water, air, soil, result in unpleasant odors, promoting the growth and multiplication
of insects, rodents and vermin, and can lead to the transmission of diseases such as typhoid, cholera,
human immunodeficiency virus (HIV) and hepatitis (B and C)” 21, 22.
For these reasons, some authors use the general division of MW into medical general waste (or
non-hazardous waste) and medical hazardous waste. The second type of waste is considered as
medical risk waste 23. Also, it is concluded that MWM, and medical waste risk management
(MWRM) must be necessary parts of the management of any healthcare institutions/facilities,
bearing in mind that “healthcare organizations are routinely in a state of crisis management” 24.
Interestingly, that the modern concept of crisis originates from medical literature in which it
indicates a dangerous state of health of the organism from which it cannot recover without
permanent damage, external intervention or without fundamental restructuring since the body's
defense (immune) mechanisms are not enough to pull the organism out of the crisis. Social
scientists have borrowed this basic medical metaphor to describe the crisis in economic, political,
social, and cultural systems 25. Crisis management can be defined as an activity aimed at planning
and implementing measures to resolve dangerous situations. As an area of action in the field of
crisis resolution, whose goal is to overcome the crisis, crisis management has recently become a
dominant area of interest in all organizations, including health institutions. Taking measures of
crisis management in health care as an important area of functioning of human society is a specific
subject of crisis management. The foundations of crisis management in healthcare are based on the
creation of knowledge and the ability to respond to a crisis, and one of the goals of crisis
management is both MWM and MWRM.
The main goal of health crisis management is to reduce the risk to the life of the population that
has been imposed on potential crisis situations. The secondary goal is to reduce damage, ensure
public safety during the crisis and the consequences of the crisis, and care for survivors and victims.
It is certainly necessary to mention here the risk analysis, i.e. the assessment of vulnerability and
risk that are complementary aspects of the same phenomenon; interactions of physical forces with
human or environmental systems. Therefore, risk analysis and management in the MWM process
include identification, hazard analysis as well as taking measures related to exposure to these
hazards to prevent a crisis. This is extremely important because medical institutions have a special
responsibility for making quality decisions based on quantitative methods, the results of which
provide a comprehensive and exact basis for efficient MWM (where efficiency can be defined “by
the phrase „do things right‟” 26). Some of the most commonly used methods include Risk matrix,
Failure Mode Effects Analysis (FMEA), Root cause analysis (RCA), Event tree analysis (ETA),
Data envelopment analysis (DEA), Preliminary Hazard or Risk Analysis (PHA/PRA), Hazards and
Operability Study (HAZOPs), Fault Tree Analysis (FTA), goal programming and others whose task
is to identify, quantify, and mitigate the risks of MW 23. Thus, obtained quantitative indicators in
the process of crisis management, allow to align organizational resources with the goal of carrying
out the mission of the organization as well as to improve the awareness of all involved stakeholders
about the importance of MWM.
This is crucial nowadays, having in mind the current global COVID-19 pandemic and its rapid
progress 27, 28 with the consequential rise of the amount of infectious MW and the need for
improvements in the field of MW disposal, MWM, and MWRM to reduce the further spread of
COVID-19 as well as other diseases.
Unfortunately, for the time being, there is no method of optimal MWM, treatment, or disposal of
MW that eliminates all of the risks caused by MW to humans or the environment 29. This is
especially the case in Serbia, which produces a large amount of MW and there is no systematic
presentation of data on the amount of MW generated in health care institutions. It is estimated that
48,000 tons of MW are generated annually in clinics and hospitals in Serbia, of which 9,600 tons is
hazardous MW (of which 5,300 tons are generated in hospitals, 2,410 tons in health centers, 1,700
in other dispensaries, and 200 tons in health protection institutions) 9, 30.
