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A Cost Optimization Model for Hazardous Medical Waste Management in Portugal
João Maria de Souza Coutinho Nunes de Almeida
Dissertação para a obtenção do Grau de Mestre em
Engenharia Civil
Júri
Presidente: Prof. Augusto Martins Gomes
Orientadores: Profª Cristina Marta Castilho Pereira Santos Gomes
Prof. João Torres de Quinhones Levy
Vogal: Profª Ana Barbosa Póvoa
Maio 2010
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AKNOWLEDGEMENTS
This dissertation represents, not only the work done in order to write the following pages, but also
the conclusion of several years of study and the overcome of quite a few obstacles. It would not
have been possible to thoroughly complete this cycle with both the help of those who contributed to
the conclusion of this dissertation and of those whose support along this cycle was extremely
helpful.
Firstly I would like to thank my thesis coordinators: Prof. João Levy for helping me during the whole
process of developing this final project, and specially Profª Marta Gomes who apart from helping
and supporting the construction of this thesis, also gave me the opportunity to participate in new
challenges such as the IO2009 conference.
I would also like to thank Eng. Luis Cordovil, Engª Ana Pinela and Drª Sofia Sá for the promptness
with which they cleared my doubts and supplied the necessary data to go on with my work.
I express my appreciation to Prof. Alexandre Gonçalves for re-explaining the basics of cartography
and coordinates systems.
I am grateful to my friend and colleague Francisco Meneses for the tutorials given on how to work
with ArcGis and also for patiently clearing all my subsequent doubts on the use of that software.
As I said before this is the end of a long cycle which completion would not have been possible
without the support of my friends and colleagues Bernardo Guimarães, Pedro Sanches, António
Dominguez, Pedro Fino, Stefano Nigra, José Medeiros, Diogo Araújo, Mariana D’Orey, Teresa
Montalvão, Tomás Eiró and Miguel Ferreira.
In that perspective I would also like to thank my friend and colleague Inês Almeida for all the
course notes and summarized syllabus that helped me through the Engineering degree.
Finally I run short of words in expressing my gratitude to my family, for the unwavering support
along all these years and for the several opportunities given to expand both my academic and
personal horizons.
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RESUMO
A gestão de resíduos sólidos hospitalares é uma área muito particular da gestão de resíduos
sólidos pois este tipo de resíduos está sujeito a regras específicas referentes ao tratamento ou
eliminação dos mesmos. Segundo a legislação Portuguesa e Europeia, as operações relativas à
gestão de resíduos deverão ocorrer preferencialmente em território nacional de forma a reduzir os
movimentos transfronteiriços dos mesmos. Dado que a produção de resíduos hospitalares
perigosos (RHP) já ultrapassou a capacidade de incineração, existe uma necessidade urgente de
expandir a capacidade instalada. Em Portugal os RHP estão divididos em dois grupos, os que são
de incineração obrigatória e os que têm de ser descontaminados antes de poderem ser
transportados para aterros. As operadoras, licenciadas para tais actividades, trabalham com
ambos os grupos de RHP ao mesmo tempo, logo o sistema de gestão de RHP deverá ser tratado
como um só. Neste trabalho desenvolve-se uma ferramenta (modelo em programação linear
inteira mista – MILP) que forneça uma solução optimizada em termos de custos onde constem a
localização das diferentes infra-estruturas relacionadas com a gestão de RHP assim como a
determinação dos fluxos de resíduos entre diferentes nós. O objectivo desta ferramenta será
fornecer ao decisor, num período de tempo aceitável, uma solução optimizada em termos de
custo. Este modelo será aplicado a dois cenários. No primeiro não serão consideradas as infra-
estruturas existentes, sendo que as localizações de todos os tipos de infra-estrutura serão
variáveis do modelo. No segundo apenas serão variáveis do modelo a localização das
incineradoras, a localização de todos os outros tipos de infra-estrutura serão parâmetros do
modelo.
Palavras-chave: Programação linear inteira mista (MILP), Gestão de resíduos hospitalares perigosos, Modelos para a localização de infra-estruturas e Optimização de custos.
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ABSTRACT
The hazardous medical waste management (HMW) is a very particular field of solid waste
management as it requires following specific rules in order to correctly eliminate and treat the
hazardous waste. According to Portuguese and European legislation the waste management
operations should occur preferably in national territory, thus reducing inter-borders waste-flows.
This poses a problem as the Portuguese incineration capacity for HMW is lower than the actual
production; as a result there is an urgent need to expand such capacity. HMW in Portugal can be
divided into two groups, roughly those that have to be incinerated and those that need to be
decontaminated before being transported to landfills. The HMW companies work with both groups
at the same time; therefore the HMW management system should be treated as one whole system
instead of two separate ones. In this work a tool is proposed (Mixed Integer Linear Programming -
MILP - Model) which will optimize in terms of cost, both the location of the facilities related to HMW
management as well as the allocation of waste between the different nodes. The aim of this tool is
to present the decision maker, in a reasonable amount of time, the optimal solution to the problem.
This model will be applied to two different scenarios. The first one will consider none of the existing
infrastructure; the locations of all the facilities will be treated as model variables. The second one
will only locate the incinerator(s); all the other facilities’ location will be considered as model
parameters.
Keywords: Mixed Integer Linear Programming (MILP), Hazardous medical waste management, Facility location model and Cost optimization.
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INDEX
1. INTRODUCTION ....................................................................................................................1
2. MEDICAL WASTE ..................................................................................................................4
2.1 Definition ........................................................................................................................4
2.2 Requirements for handling and disposal of Group III and IV ............................................5
2.3 Producers .......................................................................................................................6
2.4 Medical waste management companies ..........................................................................7
2.4.1 AMBIMED ...............................................................................................................7
2.4.2 AMBITRAL ..............................................................................................................7
2.4.3 CANNON ................................................................................................................8
2.4.4 SUCH .....................................................................................................................8
2.4.5 TRATOSPITAL .......................................................................................................8
2.4.6 Location of the HMW management infra-structure in Portugal..................................8
2.5 Quantifying hazardous medical waste in Portugal............................................................9
2.5.1 Main aspects to be considered ................................................................................9
2.5.2 HMW production in Portugal for 2006 ......................................................................9
2.5.3 HMW production in Portugal for 2016 .................................................................... 13
2.5.4 Market value of HMW in 2016 ............................................................................... 16
3. THE MEDICAL WASTE MANAGEMENT PROBLEM ............................................................ 18
4. LITERATURE REVIEW ........................................................................................................ 23
4.1 Solid waste management models .................................................................................. 23
4.2 Facility location models ................................................................................................. 25
4.2.1 The different approaches to facility location models ............................................... 25
4.2.2 Static/Deterministic location models ...................................................................... 26
4.2.3 Dynamic location models....................................................................................... 28
4.2.4 Stochastic location models .................................................................................... 28
4.2.5 Hierarchical facility location models ....................................................................... 29
4.3 Facility location models applied to solid waste management ......................................... 30
4.3.1 General overview of the facility location models applied to SWM ........................... 30
4.3.2 The location-allocation models applied to solid waste management ....................... 32
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4.4 Conclusion .................................................................................................................... 36
5. MODEL FORMULATION ...................................................................................................... 37
5.1 Modeling a real world problem ...................................................................................... 37
5.2 Mathematical modeling ................................................................................................. 37
5.3 Constraints and considerations of the HMW management model .................................. 38
5.4 HMW management mathematical model ....................................................................... 42
6. DATA COLLECTION AND ESTIMATION ............................................................................. 47
6.1 Geographical distribution of the HMW producers in continental Portugal ....................... 47
6.2 HMW production amounts associated with each node ................................................... 48
6.3 Geographical distribution of the waste management facilities ........................................ 50
6.4 Cost data estimation ..................................................................................................... 52
6.4.1 Removal/Collection/Transportation costs ............................................................... 52
6.4.2 Operating and construction costs of facilities ......................................................... 54
6.4.3 Operating cost function of each facility .................................................................. 58
7. APPLICATION TO THE PORTUGUESE CASE STUDY ....................................................... 60
7.1 The chosen interface and commercial solver ................................................................. 60
7.2 Global optimization ....................................................................................................... 61
7.2.1 Results presentation ............................................................................................. 61
7.2.2 The effect of the technology choice ....................................................................... 66
7.2.3 Comparing the obtained solution against reality ..................................................... 68
7.3 Sensitivity analysis ........................................................................................................ 70
7.3.1 Transfer Station fixed cost ..................................................................................... 70
7.3.2 Treatment vs. Transportation cost ......................................................................... 73
7.4 Partial optimization ....................................................................................................... 76
7.4.1 Constraints and considerations of the partial optimization model............................ 76
7.4.2 Simplified model formulation.................................................................................. 78
7.4.3 Data generation .................................................................................................... 79
7.4.4 Analysing the results ............................................................................................. 79
7.5 Conclusion .................................................................................................................... 80
8. CONCLUSION AND FURTHER RESEARCH ....................................................................... 82
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8.1 A Summary of the work developed ................................................................................ 82
8.2 Contributions and results .............................................................................................. 84
8.3 Future developments .................................................................................................... 85
REFERENCES ............................................................................................................................ 87
APPENDIX I – PORTUGUESE MEDICAL WASTE CLASSIFICATION ......................................... 90
APPENDIX II – LINKAGE BETWEEN THE EWC AND THE PORTUGUESE MEDICAL WASTE
CLASSIFICATION ....................................................................................................................... 91
APPENDIX III - HMW PRODUCTION PER TYPE AND PER NODE ............................................. 92
APPENDIX IV - OPTIMIZED HMW FLOWS ................................................................................. 97
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TABLE INDEX
Table 1 – Quantity of HMW produced in 2006 .............................................................................. 10
Table 2 – HMW production by SNS Hospitals and PHC for 2006 .................................................. 10
Table 3 – HMW production by type of facility ................................................................................ 11
Table 4 – HMW production estimate for 2001 ............................................................................... 11
Table 5 – Estimate of the total medical waste production (ton/year) .............................................. 13
Table 6 – Lower and higher bound estimations for the production of HMW in 2016 ....................... 14
Table 7 – Production vs. treatment capacity ................................................................................. 14
Table 8 – Estimation of the HMW produced in 2016 (ton/year) ..................................................... 16
Table 9 – Consumer price index from 2003 to 2009 ...................................................................... 17
Table 10 – Coordinates of the facility sites’ nodes ........................................................................ 51
Table 11 – Calculated transportation and fixed costs .................................................................... 58
Table 12 – Summary of the model and solution characteristics ..................................................... 62
Table 13 – Location of the opened infra-structure ......................................................................... 62
Table 14 – Comparison between the locations chosen and the existing locations ......................... 68
Table 15 – Geographical distribution of T.S. when its fixed cost varies.......................................... 71
Table 16 – Geographical distribution of D.S. when T.S. fixed cost varies ...................................... 72
Table 17 – Geographical distribution of INC. when T.S. fixed cost varies ...................................... 73
Table 18 – Geographical distributions of T.S. for different Transportation/Treatment cost ratios .... 74
Table 19 – Geographical distributions of D.S. for different Transportation/Treatment cost ratios ... 75
Table 20 – Geographical distributions of INC. for different Transportation/Treatment cost ratio ..... 76
Table 21 – Group IV waste “produced” at the DS.......................................................................... 79
Table 22 – Amounts of Group IV waste eliminated by each incinerator ......................................... 80
Table 23 – Summary of the different models and solutions studied ............................................... 81
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FIGURE INDEX
Figure 1 – Location of the HMW management infra-structure in Portugal ........................................9
Figure 2 – Evolution of waste production in Portugal (2001-2006) ................................................. 15
Figure 3 – Waste collection cycle ................................................................................................. 18
Figure 4 – Process to solve a real world problem with a mathematical model (Figueiredo, 2007) .. 37
Figure 5 – Possible waste flows considered by the model ............................................................. 39
Figure 6 – Alternative flow paths .................................................................................................. 40
Figure 7 – Costs associated with PATH nº 1 ................................................................................. 40
Figure 8 – Waste flows for a two node (Incinerator/Disposal site) example ................................... 41
Figure 9 – Third and Fourth path represented in the real situation ................................................ 41
Figure 10 – Linear and Concave cost functions ............................................................................ 42
Figure 11 – Evolution of the Portuguese population 2016-2060 .................................................... 49
Figure 12 – Position of the Centroids and the District Capitals ...................................................... 51
Figure 13 – Piece-wise linear cost function considered ................................................................. 59
Figure 14 – Piece-wise linear cost functions of DS and INC .......................................................... 59
Figure 15 – Influence areas of the T.S. ......................................................................................... 64
Figure 16 – Influence areas of the Disposal Sites (Group III) ........................................................ 64
Figure 17 – Influence area of the incinerators ............................................................................... 66
Figure 18 – Waste flows between DS and INC ............................................................................. 80
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ACRONYM LIST
ARS - HEALTHCARE ADMINISTRATIVE REGION
CBA - COST BENEFIT ANALYSIS
CPI - COST PRICE INDEX
DGS - DIRECÇÃO-GERAL DA SAÚDE
DM - DECISION MAKER
DS - DISPOSAL SITE
EU - EUROPEAN UNION
EWC - EUROPEAN WASTE CATALOGUE
GA - GENETIC ALGORITHM
HMW - HAZARDOUS MEDICAL WASTE
INC - INCINERATOR
INE - INSTITUTO NACIONAL DE ESTATÍSTICA
LCA - LYFE-CYCLE ANALYSIS
LP - LINEAR PROGRAMMING
MCDA - MULTI-CRITERIA DECISION ANALYSIS
MILP - MIXED INTEGER LINEAR PROGRAMMING
PHC - PUBLIC HEALTHCARE CLINICS
SNS - NATIONAL HEALTHCARE SERVICE
SUCH - SERVIÇO DE UTILIZAÇÃO COMUM DOS HOSPITAIS
SWM - SOLID WASTE MANAGEMENT
TS - TRANSFER STATION
USW - URBAN SOLID WASTE
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1. INTRODUCTION
Waste management has been an important topic since the late 19th century. With the increase of
population and its migration to cities, it became necessary to establish infra-structures that would
remove the solid waste away from the city population. As the population kept growing and as
society shifted to high consumption habits, booming the production of solid waste, more people
started to be interested in understanding how one could process such amounts of waste. It was
only in 1874 that “the Destructor”, the first systematic refuse incinerator was presented (U.K.).
At the end of the 19th century people started to be concerned with the shortage of space to dispose
the huge amounts of waste produced, realizing that landfills were not an option for the disposal of
solid waste. In 1889, Washington D.C. reported that the country (U.S.A.) was running out of
appropriate places to dispose refuse. So it was not long ago, on the turning of the 20th century, that
waste management became a real problem for authorities.
With the growing environmental concerns of the population the tendency was, and still is, to
converge to a sustainable future where waste production is minimal and refuse is recycled as much
as possible. This interest in waste management led to research made in several fields, namely
operational research but also health and safety. The waste started to be segregated depending on
its origin (e.g. industrial waste, medical waste) but also its hazardousness to public health and the
environment. Special requirements in terms of handling and disposing, among others, were
associated to these different categories. Nonetheless it was only in 1990 that proper legislation
regarding the disposal of medical waste was issued in Portugal.
Refuse that results from human and animal healthcare activities can be hazardous to both human
health and to the environment. As a result there is the need of properly disposing such type of
waste in order to prevent contamination of human beings. Nowadays in Portugal, as well as in most
of the developed countries, hazardous medical waste storage, transportation and disposal is
regulated by strict legislation. This means that the destination and intermediate processes of
hazardous waste, between its production and its disposal, are clearly defined and quite controlled.
In the medical waste sector the disposal of such waste is the responsibility of the producers which
are the healthcare facilities, namely hospitals which account for the biggest share in production. In
Portugal around 75% of the total number of hospital beds are held by public hospitals consequently
the Portuguese government is the most affected by hazardous waste management fees, which in
the end are paid by the taxpayers. In order to focus the funding of healthcare services mostly in
activities related directly to healthcare, there is a need of having an efficient layout of the
hazardous medical waste management infra-structure. This will allow obtaining the most cost
effective system lowering the fees paid by the healthcare system to dispose medical waste.
The situation in Portugal, as it will be discussed further on, is clearly not cost effective. Portugal has
a total decontamination capacity which is almost twice the production of medical waste that has to
be processed that way. Still, there are companies which are presently expanding their
2
decontamination capacity. Assuming that, as in almost every type of industry, the processing cost
per unit falls with the increase of amount processed (scale economies), it is understandable that
the inefficiency seen in the medical waste management area is related to the fact that it is a recent
market which has not had the time to reach an equilibrium position. This resulted in a not so
competitive market where fees are higher than they should.
On the other hand the incineration capacity in Portugal has already been surpassed by the
production of mandatory incineration waste, which leads to the need of exporting the surplus
hazardous waste resulting in higher elimination costs. Also due to the actual legislation which
states that there should not be waste flows between countries in the EU and which points to
countries being auto-sufficient regarding waste disposal, it is easily perceptible the urgent need of
expanding such capacity.
So on the one hand Portugal has a lack of incineration capacity resulting in higher costs because of
the need to export waste, but on the other hand it has twice as much the necessary capacity in
decontamination treatments which leads to low capacity usage of the facilities and higher treatment
costs. The facilities involved in disposing hazardous medical waste are expensive to build, and it is
a regulated market as one must obtain a license to operate a waste treatment facility or to merely
transport hazardous medical waste. However it still is a free market, majorly driven by economic
incentives (demand-supply laws).
Since the current scenario seems quite unbalanced, it seems appropriate to focus on what could
be the optimized layout of the hazardous medical waste management market in Portugal. Such
study would contribute positively by presenting estimations of the savings that can be made when
reaching the optimal solution, but could also help companies, operating in this sector to redefine
their strategy in order to become more cost efficient and at the end charge lower fees. The ultimate
beneficiary of this reduction in treatment cost would be the final user, as he would be able to have
a cost structure of the healthcare services with a lower share on waste management meaning that
more money could be diverted into direct healthcare services.
It is understandable that the decision makers who issue such licences or strategically plan the
bearing of the hazardous medical waste system in Portugal have to consider an enormous set of
factors. However, since the economic factors drive the market, one can therefore say that cost is
among all other factors the most important one in a strategic point of view. Thus a helpful tool to
optimize such system should firstly regard cost optimization.
Even so this tool would also have to allow the introduction of other constraints, according to
parameters such as social, environmental and political, in order to take into account certain factors
that cannot be avoided. This flexibility in manipulating constraints would permit an interaction
between the user and the solutions proposed by such tool, but it would also give the user a
perception of the cost induced when manually adding or subtracting a constraint from the problem.
In this dissertation the objective will be to provide the tool described previously. This tool will be
presented as a Mixed Integer Linear Programming (MILP) model and the yielded solution will
3
contain the cost optimized location of the different types of infra-structure involved in the hazardous
medical waste management process, as well as the allocation of waste to the different facilities.
In the second chapter a further definition of medical waste, and specially the classification used in
Portugal, will be presented, as well as the special requirements in storage, handling and disposing
of such waste defined by law. Chapter two will also cover the identification of medical waste
producers, of the companies who manage hazardous medical waste and their existing infra-
structure. To conclude this chapter an estimation of what was the value of the medical waste
management market in 2006 and also a prediction of what will be its value in the year of 2016 will
be shown.
The third chapter consists of an extensive introduction to the medical waste management
problem, its main constraints, the possible perspectives one can pursue to reach a solution, and
the approach followed in this dissertation to solve the problem.
Chapter four is an extensive literature review concerning mainly mathematical modelling and its
application to solid waste management.
The fifth chapter will be dedicated to the presentation of the model formulation, with an objective
function and constraints.
The case study presented concerns the Portuguese continental territory and so the sixth chapter
regards the collection and estimation of the several sets of data required to run the mathematical
model.
The seventh chapter will focus on presenting the results, on comparing the optimized theoretical
scenario with the Portuguese reality and on discussing several aspects related to the interactive
use of the model and the effects of the parameters variability on the solution.
Finally chapter eight summarizes the work done, presents the contributions and results of this
dissertation and suggests future research that can be done in this area.
4
2. MEDICAL WASTE
2.1 Definition
Waste, in general, is defined, by the Compact Oxford English dictionary, as “unused and unwanted
material”. Waste can come in several forms - solid or liquid, from several sources - households,
industries, public services facilities, and can be hazardous, or not to human beings.
Medical waste has several definitions though it can be in a general way defined as waste produced
in healthcare facilities, e.g. hospitals, clinics and nurseries.
Whereas Urban Solid Waste (USW) is normally not hazardous a great part of the waste generated
in healthcare facilities can be considered as hazardous. Therefore there is a need to use a
classification system for waste produced in such facilities in order to have a more efficient storage,
transportation and disposal of the waste generated by activities such as medical procedures.
Medical waste in Portugal is legally defined by the Decreto-Lei nº 178/2006, 5th of September in
section z) of article nº3 as “the waste generated by medical procedures occurring in healthcare
facilities, activities of prevention, diagnosis, treatment, rehabilitation and research related to human
beings or animals, in pharmacies, in forensic medicine, in teaching and in any other invasive
procedure such as acupuncture, piercing and tattoos”.
The Portuguese law defines a classification system for medical waste composed by four
categories: Group I, II, III and IV. According to the Despacho nº242/96, 13th of August in article nº2,
the first two groups of waste are considered as non-hazardous waste while the last two are
considered hazardous waste.
The waste which is included in the first two groups is considered to be equivalent to USW,
therefore not needing any special requirements related to handling, storage, transport or disposal.
Group III includes waste associated with biological risk and Group IV includes hazardous waste in
general. These two last groups, due to their hazardous nature, have specific rules in matters of
handling, storage, transportation and disposal. The types of waste included in each group are
defined in Appendix I.
In terms of legislation, one of the objectives of the European Union (EU) is to create uniformity for
its members. For that reason the European Waste Catalogue (EWC) was created. It consists of a
six numbers code which refers to a specific type of waste. The first two numbers refer to the
chapter, being the 18th chapter the one related to waste generated in healthcare facilities for
humans, or animals, and research facilities. The EWC is a mandatory classification for all EU
members but it does not make reference to the elimination/treatment needs of the different types of
waste.