In health care facilities, where there was no possibility of sterilization of used syringes and
needles, swabs, bandages, and other infectious waste, typical waste was mixed with municipal
waste and referred to the city dump 31. Besides the installed autoclaves and shredders for
sterilization of MW in Serbia, there are no other modern facilities for MW treatment, especially its
incineration 9. Knowing all that, it is no surprise that establishing MWM and incineration facilities
is included within the goals of Waste Management Strategy for Serbia for the period 2010-2019 9.
The incineration of MW is one of the methods to reduce and remove MW. The main advantages of
this type of MW treatment include a significant reduction in the quantity of waste, eliminating
dangerous pathogens and organic matter, transforming waste into ash. A downside to this method of
MW disposal is emissions of pollutants such as dioxins and furans (e.g. polychlorinated dibenzo-p-
dioxins (PCDD), polychlorinated dibenzofurans (PCDF)), toxic metals, as well as particulate
matter, which have negative impacts on the environment and human health 31, 32 because they “have
been associated with a range of adverse health effects” 7.
Under the framework of the European Commission's Guidelines for Waste and the National
Strategy of the Republic of Serbia for waste management, the treatment of MW by incineration is
carried out concerning all defined rules and regulations regarding possible emissions to air, water
and land 9, 33. Nevertheless, the fact that waste incineration creates energy must be considered in the
context of an integrated approach to waste management, which should include reduction, reusing,
and recycling 9.
These are the reasons why this paper emphasizes adequate MWM, which involves solving the
optimal location, routing and scheduling problems of MW collection, and incineration, as it is
shown as good practice in other countries 33-43. This is especially significant today when authors like
Yu, Sun, Solvang, and Zhao 44 prove the importance of MW and optimization as one of the key
tools in searching for possible solutions during the COVID-19 pandemic. Therefore, the authors of
the paper imply the need to develop an appropriate methodology for selecting the optimal location
for a MW incineration facility as one of the necessary activities of MWM and MWRM. For these
reasons and due to the availability of data, the region of Šumadija and Western Serbia and one
scenario were selected.
Methods
One of the long-term goals of the Strategy on Waste Management of Serbia is defined as the
provision of capacity for incineration of MW. This implies the necessary choice of location that
would represent the most favorable location for incineration. The methodology presented in the
paper shows that it is first necessary to determine a region from which potential locations and
criteria will be selected, which will then lastly provide us with the optimal location for the MW
incineration facility. Selected efficient locations used in this research are obtained from the results
of previous research of Stanojević, Makajić-Nikolić, and Savić 45. The final results refer to the
application of the DEA method and are used further on for choosing an optimal location by goal
programming. The location selection process is presented in Figure 1 (the results of Stanojević,
Makajić-Nikolić, and Savić 45 were complemented).
< Fig. 1 - The selection procedure for an efficient and optimal location. >
The first step of choosing a location is to consider the geo-economic map of Serbia, which is
divided into 30 administrative areas, 29 cities, 30 urban municipalities, 149 municipalities, 6,158
villages, and 193 urban settlements 46. Regions according to the number of cities, population, area,
the number of cities/municipalities with more than 40,000 inhabitants (this number is determined
based on the city with the smallest population in Serbia, which is Prokuplje with 44,000 inhabitants)
47 and the number of health facilities are given in Table 1.
< Table 1 Regions according to the number of cities, population, area, number of
cities/municipalities with more than 40,000 inhabitants and the number of health facilities 45 –
48>
Šumadija and Western Serbia occupy a central place in Serbia: the most registered medical
institutions are located there, it is the largest area, with the most inhabitants, and with the most cities
and the most towns/municipalities with more than 40,000 inhabitants. That is why it was elected as
the region in which the efficient locations for the treatment of MW should be defined. Šumadija and
Western Serbia, within the eight areas, have 14 towns/municipalities with more than 40,000
inhabitants 47. Featured cities are regarded as possible locations for effective MW treatment. In
regions of Zlatibor and Kolubara, there is a city that has more than 40,000 inhabitants, while in other
areas we have two potentially efficient locations. MW from municipalities and cities that are located
within the same area, but have less than 40,000 inhabitants, “belong” to the city which is the closest to
them.
Criteria for the selection of efficient locations within the region and determination of an optimal
location were 45: the amount of generated MW that needs to be transported to a given location;
duration of transport from all other locations to given locations; current pollution of each location;
the unemployment rate; the safety of the location from natural disasters and accidents. The
descriptions of criteria are given respectively: the amount of MW is directly in the relation with the
increase of the consequences of possible risk of the spillage of MW which can produce pollution of
air, land, and water; duration of transport has impact to traffic and wherefore significant negative
effects on the quality of air (emissions of CO2, NOx, CH4, O3, greenhouse gases (GHG) and their
consequentially responsibilities “for acid deposition, stratospheric ozone depletion and climate
change” 49; this criterion is very important, having in mind that “incineration of medical waste
involves the creation of certain gases such as CO2, NO2, CO and other gases, it is necessary to
choose locations that have the least air pollution, specifically have the lowest risk of crossing the
permissible limits of pollutants” 45; the unemployment rate has great importance as chosen criteria
having in mind that this rate represents an important indicator in the evaluation of “socioeconomic
development and welfare of countries” 50; consequences of natural disasters and accidents beside
their devastating influence on people and material goods (infrastructure, households, firms, and
plants) in the affected area with medical waste incineration facility, could be especially dangerous
having in mind possible catastrophic emissions of MW of which 10-25% presents hazardous waste
with infectious, radioactive, or toxic characteristics 14.
So, in the contest of the DEA method, inputs are: the amount of generated MW, duration of
transport, and pollution; while outputs are the unemployment rate, and safety of the location from
natural disasters and accidents. In the scenario of the methodology presented in this paper, all input
and output criteria are equal (for the decision-makers). In other scenarios, weights of input and
output criteria can be different according to the decision-makers' opinions. Consequently, efficient
locations could be different.
Based on the chosen criteria, values, descriptions, and results obtained by using the DEA
method, the authors further analysed gained efficient locations presented in Table 2.
< Table 2 Efficiency locations 45>
The obtained results showed that there are seven efficient locations (the efficiency is equal to 1).
To determine the optimal location, a model of goal programming, that integrates the same multiple
criteria as the DEA method is created. Charnes and Cooper 51 illustrated how that deviation could
be minimized by placing the variables that represent the deviation directly in the objective function
of the model. This allows multiple (and sometimes conflicting) goals to be expressed in a model
that will permit a solution to be found.
Results
Efficient locations determined by the DEA method represent potential locations for the MW
incineration facility. These locations should be further analysed to get an optimal solution which
should have a minimal total deviation from an ideal location. The ideal location is obtained using
the best input and output values, i.e. all criteria values of all observed locations. None of the
selected locations have such values, so the goal is to find the location that deviates the least from
the ideal one. The obtained values of inputs and outputs are given in Table 3.
< Table 3 Values of inputs and outputs 45>
Let us suppose that N is a subset of efficient locations (|N|≤ n).
The parameters and variables used in a mathematical model of the proposed problem are
following:
brj - normalized value r-th output for j-th location (brj = ylmax, r є{1, 2}, j = 1, …, n),
alj - normalized value l-th input for j-th location (alj = xlj / xlmin, l є{1, 2, 3}, j = 1, …, n),
1 if insineration facilityisonthe -thlocation
=0 otherwise
j
zj
dl+ - deviation from the best value l-output,
dr- - deviation from the best value r-output.
The mathematical model of this problem has the following notation (1-5):
32
-
min ( ) 1
1
f x d dr
lr
l
,
(1)
s.t.