According to the benchmarking study in Levy, Cordovil, Pinela and Sá (2009), each European
country has its own legislation regarding medical waste. In all the studied cases, Spain, France,
Holland, Belgium, Italy, United Kingdom there is a common base, the EWC, which explains, in all
5
those countries, the separation defined by law between ordinary medical waste and Hazardous Medical Waste (HMW). It also explains the need of differentiated treatment for HMW. Another
important point is that the most common course of action for the HMW is incineration.
As it is said, it is possible to link the Portuguese medical waste classification and the 18th chapter of
the EWC. This linkage is presented on Appendix II.
In terms of disposal the distinction between Group III and IV waste and USW resides in the fact
that, Group III and Group IV refuse is subject to different rules in terms of storage, handling,
transport and elimination/treatment. These requirements are explained in the following sub-chapter.
2.2 Requirements for handling and disposal of Group III and IV
The Portuguese legislation is clear about the requirements to handle the Group III and IV waste. It
is not the purpose of this thesis to describe extensively those requirements and the laws abiding
those procedures. Though there is the need to understand the obligations and limitations regarding
storage, transport and disposal/elimination of HMW.
The Group III and IV waste must be stored in a different place from the waste belonging to Group I
and II. The storage area must have a minimum storage capacity equivalent to 3 days of production.
In case of a collection period longer than 3 days, the storage area must be equipped with
refrigeration system. The period between collections should never exceed 7 days.
Group III waste can be eliminated the same way as Group IV, or it can be subject to
decontamination, reducing its danger for human and animal health but also reducing the
associated environmental impact, and then disposed as USW. The technologies available to
decontaminate Group III waste are, according to Levy et al. (2009), Chemical disinfection,
Autoclave, Microwave and Ionization. For more information about these techniques, its advantages
and disadvantages please refer to Levy et al. (2009).
In the case of Group IV waste, elimination is the only legal procedure. In terms of technologies
available Levy et al. (2009) refers two examples: Incineration and Plasma Systems.
The transportation condition of hazardous medical waste is defined by the Portaria nº335/97 of the
18th of December. According to the legislation, HMW should be transported in adequate environmental conditions, in order to avoid its scattering or spillage. The transport of HMW
should also obey to the Regulamento Nacional do Transporte de Mercadorias Perigosas por
Estrada. According to Direcção Geral de Saúde (DGS) (APA, 2009), the adequate environmental conditions correspond to the use of trucks equipped with isothermal containers,
though in reality not all of the companies’ authorized to transport HMW use this type of vehicles. In
fact after a quick survey we concluded that some companies use regular small trucks for short
distance routes and isothermal equipped large trucks for long route which does not abide with the
regulations.
6
2.3 Producers
The producers of medical waste can be public institutions or private companies. The main types of
producers are:
- Hospitals;
- Maternities
- Public Healthcare Clinics (PHC) - Centros de Saúde e extensões;
- Private health clinics with or without admittance;
- Nurse clinics;
- Private practice medical offices (Consultórios);
- Dental clinics;
- Laboratories;
- Veterinaries;
- Other health care facilities (human and animal healthcare);
Since the approval of the Portaria nº187/97, from the 11th of March, producers are obliged to fill an
electronic form – SIRER – every year to report their waste production. Nevertheless, as it will be
shown further on, the accuracy of the data supplied by the producers, when filling these forms, is
very low resulting in untrustworthy results. The companies licensed to treat or eliminate HMW are
also compelled to make an annual inventory and to submit it to the DGS and the Agência
Portuguesa do Ambiente. Due to the fact that the service offered by these companies is waste
treatment/elimination, they need to accurately control the waste processed for charging purposes
which results in a more reliable set of figures, in terms of the amount of medical waste treated.
Two types of hospitals can be distinguished in Portugal, those belonging to the National Health Service – Serviço Nacional de Saúde (SNS), which are owned by the government but can be
managed by a private company, and those whose property and administration depend on a private
company.
In terms of Public Healthcare facilities, the SNS is divided into seven administrative regions
(ARS), Norte, Centro, Lisboa e Vale do Tejo, Alentejo, Algarve, Região Autónoma dos Açores and
Região Autónoma da Madeira. The first five are located in the European continent whilst the other
two are archipelagos.
In the continental part of Portugal most of the hospitals (63% - 2005, Tavares, Espada, Pité-
Madeira and Gonçalves,2007) are located in the regions north of the Lisbon region. The Algarve
and Alentejo ARS in 2005 accounted for only 6% of the hospitals (Tavares et. Al, 2007). According
to APA (2009) the number of SNS hospitals in 2006 was of 85 and the percentage of waste forms
delivered was 100%. Although the percentage of compliance, in filling the waste forms, was low in
the early years (45% - 2000) the tendency allowed to get a full compliance rate in the hospital
sector by 2006.
In terms of PHC the evolution seen, regarding the compliance filling waste forms, was similar to the
one presented for the SNS hospitals. According to APA (2009) the number of PHC in 2006 was
7
347 and the percentage of forms filled was 100%. In the PHC case the distribution of facilities in
Portugal is less heterogeneous. This is probably due to the fact that each municipality has to have
at least one PHC; therefore the distribution of these facilities is not only related to the population
distribution but also to the Portuguese administrative divisions.
The growing tendency on filling the waste forms in both the hospitals and PHC is probably due to a
bigger control among the competent authorities as well as better informed producers (about their
responsibilities).
In terms of HMW production per facility the more important producers are the ones described
above. Their weight in total production will be discussed further on. There are also other types of
facilities whose single production is not important but whose production as a group is relevant to
the total. Those producers are stated below:
State dependent laboratories and pharmaceutical warehouses;
Private healthcare facilities such as clinics with admittance, laboratories, mobile blood
collection facilities, facilities where radiation, ultrasounds or magnetic fields are used,
Dialysis facilities, other facilities where medical procedures occur;
Pharmacies;
Veterinary activities.
2.4 Medical waste management companies
In Portugal there are five licensed medical waste management companies:
1) AMBIMED – AMBIMED, Gestão Ambiental, Lda;
2) AMBITRAL – AMBITRAL, Transporte de Resíduos, Lda;
3) CANNON – Cannon Hygiene – Portugal, Lda;
4) SUCH – Serviço de Utilização Comum dos Hospitais ;
5) TRATOHOSPITAL – TRATOHOSPITAL, Tratamento de Resíduos Hospitalares, Lda.
2.4.1 AMBIMED
Ambimed has three operating units and one waiting for its operating licence. Of the already
operating units Ambimed has one transfer station for both Group III and IV waste in Estarreja and
two Autoclave facilities, Beja (5.321 ton/year) and Barreiro (15.650 ton/year). These two last units
also include a transfer station for Group IV waste. The Braga facility has not got its operating
licence yet but it is planned to hold an Autoclave facility with a capacity of treating 10 tons per day
of Group III waste and to serve as transfer station for Group IV.
2.4.2 AMBITRAL
Ambitral is the youngest of the Portuguese licensed medical waste managers. Its first and only
facility got its operating licence in 2006 and is located in the municipality of Aljezur. They have a
capacity of treating 2.200 tons per year of Group III waste by Autoclave. They can also use their
facility as a transfer station for Group IV waste.
8
2.4.3 CANNON
Cannon Hygiene Portugal is held by Cannon Hygiene Limited, a United Kingdom based company.
It has six licensed facilities; one of them is currently deactivated. Cannon is also waiting for the
operating licence of a seventh facility. On the active facilities, Cannon is licensed to treat by
chemicals Group III waste and store temporarily some of the Group IV waste (sharps and rejected
pharmaceutics). Those facilities are located in Portimão (21 ton/year), Setúbal (70 ton/year), Lisboa
(211 ton/year), Castelo Branco (17 ton/year), Gondomar (75 ton/year), Batalha (deactivated facility)
and Leiria (31 ton/year – waiting for the operating licence). The Group IV waste is transferred to
SUCH for incineration or exported to Belgium to be treated by a company called INDAVER.
2.4.4 SUCH
SUCH, is an organization held by hospitals, public healthcare clinics among others. It detains the
operating licence for the only incinerator authorized to incinerate Group III and IV waste in
Portugal. SUCH operates a transfer station for both Group III and IV waste in Pombal, an
Autoclave facilitiy in Vila Nova de Gaia (3.120 ton/year) and a HMW incinerator in Lisboa (2.000
ton/year). It is necessary to add that the Group III waste collected by this company is treated in its
facility in Vila Nova de Gaia or sent to an autoclave facility of Tratospital or Ambitral. The Group IV
waste is either incinerated in Lisbon or exported to Belgium (INDAVER). The Lisboa and Vila Nova
de Gaia facilities can store temporarily Group IV waste.
2.4.5 TRATOSPITAL
Tratospital is licensed to treat by autoclave Group III waste and temporarily store Group IV waste. It
possesses only one licensed facility in Cascais with capacity for treating 10.950 tons per year of
Group III waste. It treats the collected Group III waste in its facility and sends its collected Group IV
waste to be incinerated in SUCH.
2.4.6 Location of the HMW management infra-structure in Portugal
The geographical distribution of the infra-structure related to HMW management in Portugal can be
seen in figure 1.
Both the operating facilities, as well as the ones waiting for an operating license are shown in figure
1. From figure 1 it is noticeable the high number of Group III treatment units in Portugal. They are
located mostly next to the coastline, where the population is also more concentrated. The only
HMW incinerator in Portugal is located roughly in the middle area of the country. Another
interesting fact is the small number of Transfer Stations (TS) for both groups, only two locations
are purely TS and not TS associated with other facilities. TS are locations where waste is stored
temporarily and subsequently transported to the incinerators or Group III waste treatment facilities.
9
Figure 1 – Location of the HMW management infra-structure in Portugal
2.5 Quantifying hazardous medical waste in Portugal
2.5.1 Main aspects to be considered
The information relative to this subchapter can be extracted from several sources. For example the
statistics from the Instituto Nacional de Estatistica (INE), the annual reports from the DGS, the
database of the Agência Portuguesa do Ambiente and other publications that resort to the data of
these three organs and compile it for other purposes, e.g. Levy, Teles, Madeira and Pinela (2002),
Tavares et. al (2007) and APA (2009).
The data concerning HMW production in Portugal will be taken mainly from the already quoted
report: APA (2009), as it is the most recent study available. However several other sources will be
consulted in order to check for more reliable information.
There are three main aspects which this quantification must approach: (1) the amount of HMW
produced, (2) the production distribution by geographical location and/or type of facility, and (3)
how much does it cost to dispose HMW (the medical waste market in Portugal).
HMW production in Portugal will be analysed for two distinct periods. Firstly for the year of 2006,
which is the most recent data set found, and secondly for the year of 2016, which is the farthest
prediction found in the literature.
2.5.2 HMW production in Portugal for 2006
As it was said in 2.3, there is an obligation, since 1997, for the producers and companies treating
or eliminating HMW to provide annual inventories of the waste produced, treated and eliminated to
10
the competent authorities. The compliance rate of the producers in filling these forms was very low
at the beginning (1997) and has been increasing in the past few years. However estimates from
different sources, seen in the literature, on the amount of HMW produced in the past years point
out to different results.
The most recent data available on HMW production in Portugal is presented by APA (2009) for the
year of 2006. In table 1, it can be seen the sum of all quantities stated in the mandatory waste
inventories for HMW, first in the producers perspective and then in the companies perspective.
Table 1 – Quantity of HMW produced in 2006
Group Quantity (ton)
Producers Companies
Group III 56.261 21.325
Group IV 7.298 1.646
Total 63.559 22.971
Source: (A.P.A., 2009)
A sharp difference between the two amounts can be observed. According to APA (2009) this
difference can be explained by units errors made while filling the electronic form at SIRER, by
information duplication or by erroneous EWC codes. The accuracy of this data can also be
questionable due to the fact that not all the producers filled the forms or use the correct means to
dispose their HMW.
However, the official amount of HMW produced in Portugal, meaning the amount of HMW that is
declared and goes through the specific disposal cycles defined by the legislation, is represented by
the figures resulting of the inventories supplied by the waste management companies. This data
can be considered reliable since these companies have to bill their clients and therefore have to be
precise in measuring the amounts processed. For that reason the numbers presented by the waste
management companies are the most reliable source of data in terms of the HMW produced in
Portugal.
The HMW production of the SNS hospitals and PHC is available in Tavares et al. (2007) for the
period of 2000-2005 and in SIRER for 2006. The amounts produced in 2006 are presented in table
2.
Table 2 – HMW production by SNS Hospitals and PHC for 2006
Group
2006 (ton)
SNS Hospitals P.H.C.
Group III 12.097 637
Group IV 1.335 55
Total 13.432 692
Source: (A.P.A., 2009)
There are more hospitals in Portugal than those belonging to the SNS. Consequently to understand
the weight of hospital in the HMW production there is the need to take into account the non SNS
11
hospital production. As no information was available APA (2009) estimated the total production of
HMW by hospitals, assuming that the production of HMW in each hospital is only dependant of its
number of beds. Seen that the ratio of SNS hospital beds over the total number of hospital beds
was 75% in 2007, it was possible to estimate the total hospital production of HMW for 2006 –
Group III: 16.089 t and Group IV: 1.775 t.
With the estimations above it is possible to present the distribution of HMW production by Hospitals
and PHC (table 3).
Table 3 – HMW production by type of facility
Group
2006
Companies (t) Hospitals P.H.C.
(ton) (%) (ton) (%)
Group III 21.325 16.089 75% 637 3%
Group IV 1.646 1.775 108% 55 3%
Total 22.971 17.864 78% 692 3%
Total (%) 81%
Table 3 shows incongruence in the estimated amount of Group IV waste produced by hospitals.
The estimated value is higher than the amount stated by the waste management companies. This
error can be explained by three factors. The first is the possibility that not all the hospitals
separated and declared their Group IV waste. The second is the fact that non-SNS hospitals might
have different Group IV waste production rates from the ones of the SNS hospitals.
Finally the third factor is related to the fact that the estimation of HMW production by hospitals and
PHC is taken from the producers data set, presented in table 1, which was assumed as containing
input errors and is subsequently compared to the companies’ data set. However, in terms of SNS
hospitals and PHC the production amounts of HMW supplied by SIRER – inventories made by the
producers - for 2006 are consistent with data from at least the three previous years.
A comparison with other studies would be relevant, in order to try to validate the distribution of
waste production by facility type. The problem is that the information available is fragmented and
so it would be difficult to compare the previous results with other information in a timely fashion.
Nevertheless, Levy et al. (2002) estimate the total production of HMW for the year of 2001 as it can
be seen in table 4.
Table 4 – HMW production estimate for 2001
Group Year Total Production estimative (ton)
SNS hospital production
(ton) Ratio
Group III
2001
20.741 13.639 (a) 66%
Group IV 2.269 2.942 (a) 130%
Total 23.010 16.581 72%
Source: (Levy, Teles, Madeira, & Pinela, 2002), (a) (A.P.A., 2009)
12
When comparing the Group IV waste produced in hospitals (APA, 2009) and the total production
(Levy et al., 2002) the same incongruence is observable. At this point what seems to be more
probable is having different Group IV production rates for the two types of hospitals, still one cannot
confirm this hypothesis. Another important aspect that can be observed is the high weight of
hospitals in the total HMW production.
As it can be seen, in table 1, there is clearly a difference between the amount of HMW treated and
the amount of HMW produced. If the estimates for hospitals and PHC are considered reliable it can
be stated that hospitals and PHC represent approximately 80% of the total HMW production that is
declared in Portugal. This leaves a 20% margin that is supposed to account for the production of
facilities such as dental clinics, laboratories and continuous healthcare facilities among others.
Such margin does not seem an appropriate representation of the production of HMW by facilities
other than hospitals and PHC. There are still a lot of medical activities that do not report their HMW
production to the competent authorities, or that do not do a correct triage of its medical waste. Still
the main healthcare facilities, such as Hospitals and PHC, by the services they supply should
account for a big share of the total HMW production.
The amount of HMW reported to SIRER for sectors other than hospitals and PHC such as nurse’s
activity, dental clinics, analysis laboratories and veterinary activities are very low and are not
representative of their sector’s production (APA, 2009).
This leads to two important issues; firstly there is a need to increase the supervision on HMW
producers in order to make sure the HMW is conveniently separated from the other sources;
secondly there is a need of obtaining better estimations of the amount of HMW that is actually
produce taking into account the “illegal” producers.
The APA (2009) publication also refers the treatment costs for the different types of medical waste.
These costs include the activities of triage, removal, transportation, treatment and the disposal site
fee. The values are:
Groups I and II: 0,06 €/kg;
Group III: 0,4 to 0,6 €/kg;
Group IV: 0,8 to 1,20 €/kg.
With these costs and the estimates for the medical waste produced for 2006 (97.080 tons for
Groups I and II, values in table 1 for HMW) they assess that the market value for medical waste
treatment in 2006 is approximately of 19 million of Euros (13 million of Euros for HMW).
In Levy et al. (2002) the authors study the waste treatment market in Portugal concluding that the
medical waste market value for 2001 was around 60 millions of Euros. The big differences in these
values and the rather illogical tendency of a decreasing market value are most probably explained
by the reduction in treatment fees as the equipments become less expensive. In table 8 it is
noticeable that the evolution of medical waste production along the past few years is rather
unstable. Between 2001 and 2006 a distribution with alternate high peaks, around 120.000 tons
(exception is 2004) and low peaks, around 100.000 tons is observed.
13
Table 5 – Estimate of the total medical waste production (ton/year)
Year 2001 2002 2003 2004 2005 2006
Group I + II 93.106 76.739 88.868 131.472 69.686 97.080
Group III 23.215 19.642 18.665 20.644 19.432 20.741
Group IV 5.007 3.411 2.458 2.557 2.301 2.269
Total (tons) 121.328 99.791 109.991 154.673 91.420 120.090
Source: (A.P.A., 2009)
For this work the data presented before has the purpose of giving the reader some framing of the
Portuguese situation in terms of the medical waste production, its distribution by facility types and
the market value. It is not the scope of this dissertation to assess the production of HMW in
Portugal. However such data is very important in order to apply the intended model.
In short the objective here is to present a model that optimizes the flows of medical waste and the
location of the different types of infrastructure. Therefore, even if some of the data presents
inconsistencies, those are acceptable to the level of detail needed.
Moreover, as the objective is to present an optimized scenario for the future it will be necessary to
estimate data for future periods which will add possible variability to the estimation factors.
The Portuguese strategic plan for medical waste refers to the period 2009 to 2016 – APA (2009). In
order to maintain the data variability as low as possible, the production data presented will be their
estimation for the 2016 HMW production in Portugal
2.5.3 HMW production in Portugal for 2016
To estimate the HMW production for 2016 the data was again taken from APA (2009).
As the production amounts for the last couple of years had a high variability, suggesting some
biased data, there is a need to supply lower and higher bound estimations.
For the lower bound estimation APA (2009) used the values presented before (medical waste
produced in 2006) and considered that the medical waste production would increase at the same
rate as the population. Considering the estimation for the population, in 2016, it was possible to
obtain a set of figures concerning HMW produced in that year (table 6).
For the higher bound estimation, APA (2009), in a short description separated the producer into
different sectors and chose a variable that would describe the amount of work done by each type of
facility, e.g. the number of beds for Hospital, the number of medical appointments for PHC and the
number of students for schools. With the available data the production per variable was calculated.
Assuming the production per unit (variable) would not change and with the estimations of the total
number for each variable in 2016, it was possible to obtain the total amount of medical waste
produced in 2016 (table 6).
Finally to cross over all the relevant information it is compared in table 7 the estimated production
for 2016 and the expected treatment capacity in Portugal for the same year. It is necessary to add
that according to EU legislation but also to Portuguese legislation (Decreto-Lei nº 178/2006, 5th of
14
September) the waste management operation should occur preferably in national territory, thus
reducing the inter-borders waste flow.
Table 6 – Lower and higher bound estimations for the production of HMW in 2016
Group 2016 (ton)
Lower bound Higher bound
Group III 20.955 28.962
Group IV 2.356 5.205
Total 23.311 34.167
Source: (A.P.A., 2009)
Table 7 shows that, on the one hand the treatment capacity of Group III waste is enough to deal
with the higher bound and still have an excess of 12.000 ton/year. On the other hand, even in the
more optimistic scenario, the treatment capacity for Group IV will not be able to process all the
waste produced resulting in a deficit of 350 ton/year.
Table 7 – Production vs. treatment capacity
Group III (ton/year) Group IV (ton/year)
Lower bound Higher bound Lower bound Higher bound
Treatment Capacity 41.316 2.000
Estimated production for 2016 20.955 28.962 2.356 5.205
Differential 20.361 12.354 -356 -3.205
Source: (A.P.A., 2009)
The Group IV treatment deficit poses a problem as the legislation cited above states that the
optimal situation is attained when all the waste produced in national territory does not cross
borders for treatment/elimination. As a result there is a need to increase the treatment capacity of
Group IV waste in Portugal by 2016. So the possibilities of building a new incinerator, or expanding
the actual incinerator, are urgent measures that have to be taken in a short term.
In terms of the distribution of HMW production by type of facility, it is considered to be the same as
in 2006.
As it was seen in table 5 the total amount of medical waste produced per year is very variable and
does not represent a clear tendency. The evolutions of the amounts of medical waste produced in
each group are represented in figure 2.
It can be observed that the only waste Group which presents high variability and no clear tendency
is Group I + II which, for the period between 2001 and 2006, accounted on average for 80% of the
total medical waste production. Therefore this waste group is responsible for the oscillations seen
in the total values of table 5. This variability can be explained by the lack of special treatment
required by this type of waste; it can be treated as USW with almost insignificant treatment costs
when compared to HMW. This leads to poorer information on the production amounts. The 55%
decrease in Group IV waste production can be explained by a better triage of waste at the origin. In
Levy et al. (2002) the cost of eliminating Group IV waste in 2001 was equal to 60% of Group III
treatment cost, therefore producers were not stimulated to do a good triage of medical waste. In
15
2009 the estimated cost of eliminating Group IV waste was 200% of Group III waste treatment cost,
meaning that producers are now stimulated to do a better triage in order to spend less money in
waste management operations.
Figure 2 – Evolution of waste production in Portugal (2001-2006)
Of course the previous scenario assumes that the treatment costs estimation was accurate. If the
ratio between disposal cost of Group IV and disposal cost of Group III waste was always over the
unit, then the previous scenario is erroneous and the decreasing tendency of Group IV waste
production can be associated with a worst triage from the producers in order to avoid costs.
It is my belief that between 2002 and 2009 progress has been made in this area, in terms of the
producers sensitivity for these issues, and with the reduction of Group IV disposal costs (average
cost per kg in 2002, 1,2€, in 2009, 1,0€) there are more concerns among the producers to do a
better triage.
In terms of HMW production the expected tendency is to have a stable production which will have a
low growth rate. The factors that are relevant to explain the future amount of HMW produced are:
1) The growing environmental concern among the population, which will yield in a better
usage of resources therefore contributing for lower productions of waste;
2) The population growth, which is directly related to the amount of waste produced;
3) The healthcare needs of the population. The less healthcare the population needs, the less
HMW will be produced;
4) The control over HMW producers, to dispose the waste with the correct procedures.
Apart from the population growth it is difficult to predict the evolution of the other three factors and
its real influence in the HMW production. Assuming that the population concern is not very influent
in the HMW production, that the population maintains its needs to healthcare treatments and that
the control over HMW producers is reinforced, it is likely to have a steady growth of the HMW in
Portugal until all the producers comply with declaring their HMW production. After having attained
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
2001 2002 2003 2004 2005 2006
% o
f pro
duct
ion
in 2
001
Years
Group I + II
Group III
Group IV
16
that mark it is not expectable to have a growth on HMW production since the population
estimations for the future point to stagnation in growth, leading to stagnation in HMW production.
To take into account these several factors, the first step will be to estimate the HMW production of
hospitals and PHC, which are the biggest producer of HMW, for 2016, using the population
estimates.
Table 8 – Estimation of the HMW produced in 2016 (ton/year)
Years 2009 2016 Cesur estimates
Hospitals + PHC Hospitals + PHC Total Production Lower Bound Upper Bound
Population 10.599.095 10.708.332 Group III (t) 16.726 16.898 25.998 20.955 28.962
Group IV (t) 1.830 1.849 2.844 2.356 5.205
Total (t) 18.556 18.747 28.842 23.311 34.167
It is a general belief that the amount of undeclared HMW in Portugal is approximately 10% to 20%
of the total amount produced. Considering that the reinforced control over producers will force the
100% compliance rate to declare HMW, lowering the weight of hospitals and PHC from 80% to
66% of the total amount produced. Assuming that the proportion of Group III and IV waste
production stays unaltered, the total amounts of HMW produced in 2016 estimated will be as
shown in table 8.
It is necessary to add that, even if the hospitals and PHC constitute the most reliable source of
information, due to the high number of facilities and users, there are probably errors made during
the triage. Considering that 10% of the HMW produced in such facilities is misdirected from the
correct disposal category, which means that the 66% (hospitals + PHC declared production)
correspond to 9/10 of the actual production, and assuming that these misdirected 10% are included
in the undeclared amount of waste, by 2016 the average weight of HMW produced in hospitals and
PHC will be 73% of the total amount. It would be distributed as 71% for hospital 2% for PHC.
When comparing the values obtained in table 8 with the ones given by APA (2009) it is possible to
observe that both production values, for Group III and Group IV waste, are between the author’s
lower and upper bound, being close to the middle point between the two bounds.
2.5.4 Market value of HMW in 2016
The Consumer Price Index (CPI) ratio for a 12 month period, according to the Bank of Portugal, is
presented in table 9.
Admitting that the CPI for the next few years will be on average a little bit lower than the average
value from 2003 to 2009 – an average value of 2.0% will be considered instead of the average
value of 2.4% seen in the past 7 years – and assuming the prices will not change drastically
because of technology improvements (as they did in the past) but will rise accordingly to the CPI,
the estimated average cost of disposing Group III and Group IV waste in 2016 will be
approximately of 0,6 €/Kg and 1,2 €/Kg respectively. These values represent a total HMW market
17
value between 15,4 and 23,6 million of Euros per year, considering the lower and upper bound
productions or a market value of 19 million of Euros for this disertation production estimates.
Table 9 – Consumer price index from 2003 to 2009
C.P.I. for 12 months
period (%) C.P.I. relatively to
Jan-02 (%)
Jan-03 4 4,000
Jan-04 2,3 6,392
Jan-05 2 8,520
Jan-06 2,7 11,450
Jan-07 2,6 14,348
Jan-08 2,9 17,664
Jan-09 0,2 17,899
Source: Banco de Portugal
The market value of this sector is one justification among others to the need of a careful planning of
the infra-structure used to manage HMW.
18
3. THE MEDICAL WASTE MANAGEMENT PROBLEM
In the medical waste area there are several active shareholders who have different objectives and
concerns. Many problems arise with the production of medical waste, such as: the environment
concerned person who wants to find a solution to reduce the medical waste production at its
source, the health professional who wants to understand what is the cleanest treatment solution for
HMW or the public authorities who want to plan an efficient waste management system.
In the case of this dissertation, the problem being looked at is the optimization of the HMW
management system. As it was shown in the previous chapter the HMW sector is a much regulated
area in terms of legislation. Therefore there are few choices to be made in terms of planning
regarding the layout of the system.
Medical waste is produced in the facilities described in a previous chapter, where it is separated
into four different categories and put into different containers accordingly. The last two categories,
known as Groups III and IV, are considered HMW. As a result, they need to be processed in a
specific way in order to be disposed of. For Group III this is previous decontamination and for
Group IV incineration.
The HMW management system can be characterized by a first level node, the producers, and a
sinking node, a processing facility, which varies according to the waste category and as its name
indicates, is the last considered node in the disposal waste cycle. For this to happen, waste must
be transported from a node to the other.
As the amounts of both types of waste produced are relatively low (when compared to USW), their
transportation costs are higher than for USW. In order to reduce these costs there is the possibility
of using a TS. This facility, a storage unit for HMW, is an intermediate node which concentrates
waste streams from different origins and later transports them together to the final node. This
procedure benefits from scale economies, which result is reflected on lower transportation costs,
generally due to the use of bigger capacity vehicles, between the TS and the sink nodes, than the
ones used to collect HMW from the generating nodes. Figure 3 shows the HMW management
system composed by three nodes and the two possible paths for the waste.
Figure 3 – Waste collection cycle
19
The amounts of HMW produced at each node makes the management system design a problem to
be treated in a small scale area. In the case of Portugal all continental territory should be included
but in the case of the U.S.A. treating this problem at a state level would probably be more
adequate.
The disposal of HMW has several costs associated, like transportation costs, storage costs at the
TS and processing costs at the final node, among others. The optimization of the HMW system in
terms of cost is something valuable for the operating companies as they can minimize resource
consumption. But it is also valuable for the public authorities as by optimizing costs the fees for
disposing the HMW can be kept at a low level for the public hospitals and also for the final user, the
taxpayer.
The difference between operating companies and public authorities is that if the former are
concerned only with minimizing costs to increase profits, the later besides being concerned with
costs have to take into account several other factors.
In the specific case of HMW the processing facilities are not socially or environmentally friendly. If
these two last factors were the only taken into account the optimal location for these facilities would
be in the most deserted place of the territory. The problem is that this would probably be the worst
solution in terms of costs as it would result in impracticable fees to the users. So, in order to find
the optimal solution a balance must be found between the different factors the Decision Maker
(DM) has to take into account.
As these are intricate decisions, this dissertation proposes a tool to help the DM’s process of
decision. There are two aspects to optimize in this problem: (1) how to optimize the routes of waste flow from the different production nodes to the different sinking nodes and (2) how to optimize the location and number of the different facilities in the system.
With various factors to be taken into account the DM faces a universe of solutions that can be
rather complex. It would be difficult, due to the number of variables in this problem to define the
entire layout in one go. So a Solid Waste Management (SWM) problem, and in particular the
HMW management problem should be viewed as a multi-stage decision process, where there is a
need to move back and forth between the results obtained by the tools that optimize the layout and
the DM.
When comparing an optimization model, where the presented solution is supposed to be the final
solution, to an interactive tool, it is clear that the second one will have more acceptance by the DM,
who most of the time holds a political position. The interaction not only gives the DM the
opportunity to participate in the construction of the system, thus motivating him but also provides
perspective to the DM, this meaning the DM will be more conscious on the consequences of minor
adjustments to the layout, which most of the times are due to political reasons.
The tool will be a mathematical model which will optimize, having cost as the objective, both the
location of the transfer stations and sinking nodes as well as the allocation of the different waste
flows. This tool should provide the DM support for a first analysis of possible locations, which
20
means that the result of the model will not be the precise optimal location of the different facilities
but an approximate zone in which the facility should be located. This approximation will point out to
a zone where the costs are near to minimal and will provide a small area where the facilities can be
placed according to other factors. The model will be flexible enough in order to allow the DM to
impose constraints which he finds necessary - e.g. number of facilities to be opened, capacity of
the facilities, and forcing a facility to be opened. The final solution will represent what could be the
most cost efficient solution for HMW management.
This strategic approach will have consequences to the model formulation since it will not consider
certain operational and micro-management factors, such as the availability of vehicles and
crews or even the optimal routing. With the large area being covered by the model, the whole
continental part of the Portugal, considering such factors would make the optimization rather heavy
and would not serve the main objective: interaction with the DM.
Though the rules for HMW management change from country to country, the basic concepts, such
as a hierarchical facility scheme with few levels and few final disposing possibilities for HMW are
quite common in countries where there is legislation concerning HMW disposal. Therefore the
purpose of this dissertation is to develop an optimization model that focuses in those basic
concepts. However to develop such model and present results it is necessary to apply it to a
particular case. The model will focus on the specifics of the Portuguese reality.
In Portugal, as it was seen before, the disposal services and its auxiliary tasks are supplied only by
private companies who already possess different market shares and a portfolio of clients. One of
the possible perspectives would be to model this system considering the interactions between
those companies and their weight on the market. This perspective is one of two separate types of
optimization perspectives that can be accomplished.
This first approach would be equivalent to optimize in a short to medium term perspective. The
resulting solution would be obtained by optimizing only the available variables, which can be
considered as optimizing the system partially. It was mentioned before the need to expand the
HMW incineration capacity in Portugal. A partial optimization would only focus on locating the
incinerators not contemplating a possible change in the already existing infra-structure, therefore
not considering possible changes in the existing layout. The results taken from this optimization
would represent the best scenario in terms of costs for a near future situation.
However the HMW management system is composed of expensive facilities and it is a complex
system. So one should try to understand what could be, in a long term perspective, the highest
degree of efficiency that this system would reach. The second perspective considers this long term
optimization. In this case the objective is to attain global optimality, meaning that the objective is to
have the optimal layout for the entire system. By considering all possible locations as variables the
optimized solution given by the model will represent the best solution possible (more efficient),
which most certainly will be attained in a farther future when the system layout converges into the
global optimized scenario. This would result, at the end, in a more economical solution.
21
Change comes with a cost and it is the market competitiveness which will dictate how fast a cost
efficient system will be attained. So in a short term one is expected to observe the partial optimization results but in a long term and in a free market one should expect to attain the global
optimization layout.
The main scope of this work is to present a global optimization application to the Portuguese HMW
management system, which will be the tendency followed by the HMW market when trying to be
more cost effective.
As it will be shown further on when analyzing the results of the proposed model, the Portuguese
HMW system is poorly based on TS which are inexpensive facilities that can provide transportation
cost economies. In Portugal it was only in 1990 that the legislation started differentiating HMW from
the other types of waste, stating that this type of waste had to be incinerated. Due to that fact small
capacity incinerators started to be installed in several hospitals. The medical waste classification
into four groups only appeared in 1996, allowing alternative types of treatment for Group III waste –
other than incineration. From 1996 on, several private held companies were created working in this
new HMW alternative treatments market. Due to the poor environmental conditions the hospitals
incinerators had, from 1999 on most of those units were closed to the extent of having only one
HMW incinerator operating in Lisbon.
The hospitals which, as seen before, account for most of the production, were now faced with the
need of transporting the Group IV waste produced to the Lisbon incinerator instead of treating that
waste themselves. The amounts produced by each facility are quite small and the fact that that it
cannot be stored, in a worst case scenario more than 7 days, poses a problem mainly to the
hospital units and creates a new market for the Group III waste treatment companies.
The fact that those companies already had to go collect Group III waste periodically at the hospitals
gave them a very competitive advantage for this new Group IV waste transportation market. These
companies adaptation to these changes can be resumed to the construction of TS in their already
existing disposal sites so that they can concentrate Group IV waste and then transport slightly
higher amounts in each trip to Lisbon at lower costs.
This leads to a current scenario where the HMW system is far from being efficient, and two main
issues concerning that efficiency arise.
The first one is the oversize of Group III waste treatment facilities which led to having twice the
necessary treatment capacity installed when the production for the coming years is expected to be
stable. The size of the facilities, on average each one has the capacity of treating approximately
26% of the annual Group III waste production, would suggest a layout mostly concentrated on a
few waste treatment facilities and mostly based on a high number of “pure” TS – sites used only as
TS. But reality indicated the opposite. There are a lot of these treatment facilities and only two
“pure” TS. This means that to increase the efficiency of the system there are two possible
outcomes for this market. In the first one, companies understand that they can be more competitive
by downsizing facilities which will lead to a decrease in treatment cost per unit of waste. In the
22
second one some of the companies, which have lower market shares and cannot increase them,
will be going bankrupt and the companies that have high market shares will try to concentrate the
treatment in a few of their facilities by basing the waste transportation system mostly in TS. The
final outcome depends on the impact of transportation cost on the overall costs. If transportation
costs impact is high then the first outcome will be more probable, otherwise the second outcome is
expected.
These two outcomes will also have an effect on the Group IV waste market whose transport is
closely linked to the Group III waste. If the first outcome is reached then a small number of
incinerators (possibly more than one) will be opened. In case the second outcome is reached then
the incinerators location will converge into a more concentrated layout.
The second issue is the incineration capacity expansion. This issue is easily optimized by using the
partial optimization model. But as it could be seen in the previous paragraph the markets for
managing both groups of HMW are closely linked. So if a global optimization approach is taken, it
will be possible to solve these two main issues at once.
In conclusion in this dissertation the work will be mainly focused on presenting a global optimization (long term) model for HMW management considering only the cost point of view,
which is possibly the most important decision factor.
In an analogy to the reasoning made by Antunes, Teixeira, & Coutinho (2008), if a HMW incinerator
is set in an industrial site of appropriate size, then its main environmental impact will be related to
the transportation of solid waste as the surrounding facilities will also be heavy polluters, and the
impact of transportation is directly linked to its cost.
Since the Portuguese HMW market is a free market, this model would be equivalent to supplying
the DM a tool to set up the system layout from scratch, in a place where no previous facilities
existed. The outcome of the model will present the optimized scenario which will be attained in a
far future, when the market reaches its equilibrium point. The option of considering costs as the
only optimizing factor resides also in the will of presenting a tool that could quickly present an
accurate estimation of the HMW system layout and its costs.
23
4. LITERATURE REVIEW
This chapter will first give a general idea of the models used in SWM problems depending on their
objectives. Afterwards it will focus on cost benefit analysis models and how they are structured.
Concepts like Static/Dynamic models and Deterministic/Stochastic models will be approached.
In this second part an introduction to the concept of facility hierarchy will also be put together.
Finally it will converge into the application of Facility Location models to SWM specially the
Location-Allocation models, which are of most interest for this dissertation.
4.1 Solid waste management models
“A model is a representation of an object, system or idea in some form, other than that of reality
itself” (Qureshi, Harrison and Wegener in Morrissey and Browne (2004), p. 1). So the purpose of
building a model is to reproduce, understand or predict the behavior of a particular system when
confronted to different conditions or restrictions.
In the SWM field several types of models have been developed in the past years. The purposes of
such models have influenced the way they are solved and their final objectives. In the beginning
(early 60s) simpler models were produced with the objective of optimizing only one aspect of the
system, e.g. the optimal collection route, the sitting of landfills, the determination of waste flows. In
these earlier models there was no concern with social and environmental aspects nor with the
negative impacts on the population and the pollution produced by the chosen technology.
As the computational capacity grew so did the complexity of the models produced. However the
accessibility to more powerful computers was not the most important reason for this increase in the
models complexity. The raising concerns about the environment and the possibility to adopt new
cleaner and more sustainable technologies for waste disposal were the main reasons that led to
the adoption of more complex models. The DMs, who once had only the possibility of choosing
between landfills and incinerators and did so based only in the pure economical cost, are now
faced with numerous possibilities, ranging from recycling, only one type of waste or all the waste,
composting, etc. Also the decision criterion is no longer the economical cost but the real cost which
includes environmental and social costs.
In terms of model formulation the perspective changed from optimizing to compromising models. In
these last models the objective is to analyze the system in a way where several factors are taken
into account, such as the impact of the pollutants emission in a specific population and the
sustainability of a specific technology over another. Morrissey and Browne (2004), divide the waste
management models in three categories, (1) Cost Benefit Analysis (CBA), (2) Life Cycle Assessment (LCA), (3) Multi Criteria Decision Analysis (MCDA). What distinguishes the use of
each one of these three categories is the decision making criterion of the model.
In CBA the model tries to convert every single aspect to a common scale, such as the monetary
scale, in order to globally optimize the solution. This model can be rather unsatisfactory in cases
where a lot of environmental and social factors have to be considered, due to the fact that they
24
have to be converted into money. Furthermore this type of model optimizes only one perspective,
which means that in cases where there is a group of DMs, e.g. regional council, the unanimity will
be hard to attain. On the other hand in rather non-complex models where there are few decision
variables and few decision makers this type of models can be of great help as they provide rather
accurate model formulations.
The LCA is a type of approach that in the beginning was used to calculate the environmental
impact of a material and to compare between different types of materials in a production set. But a
more holistic use of the method made it become useful in SWM. These types of models determine
the path to be undertaken by a type of waste by evaluating the environmental costs it incurs in the
different waste processing facilities and selecting the least expensive as the solution. Its application
is rather in an environmental perspective and is limited to the “environmental” optimization of the
system. As environmental impacts are hard to convert to a monetary scale these models are to be
used more as tool providing information to the DM rather than as a model giving an optimal
solution.
The MCDA are the more complete models in cases where a high level of complexity is presented.
In these types of models the solution reached is not the optimization of one factor but the reach of
a compromise between different factors. This type of models takes into account several
perspectives trying to get the solution or set of solutions that better adapts to the different decision
makers profile. In case of very complex systems, as the urban waste systems of today where
numerous possibilities are presented regarding waste treatment, a conversion to monetary scale
would not be enough to solve the problem because the different stakeholders evaluate differently
the several options available. So a compromise has to be found and a fair solution has to be
attained, which is clearly covered by MCDA models. The notion of compromise and fairness in the
solution is presented by Erkut, Karagiannidis, Perkoulidis and Tjandra (2008); the authors present
a MILP approach with multi-objectives to solve a waste management problem in central
Macedonia. As a result they obtain a fair location for transfer-stations in the different administrative
regions.
In conclusion it all depends on the type of problem being considered. In this dissertation specific
case the reality is pretty simple. When considering the Group III and Group IV waste, a limited set
of destinations are possible, Chemical Disinfection or Autoclave, for Group III and Incineration for
Group IV. Moreover the problem being treated here can be described as follows. There are already
existing generating sources, which are the ones described in the first chapter, from these
generating sources the waste can be transported directly to the disposal destination or it can pass
through an intermediate facility, the transfer station.
In this specific case the objective is to supply the DM with a tool which will optimize the system only
in a cost point of view. Any environmental and social costs associated to the treatment facilities
location, if they were to be accounted, can be introduced in the model as penalties associated with
the locations. Consequently the model to be considered should be a CBA, where the only objective
to be optimized is cost.
25
This decision to use an approach depending only in one perspective is due to the already
explained fact that cost is the most important factor when determining what would be the optimal
layout of the HMW management system. That is the areas where facilities should be built and the
distribution of waste streams.
Although out of the scope of this work and as a small note, it was observed that all the models
described in the reviewed literature consider the waste management problem from its collection to
its disposal and so they do not include measures to prevent or control its production. That seems
logical as the production itself is sometimes difficult to predict and so the inclusion, for instance, of
waste taxes would lead to a new production scenario which would be even more difficult to predict.
Nevertheless the consequences of generating big amounts of waste are damaging to the
environment, thus prevention policies should be considered in the complex USW management
models.
The problem to be solved in this dissertation has been largely studied and can be labeled as the facility location problem. In this type of problems the location of facilities and the allocation of
goods (waste streams in this case) are the variables and the models are optimized following
different approaches depending on the case studied. In the literature the more common
approaches have “been directed to formulating new models and modifications to existing models
which have many potential applications” (Current, Daskin and Schilling, 2002, p.2). The lack of
application approaches in the literature can be explained, according to these authors by three
reasons: (1) Applications are not viewed “as scientific advances by the research community” (p.2),
(2) applications are often developed by consultants and planners who “are rarely motivated to
publish in research journals” (p.2) and (3) “Private sector advances in location modeling […] give
the firm a competitive advantage, consequently, they are not shared” (p.2).
Also the variability of constraints, variables and objectives makes each case a different application.
As a result it is quite hard to create a general model which would directly cover all kinds of
situation. Even so this type of problems has four components that are present in every case; these
are according to ReVelle and Eiselt (2005) “(1) customers, who are presumed to be already located
at points or on routes, (2) facilities that will be located, (3) a space in which customers and facilities
are located, and (4) a metric that indicates distances or times between customers and facilities”
(p.1). So in this work there is a hybrid objective consisting in formulating and adapting a model to
our reality but also to present a practical application of this model.