- 1, {1,2,3}
1
na z d l
j
lj l
j
,
(2)
-1, {1,2}
1
nb z d r
r
j
lj
j
,
(3)
1
1
nzj
j
,
(4)
{0,1}, 1,...,z j n
j
,
(5)
As was mentioned before, it was assumed that all of the criteria (inputs and outputs) are equally
important for the decision and that the only negative deviation is permitted i.e. decreasing the input
criteria (
-
0, 0, {1,2,3}, 1,...,d d i j n
ll
) and the positive deviation i.e. increasing output criteria
is (
-0, 0, {1,2}, 1,...,d d i j n
rr
).
After solving the presented mathematical model, only for efficient locations, the obtained values
are shown in Table 4 and Table 5.
< Table 4 The values of variables zj>
The real deviation from the obtained ideal values and results of the authors Stanojević, Makajić-
Nikolić, and Savić 45 are given in Table 5.
< Table 5 The values of deviations and objective function >
From the given tables Location 13 was chosen as the optimal location for the building of MW
incineration facility. Regarding total transportation time Location 13 is not the best (since it requires
more time than is calculated ideal value of 7,201 minutes). Even though Location 13 does not have
an ideal value for any of the other criteria observed, it still proved as the most efficient location,
given the reasons that the amount of MW (5,644.52 kg) which has to be transported to this location
is much larger than the quantity that the other locations require, but the transportation time (8,910
minutes) and pollution (0.24044) are considerably lesser than at the other locations, namely, they
are closer to the best values of these criteria. Safety (0.9457) and unemployment rate (0.2439) of
this location are characterized by a relatively small deviation from the best value, so the minimum
value of the objective function is equal to 0.807768.
Discussion
To reduce the risks that MW carries, developing countries, such as Serbia, must focus on solving
this problem as soon as possible. The previous practice of sterilization and shredding MW and its
disposal in a landfill or export abroad is a short-term solution. The consequences that may occur
due to possible adverse events during MWM can be dangerous not only for human health but also
for the entire ecosystem of the region. Therefore, the location, where it is possible and appropriate
to dispose and treat MW, should be considered through the integration of different elements that
meet environmental, social, economic, and technical criteria.
This paper takes into consideration the amount of waste that needs to be transported, the time of
transport, the current pollution of the location, the unemployment rate, and the safety of the location
of possible natural disasters and accidents. In the proposed methodology, the authors of the paper
analysed these criteria using the DEA method, and as the results, they have obtained seven efficient
locations for MW incineration facility on the case of Serbia. In the presented research, it was used a
goal programming model for further formulation and analysis to achieve an optimal location for the
incineration of MW. In the chosen scenario, the location was Location 13.
Bearing in mind that the limitation of the present research is related to the lack of adequate
database on the amount of MW generated by each health institution, the future directions of
research should include the promotion and creation of a single database of health facilities, their
capacity, and resources at their disposal, which would allow better management of the health
facilities, and would lead to an improvement of the process of MWM, as well as problems with
which every institution of this type meets. Another limitation regarded to the obtained location
itself, which is the result of the assumption that all of the criteria (inputs and outputs) are equally
important for the decision-makers. Namely, when it comes to the location of MW incineration, it
must be noted “that selected sites should be located away from sensitive land uses e.g. residential
areas, educational and health services, etc.” 52 This, consequently implies that the obtained location
has to be carefully qualitatively reviewed to avoid unnecessary possible increase in pollution. Also,
future research must consider different scenarios, with relation to different weights all of the criteria
(inputs and outputs) for a goal programming model which in that case can give different results.
Besides, cost-benefit analysis would show the long-term financial effects of such a decision.
Conclusion
The problem of MW and its disposal is growing rapidly throughout the world as a direct result of
fast urbanization and population growth, requiring specialized treatment and management. As is
mentioned before, poor MWM can potentially cause hazards such as exposed “health care workers,
waste handlers, patients and the community at large to infection, toxic effects and injuries” 7, as
well as risks of environmental pollution and degradation. Thus, the importance of MWM is
reflected in the reduction of all possible negative impacts of MW both on the people and the
environment.