4.2 Facility location models
4.2.1 The different approaches to facility location models
The available literature on facility location problems is very extensive. First it is necessary to
distinguish between static/dynamic models or deterministic/stochastic models. The first group
refers to the time set of the model. Static problems consist in studying a case in a unique time
frame whereas the dynamic models consist in analyzing the model in several time frames. The
second group considers the input data. In the deterministic models the input data is considered to
26
be known, a set of determined constants, while the stochastic approach regards models where
the information relative to the inputs is not well known and easy to obtain and therefore has some
sort of probability associated.
In the available literature it is more common to have models where the dynamic approach is used
together with the stochastic, rather than the deterministic approach, since the input information is
in most cases difficult to predict during the course of time and so it is better to associate probability
to those values (Current et al., 2002). The deterministic approach is more commonly used
together with the static approach, still several examples of deterministic dynamic models can be
found.
The study of location theory formally began in 1909 with Alfred Weber (Owen & Daskin, 1998;
ReVelle & Eiselt, 2005) who presented a static model whose objective was to “position a single
warehouse so as to minimize the total distance between it and several customers” (Owen &
Daskin, 1998, p.3). These kinds of models have been largely used as they present simpler and
lighter computational approaches than the dynamic models. Although they are simplified
representations of reality it has to be considered that reality is constantly changing, market trends
evolve, costs vary and technology improves, hence the necessity of considering time as a variable
in cases where change is imminent. The optimal solution of today is not necessarily the global
optimal solution of the time period in study. However, location models in most of the cases are
particularly difficult to optimally solve consequently the application of complex models did not arise
until more powerful computers were available (Current et al., 2002).
In this dissertation’s framework a static/deterministic approach will be taken. This is on the one
hand due to the fact that the objective is a long term planning of costly facilities and as a result few
changes in the layout are desirable. But also on the other hand due to the small variability of
production along the coming years (which will be explained further on). Therefore the literature
review of dynamic and stochastic models will be limited to the transmission of a general idea
about these approaches.
4.2.2 Static/Deterministic location models
There are several types of static deterministic location problems that can be divided according to
their objective (Sahin & Süral, 2007). For this work four main categories were considered those
are: covering, center, median and fixed charge. Although Sahin and Süral (2007) only consider
the first three categories it was decided to include the center problem as it represents many of the
waste location models presented in the literature. The first two models can be viewed as having an
“equity” objective, as their purposes is to minimize the maximal distance, and the last two as
having an “efficient” objective, as their purpose is to minimize the total distance (Current et al.,
2002). Those problems can also be divided into single or multi-objective problems, although since
the only variable to optimize is cost, this literature review will be converging to a single objective
method as it is more representative of our reality.
27
ReVelle and Eiselt (2005) consider the division of static deterministic location problems according
to their objective but also according to the “space of location decisions”, that is they divide the
problems according to the type of space the model represents (d – dimensional real space or
network location problems) and for each of these options they sub-divide according to the location
possibilities for the facilities (continuous or discrete location problems). This first sub-division
category refers to problems where the location possibilities are continuously distributed while the
second one refers to location problems where there is a discrete set of possibilities for the
locations. Normally what distinguishes the two situations is that in the discrete location problems
there is a pre-evaluation of the possible/desirable sites thus narrowing the options down to a set of
locations. The authors also refer that the “continuous location problems, […] tend to be non-linear
optimization problems, while discrete location problems, […] involve zero-one variables that result
in integer programming/combinatorial optimization problems” (p.3).
The covering problems are normally applied to public services such as hospitals, emergency
vehicles services, police, firemen, schools etc. The covering problems consist in locating the
facilities such as all nodes are at a maximum travel distance/time of a facility insuring that a
minimum coverage is offered to clients. Sometimes the execution of this sort of models can present
results that are infeasible as the allocated resources are not sufficient to build the facilities for the
desired coverage level. A more realistic set up of this problem consists in limiting the number of
facilities to be built thus giving the coverage level only to a number of users. This last formulation is
called the maximal covering problem (Owen & Daskin, 1998; Current et al., 2002; ReVelle &
Eiselt, 2005).
The center problem, also known as the minmax problem, is a formulation used to minimize the
maximum distance between any demand and its nearest facility (Owen & Daskin, 1998). In this
case the resources to build facilities are established (N facilities can be built) so the model tries to
find the location of those facilities in order to have the minimum distance possible between the
facilities and demand. The difference between the center and the maximal covering problem is
that in the last one the objective is to serve the maximum number of users by positioning the
facilities at a distance inferior to the recommended and in the center problem the objective is to
minimize the average maximum distance between a user and its closest facility.
The objective in median problems can be defined as minimizing the total demand-weighted travel
cost (distance or time). In this type of problem the solution resides in locating a P number of
facilities in order to obtain the minimum cost while satisfying the demand. Only variable costs, such
as the transportation costs, are taken into account. In the general formulations presented by Owen
and Daskin (1998), Current et al. (2002), ReVelle and Eiselt (2005) and ReVelle, Eiselt and Daskin
(2008) it is said that Hakimi in 1964 proved that for a network facility location problem “relaxing the
problem to allow facility location on the arcs of the network would not reduce total travel cost”
(Current et al., 2002, p.11). This means there is at least one optimal solution where all the facilities
are located in the network nodes. Therefore this “formulation includes only nodes as potential
facility sites and yet does not penalize the objective function value” (Owen & Daskin, 1998, p.4).
28
The fixed charge problem is similar to the median but it also includes the construction, capital or
expansion costs associated with opening the facility, therefore demand may not be assigned to the
closest facility but to a farther facility whose fixed cost is lower.
The location-allocation problems which define the location of the facilities and establish the flows
between nodes are normally solved with median or fixed charged approaches (Owen & Daskin,
1998).
Apart from the formulations presented above there are numerous other variants, such as the hub
problem, the antimedian problem, the anticenter problem and the p-dispersion problem that are
not presented in this work as it is not the aim of this research. General formulations of these
problems are presented in Current et al. (2002).
All the models presented above consider that the flows between nodes are represented by direct
travels, which means that the cost of transportation is equivalent to the round trip cost between the
two nodes. In certain cases, such as solid waste systems, the collection of waste in a group of
nodes is often made by the same vehicle which has a collection route associated. In these cases,
in addition to the facilities location, another problem has to be solved which is the optimization of
the collection routes. Those models are called by Current et al. (2002) as location-routing models.
4.2.3 Dynamic location models
The dynamic location models, as the name states, define models that study a problem over a time
period with inputs that are variable. They can be classified into two categories; (1) implicitly dynamic or (2) explicitly dynamic (Current, Ratick, & ReVelle, 1997). The first one refers to
models that are dynamic because they consider the evolution of the parameters (time, cost,
production/demand) in time but they do not allow facilities to open or close during the period where
they are running, thus giving a “static” solution. The second also allows the evolution of
parameters and additionally allows facilities to be opened or closed during the time horizon of the
optimization; in this case the solution layout refers to a set of time-periods that can be smaller than
the defined time horizon. For more information on these models and examples of application refer
to Current et al. (1997), Owen and Daskin (1998) and Current et al. (2002).
4.2.4 Stochastic location models
The stochastic methods differ from the deterministic due to the fact that they add variability to the
value of the input parameters. The models presented in section 4.2.2, all presume that the input
parameters are known with certainty.
According to Owen and Daskin (1998), there are two main approaches to stochastic location
models. They are referred to as the probabilistic approach and the scenario planning approach. In both cases all of the system parameters (such as demand, travel cost, construction
cost and discount and capital rates) can be considered uncertain. What separates the first one from
the second one is that the first one is more complex. The probabilistic approach considers the
probability distribution of each parameter (“standard formulation”) or formulates within a queuing
29
framework, instead the second approach tries to find the more robust solution among a sample of
scenarios, each one of them being a “generated set of possible future variable values” (Owen &
Daskin, 1998, p.13).
Current et al. (2002) also separate the different stochastic location problem approaches in these
categories and provide several examples of application. Current et al. (1997) also present
examples of application.
4.2.5 Hierarchical facility location models
Hierarchical systems are complex systems that present an organized set of different levels.
Hierarchical facility location problems are normally associated with healthcare facilities. For
instance the healthcare services are composed in its lower levels by some local numerous facilities
which treat simpler types of diseases and have fewer resources. In case the patient requires further
tests or more complicated procedures, he will be referred to upper level facilities which are more
scarce (regional level) and offer the same services as the lower levels, plus specific types of
treatment. For example if you present yourself to a local clinic needing a complicated surgery
doctors will transfer you to a hospital for being submitted to that procedure. So the optimization
model applied in these cases is most commonly a covering problem where the display of the
facilities is such that all people are covered firstly for basic service and then for specific services.
Another area where a hierarchical system can be found is in the production system of goods and
its supply chain. One simple example of this hierarchy is: the raw material being extracted at one
place, transported to a transformation facility and finally to a store to be commercialized. In this
case the flow has to pass through all the hierarchical levels in order to reach the last one with the
desired form and to the desired clients.
The organizational structure of the SWM system, allows it to have an explicit hierarchy. Compared
to the second example, SWM models are the reverse version of manufacturing a product. It all
starts with clients: a large number of nodes producing small quantities, therefore equivalent to
shops with small demands. The waste needs to be collected from these nodes and directed most
of the times to a transfer station in order to lower transportation costs, taking advantage of scale
economies by concentrating big quantities of waste to be transported together. The TS step would
be equivalent to distributors warehouses. Finally the waste is delivered firstly to a treatment plant
and then disposal site or directly to its DS (for example landfills). This would be the equivalent to
the raw material extraction and transformation into goods. This procedure is known as reverse logistics.
Sahin and Süral (2007), classify the hierarchical systems according to four parameters:
1) Flow pattern, which represents the type of flow products can have in the system. Single-flow means that the product can only travel from a level to the level immediately above
while multi-flow means that products can travel directly from any lower level to any upper
level;
30
2) Service varieties, which concerns the presence of services in the different hierarchical
levels. A system is considered to be nested if in each hierarchical level the services
provided are the same as the provided by its inferior level plus one different service (the
healthcare facilities example). In case each hierarchical level provides different services
the system is considered non-nested (the production and supply chain example);
3) Spatial configuration, which corresponds to a system being single-sourced or not. The
system is considered coherent if the demand of a determined level is satisfied only by one
superior level facility – single-sourced. The non-coherent system would therefore
correspond to having several higher-level facilities supplying at the same time a lower-level
facility;
4) Objectives, representing the already quoted classification of median, covering and fixed charged objectives.
4.3 Facility location models applied to solid waste management
4.3.1 General overview of the facility location models applied to SWM
A waste management system is normally composed by a group of production sites, a group of
transfer stations or other type of intermediate treatment and a group of disposal facilities.
In the specific case of this thesis, waste is produced in a big group of facilities, including hospitals
and other healthcare clinics, as described in chapter 2. Those facilities produce four types of waste
of which only two are considered in the context of this work. Those are the Group III and IV waste
which are considered hazardous and so cannot be treated as USW.
As it was already explained the waste produced, independently of belonging to Group III or IV, has
to be collected and transported to a transfer station or directly to the treatment facility (or
incinerator in case of Group IV waste). The waste transported to a transfer station is later
transported to the treatment facility taking advantage of the reduced costs of transport due in part
to scale economies. Finally both types of waste are transported to USW landfills (in case of Group
III waste) or to non-hazardous industrial waste landfills (ashes originated by the incineration of
Group IV waste). This final destination is defined by law.
This hierarchical design can be classified as a multi-flow, non-nested and coherent system. In
the specific case of Group III and IV medical waste, the layout is not as complex as the layout seen
in the later papers on SWM. The reason for the downgrade in complexity is related to the low
number of possibilities in terms of treatment for medical waste. This type of layout is also seen in
the early papers published on SWM, where the possibilities of disposing waste were only landfills
and incinerators (with presence or absence of transfer stations) and where no separation of the
refuse was made in its origin, e.g. Esmaili (1972).
When reviewing the literature on SWM, it was possible to have a clear view on the evolution of the
approaches taken by the published authors along the years. The first papers on SWM (published in
the 50s and 60s) treated subjects like vehicle routing, facility location and waste allocation, with
31
systems as simple as production-disposal. The reason behind such simplicity was the quite
reduced number of different disposal technology available but also the computing capacity at that
time.
These first approaches to location-allocation problems evolved to more complex models where
optimization is made through the allocation of waste to several facilities with different technologies.
Models where the possibilities of treatment were none (only production and disposal) and where
the objective was to minimize the system cost (Helms & Clark, 1971) evolved to much more
complicated models, in terms of treatment possibilities, and where the optimization is not only from
the economical point of view but also from the environmental point of view taking into account
criteria like noise control, air pollution and traffic congestion (Chang & Wang, 1996) or criteria like
greenhouse gases production, reduction of waste disposed directly to landfill opposed to the
increase of energy and material recovery (Erkut et al., 2008). In other types of approaches it is
possible to see the inclusion of an equity criterion to the economical and environmental criteria in
order to avoid penalizing “excessively some zones for the benefit of others” (Caruso, Colorni, &
Paruccini, 1993, p.2), i.e. concentrating all the treatment/disposal facilities in one area. This equity
criterion leads to solutions that are socially acceptable.
The appearance of these more complex models follows the tendency of the booming evolution of
computer resources, which have greatly increased in the past few years, allowing for a faster
resolution of complex algorithms. The multi-criteria approaches, with the inclusion of environment
impacts and equity, are the result of our society’s awareness to the environmental problems and
the access to information the general population nowadays has.
This increased flow of information leads, in many cases, to local opposition to the opening of waste
management facilities. It is common nowadays to hear acronyms like BANANA (Build Absolutely
Nothing Nowhere), LULU (Locally Unwanted Land Use), NIMBY (Not In My Back Yard), NOPE
(Not On Planet Earth) or NOTE (Not Over There Either) that reflect the opinion of the local
population to certain types of facilities being built (Erkut et al., 2008). This opposition is an extra
concern for the DM who most of the time is in a political position and has to choose an option not
only based on a technical point of view but also from a political point of view. The solution of
applying the kind of models that locate facilities in order to maximize the distance to population, as
the only criteria, is also not viable because of the costs incurred. So in most of the cases the DM
has to consider both the technical and social point of view in order to achieve its goal. Antunes et
al. (2008) considered both these points of view when locating one incinerator in central Portugal by
developing a model with three optimization stages. The first two stages are optimized through
facility-location models whereas the third stage is a multi-criteria analysis. In the first stage it
decides on a set of locations for the incinerator by minimizing cost, in the second stage it optimizes
the incinerator location by maximizing the distance to the population and in a third stage it
evaluates the different industrial sites according to several criteria.
Despite of the concern in developing complex models where several perspectives are taken into
account, there still are some rather innovative, useful and not as complex approaches to SWM,
32
which can be considered so by the originality of the approach taken, e.g. the use of genetic
algorithms to help locate a treatment facility and its necessary transfer stations (Ortega, Delgado, &
García, 2007), or the context in which they are applied, e.g. an allocation model applied the
complex city of Mumbai (Rathi, 2007).
After this general overview on SWM models a more extensive literature review will be presented,
regarding the work that is directly related to the location of SWM facilities and the allocation of
waste to these facilities.
4.3.2 The location-allocation models applied to solid waste management
In the first works presented in the literature (1971 to 1988) what differentiated them was not the
model nor the problem to be solved, normally a three level problem with waste generating centroids
at the base level followed by already built and future transfer stations and finally a disposal facility
(in general landfills or incinerators), nor the approach taken and objective, which was minimizing
the total cost using a fixed charge or a median model. During this time the innovation/originality
was mainly the way the problem was solved. This is justifiable seen that the available
computational means were not as powerful as today, therefore making large scale problems time
costly or even impossible to solve.
Helms and Clark (1971) presented a fixed charge model to locate and allocate the USW to seven
possible disposal sites. They include fixed costs associated with the utilization of each of the
disposal sites, considering this fixed cost equal to zero when the facility already exists, and a
variable cost which represents the cost of hauling and disposal fee of the waste. They refer that
collection and haul are different concepts, the first one being the time/distance that a vehicle takes
from the garage to the last collection point, and the second is the time/distance that the vehicle
takes from that same collection point to the disposal site. The model only considers the haul part
(considering centroids of the production areas) as it is stated that the inclusion of collection would
turn the model intractable.
Marks and Liebman (1971) propose a fixed charge location-allocation model with a three level
hierarchy, where sinking nodes location is already known. This model’s objective is to locate the
transfer stations necessary to the SWM system and allocate the waste flows. It considers as
variable costs three components: (1) transportation cost, (2) TS fees and (3) sinking node fees.
The model does not optimize collection routes as the production nodes considered are the
centroids of the different collection areas. In this approach, the authors’ model locates only one
type of facility.
Harvey and O'Flaherty (1973) also present a fixed charge model, but their approach has the
objective of locating two different types of facilities, landfill and TS. For that purpose the model
includes another fixed cost related to the second type of facility to be located. In this model
formulation the variable costs associated with the different facilities are considered separately. The
formulation also considers the centroids of the production zones; the authors state that this
simplification will increase the collection capacity at most ten percent.
33
Greenberg, Caruana and Krugman (1976), propose a linear programming model (p-median) for
managing a solid waste system with a three level hierarchical layout; (1) the source, (2) an
intermediate facility – for waste processing - and (3) landfills. They do not use fixed costs in their
formulation, only the hauling and fees associated with the facilities. The objective of this model is
not to decide which type of facility should be opened and its location but to test different SWM
strategies, e.g. centralized landfill versus disperse landfills, use of intermediate facilities to reduce
the amount of waste sent to landfills. Therefore the inclusion of fixed costs associated with the
construction cost of the different facilities would make the model heavier and more difficult to solve.
The authors justify the simplification of using a Linear Programming (LP) model instead of a MILP
model with the fact that the algorithms available were deficient in solving this type of problem.
However the operating costs still have to be included in the model formulation. For that purpose the
authors included the economies of scale by manually executing “repetitive test runs of different
scale plants” (p.4) which is “inexpensive to run, flexible and works” (p.4). When comparing the LP
approach versus the MILP approach the authors state that when “the fixed-charge model
programming is improved, the user faces the trade-off between the added computer costs and
complexity of the fixed-charge model, and the additional keypunching and deck setups and
submission of the linear model” (p.4). Nowadays with the personal computers capacity of solving
complex models it is clearly worthwhile opting for MILP approaches.
Kirca and Erkip (1988), present an approach to locate transfer stations which is composed by four
stages. (1) Validation of available data, (2) modeling allocation problem with fixed transfer station
locations, (3) a static location problem and (4) implementation of the results over the time horizon.
The two intermediate stages represent a good approach to the SWM problem as they try to include
the DM in the process. In the second stage the LP model is run to see which will be the allocation
of waste flows. In that stage the DM will be providing the possible locations for the TS and the
solution will be a refined set of the possible locations for TS. In the third stage the constraints of
building TS are included and the outcome is the optimal locations for the transfer stations. This
approach is applied to the municipality of Istanbul and the authors present a practical technique to
overcome the problem when cost data is insufficient or unavailable. Instead of using the transport
costs of both collection vehicles and trucks, they reduce these two parameters to a relative one
(the ratio between the two costs).
The previously presented articles sum up the first static approaches in location-allocation models.
Although not very common some of the models that can be seen in this period already contain
dynamic approaches like the ones presented by Esmaili (1972), Walker, Aquilina and Schur (1974)
and Jenkins (1982a), with its multi-period approach, to solve the location-allocation problem of solid
waste.
Walker et al. (1974), present a heuristic algorithm (Solid Waste Allocation Model - SWAM) to solve
a SWM problem with a fixed charge allocation model. In terms of costs they consider the same
costs as the models presented before – transportation cost, fixed and variable cost associated with
the facilities – although they present two approaches to the consideration of variable cost in
34
incinerators, a linear cost function and a piece-wise cost function. The last cost function considers
the economies of scale in the variable costs, the result of treating bigger amounts of waste. The
SWAM optimization strategy is to break the total period of study into smaller periods, treating these
last periods as singular independent fixed charge problems and update the information from a
previous period to its subsequent period. As a result facilities such as landfills can be closed when
its capacity is reached. Although this model allows facilities to be opened and closed during the
study period, it cannot be called an explicitly dynamic model; as the facilities opening and closing
dates have to be determined by users (with the exception of landfills which can be closed
automatically when full capacity is attained). Nonetheless this model is an implicitly dynamic
model as input parameters can be changed during the study time period.
Earlier, Esmaili (1972) also presented a dynamic model that can be categorized as a deviation
from the explicitly dynamic definition given earlier. His fixed charge location-allocation model
considered that at the beginning of the study period all facilities were available but it did not allowed
the user to change parameters such as the production or cost during the optimization routine. The
waste management system was composed of possible locations for landfills and transfer stations,
therefore a 3 level hierarchy. The model would divide the whole time period into smaller stages and
for each stage the waste allocation was made to the facilities that presented the least costly
solution. The locations for landfills had a maximum capacity attached. When this capacity would be
attained the model would exclude this location from the available set, and rerun the fixed charge
function to find the new set of location that optimized the cost.
When running a purely static method for a distant time horizon the optimized result considers the
production at the horizon. If an approach similar to Esmaili (1972) is taken there will be a wiser
planning of resource usage resulting in a more economical solution. However the fact that in the
previous model the production is maintained constant results in a distorted approximation of reality.
Also these results are valid for waste management problems where expanding the capacity of its
facilities – landfill – is complicated or unwanted.
Finally among the models where the only optimization parameter is cost, Clark and Gillean (1974)
presented a model which is not aimed at setting the outline of the entire waste management
system but rather to optimize the operational parameters of collection. The authors present a
model which studies the cost of collecting and disposing USW, optimizing it by changing a set of
operational parameters, such as the type of collection – back yard versus curbside, or the type of
vehicle. This model is an allocation model as it studies which amount of waste is going to each
disposal site but it does not locate any type of facilities and does not optimize collection routes.
However this paper consist in a good tool to further study the results of a location-allocation model
and therefore is included in this literature review.
In the more contemporary publications, one of the first approaches to multi-objective models can
be seen with Caruso et al. (1993), which is followed by Chang and Wang (1996), by Karagiannidis
and Moussiopoulos (1998), whose application consists in a system with four hierarchy levels and
the inclusion of citizen acceptance among others, and by Chambal, Shoviak and Thal (2003)
35
whose purpose is to help the DM choose the best municipal SWM strategy using a decision
analysis technique called value-focused thinking method.
Nevertheless at the same time Kulcar (1996) developed a model applied in the region of Brussels
where the objective was in a first part to locate the transfer stations and in a second part to locate
the depots where the trucks are stored. In this paper the author uses a fixed charge model to
express the fixed costs of the depots and transfer station. He takes traffic into account by
multiplying the distance between two nodes by a certain factor.
In Badran and El-Haggar (2006) the authors apply a fixed charge model to the region of Port Said
in order to determine the optimal location of collection stations and the optimal waste flow
allocation. For that they consider the technology already available for treatment and disposal and
they design the complete waste management system in terms of collection stations and types of
vehicles. They include a sketch of what should be the typical collection station.
In Komilis (2008) the author, based on previous mentioned work, presents two different
approaches for optimizing the haul and transfer of municipal solid waste. The model has a three
level hierarchy: generating nodes, transfer stations and disposal sites. The author presents the
model in two perspectives of optimization, (1) time and (2) cost. The first one is rather practical
when information on cost is not available or takes a big amount of time to be collected. This
approach presents itself as a reasonable and quick solution for an allocation model. However the
author states that the time approach “would be ideal in situations that one type of vehicle is used
throughout the MSW system and no intermediate nodes (transfer stations) are included” (p.7), so in
cases where location models with several levels are being used the time approach is not a good
solution as it does not take into account the differences between the vehicles used. On the other
hand when using the cost approach the DM should insure that the data used is reliable and
accurate, “the use of default cost data is not always a safe approach” (p.7).
Finally Li, Huang, Yang and Nie (2008) present a much more complex stochastic and dynamic
model which is able to generate “a range of decision alternatives under various environmental,
socio-economic, and system reliability conditions” (p.1). This model is no longer an attempt to
optimize a system but a tool designed to help the DM observe the consequences of different
alternatives under different scenarios where a large set of variables is taken into account.
As it has been observed the literature review exposed in this dissertation concerns work based on
solving USW management problems rather than medical waste management problems. Truth is
during the research almost no references to medical or hospital waste management were found,
regarding location-allocation optimization models. Many of the research made in the medical waste
field concerns mainly how to efficiently treat it or how to manage it in a hospital scale. This lack of
research might be the consequence of a highly regulated sector where in most cases the options
available are so little that researchers feel that there is no need in applying or creating new models
to optimize the HMW system.
36
Nevertheless a few interesting papers, concerning this subject, were found. Shi, Fan, Gao and
Zhang (2009), present a MILP model in order to solve a location-allocation problem of medical
waste. Their system’s layout is composed by 4 hierarchical levels, the producers (hospital),
collection facilities, processing facilities and factory. The two intermediate levels facilities are the
ones to locate, and the waste flow needs to go form an inferior level to its directly superior
hierarchical level making this a single-flow model. It considers the transportation of several
different types of waste. However the main point the authors want to show, is how they solve the
problem. They use a genetic algorithm (GA) to solve the MILP model. The GA population is
composed of only one chromosome whose genes are the binary variables associated with the
opening of the facilities and the variables representing the different waste flows. The fitness (the
parameter that rank each chromosome) of a population sample is measured as the difference
between a penalty value and the objective function (minimize costs). The example shown on this
paper is quite small, two types of waste, six producers, five potential collecting centers, three
potential processing centers and one factory location. This model is therefore very similar to the
ones developed in the period of 1971-1988, with the exception of its solving method, which applies
the use of GA.
Finally, Medaglia Villegas and Rodríguez (2009) also present a medical waste management model
which purpose is to locate transfer stations in order to minimize cost but also to minimize the
neighbor populations. For solving this model the authors apply a GA, more specifically a multi-
objective evolutionary algorithm.
4.4 Conclusion
To conclude, after this literature review one can see the enormous set of different perspectives in
which the HMW problem can be studied. However due to the particularities seen in chapter 2
regarding the disposal of this type of waste and the objectives of this work seen in chapter 3, it is
possible by now to have an idea of what type of model will be developed in this dissertation. In the
next chapter the model formulation will be extensively explained, though it is already possible to
predict that the approach taken will be to develop a MILP model which takes into account the
transportation costs, the variable and fixed costs of facilities and that optimizes the location of three
different types of facilities (TS, Group III disposal sites and incinerators) but also the allocation of
waste to the different nodes. As it was said before, due to the several factors, such as the evolution
of HMW production, this model will be a static/deterministic model.
37
5. MODEL FORMULATION
5.1 Modeling a real world problem
After describing the HMW problem and revising the literature related to SWM optimization models,
it is now possible to present the model proposed in this dissertation. Finding the solution of a
problem by recurring to a model can be briefly characterized by a five step process (figure 4).
Figure 4 – Process to solve a real world problem with a mathematical model (Figueiredo, 2007)
As it can be seen in figure 4, the first step to solve a problem is to identify it. After the identification
of the problem there is the need of defining its details and also to define the surrounding conditions;
this will be attained by defining the objective and the constraints imposed by the scenario, this is
followed by the model formulation and by the choice of a solving method – optimization algorithms
(general purpose or tailored specifically to the problem) or heuristic methods. Finally the solution
given by the model has to be applied but not without confirming the feasibility of this change. So an
analysis to the solution has to be made in the perspective of feasibility but also to understand what
can be improved in order to obtain better results.
5.2 Mathematical modeling
When developing a mathematical model the objective is to represent reality by mathematical
formulas. The model can be summed up to a set of objectives and constraints. The objectives are
defined by the approach taken to the problem “what do we want to optimize?”, the constraints are a
set of expressions that allow the model to take into account the surrounding limitations, adapting
itself to reality.
When developing a model there are two important characteristics that greatly influence its final
form: authenticity and flexibility (Figueiredo, 2007). These two characteristics should always be
taken into consideration.
Real world problem
Definition of CONSTRAINTS
and OBJECTIVES
Mathematical model
FORMULATION
SOLVING method
APPLICATION of the SOLUTION
and CONCLUSIONS
IMPROVEMENT
38
Authenticity represents the proximity between the problem perception in the real world and the
problem representation in the model. This characteristic is not directly referred to the degree of
detail in which the problem aspects are described, but to the way that the relevant aspects are
taken into account in the model formulation. This means that unnecessary or inappropriate details
of the model will not contribute to its authenticity (Figueiredo, 2007). In all models there is the need
to consider some kinds of simplifications from the real world scenario in order to make it more
efficient in terms of resolution. A highly authentic model can be described as a model which
considers the real problem in almost its whole, whereas a lowly authentic model tends to ignore
aspects that have a great impact in the final results.
Flexibility represents, as it is indicated by its name, the extent to which the model can quickly be
modified in order to comply with new or modified factors that are now important to include. This
means that the more flexible the model is, the easier it is to adapt it to new situations or
perspectives.
When formulating a model a balance has to be made between both features. On the one hand it is
necessary that the model is authentic enough so that its solution is relevant to solving the real
world problem, but on the other hand it is also necessary to have some flexibility in the model to
facilitate its adaptation to new elements, therefore creating a tool that can be used in different
situations.
Solving the problem, reaching the optimal solution, is also a very important step of the process. As
nowadays the computational resources are well developed and several commercial solvers are
available to users, reaching the optimal point is no longer as relevant as it was before – at least for
models that can be solved with these applications. Although the solving tools are a very complex
and important aspect of solving the problem, the objective of this dissertation is not directly related
to this field of study.
5.3 Constraints and considerations of the HMW management model
As already mentioned, the objective of the model is to minimize the total cost incurred in the
disposal process of HMW. Each country has its own medical waste management policy with its
specific set of rules. Hence, to present an application the model will be shaped according to the
Portuguese case. However the model should be flexible enough to be adapted to new realities if
necessary. In the next figure the options for the path to be taken by both Groups III and IV waste
are shown in order to enhance understanding of the mathematical model.
As it is shown, in figure 5 the Group III waste can go from its generating node to an intermediate
TS and then to the Disposal Site (DS) – from now on the Group III treatment facilities will be
referred to simply as disposal sites – (GIII-1), or directly from the generating node to the DS (GIII-2).
The Group IV waste flow can go directly from the generating node to the incinerator (GIV-1) or, it
can also go through a TS in its path from the generating node to the Incinerator (INC). The only
39
difference is that the Group IV waste flow can go to the same (GIV-3) or to a different (GIV-2) TS
than the one where Group III waste, from the same generating node, goes. The two possibilities
have different costs. As it was already observed, the quantities of Group IV waste produced are
very low in comparison to the quantities of Group III waste produced by the different facilities. Of
the total HMW produced in Portugal in 2006, 10% is Group IV waste and the other 90% is Group
III. Therefore if Group IV waste travels along with Group III refuse it will be more economical since
the vehicles which transport the waste will not have to do specific travels to pick up the Group IV
waste. In this optic the cost of transporting only Group III waste or both groups together is the
same, as the joint transport would increase the vehicle load by only 1/9.
Figure 5 – Possible waste flows considered by the model
Even though this model considers the Autoclave and Disinfection facilities as sinking nodes to
Group III waste and the incinerators as sinking nodes to Group IV waste, it must be said that one
could have considered as sinking nodes the landfills. Group III treated waste is disposed in USW
landfills and the ashes, result of the Group IV waste incineration, have to be transported to a non-
hazardous industrial landfill.
The omission of these final steps are justified by the fact that (1) USW landfills are present all over
the country and so the location of the Group III waste treatment facility will not have relevant
influence in the costs of transporting the refuse to the landfill, and (2) concerning the Group IV
ashes, its transportation cost to non-hazardous industrial waste landfills is significantly inferior to
the cost of transporting Group IV waste. Therefore the weight of this last cost is not significant
enough to alter the incinerator location choice.
It is also necessary to emphasize four other paths that could be considered as plausible (figure 6).
They represent the hypothesis of transporting Group III and IV waste together in the same vehicle,
making two stops, the first stop to “drop-off” part of the cargo and then follow to the vehicle final
destination.
The first two paths are literally “drop-off” situations. The vehicles transporting Groups III and IV
waste go from the production node to a disposal site or incinerator to “drop-off” respectively Group
GENERATING
NODE INCINERATOR
DISPOSAL
SITE
TRANSFER
STATION 1
TRANSFER
STATION 2
Group III Flow
Group IV Flow
GIV-2 GIV-2
GIV-3 GIV-3
GIII-1
GIII-1 GIII-2
GIV-1
40
III or Group IV waste and then follow to unload the rest of the cargo in another incinerator or
disposal site node.
Figure 6 – Alternative flow paths
The choice of the first path (Generating node/Disposal Site/Incinerator) can be considered illogical
as the cost of transportation will always be superior to other alternatives. In figure 7 an illustration
of the costs incurred and a comparison between path 1 and 2 can be seen. Consider that the
distance between generating node and DS is D1 and that the distance between DS and INC is D2
and that the cost of transporting both groups of waste is Ct. A best case scenario for this option is
having D2 close to zero, this would lower the total cost of transporting only Group IV waste,
between the DS and INC, as this cost per unit of waste transported is higher than transporting
Group III waste since the vehicle will circulate with only 10% of its cargo capacity – the chosen
value of 10Ct will be explained further on. Therefore, when comparing path 1 with path 2, it is
understandable that the second path is always preferable to the first one. The option of not
“dropping-off” at the disposal site first will force the vehicle to do D1 + D2 (the same as path 1)
plus D2 again at a cost of Ct, which means a total cost of 퐶푡 ∗ (퐷 + 2퐷 ). This represents a lower
cost alternative to path 1 which can be represented by 퐶푡 ∗ (퐷 + 10퐷 ).
Figure 7 – Costs associated with PATH nº 1
The second path (Generating node/Incinerator/Disposal site) can also be discarded from the
model. This path will not be chosen because there will always be a more economical way of
making the trip. The Group III disposal units have high building costs and in most cases present
processing costs per unit which decrease when the amount of treated waste increases. Therefore it
is expected to have few of those facilities in the final layout. Incinerators are even more expensive
than disposal units so in the final layout there should be a certain number of TS followed by a lower
number of DS and an even more reduced number of incinerators.
41
Let us consider a simplified situation with only one incinerator and one disposal site. In this case
the generating nodes, which are closer to the incinerator than they are to the DS, would go drop-off the Group IV waste at the incinerator and then would follow their way to the DS (path 2) –
figure 8 – as this would be the more economical solution. Due to the costs associated with the
several facilities, the influence areas of incinerators and DS are always larger than those of TS.
This means that in this case the bigger area of influence of the incinerator would lead to a bigger
concentration of waste than the one seen if there was only a TS at the same point. This bigger
concentration of waste makes the construction of a TS, at these nodes - incinerator and DS –
economically viable, which would lead to the following path generating node/TS/Sinking node. So
this justification allows to eliminate the second path, but also to reinforce the idea that the first
drop-off situation (path 1) will never occur.
Figure 8 – Waste flows for a two node (Incinerator/Disposal site) example
The third and fourth path (Generating node/Sinking node 1/TS/Sinking node 2) can also be
excluded from the possible paths to include in the model. This can be justified with the same
reason given for the second path. As the sinking nodes facilities are expensive to build, their area
of influence will be large and therefore there will be with great probability a TS in these nodes. This
will lead to the distance between Sinking node 1 and TS being zero (they are located at the same
point), thus the third and fourth path are equivalent to the path illustrated by figure 9 which is
contemplated by the model. These justifications validate that the waste paths contemplated by the
model represent the only real possible situation.
Figure 9 – Third and Fourth path represented in the real situation
Still concerning alternative paths, it was said in the second chapter that the Group III waste could
also be eliminated. Such alternative is not considered by the model as the cost of elimination is
almost double the cost of decontamination; therefore it is never a more economical solution.
42
Another concept introduced in the model is that of cost curves (figure 10). A facility running at full
capacity must have a lower processing cost per unit than another facility running at 50% of its full
capacity. This decrease in treatment cost per unit can be perceived in the total cost function as a
decrease tendency of its first derivative resulting in a concave total cost function similar to the one
presented in figure 10 (blue line).
As the proposed mathematical programming model is linear, there is the need to linearize the cost
function. The approach taken was the one used by Walker et al. (1974), where the authors
transform a non-linear cost curve into a piece-wise linear concave cost function (in red – figure
10). Each piece of this linear cost function has a different fixed cost associated (intersection with
the cost axe) and a different slope (decreasing with quantity treated). As proven by the cited paper,
there is no need to introduce lower and upper bounds constraints to the different pieces of the cost
function as for this type of curves the quantity processed will always be between the correct
bounds.
Figure 10 – Linear and Concave cost functions
5.4 HMW management mathematical model
The mathematical programming formulation presented in this work is an adaptation of the
formulations presented in the literature with adjustments to the HMW problem and more specifically
to the Portuguese case. The two authors whose formulations influenced mostly the developed
model are: Komilis (2008) with the path binary decision variables and Walker et al. (1974) with the
piece-wise linear cost functions as stated before.
The following indices, parameters and variables are defined:
Indices i Generating nodes – i {1,…,m} j Transfer Station nodes (TS) – j {1,…,n} k Disposal Site nodes (DS) – k {1,…,p} l Incinerator nodes (INC) – l {1,…,q} x Cost function index – x {1,…,r}
0102030405060708090
100
0 20 40 60 80 100
% o
f tot
al c
ost
% of total capacity used
Piece-wise linear cost functionConcave cost function
43
Parameters
Cs Cost per ton*Km of transporting Group IV waste from a generating node to a transfer station or incinerator individually in a small capacity vehicle
Ct Cost per ton*Km of transporting Group IV together with Group III from a generating node to a transfer station in a small capacity vehicle, or Group III from the generating node to a transfer station or directly to the disposal site
Cts Cost per ton*Km of transporting all types of waste from the transfer station to its a disposal site or an incinerator in big capacity vehicles
PG4i Group IV waste production at a specific node i (ton per year) PG3i Group III waste production at a specific node i (ton per year) FixTSj Fixed cost of using/opening a TS at a specific location j
FixDSkx Fixed cost of using/opening a DS at a specific location k, associated to a specific cost curve x
FixINClx Fixed cost of using/opening a INC at a specific location l, associated to a specific cost curve x
VarDSkx Variable cost (per ton) of treating waste at a DS in location k, for cost curve x VarINClx Variable cost (per ton) of eliminating waste at an INC in location l, for cost curve x
δ Control parameter equal to the highest ratio "Group IV waste produced at node i divided by Group III waste produced at the same node" plus 1
β Control parameter which has to be greater or equal than the total amount of HMW in the system
dij
Euclidean distances between the different sets of nodes (km) dik dil djk djl Positive variables QtDSkx Quantity of waste being treated at a certain DS (k) associated to a certain cost curve (x)
QtINClx Quantity of waste being eliminated at a certain INC (l) associated to a certain cost curve (x)
Binary variables
Z1il = 1 If Group IV waste is transported from node i to incinerator l
GIV-1 (figure 5) = 0 Otherwise
Z2sijl = 1 If Group IV waste is transported individually from node i to TS j, and
then to INC l GIV-2 (figure 5)
= 0 Otherwise
Z2tijl = 1 If Group IV waste is transported together with Group III from node i to
TS j, and then to INC l GIV-3 (figure 5)
= 0 Otherwise
Z3ik = 1 If Group III waste is transported from node i to DS k
GIII-2 (figure 5) = 0 Otherwise
Z4ijk = 1 If Group III waste is transported from node i to TS j, and then to DS k
GIII-1 (figure 5) = 0 Otherwise
44
Y1j = 1 If TS at node j is open = 0 Otherwise Y2kx = 1 If DS at node k is open and cost function x is being used = 0 Otherwise Y3lx = 1 If INC at node l is open and cost function x is being used = 0 Otherwise Δ1jk = 1 If it is the path chosen between TS (j) and DS (k) / INC (l) Δ2jl = 0 Otherwise
The big capacity/small capacity term used previously to define some of the parameters is related to
the before mentioned scale economies in the use of TS. Due to the concentration of waste at these
facilities its expectable to have larger vehicles doing the transport of waste between the TS and the
sinking node.
As the objective is solely related to costs, the objective function represents the sum of all costs
considered:
푀푖푛 퐶표푠푡 = [푍1 ∗ 푃퐺4 ∗ 푑 ∗ 퐶푠]
+ 푍2푠 ∗ 푃퐺4 ∗ 푑 ∗ 퐶푠 + 푑 ∗ 퐶푡푠
+ 푍2푡 ∗ 푃퐺4 ∗ 푑 ∗ 퐶푡 + 푑 ∗ 퐶푡푠
+ [푍3 ∗ 푃퐺3 ∗ 푑 ∗ 퐶푡]
+ 푍4 ∗ 푃퐺3 ∗ 푑 ∗ 퐶푡 + 푑 ∗ 퐶푡푠
+ 퐹푖푥푇푆 ∗ 푌1
+ [푄푡퐷푆 ∗ 푉푎푟퐷푆 + 퐹푖푥퐷푆 ∗ 푌2 ]
+ [푄푡퐼푁퐶 ∗ 푉푎푟퐼푁퐶 + 퐹푖푥퐼푁퐶 ∗ 푌3 ]
(1)
The objective function is represented by eight expressions of sum. The first five are related to the
transportation costs and the last three to the facility related costs (variable and fixed costs). The
constraints to the model are the following:
푍4 ∗ 푃퐺3 + 푍2푡 ∗ 푃퐺4 ≤ 훿 ∗ 푍4 ∗ 푃퐺3 , 푖 = 1, … ,푚; 푗 = 1, … ,푛 (2)
[푍1 ] + 푍2푠 + 푍2푡 = 1 , 푖 = 1, … ,푚 (3)
45
[푍3 ] + 푍4 = 1 , 푖 = 1, … ,푚 (4)
푃퐺4 ∗ 푍2푠 + 푍2푡 + 푃퐺3 ∗ 푍4 ≤ 훽 ∗ 푌1 , 푗 = 1, … ,푛 (5)
푃퐺3 ∗ 푍4 + [푃퐺3 ∗ 푍3 ] ≤ 훽 ∗ 푌2 ,푘 = 1, … ,푝
(6)
푃퐺4 ∗ 푍2푠 + 푍2푡 + [푃퐺4 ∗ 푍1 ] ≤ 훽 ∗ 푌3 , 푙 = 1, … , 푞
(7)
푄푡퐷푆 ≤ 훽 ∗ 푌2 ,푘 = 1, … ,푝;푥 = 1, … , 푟 (8)
푄푡퐼푁퐶 ≤ 훽 ∗ 푌3 , 푙 = 1, … , 푞;푥 = 1, … , 푟 (9)
푌2 ≤ 1 ,푘 = 1, … ,푝 (10)
푌3 ≤ 1 , 푙 = 1, … , 푞 (11)
[푃퐺3 ∗ 푍3 ] + 푃퐺3 ∗ 푍4 − 푄푡퐷푆 = 0 ,푘 = 1, … ,푝 (12)
[푃퐺4 ∗ 푍1 ] + 푃퐺4 ∗ 푍2푠 + 푍2푡 − 푄푡퐼푁퐶 = 0 , 푙 = 1, … , 푞 (13)
Constraint (2) allows the flow of Group IV waste to be transported at reduced cost only when it
goes from the same generating node, i, to the same transfer station, j, along with Group III waste.
The coefficient δ serves as a control parameter, i.e. whenever the flow of Group III waste in a
certain arch is equal to 0 then δ*0=0, which means that the Group IV waste flow in the same arch
has to be 0 (since the right hand side of (2) cannot be negative). If the Group III waste flow is ≥ 0
then δ, which is a big number, allows Group IV waste flow to travel along this path.