This problem can be solved by the right investment in the incinerator facility at the adequate
location which will meet diverse multiple environmental, social, economic, and technical criteria to
adequately manage the final processing of MW, and provide proper MWRM, having in mind that “a
single large modern incinerator designed with emission control will help reduce pollution and such
a center could serve as an emission monitoring point for authorities” 53. This adequate location i.e.
optimal location can be obtained by developed methodology in this paper that is using the DEA
method and the goal programming.
Last but not least, as well as the authors Klemeš, Van Fan, Tan, and Jiang 27 we can conclude
that: “To work towards a safer and greener planet, every single step considering the complexity of
various issues becomes an imperative goal of humankind.”
Disclosure statement
All authors declare no conflicts of interest.
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18
FIGURES
Locations
Defining criteria for the
selection of efficient
locations
Data collection
DEA
Goal programming
Efficient locations
Optimal Location
Output
Unemployment
Safety
Input
Amount of waste
Transport
Pollution
Fig. 1 - The selection procedure for an efficient and optimal location.
19
TABLES
Table 1
Regions according to the number of cities, population, area, number of
cities/municipalities with more than 40,000 inhabitants and the number of health
facilities 45 – 48
Region
Vojvodina
Belgrade
Šumadija
and Western
Serbia
South and
Eastern
Serbia
Kosovo
and
Metohija
Number of
cities
8
1
10
9
1
Population
1,659,440
1,931,809
2,031,697
1,563,916
-
Area km2
21,614
3,234
26,493
26,248
10,910
Population
density per
1km2
89.40
513.10
76.70
59.60
-
Number of
cities/
municipalities
with more
than 40,000
inhabitants
13
17
14
12
-
Number of
health
institutions
92
54
101
93
-
20
Table 2
Efficiency locations 45
Location
Efficiency
Rank
Location 1
1
1
Location 2
0.9012
14
Location 3
0.9901
9
Location 4
0.917
13
Location 5
1
1
Location 6
1
1
Location 7
0.9832
10
Location 8
0.9804
11
Location 9
0.9945
8
Location 10
1
1
Location 11
0.9225
12
Location 12
1
1
Location 13
1
1
Location 14
1
1
21
Table 3
Values of inputs and outputs 45
Inputs
Outputs
Location
Amount
of waste
Transportation
time
Pollution
Unemployment
Safety
Location 1
5,017.73
9,291
0.805
0.1894
0.9792
Location 2
5,339.86
9,749
0.56333
0.1724
0.8939
Location 3
5,486.32
14,292
0.5975
0.3322
0.9459
Location 4
5,337.43
11,742
0.602
0.2126
0.9067
Location 5
5,713.94
7,201
0.24044
0.1534
0.9387
Location 6
5,358.02
7,274
0.42333
0.1994
0.9441
Location 7
5,468.85
9,260
0.3253
0.2634
0.8995
Location 8
5,597.55
9,723
0.6675
0.2768
1.0000
Location 9
5,316.27
9,829
0.43333
0.3006
0.8246
Location 10
5,671.17
9,001
0.2263
0.2094
0.9898
Location 11
5,401.67
7,720
0.8775
0.2241
0.8922
Location 12
5,392.39
13,514
0.26873
0.3687
0.9011
Location 13
5,644.52
8,910
0.24044
0.2439
0.9457
Location 14
5,195.40
7,636
0.6725
0.2829
0.9387
Table 4
The values of variables zj
Location
zj
Location 1
0
Location 5
0
Location 6
0
Location 10
0
Location 11
0
Location 13
1
Location 14
0
22
Table 5
The values of deviations and objective function
Location
Amount of
waste
Transport
time
Pollution
Unemployment
Safety
Deviation
626.79
1,709.00
0.01
-0.12
-0.04
Location 13
5,644.52
8,910.00
0.24
0.24
0.94
Ideal
5,017.73
7,201.00
0.23
0.36
0.98
Received on May 21, 2020.
Revised on July 6, 2020.
Accepted Jule 7, 2020.
Online First Jule, 2020.