Constraints (3) and (4) confirm that for each node i only one path is taken, regarding respectively
Group IV and III waste collection. This means that the waste produced at a certain node can only
be transported through one path (method of transportation), avoiding having more waste
transported than the one produced.
Constraints (5), (6), (7), (8) and (9) can be considered as capacity constraints, though in this case
they prevent waste flow to go through facilities that do not exist (when Y=0). The first three
constraints of this group ensure that the path chosen for a certain node i, (Z=1) is going through
46
existing facilities (Y=1). The last two constraints ensure that if a certain amount of waste is billed
with a certain cost curve at a facility then the fixed cost associated with that curve must also be
taken into account. The coefficient β serves as a control parameter. This coefficient can quickly
transform these constraints into capacity constraints being β the capacity limit. The role of β in
these constraints is analog to the role of δ previously mentioned.
Constraints (10) and (11) ensure that only one cost curve is used per location, meaning that all the
treatment costs of one location (k or l) are taken from the same cost curve.
Finally constraints (12) and (13) guarantee that all the waste coming to a certain facility is charged
with the according variable treatment cost.
Apart from the constraints already mentioned, four control constraints were introduced to ensure
that all waste of the same group flowing through TS has the same final destination. This ensures
that the model is coherent as described in 4.3.1, meaning that a lower-level facility can only send
waste to a single higher-level facility.
∆1 = 1 , 푗 = 1, … ,푛 (14)
∆2 = 1 , 푗 = 1, … ,푛 (15)
푍4 − ∆1 ≤ 0 , 푖 = 1, … ,푚; 푗 = 1, … ,푛;푘 = 1, … ,푝 (16)
푍2푠 + 푍2푡 − ∆2 ≤ 0 , 푖 = 1, … ,푚; 푗 = 1, … ,푛; 푙 = 1, … , 푞 (17)
Constraints (14) and (15), ensure that only one path is chosen between the TS and the sink nodes
(coherency of the model) and constraints (16) and (17) confirm that the waste flows between the
TS and sink nodes are going through an open path.
In conclusion this is as mixed integer linear programming model (MILP model) that can be
solved recurring to a commercial solver. With the model formulation being completed it is now
possible to present an application of the model, still it is necessary to define beforehand the values
of the different parameters.
47
6. DATA COLLECTION AND ESTIMATION
To apply the model developed in the previous chapter to the Portuguese case study there is the
need to gather reliable data or estimate parameters if there is no data available. The input data
necessary to apply this model can be divided into four different sets:
1) The geographical distribution of the HMW producers in the continental part of Portugal;
2) The HMW production of each node;
3) The location where it will be possible to build the infra-structure (TS, DS and INC);
4) The different types of costs.
In this chapter, the collection or estimation of the several data sets will be explained in detail. The
main purpose of this chapter is to describe all the types of data this model needs to yield a solution.
However when data is not available estimations will be made and all the assumptions will be
presented, in order to be possible to run an application of this model.
6.1 Geographical distribution of the HMW producers in continental
Portugal
To represent the real geographical distribution of the HMW producers in Portugal it would be
necessary to associate a node to each of the producers mentioned in the second chapter
(Hospitals, Public Healthcare Clinics, etc). The number of nodes obtained would be extremely high
and their precise location and associated production would be very difficult to get. Furthermore the
inclusions of all nodes (circa of 10000, only considering hospitals, PHC, dental clinics and
pharmacies) would make the model almost intractable and very difficult to solve.
The intention of this work is to provide a strategic level solution; hence the exclusion of route
optimization and other operational factors, and so there is a need to simplify the distribution of
producers, concentrating the productions of minor nodes into more important nodes.
As it was seen before, the information on production is rather scarce and not one hundred percent
reliable. The most recent data on production comes from APA (2009), which was in part adapted in
a previous chapter to estimate the distribution of HMW production in Portugal.
From the analysis of that data set it could be concluded that hospitals contributed for a big part of
the HMW produced in Portugal (circa of 80%). Hospitals constitute specialized healthcare units of
the higher hierarchical level. People are referred to hospitals or go there for special procedures that
cannot be accomplished in lower level healthcare facilities such as PHC. Many of these users do
not live in the surrounding areas of the hospital and therefore make special trips in order to benefit
from these treatments. So the use of hospitals could be characterized by one time or necessity
users rather than day-to-day users.
PHC, dental clinics, private clinics, pharmacies and other healthcare facilities are lower level
facilities which the population uses in a more frequent base to satisfy their more basic healthcare
needs, such as regular medical appointments. In Portugal each municipality has at least one PHC
48
that provides the population some basic healthcare assistance. The previously mentioned facilities
(excluding the PHC) are built in a free market perspective; where there are clients with needs to
satisfy there is also a business opportunity and so there will probably be someone interested in
opening one of these private held facilities, such as pharmacies. Additionally, as these are facilities
which purpose is to satisfy basic day-to-day needs, it is expected that the clients will opt for the
closest facility to their residence area and not to drive to a distant place to satisfy their needs. So in
this case, as opposed to hospitals, it is possible to say that the HMW production depends on the
resident population rather than on the number of facilities present in the area.
In terms of data available it was only possible to obtain the total amounts of waste produced in
Portugal by district. The option taken was to concentrate production around nodes that would
represent an administrative region.
In Continental Portugal there are 18 districts, although the objective here is to develop an
optimization tool in a strategic point of view, this scale is considered to be insufficient for modeling
the generating nodes. The smallest administrative area in Portugal is called “freguesia”
(community); there are 4.050 communities in continental Portugal. The precision level associated
with having the communities as generating nodes would bring a high amount of additional
computational time and needs without bringing any extra precision, in the form of valuable
information (authenticity), to the model.
So the decision was to analyze the problem at a Municipality scale. In the continental part, Portugal
has 278 Municipalities, which is considered an appropriate scale to solve the problem.
6.2 HMW production amounts associated with each node
Once the nodes are chosen there is the need to know which will be the production associated to
each node.
On the one hand there are the necessity facilities (hospitals) and on the other the day-to-day
facilities. The information available related to production is given by districts, so they will be
considered as independent producers, and the production of each municipality will be estimated
according to other available data.
For the day-to-day production the solution found was to consider that it was directly proportional to
the resident population of each municipality. For the necessity facilities, their best waste
production indicator was the number of hospital beds, therefore the part of HMW produced
associated with this type of facility will be distributed by the different municipalities according to the
available number of hospital beds in each one of those administrative regions.
In terms of available information the following was taken from INE:
1) The projections for the resident population of Portugal, undiscriminating the area of
residence;
2) The resident population by area of residence for 2008;
3) The number of hospital beds per municipality for the year of 2004, 2005 and 2006.
49
The use of several data sources to obtain the number of hospital beds available in each
municipality was due to the fact that the data available was incomplete. When it was not
possible to obtain, in the statistics referring to the years of 2004, 2005 and 2006, the number of
beds for a certain municipality in Portugal, a value of zero was assumed. This action was taken
due to the fact that looking into older surveys might conduce to biased information for the
municipalities with no data available.
To predict the HMW production of each node it will be assumed that:
1) The percentage of the population living in each district will be constant along the coming
years, as well as the percentage of the district population living in each municipality. Those
percentages will be equal to the 2008 INE statistics;
2) The ratio of number of beds per inhabitant plus it distribution will be constant;
3) 71% of the production will be directly proportional to the number of hospital beds in each
municipality and the remaining 29% will be directly proportional to the resident population;
4) The total HMW production estimate methodology used will be the one exposed in 2.5.3.
The first two assumptions are equivalent to say that the distribution of HMW per municipality will be
equal in 2016 to the 2008 distribution. With these assumptions we are able to estimate the
distribution of the production on the continental part of Portugal.
Figure 11 – Evolution of the Portuguese population 2016-2060 Source: Projecções de População Residente (2008-2060), INE
As the infra-structure being considered is expensive and has an expected life span of several
years, the model should plan the layout considering all those periods. The question to be asked is if
the production is going to undertake a lot of changes in the forthcoming years.
Assuming that the amount produced is directly dependent of the resident population in Portugal
and that from 2016 on the production per capita will be stable, it can be considered that the
production of HMW will vary in the same way as the population. The projection for the resident
population in Portugal, according to the INE, is shown on figure 11.
93949596979899
100101102
2016
2019
2022
2025
2028
2031
2034
2037
2040
2043
2046
2049
2052
2055
2058
% o
f the
pop
ulat
ion
in 2
016
Years 2016-2060
Population
50
As it is observable the peak will be around the decade of 2028-38, but its biggest value will not
surpass the value projected for 2016 by more than 1,5%. Therefore it is justifiable that a static
model is used as the production, for at least the next 50 years, will be more or less constant –
higher on average 0,8% until 2047 and lower on average 1,8% form 2048 to 2060. These small
variations make the use of a dynamic model or a multi-period approach useless, as the results
would be the same. Of course there is also the possibility of variability on the data set supplied and
also on the conditions assumed. This variability could lead to different scenarios that would require
the use of other models than the static deterministic approach.
In conclusion the data used to solve the proposed model, regarding the amount of HMW to be
disposed, will be the set referring to 2016. Of course this simplification can only be made for the
Portuguese case study. If this model was to be applied to a region where there was a high
variability of the HMW produced over the next few years, then a multi-period approach should be
taken in order to define the infra-structure opening and closing timing.
This sub-chapter had the objective of explaining the methodology used for estimating the
production at each node. The estimated production quantities for each municipality are given in
Appendix III.
6.3 Geographical distribution of the waste management facilities
In terms of the possible locations (nodes) for the facilities, such as TS, DS and INC, it would be
logical to assume that the possible locations would be the nodes representing the municipalities.
However given that the purpose of this dissertation is to point out a region where it would be
optimal to locate a certain facility it was decided to choose only one node per district.
This option was also justified by the increase in computational time required for solving the model
with one possible location for each type of facility per municipality (834=1*3*278).
It is necessary to define a set of coordinates in each district which will represent the node –
possible location for the facility. One possible approach would be to choose the district capital city.
This choice would not represent the best solution regarding the management of the HMW
produced in the district’s municipalities. The optimization of hauling distances to a possible facility
inside the district is obtained by calculating the coordinates to its gravitational center, considering
the HMW produced as the mass of each generating node (municipality). The gravitational centers
of each district will be referred to as the centroids.
Using the HMW estimated production for 2016 it is possible to calculate the coordinates of the
centroids. A weighted mean was calculated using the production amount stated in 2.5.3 for the
year of 2016, having as weight factors the production of each municipality. The coordinates of each
node are presented in table 10.
In figure 12 a schematic of the position of the centroids and the capitals of districts is presented.
This scheme is to give an idea, to the reader, of the differences between choosing the district
capitals or the centroids as possible locations for the facilities. From a general overview it is
51
noticeable that when presenting the results, the reader can in most cases associate the facilities
location as an area very close to the district’s capital. On average the centroids are 12 km away
from the district’s capital. If the four farthest centroids, Santarém, Castelo Branco, Faro and Vila
Real are excluded from the average distance, the value decreases to only 9 km. Considering that
Lisbon is approximately 14 km long and 7 km wide, the values obtained suggest that in conceptual
terms the DM can actually consider the location for the facilities as the surrounding area of the
district’s capital, the exceptions are the 4 districts nominated above.
Table 10 – Coordinates of the facility sites’ nodes
District M Centroid P Centroid District M Centroid P Centroid
AVEIRO 164653,56 422543,87 LEIRIA 137565,84 300753,15
BEJA 219837,16 110764,21 LISBOA 108096,59 199523,79
BRAGA 172782,89 506692,56 PORTALEGRE 263211,15 246354,02
BRAGANÇA 310802,86 530574,32 PORTO 164050,30 468103,29
CASTELO BRANCO 252765,68 343558,32 SANTARÉM 164046,46 271234,65
COIMBRA 173781,76 360513,40 SETÚBAL 124078,45 179006,94
ÉVORA 221315,92 180627,42 VIANA DO CASTELO 147488,27 530820,69
FARO 198206,77 13535,86 VILA REAL 241349,98 500313,36
GUARDA 259823,82 400142,33 VISEU 219740,92 426615,74
Figure 12 – Position of the Centroids and the District Capitals
52
6.4 Cost data estimation
Regarding costs, it can be said that for the scenario being studied, costs can be separated in two
groups, (1) fixed and (2) variable. Before exposing the list of cost belonging to each category it
should be said that the aim of the model is not to choose between the technologies available.
Therefore for each type of infra-structure only one technology will be considered. This does not
mean that it is impossible to manipulate the model in order to adapt it to our reality. Several runs
can be made with technology sets chosen by the DM, who can subsequently study the results
obtained. Originally the purpose of this work was to study the optimization of the Group IV waste
disposal system. After understanding that Group IV represents only 10% of the HMW produced at
each node, being the other 90% Group III waste, and that the companies of this sector operate with
both types of waste, it was understood that optimizing this system only made sense if both Groups
III and IV were treated together in the same model.
For gathering the data related to costs two approaches were taken. The available literature was
searched in order to find values for costs and companies were contacted to see if they could supply
some information related to costs. The first approach revealed itself as the most complete although
the detailed information obtained was in general outdated. The second approach was also not very
rewarding as most of the companies contacted did not supply data, and the one that did could not
get into the degree of detail needed.
So the costs that will make sense to include will be:
1) The Removal/Collection/Transportation costs. These are associated with the transportation
from the producing/transfer nodes to transfer/disposal nodes. They will be considered as
variable;
2) The fixed cost of setting up a new facility. This cost will help to decide on the number of
facilities to set up and will be taken as constant in all the new locations;
3) The variable cost associated with the % of capacity used by each facility.
6.4.1 Removal/Collection/Transportation costs
According to Levy et al. (2002) the price of collection and transport of Group I and II medical waste
in 2002 was between 0,025 and 0,035 €/Kg.
The data present in the literature shows that for USW management systems the biggest part of the
cost incurred in the disposal process is due to collection and hauling – 85% according to Marks and
Liebman (1971), 80% according to Clark and Gillean (1974). It is necessary to refer that in the
specific case of HMW, the process of collection, hauling and disposing of HMW is not as industrial
as the USW system and it is a more complex system. Therefore the previously mentioned
proportions should not be directly taken into account but serve more as a guideline.
The collection process for HMW can be characterized by a small number of locations that produce
big amounts of waste (Hospitals) and an enormous set of small producers (day to day facilities).
53
Therefore it is expected that the proportion of collection in total cost will be very high for the day to day facilities but lower than the USW for the hospitals.
Also, when comparing the disposal activities and handling concerns of HMW against those of
USW, it is noticeable that HMW has more complex treatment and handling requirements. The
handling requirements increase both the cost of collection - special containers - but also the
disposal fees.
Consequently it is expectable to have a lower weight of collection on the total disposal cost but not
very far from the one seen in the literature. For the purpose of the case study a collection cost
proportion of 70% will be assumed.
In the mathematical model exposed in chapter 5 there are three types of transportation cost:
1) Cs, Small capacity vehicles transporting only Group IV waste;
2) Ct, Small capacity vehicles transporting Groups III and optionally Group IV waste;
3) Cts, Big capacity vehicles transporting one type of waste only.
The cost of transporting the waste from the transfer stations to the disposal site (Cts) will be
considered 1/3 times Ct, this value is taken from Kirca and Erkip (1988). The authors considered
that the reduction in transporting USW in big capacity rather than in small capacity vehicles is a
third of the small capacity vehicle cost, but they stated that in the literature the proportion is located
in the 1/4 to 1/5 range. Medical waste needs special requirements in the transportation and
collection, consequently a fewer difference in cost is expected when changing the transport means.
In each municipality the Group IV waste production is equivalent in weight to 1/9 of the Group III
waste production. So for each stop that a vehicle, which is collecting Group III waste, does, the
same vehicle, this time collecting only Group IV waste, has to do 9 more stops to get the same
amount of cargo. As a result in order to penalize the transportation of Group IV waste exclusively,
between the generating node and its first destination, it will be assumed that the cost of
transportation is 10 times higher than collecting and transporting both types of waste together. This
difference will reflect the bigger number of kilometers the vehicle has to do before it gets to full
load.
The total costs given by APA (2009) are supposed to be rough estimations of the real costs. In
order to obtain the cost per km, it is necessary to know on average how many kilometers a ton of
waste travels. The only way to estimate such value was to consider the existing infra-structure (DS
only) and to optimize a model where the only transportation possibility for the waste to be
transported was from the generating node directly to the sinking node. Although this representation
considers some simplifications, the prediction should be accurate enough to give an estimate of
transportation cost (per ton*km). In this scenario, it was found that waste will travel on average
approximately thirty kilometers. Therefore the transportation cost between generating nodes and a
first stop will be:
(0,1 ∗ 1,2 + 0,9 ∗ 0,6) ∗ 0,7 = 0,462푒푢푟 퐾푔 →0,462
30 = 0,0154 ∗푒푢푟
퐾푔 ∗ 퐾푚
54
This means that the cost of transporting Group III (and Group IV) waste in small capacity vehicles,
will be of 15,4 Euros/ton/Km
So if Ct = 15,4 Euros/ton/Km, then Cs will be equal to 10 times this value (154 Euros/ton/Km) and
Cts will be equal to a third of Ct (5,13 Euros/ton/Km)
As it was seen in chapter 4, in the literature reviewed almost all of the models considered the
transportation cost as representing a return trip. In the case of this dissertation the transportation
costs estimated represent the cost paid by the producer (per ton*km). Consequently from the way it
was estimated, this cost should only multiply the distance between the initial node and the final
node.
The most relevant paper seen in the studied literature, in terms of time proximity and case study
location was Komilis (2008). The author in this paper considers an USW system in Athens. The
hauling cost parameters are, for a 13 m3 collection vehicle operating at full capacity, 0,075 € -
0,086 €/ton/Km. Therefore the cost of hauling and collecting HMW is approximately 180 times
higher than the cost of hauling and collecting USW. In the HMW specific case the hauling activity is
not as industrial as the hauling of USW, the vehicles used have smaller capacities and have
specific needs such as refrigeration, the amounts collected at each node are much smaller than in
the USW case, and HMW needs special handling requirements that inflate the transportation costs.
Due to the facts quoted above, the big difference seen between the collection and hauling costs of
the two waste systems seems acceptable.
Levy et al. (2002), state that for a similar scenario the collection and haul costs would be between
0,5 to 1,5 Euros/Kg. Admitting that in their scenario waste travels on average the same thirty
kilometers, the cost per kilometer will be between 0,0167 – 0,05 Euros/Kg/Km. Although the lower
bound of Levy et al. (2002) is superior to the value found, it is possible to say that the greatness of
the values obtained is similar and therefore validate the estimation on the transportation costs.
6.4.2 Operating and construction costs of facilities
The costs associated with the disposal of HMW should be equivalent to 30% of the total cost of
disposing a unit of HMW. This value assumes the split between transportation and treatment costs
seen in the previous sub-chapter. The total cost for each waste group are given in APA (2009).
It is understandable that with the rate at which technology evolves, the expected life-span of the
equipment, used in treating or eliminating HMW, should be considered as rather low when
comparing to infra-structure such as office buildings for example. The truth is every year cleaner
and more efficient technology appears on the market. However there is an important part of the
facility cost associated with the land acquisition and with building the structure that holds the
equipment, as well as associated with equipment related to secondary activities, such as cold
storage or loading/unloading vehicles.
Due to these important fixed costs and considering the possibility of adapting that location to other
type of equipment with the same purpose, it is understandable that when planning the locations of
55
waste management facilities the life-span considered, for the whole strucutre is rather high. For the
sake of this model application the life-span of the facilities will be considered as twenty years,
which is the most common value for these types of projects.
In terms of data available, Levy et al. (2002) present some values for the different units involved in
disposing HMW. This data is rather outdated as the first edition of the book mentioned is form
2002. Tsilemou and Panagiotakopoulos (2006) present some approximate cost function for the set-
up cost and the operating cost of four types of waste treatment facilities. One of the included types
of facilities is waste-to-energy, which by their assumptions can be considered as having more or
less the same costs as a HMW incinerator. The problem is that their cost functions can only be
applied to a certain capacity range, which is far beyond the ones considered in this work.
Nevertheless, the values presented by these two sources are the closest estimations that could be
found. So in order to estimate the set-up cost of these facilities such sources will be used. Though
Levy et al. (2002) book dates from 2002 the growing inflation and the price devaluation of the
technology used can be considered as positive contributes, since their contradictory effect brings
the 2002 estimation closer to a price estimation for 2009. The cost functions presented by Tsilemou
and Panagiotakopoulos (2006) are not that adaptable to this problem since their application range
falls far from the range considered in this thesis.
In Levy et al. (2002) the initial cost given for an incinerator with a capacity of 5.000 ton/year is
2.500.000 Euros. The estimated production of Group IV HMW for 2016 is of approximately 2.600
ton/year. The technology has to be chosen before running the model; therefore the first approach
will be to predict a single facility with the installed capacity of 2.600 ton/year. Admitting that the
construction of these facilities present strong scale economies; it is possible to say that a 30%
reduction in set-up cost will be assumed for a 50% reduction in incineration capacity.
Consequently, assuming that the values presented in the previously quoted book can be
considered up-to-date, the set-up cost for a 2.600 ton/year incinerator should be 1.750.000 Euros.
The capacity range for waste-to-energy facilities given by Tsilemou and Panagiotakopoulos (2006)
goes from 20.000 to 600.000 ton/year which, as it was said before, does not include the capacity
ranges that are used in the HMW treatment. Nonetheless, by using the cost function given by the
article an initial set-up cost of 2.643.472 euro is obtained. This value can be considered as an
upper-bound value for the set-up cost of an HMW incinerator since the technology considered in
the cost function is more costly and the capacity chosen is outside the capacity range definitely
reflecting a biased value.
To include the set-up cost into the model in a fair way, it is necessary to convert it to the same
temporal scale (per year).So the set-up cost will be converted to an annuity (amortization). For that
matter it will be considered that the set-up cost can be allocated as an annual cost calculated as an
annuity which will be paid during the equipment life-span (20 years) and assuming a capitalization
tax of 4% (approximately the Portuguese government bonds tax). The present value of a
discounted amortization is equivalent to the sum of the geometric progression terms with a
56
common ratio equal to , in this case r is equal to 4%. The generic formula for summing the
terms of a geometric progression is:
퐺푒표푚.푃푟표푔푟. =
퐹푖푟푠푡 푡푒푟푚푟 ∗ 1−
1(1 + 푟) (18)
For an incinerator with an annual capacity of treating 2.600 tons of Group IV waste the following
annual cost will be considered:
퐴푛푛푢푖푡푦 =1.750.000 ∗ 4%
1 − 1(1 + 4%)
= 128.768 퐸푢푟표푠/푦푒푎푟
The average cost of disposing a kg of Group IV waste is 1,2 Euros as stated before. Therefore the
total annual market value for eliminating Group IV waste would be:
퐴푛푢푎푙 푐표푠푡 푎푠푠표푐푖푎푡푒푑 푤푖푡ℎ 푒푙푖푚푖푛푎푡푖표푛 표푓 퐺푟표푢푝 퐼푉 푤푎푠푡푒 = 30% ∗ 푇표푡푎푙 퐶표푠푡
→ 30% ∗ 1,2 ∗ 2.600.000 = 936.000 퐸푢푟표푠/푦푒푎푟
From these 936.000 Euros, 128.768 Euros are spent in amortizations, and the other 807.232 Euros
account for direct plus indirect costs and profit.
For the Group III facilities a similar approach was taken to estimate the initial cost. It has to be
referred that there are only two types of treatment facilities for Group III waste available in Portugal;
(1) chemical disinfection and (2) autoclave.
By 2016 there will be at least six of the chemical disinfection facilities running in Portugal. They are
all property of Cannon Hygiene and their treatment capacity is rather low (on average: 71 ton/year)
when compared to autoclave facilities.
In terms of autoclave facilities, there will also be six facilities running by 2016, as it could be seen in
a previous chapter. Their average capacity is of approximately 6.850 ton/year.
Assuming that the market share of all companies is directly proportional to their treatment capacity,
this meaning that the capacity factor of all facilities is considered to be the equal, on average the
facilities will be working at 57% of their full capacity.
푇표푡푎푙 퐺퐼퐼퐼 푝푟표푑푢푐푡푖표푛 2016 푖푛 푡ℎ푒 푐표푛푡푖푛푒푛푡푇표푡푎푙 푡푟푒푎푡푚푒푛푡 푐푎푝푎푐푖푡푦 2016 =
23.723 푡표푛41.316 푡표푛 = 57%
As it was said before the model will not contemplate the technology choice. Therefore it is the DM
responsibility to choose the correct one by testing the model under several scenarios. For the
purpose of this work the initial cost estimated will be for an autoclave unit with a capacity of 6.850
ton/year. This type of facility is the most representative of the data available.
The same capitalization tax (4%) is assumed, as this only depends on indirect factors, such as the
state of the economy.
57
Again, the best cost estimates available are the ones given by Levy et al. (2002). The authors
estimated in 2002 a cost of 950.000 Euro for the acquisition of the autoclave unit with a capacity of
5.000 ton/year, plus a cost related with the structure building of 450.000 Euro and a quick
benchmarking research on the internet revealed that an industrial lot situated around Lisbon with
an area 1.000 square meters would cost around 125.000 Euro. This adds up a total cost for an
Autoclave unit of around 1.525.000 Euros. In reality the dimensions of the facilities vary a little bit,
but as it was said before only one type of technology will be considered so the set-up cost used to
apply the model to a case study will be the annual cost of a 6.850 ton/year autoclave:
퐴푛푛푢푖푡푦 =1.525.000 ∗ 4%
1 − 1(1 + 4%)
= 112.212 퐸푢푟표푠/푦푒푎푟
The average cost of disposing a kg of Group III waste is 0,6 Euros as stated before and the facility
is working at 60% of its capacity. Therefore the total annual market value of an Autoclave facility for
treating Group III waste would be:
퐴푛푢푎푙 푐표푠푡 푎푠푠표푐푖푎푡푒푑 푤푖푡ℎ 푡푟푒푎푡푚푒푛푡 표푓 퐺푟표푢푝 퐼퐼퐼 푤푎푠푡푒 = 30% ∗ 푇표푡푎푙 퐶표푠푡
→ 30% ∗ 0,6 ∗ 60% ∗ 6.850.000 = 739.800 퐸푢푟표푠/푦푒푎푟
From these 739.800 Euros, 112.212 Euros are spent in amortizations, and the other 627.588 Euros
account for direct plus indirect costs and profit.
Finally it is necessary to estimate the transfer station cost. In terms of the transfer stations there is
no data for comparison. The TS is a refrigerated warehouse where the HMW coming from the
generating nodes is unloaded into the warehouse and is then shipped to the sinking nodes in
bigger vehicles benefiting from the scale economies of the transport. This facility is a much simpler
facility to build and run. Firstly it does not have the equipment and personnel needs as the others
do, secondly each of the other types of facilities can easily house a transfer station with almost no
extra cost. Therefore the cost approach to this type of facility will be slightly different from the other
ones. Only a fixed cost will be taken into account to represent a penalty if the model opens one.
The fact that this penalty is not related to the usage level of the facility is due to its dimension and
its purpose. Supposing that only one standard type of transfer station is considered, opening it
brings an extra fixed cost which is related to energy, personnel and other costs and it also saves
the company money by reducing transportation cost. So it is assumed that the TS fee is in sort of a
way diluted in the transportation costs, only having to take into account separately the fixed
operating costs of the facility. This fixed cost represents the minimum cost that makes the
construction of a TS worth the investment.
Due to the nature of this facility and its purpose, the annual cost considered for opening the TS will
be of 100.000 Euros (approximate value).
After getting the best solution with the technology chosen the DM should look to the capacity
factors of the different facilities in order to decide the adjustments to be made regarding the
technology chosen. That is also the reason no capacity factor is included, an optimal result could
58
show that it would be more rewarding to concentrate more waste treatment in one area and close
facilities in other areas. This will be explained in better detail when analysing the results.
This approach of subsequent analysis compensates the possibility of biased data. Accepting the
model solution with no further analysis may result in erroneous layouts far from the optimal. A
human analysis should always be taken into account due to the extra information an experienced
person can bring to the solution of the problem.
The costs calculated are summed up as seen in table 11.
Table 11 – Calculated transportation and fixed costs
Costs Ct (€/ton/km) Cs (€/ton/km) Cts (€/ton/km) Fj (€/year) Fk (€/year) Fl (€/year)
15,4 154 5,13 100.000 112.212 128.768
6.4.3 Operating cost function of each facility
Finally there is the need to include the direct costs of treatment by each facility. It would not be an
accurate model if economies of scale were not taken into account. As it was shown before the
model can adapt itself to any kind of piece-wise linear cost curve for the incinerator and autoclave
facility, this means that it can consider from a single linear cost curve to n linear cost curves put
together into a piece-wise function.
In terms of the current application, in order to try to minimize the possibility of error in the estimates
due to the lack of data, a cost function composed by only two linear pieces will be considered.
Consequently each facility has two operating levels in terms of their running capacity, (1) warm-up
and (2) stable. In the first operating level, the capacity factor in each the facility is operating, is still
in a low range; therefore the operating costs per unit are very high as well as the variation of cost
per unit with each additional unit produced. This means that the production cost is not stable. In the
last level, the production costs have stabilized due to the already considerable capacity factor, this
means that the cost per unit will not vary a lot when an additional unit is produced. Although this
cost function is continuous in reality to include it in the model it is necessary to consider a piece-
wise linear representation (Walker et al., 1974).
The purpose of the inclusion of cost functions is to give the model a perception of the advantage of
increasing the total waste flow to one facility instead of opening a new facility. Another possible
solution for this matter is instead of considering cost functions, to determine the minimum capacity
for which a facility is allowed to be opened.
In this application the warm-up period goes from 0% capacity to 40% capacity and it represents an
increase of 60% in the total variable cost. The stable period goes from 40% capacity to 100%
capacity and accounts for the other 40% increase in total variable cost (figure 13). These values
were suggested by industry experts.
There is the need to add the annual amortization (annuity) to the variable cost. To determine the
real values of the cost function it is necessary to know the values of at least two points of the
59
graphic. For both facilities the 0% capacity corresponds to a total cost equal to the annuity. In the
incinerator case and in the autoclave case, the 100% capacity and the 60% capacity, respectively,
correspond to a total cost equal to the annual total cost seen previously. Inferring from these values
it is possible to obtain the cost curves presented in figure 14.
Figure 13 – Piece-wise linear cost function considered
The concavity of the piece-wise linear curves are guaranteed, which means there really is an
economy of scale in costs.
With the treatment costs defined it is possible to proceed to solving the model. Nonetheless it is
necessary to emphasize that the costs considered (most of them estimated) serve only as
guidelines to give an application example of the model. Further collection and better estimation
should be done in order to present other aspects of the model solution.
Figure 14 – Piece-wise linear cost functions of DS and INC
0102030405060708090
100
0 20 40 60 80 100
% o
f var
iabl
e co
st
% of total capacity used
0100000200000300000400000500000600000700000800000900000
10000001100000
0 2000 4000 6000 8000
Tota
l anu
al c
ost p
er fa
cilit
y (E
uros
)
Amount of waste treated (ton)
Group III
Group IV
60
7. APPLICATION TO THE PORTUGUESE CASE STUDY
The model presented in chapter 5 is an application of mathematical modeling to HMW
management in general but specifically considering the Portuguese legislation. The application of
this model can be described as a raw application since it optimizes the location of all the infra-
structure as if they had not been built yet (define the layout from scratch). This application is
equivalent to the global optimization concept introduced in chapter 3, meaning that the solutions
represent the layout that will be attained when the HMW market is more consolidated.
In this chapter the objective is to present an application of the model developed in chapter 5 with
the gathered and estimated data in chapter 6. As it was referred before the objective of this
dissertation is to present a mathematical model to optimize the HMW layout in a global perspective
and regarding only costs thus giving the best possible solution. In this chapter the application of the
model to the Portuguese case will be presented, as well as the discussion of some of the results
and other factors. Nonetheless to understand the difference between global optimization versus
partial optimization, at the end of this chapter an example of what could be a partial optimization
model for this particular case and an application will be presented.
7.1 The chosen interface and commercial solver
The GAMS application (version 22.9.2) was chosen as the interface between user and solver since
this application is rather reliable, simple and user-friendly. The CPLEX solver (version 11.2.0) was
chosen as the model solver, due to the fact that according to information available it is a reliable
and powerful solver.
The CPLEX solver uses a branch and bound algorithm to reach optimization. Therefore the solver
will first reach a relaxed solution, and from there it will obtain a value for the objective function.
After obtaining this value it will start the branch and bound algorithm to approximate as close as it
can the objective function’s value to its objective (a relaxed solution). The process is time and
memory consuming and as the process reaches closer to the relaxed value it takes more time to
get improvements. If the objective function value is exposed as a percentage of the relaxed
solution objective function value, it is possible to say that an improvement from 109% to 108% is
harder to get, in terms of resources, than a progress from 195% to 194%. Therefore there is the
need to understand the trade-off between having a solution that is 1% better but takes 10 times
more to be computed.
The concept of optimization gap can be extracted from this trade-off of time versus solution
improvement. The optimization gap is the user defined number that indicates to the solver that the
solution is already satisfying and therefore there is no need to carry on with the algorithm. It is
understandable that the improvements carried by such a little difference might not compensate the
computing capacities required.
Due to the nature of this model and its purposes, it was considered that a 10% optimization gap
would be adequate for presenting an “optimized” solution. Though it must be said that this value
61
is not strict and sometimes a lower upper-bound can be chosen, it all depends on the CPU time
consumption. The model presented in this work is supposed to be above all an interactive tool that
helps the DM eliminate some of the variables. Therefore the results should be presented in a
reasonable amount of time. Nevertheless if a higher upper-bound is reached the DM should take
into account the fact that the solution presented might be far from optimal.
Apart from the branch and bound algorithm, CPLEX possesses another tool that can help
improve the final solution. It consists on a built-in heuristic called polish, which slightly improves
the final results. In the different scenarios used during this application, improvements up-to 0,3%
were obtained by the polish heuristic.
7.2 Global optimization
7.2.1 Results presentation
As stated before, this model has two objectives: (1) finding the optimal location of the HMW related
infra-structure and (2) optimizing the waste flows between the different nodes.
After a first couple of tests, it was possible to obtain the first set of results. An optimization gap of
4,82% was reached by the algorithm and with the application of the polish heuristic it improved
the optimization gap to 4,59%. This represents a total cost of 14,72 millions of Euros per year for
the management of HMW in continental Portugal. This set of results will be called from now on the
model solution.
However, by analyzing some of the results given by the sensitivity analysis and other sets of
solutions obtained, it was possible by a trial and error method, where the location of the facilities
was no longer a variable but a parameter fed manually to the model by the user, to find an even
better solution. The set of results called best solution was found by fixing the infra-structure as
opened or closed (following the observations made by analysing previous results) and optimizing
only the waste flows between nodes. Still this best solution improved the objective function value
by only 0,044% to a total value of 14,71 millions of Euros per year.
In order to understand how much more time the solver would take to reach the solution found by
trial and error, the original formulation of the model was ran with the CPLEX Objllim option on
and set to a value of 14,713 millions of Euros. This option consists in setting the objective function
value’s upper bound, that once reach will order the solver to stop computing and to present the
solution. The solver was executed for over 20 hours without reaching the solution. A quick
comparison will be made between the two solutions, but in the end only the results from the best
one will be presented and commented extensively.
As it was observed before, the predicted market value of HMW management for 2016 for the whole
country would be between 15,3 and 23,4 millions of Euros, being the estimation made in this work
equal to 19 millions of Euros. Although this is only the first iteration between the results and the
choices made by the DM, such as technology and facility capacity, it is already possible to see
some improvement in the total cost. This means that the HMW market can still cut their costs by at
62
least 22,5%, with the use of the same type of facilities. One can observe from table 12 the
characteristics of the two solutions presented in terms of model and solution statistics. Table 12 – Summary of the model and solution characteristics
No. of Variables
No. of Binary
variables
No. of Equations
No. of Non
Zeroes
No. of Iterations
CPU Time (sec)
Optimality Margin
(%)
Objective Function Value (€)
Global Optimization
Model Solution 281.035 280.962 185.939 2.022.805 51.193 1.487,2 4,59% 14.724.908
Best Solution 66.427 66.400 59.050 498.625 1.155 12,3 0,00% 14.712.062
In terms of the located infra-structure, the model opened 15 TS, 11 DS and 2 incinerators among
the 18 possible locations for each type of facility. The chosen locations and the handled waste
quantity for DS and incinerators were as shown in the table 13.
When comparing the two solutions found it must be said that a few changes are noticeable from
one to the other. The number and location of TS is the same in both solutions. The best solution
differs in terms of DS and INC from the model solution by not opening a DS in Portalegre and an
INC in Coimbra. Table 13 – Location of the opened infra-structure
LOCATION T. STATION DISP. SITES INCINERATOR
LOCAT. % USED LOCAT. % USED
AVEIRO X X 18,56 - -
BEJA X - - - -
BRAGA X X 31,93 - -
BRAGANÇA X X 4,79 - -
CASTELO BRANCO X X 10,62 - -
COIMBRA X X 38,83 - -
ÉVORA X X 12,90 - -
FARO X X 12,34 - -
GUARDA - - - - -
LEIRIA - - - - -
LISBOA X X 125,81 X 48,22
PORTALEGRE X - - - -
PORTO X X 63,64 X 51,60
SANTARÉM X X 16,24 - -
SETÚBAL X - - - -
VIANA DO CASTELO X - - - -
VILA REAL X X 10,64 - -
VISEU - - - - -
As it can be observed, from table 13, only three TS serve as “pure” TS, for both groups of waste,
and out of the 18 possible locations only Viseu, Guarda and Leiria centroids do not get a TS. In
terms of used capacity of the incinerators, the two locations handle almost the same amount of
waste and their used capacity is in the stable range. The number of incinerators and their
geographic distribution is accordingly to what would be expected, one located in the middle of the
northern region (Porto) and the other in the middle of the southern region (Lisboa) of Portugal.
63
In terms of Group III disposal site it can be seen that most of the DS opened are working at a rather
low percentage. Despite the high costs of opening a new facility instead of redirecting the waste to
an already existing facility, the model chooses to open new facilities and to let them run in the
warm-up range. This can be the consequence of relatively high transportation costs, meaning that
the saves made by concentrating all the waste in these facilities are overcome by the increase in
transportation costs. This situation was predictable as in a previous chapter it was assumed that
the transportation costs accounted for 70% of all costs in HMW treatment.
The DSs, running in the warm-up range, are on average using 18% of their total capacity. There
are also two opposite cases. Porto DS is running in the stable range using 64% of its capacity and
Lisboa is a more extreme case has it is running over its capacity by 26%. This indicates that next to
the biggest production centre there is the necessity of a bigger treatment facility.
To recall the reader, while generating the cost data used in this model it was necessary to define
the capacity of the DS (6.850 ton/year) and the INC (2.600 ton/year). Therefore the percentages
used seen in table 13 are relative to the previously mentioned values. The model as it is formulated
does not impose any capacity restrictions to the different facilities. This option was considered
since it is expected to have interaction between the results provided by the model and its user.
Therefore before a subsequent iteration the user should adapt the facilities choice, e.g. by
increasing or decreasing their capacity, to the previously presented results of the model.
In conclusion it can be observed that the types of facilities chosen for this particular scenario are
not the optimal. In a following sub-chapter the effect and consequences of choosing new facilities
will be discussed. The cost functions that are currently being used are taken from the available
data and also from estimates made using the literature. Consequently it would not make sense to
estimate new cost functions for a new type of technology or a new facility with a different capacity,
since more precise and complete data, which is unavailable at the moment, would be needed. Due
to these facts the results analysis will carry on having the aspects before mentioned discussed
further on.
Figure 15 represents the influence areas of the different TSs. It allows a better perception of the
waste flows between the generating nodes and their first stop. The solution presented by the
optimization shows that the only paths considered are the ones where both Group III and IV travel
together from the generating node, firstly to a TS and afterwards each groups is directed to its final
destination. As a result the first step of transportation is common for both Groups and for all
generating nodes. These results can be seen in Appendix IV.
It is interesting to observe that the major part of the TSs are centred in their influence area, clearly
determining an action radius around them. Those TSs, that by their geography are close to natural
borders, such as Faro, Porto and Aveiro, present an area of influence that extends to the middle
distance between them and the neighbouring TS. At a first glance Setubal might seem out of the
last category, but seen that Euclidean distances are considered and each municipality is
represented by only one point, it can be concluded that this case can also be introduced in the
previous category. To better understand the TS influence areas that are not as regular as they
64
probably should be there is the need to observe both TS and DS, and the DS influence area. This
information is shown in figure 16.
Figure 15 – Influence areas of the T.S.
Figure 16 – Influence areas of the Disposal Sites (Group III)
Transfer Station
Transfer Station
Disposal Site + Transfer Station
65
Figure 16 represents the influence areas of the different disposal sites (Group III waste). In this
figure it can be seen that the influence areas are, at a first sight, accordingly to what would be
expectable. To understand why the model opened such a high number of disposal sites resulting in
low used capacity for each facility and consequently higher treatment costs per unit, as most of the
facilities are working in the warm-up range, one can look at the example of the Porto (64%) and
Braga (25,57% - Braga TS, 6,36% - Viana do Castelo TS ) disposal sites (the two north western
DS).
Once the waste gets to the TS, the two waste groups can be treated separately as there is no more
advantage in transporting them together. So in the two previous mentioned cases it would seem
logical, at a first sight and due to the proximity of the Braga DS, to concentrate the Group III waste
treatment in one single facility (probably in Porto). In the actual scenario the treatment cost for
these two facilities is of approximately:
397479 + (4360 ∗ 83,29) + 112212 + (2187 ∗ 187,40) = 1.282.679 €
For the hypothetical scenario where the Group III waste treatment would be concentrated in one
facility (Porto), the total treatment cost for that area (Porto TS, Braga TS and Viana do Castelo TS)
would be:
397479 + (4360 + 2187) ∗ 83,29 = 942.779 €
It would lead to saving 339.900 €/year in treatment costs. The savings made in treatment costs
would mean that to have two cost equivalent scenarios there would be, in the hypothetical one, an
extra 339.900 €/year to spend on transportation costs.
If Porto was chosen to house the only DS, it would mean that the 2.187 ton received annually at
the Braga DS would have to spend approximately an extra 422.647 €/year to reach the Porto TS,
this value represents the extra transportation costs. This amount is bigger than the savings made in
treatment costs resulting in a more expensive scenario.
In case the hypothetical scenario was the opposite: to open a single DS at Braga, there would be
4.360 ton/year of Group III to move from Porto TS to Braga DS. This would present an even more
costly scenario. Thus it is perceptible that most cost effective scenario, for at least this area, is the
one found by the model.
Therefore it can be concluded that the relatively high transportation costs, when comparing to
treatment costs (assumption made in a previous chapter), result in having a final solution where
most of its facilities work a lot under their maximum capacity. Although this conclusion is to general
for the single demonstration made it definitely points out to a possible cause of the high number of
facilities opened. Further on, a sensitivity analysis will be ran to understand the impact of the
relation between transportation and treatment costs.
Figure 17 shows the influence areas of the incinerators. In this case Portugal is divided into two
areas, North and South, with two incinerators, one in Porto and the other in Lisboa, eliminating
almost the same amount of Group IV waste each. Both the incinerators are located in the centre of
66
the two influence areas, in terms of North-South distances, but they are clearly located next to the
coast line instead of being located in the interior of the country. This is a clear result of the unequal
distribution of the population and the hospital resources over the Portuguese territory. It is a fact
that the Portuguese population is much more concentrated in the coastline of Portugal than in its
interior.
Although the capacity choice for the incinerators seems fair in terms of costs, due to the predicted
evolution of HMW production which will not vary dramatically in the coming years, an alternative
should be studied with incinerators of about 75% of the capacity used for this application (1.950
ton/year). It would probably result in lower elimination costs. The question is: With these new types
of incinerators would the model allow the opening of more incinerators or just a lower total cost with
the same facility layout. Although the data for elimination costs for different technologies is not
available, there is another way to study the effect of changing the elimination costs. This will be
studied as a sensitivity analysis to the variation of transportation costs relatively to treatment costs.
The scenario of choosing a lower capacity incinerator can be exemplified as a reduction of the gap
between transportation costs and treatment costs.
Figure 17 – Influence area of the incinerators
7.2.2 The effect of the technology choice
The solution presented before was meant to illustrate the application of the model developed in this
thesis. As the costs were taken from the current HMW management market in Portugal there was a
need to consider the technology which represents those costs, resulting in the choice of high
Transfer Station
Incinerator + Transfer Station
67
capacity DS facilities. The obtained layout, with its low used capacity facilities, would have allowed
the DM to understand that the technology choice was not the most correct. The relatively high
transportation costs do not allow the treatment to be concentrated in a small number of facilities,
but point to a more disperse layout in terms of treatment. The fact that the technology chosen was
not the most suitable one indicates a total cost that is for sure higher than the one that can be
attained in reality for these conditions.
If there was a more complete set of data, the next step for the user would have been to consider a
new type of technology or different capacities for the DS facilities. One of the possible choices
should have been to allow smaller capacity facilities to be opened in nodes located on the
periphery of the big production centres and to maintain the same capacity facilities in the big
production centres. This is the interaction, mentioned before, that this model is supposed to create
between the DM and the optimized solutions.
So before analysing other aspects of the solution the user should have focused in obtaining higher
capacity rates in all the facilities in order to get a mostly accurate approximation of the total cost.
In this particular case the analysis carried on without correcting the technology choices. The fact is
for that matter it would be necessary to introduce new cost functions in the model. As it was
explained before the lack of data would have made it impossible to obtain new cost function that
would reflect reality. The pursuit of more suitable facilities would have lead to the introduction of
inaccurate data and so the choice was to focus the explanation on presenting the actual solution
instead of a vague search for results that would not represent reality.
However, it is possible to predict the effects of choosing a new technology or a different capacity
facility by analysing the possible outcomes qualitatively. Let it be assumed the DM had chosen to
change only the capacity of the autoclave units, since the incinerators are working at a rather
acceptable rate, but also because they are obnoxious facilities and so it could be that DM’s
objective was to minimize the construction of such facilities. In this case the DM would redefine the
facilities located in the biggest pole to handle more waste (increase the capacity of the Lisbon
autoclave) and it would allow units of smaller capacity (e.g. 20% of the actual capacity) to be
installed in the other nodes according to the previously obtained results, therefore lowering all the
treatment costs.
From this solution two outcomes would be possible; the first one would lead to a situation where
the only factor that changes is the total cost of the system, the second one would be the opening of
more DS in remote places such as the zone around Évora, with Portalegre and Beja opening their
own DS. However, most probably after two or three adjustments in the facilities chosen for each
node, the DM would be looking at a scenario where both the location and the capacity chosen
would be optimized.
The changes in the final layout would also be conditioned by the relation between transportation
and treatment costs, reinforcing the necessity of having a sensitivity analysis done to this matter.
68
The flexibility and the fast results presentation is the purpose of this model. Rather than having a
model that presents the final optimized solution the purpose of this thesis was to present a tool that
could be used interactively with the DM. Due to the fact that the HMW market is a free market
driven by economic factors the DM using this tool, would most probably be the person in charge of
the strategic planning of one of the HMW management companies. With this interaction the DM
would be able to weight the trade-offs between the different strategies chosen, and also to weight
other factors that can be imposed by the Portuguese government. The flexibility of this model
formulation would allow the DM to adapt it to the constraints he finds necessary and to quickly
study different alternatives choosing among the ones he considers suitable.
However, due to the already installed infra-structure, one can say that the results presented by the
model as it is, will point to what will be the expectable layout of the HMW management market in a
few years.
7.2.3 Comparing the obtained solution against reality
Finally in order to compare the model’s results with the already built infrastructure, it is presented in
table 14 the already existing facilities and also the facilities suggested by the optimization process.
Table 14 – Comparison between the locations chosen and the existing locations
LOCATION OPTIMIZED SOLUTION EIXISTING FACILITIES
T.S. D.S. INC. T.S. D.S. INC.
AVEIRO X X - X - -
BEJA X - - X X -
BRAGA X X - X X -
BRAGANÇA X X - - - -
CASTELO BRANCO X X - X X -
COIMBRA X X - - - -
ÉVORA X X - - - -
FARO X X - X X -
GUARDA - - - - - -
LEIRIA - - - X X -
LISBOA X X X X X X
PORTALEGRE X - - - - -
PORTO X X X X X -
SANTARÉM X X - - - -
SETÚBAL X - - X X -
VIANA DO CASTELO X - - - - -
VILA REAL X X - - - -
VISEU - - - - - -
Total 15 11 2 9 8 1
By analysing the information presented in table 14, one can withdraw that both cases are in a
certain way similar. The system is not based in “pure” TS, only 4/15 pure TS in the final solution,
and also that there is an elevated number of DS. As one could see in the results presented before
the inefficiency of the HMW system, a very important issue to be solved, was also present in the
69
solution proposed by the model. It is important to remember that the solution presented
corresponds only to the first iteration of the solving method and so a better efficiency could be
attained in subsequent iterations. Still the results presented by the model over-perform by 22,5%
the already built infra-structure. How is it possible that using the same technology and the same
capacities one still finds room for improvement?
Firstly one must consider that in the existing facilities columns, only the districts are represented
(there can be more than one facility per district) whereas the model is limited to locating not more
than one type of facility per district. In reality, by 2016, there will be 13 DS in Portugal, which is
approximately equal to the 11 proposed by the model. However the real total treatment capacity in
2016, which is overestimated, will be lower than the one proposed by the optimal solution.
So it is the simple fact that the model’s solution proposes a more even distribution of DS facilities
that allows the total cost to decrease 22,5%. This disperse layout allows savings in terms of
transportation costs.
Nonetheless there is a need to remember that the lack of data did not allow the pursuit of the
optimal capacity (and cost) configuration. If the model would have been fitted with the new facility
types (lower capacity) it could have been guaranteed that the total capacity would be inferior to the
real one resulting in an even bigger reduction in the total cost of the system.
In terms of incinerators, the current scenario is concerning because the only HMW incinerator is
located in the centre of Lisboa. This location raises problems such as air contamination and
increased transportation costs as the vehicles must enter the city to drop the HMW. Another issue
is the fact that this incinerator will not have the capacity to incinerate all the Group IV waste
produced in continental Portugal. Therefore there is the urgent need to relocate the incinerator
and/or expand the actual incineration capacity. The solution presented by the model reflects a good
approach of splitting the capacity into two locations to avoid high transportation distances between
producer and the sinking node. As one could see the optimal solution also locates one incinerator
in Lisbon, nevertheless it is none but logical to build such a facility outside agglomerates of
population in more industrialised zones with easy access to vehicles and less impacts to the
population.
In conclusion one can say that due to the fact that the HMW management market is relatively new,
it is not cost optimized yet. The companies operating in this market started by opening big
treatment facilities in order to present competitive prices ignoring that the transportation cost are
quite an important part in the overall costs. This directed the market to an expansion with the
construction of more high capacity facilities.
Seen that the production of HMW is expected to be stable in the years to come it is my opinion that
the installed treatment capacity has to decrease in the following years. It is expectable to see the
second outcome presented in chapter 3, which is operating companies downsizing their existing
Group III waste treatment facilities to present more competitive prices but also creating a more
disperse network of DS. In terms of Group IV waste elimination, seen that the elimination costs of
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this type of waste are slightly higher, one can always expect fewer facilities of this type and a
bigger concentration of waste eliminated in each one of them. In general the system will not be
based in “pure” TS, but in TS serving mostly Group IV waste. Finally in terms of total cost the
possible reduction will be proportional to the reduction in treatment costs obtained by using smaller
capacity facilities, one can expect improvements not much bigger than the proposed 22,5%. The
fact is the decreases in costs, after having a well distributed network of facilities, will be majorly the
contribution of reduced treatment costs, which account only for 30% of the total cost. Therefore
considering the prices of today a good estimate for the lowest value of the HMW market in Portugal
would be around 14 millions of Euros per year.
7.3 Sensitivity analysis
During the results analysis it was observed that there were two parameters to which a further
analysis, regarding their influence on the model behaviour, was relevant.
The first parameter is the TS fixed cost. The costs related to opening such a facility are
approximate estimations; as a result it is important to understand how a variation in these
estimations would affect the final result. The influence of TS fixed cost will determine how relevant
is the solution presented before and will help validate the results presented.
The second parameter is the relation between the transportation costs and treatment costs. The
division 70-30 was based on general estimations given by the reviewed literature. The aim of this
sensitivity analysis will not be to validate the results but rather to validate the model. It is
understandable that if transportation costs are low – relatively to treatment costs - then the final
layout will have a rather concentrated infra-structure shape. On the other hand if the transportation
cost are high then the final layout will have a rather disperse infra-structure shape. So by changing
this ratio one can observe if the model responds accordingly to what would be expectable.
7.3.1 Transfer Station fixed cost
To evaluate the model sensitivity to the first parameter, a series of runs were made increasing
solely the fixed cost associated to opening a TS. The first run was made with a fixed cost of
30.000€ and then it was raised to 75.000€, 90.000€, 150.000€ and 200.000€. It is necessary to
recall that the model was ran with a TS fixed cost of 100.000€ (control value).
The model presents a solution discriminating both the chosen locations for the different type of
facilities as well as the waste flows between production node and sink node. In this case the
interest of this sensitivity analysis relies mostly on the facility location and their used capacity rather
than in the waste flows. In the next tables the results for each of the TS fixed cost value will be
presented aggregating the results by facility type.
The first comparison is relative to the TS location. As it can be observed, in table 15, once the fixed
cost of TS increases the total number of opened TS decreases. This observation is consistent as it
is expectable that if costs go up the number of opened facilities should go down.
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In terms of waste flows, by analysing the whole solution (not presented here), it is possible to
conclude that in all the cases both waste groups are transported together passing by a TS before
going to the respective sink node. This means that even with TS costing twice the price it is still
more cost effective to go to a farther TS before going to a sink node than to go directly to the sink
node and endure the increase in transportation costs. It can be concluded that for the 200.000€
scenario, when comparing to the 100.000€ scenario, the cost of opening 4 extra TS does not
compensate the increase in transportation costs induced by the absence of those TS. By analysing
the total number of TS opened for each of the different fixed costs it is observable that the variation
near the control value is not very high, consequently if the TS fixed cost real value is near 100.000
€/year, the model solution will be mostly accurate.
In terms of the DS distribution, after analysing the previous results it would be predictable that by
lowering the fixed costs associated with TS a decrease in overall transportation cost will be
obtained as the producing nodes will be closer to TS, therefore more ton*km of waste would be
travelling in high capacity vehicles. Consequently one can expect two scenarios depending in the
overall decrease in transportation costs. If the decrease has a high impact in total cost, then one
would expect to have a concentration of Group III waste in fewer DS, benefiting from lower
treatment costs. If the decrease has a low impact in total cost, then one would expect to have the
same number of DS in nodes where TS would also be present.
Table 15 – Geographical distribution of T.S. when its fixed cost varies
LOCATION T.S. FIXED COST
30.000 75.000 90.000 100.000 150.000 200.000
AVEIRO X X X X X X
BEJA X X X X - -
BRAGA X X X X X X
BRAGANÇA X X X X X X
CASTELO BRANCO X X X X X X
COIMBRA X X X X X X
ÉVORA X X X X X X
FARO X X X X X X
GUARDA X - - - - -
LEIRIA X X - - - -
LISBOA X X X X X X
PORTALEGRE X X X X X -
PORTO X X X X X X
SANTARÉM X X X X X X
SETÚBAL X X X X X -
VIANA DO CASTELO X X X X - -
VILA REAL X X X X X X
VISEU X - - - - -
TOTAL 18 16 15 15 13 11
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Table 16 – Geographical distribution of D.S. when T.S. fixed cost varies
LOCATION T.S. FIXED COST
30.000 75.000 90.000 100.000 150.000 200.000
AVEIRO X X X X X X
BEJA - - - - - -
BRAGA X X X X X X
BRAGANÇA X X X X X X
CASTELO BRANCO X X X X X X
COIMBRA X X X X X X
ÉVORA X X X X X X
FARO X X X X X X
GUARDA - - - - - -
LEIRIA - - - - - -
LISBOA X X X X X X
PORTALEGRE - - - - - -
PORTO X X X X X X
SANTARÉM X X X X X X
SETÚBAL - - - - - -
VIANA DO CASTELO - - - - - -
VILA REAL X X X X X X
VISEU - - - - - -
TOTAL 11 11 11 11 11 11
It must also be added that due to the 70-30 distribution between transportation and treatment
costs, the transportation cost decrease will be expected to have a low impact over the total cost.
Therefore these conclusions point out to a fairly constant DS number for the different TS fixed
costs.
As it can be seen in table 16, the predictions are confirmed by the results. The DS number and
distribution remains unaltered. In terms of waste treated the DS maintain their treated amounts with
a variation on average of around 2% of the control value (100.000 €).
Table 17 presents the distribution of incinerators for the several runs. In this case the number of
facilities and its distribution is also stable for the different runs. Incinerators are slightly more
expensive than DS (so less sensitive to variations in transportation costs) and one must bear in
mind that Group IV waste is dependent on Group III waste to be transported. So it is logical that the
variation on the incinerator location and number follow the DS tendency.
In conclusion the observed lack of variation in the distribution of the facilities other than the TS,
when decreasing the TS fixed cost, verifies the importance of transportation costs in this particular
application. Once again the choice of a 70-30 cost relation between transportation and treatment
cost leads to the conclusion that the reduced transportation costs between TS and sink nodes are
still so high that it is not worth to have a more centralized layout where the treatment costs are
lower due to the high capacity factors of the several facilities. It can also be concluded, what was
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already referred in this thesis, that for a scenario with such a distribution between costs it is better
to have a bigger number of smaller facilities.
Nevertheless this lack of variation also shows the robustness of the model to a variation of this
parameter, confirming that for TS fixed cost values of the same order the solution presented is still
very close to the optimal one.
Table 17 – Geographical distribution of INC. when T.S. fixed cost varies
LOCATION T.S. FIXED COST
30.000 75.000 90.000 100.000 150.000 200.000
AVEIRO - - - - - -
BEJA - - - - - -
BRAGA - - - - - -
BRAGANÇA - - - - - -
CASTELO BRANCO - - - - - -
COIMBRA - - - - - -
ÉVORA - - - - - -
FARO - - - - - -
GUARDA - - - - - -
LEIRIA - - - - - -
LISBOA X X X X X X
PORTALEGRE - - - - - -
PORTO X X X X X X
SANTARÉM - - - - - -
SETÚBAL - - - - - -
VIANA DO CASTELO - - - - - -
VILA REAL - - - - - -
VISEU - - - - - -
TOTAL 2 2 2 2 2 2
7.3.2 Treatment vs. Transportation cost
In terms of this second sensitivity analysis the objective of the results will be to validate the model
behaviour when subject to such changes. For this analysis all the transportation costs were
multiplied by a factor in order to vary the relation between those and the treatment costs. The
assumed control value is for transportation costs with a factor of 100% (70-30). The analysis was
done for factors of 20% (32-68), 50% (64-36) and 200% (82-18). The choice of these values was
made to have two extreme values of the relation (32-68 and 82-18) and a close value to the initial
relation (64-36).
To illustrate these different scenarios an example of the calculi made is presented. Multiplying the
transportation costs by 20% means that the overall weight of transportation costs is now equal to
0,2 ∗ 70/(30 + 0,2 ∗ 70) = 32%, therefore the treatment costs weight is equal to 68%.
It can be expected that as this relation between costs approaches the 32-68 value a more
concentrated layout will be presented as a solution, since the treatment costs become the most
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important part of total costs and so in order to have a lower total cost there is the need to have
higher usage of infra-structures. When this relation approaches the 82-18 value a more disperse
layout will be presented as a solution, given that this will only reinforce the already high impact
transportation costs have in overall costs. Consequently for the last case scenario a lower usage
rate is expected for each facility.
Again the focus of this sensitivity analysis is not the waste flow, but the location and number of the
different infrastructure.
In table 18 it is presented the TS locations for the different transportation cost factors. It is
observable that this type of infra-structure is rather important for the functioning of the layout, and
the scale economies are taken into account, as even with a reduced transportation cost impact the
number of TS opened is quite high (8). This behaviour is as expected since in reality TS are simple
and quite cheap facilities (when comparing to DS and INC) to build and run, so as a result even in
a scenario where transportation costs are not an important part of the overall cost such facilities
should be present in a quite important number. As it can be seen for a relation of 32-78 (20%) there
are almost half of the locations that hold a TS.
Table 18 – Geographical distributions of T.S. for different Transportation/Treatment cost ratios
LOCATION TANSPORTATION COSTS FACTOR
20% 50% 100% 200%
AVEIRO - X X X
BEJA - - X X
BRAGA X X X X
BRAGANÇA - X X X
CASTELO BRANCO - X X X
COIMBRA X X X X
ÉVORA X X X X
FARO X X X X
GUARDA - - - -
LEIRIA - - - X
LISBOA X X X X
PORTALEGRE - - X X
PORTO X X X X
SANTARÉM X X X X
SETÚBAL - - X X
VIANA DO CASTELO - - X X
VILA REAL X X X X
VISEU - - - X
TOTAL 8 11 15 17
The same analysis can be made to the results presented in table 19, regarding the location of the
DS for the different transportation cost factors. Once again the number of DS increases with the
increase of the transportation cost impact, going from a more concentrated to a more dispersed
layout. But as the costs of opening such facility are related to both the opening and the amount of
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waste processed it is clear that for low transportation costs the number of DS will not be as
important as the number of TS. The DS are infra-structures which in reality are costly to open and
operate, and lower costs will be attained by treating the most waste possible in each facility.
Table 19 – Geographical distributions of D.S. for different Transportation/Treatment cost ratios
LOCATION TANSPORTATION COSTS FACTOR
20% 50% 100% 200%
AVEIRO - - X X
BEJA - - - X
BRAGA - - X X
BRAGANÇA - - X X
CASTELO BRANCO - X X X
COIMBRA X X X X
ÉVORA - X X X
FARO - X X X
GUARDA - - - -
LEIRIA - - - X
LISBOA X X X X
PORTALEGRE - - - X
PORTO X X X X
SANTARÉM - X X X
SETÚBAL - - - -
VIANA DO CASTELO - - - X
VILA REAL - X X X
VISEU - - - X
TOTAL 3 8 11 16
The difference between DS/INC and TS is that the first one are more economical if they handle
higher amounts of waste whereas the TS cost economy is related to the relation between the
number of ton*kilometres made between the generating node and the TS and the number of
ton*kilometres made between the TS and sink node. So in the TS case the closer they are to
generating nodes the higher the economy made, as a result a high number of TS are opened even
when the transportation costs impact is low.
In terms of the distribution of the INC, presented in table 20, the same comment regarding the DS
can be made. The behaviour of the model is consistent with the logic exposed before. One should
only add that because of the smaller amounts of Group IV waste treated and its higher treatment
cost per unit, as expected there will be even fewer INC than DS.
Going back to the question posed during the incinerators results analysis in 7.2.1, whether the
choice of a smaller capacity incinerator would lead to the opening of new incinerators or just a drop
in the total cost, it is now possible to predict the answer. By choosing smaller capacity incinerators
(e.g. about 75% of the actual capacity) the DM would be only reducing the Group IV treatment cost
per unit, since the incinerators are quite insensitive to the relation between transportation and
treatment costs, as it can be observed from table 20. There rather stable behaviour when faced
76
with changes in that ratio leads to the belief that choosing slightly smaller capacity incinerators
would only decrease the total HMW management cost and would not point to the opening of new
facilities (INC).
Table 20 – Geographical distributions of INC. for different Transportation/Treatment cost ratio
LOCATION TANSPORTATION COSTS FACTOR
20% 50% 100% 200%
AVEIRO - - - -
BEJA - - - -
BRAGA - - - -
BRAGANÇA - - - -
CASTELO BRANCO - - - -
COIMBRA - - - X
ÉVORA - - - X
FARO - - - X
GUARDA - - - -
LEIRIA - - - -
LISBOA X - X X
PORTALEGRE - - - -
PORTO X X X X
SANTARÉM - - - -
SETÚBAL - X - -
VIANA DO CASTELO - - - -
VILA REAL - - - -
VISEU - - - -
TOTAL 2 2 2 5
7.4 Partial optimization
As it was emphasised before, the purpose of this work was not to undergo on a study for the
possible location of the new incinerator but to provide a tool that would present the optimal layout
of HMW facilities.
However in this final sub-chapter of the application to the Portuguese case-study, a simplified
version of the developed model will be presented. This new application will be focused on solving
the Portuguese incineration problem in a short/medium term perspective.
7.4.1 Constraints and considerations of the partial optimization model
Following the concepts introduced in chapter 3, a simplified model will partially optimize the HMW
management system. Basically in the partial optimization the location of the facilities other than
incinerators will become a parameter instead of a variable. To model reality with this simplified
version of the optimization model studied earlier two approaches can be taken.
The first one, slightly off reality, would be to consider exactly the same model as before with certain
small modifications. Apart from considering the TS and DS location as parameters and not
77
variables it would also be necessary to modify the DS nodes distribution in order to accommodate
the fact that certain districts possess more than one treatment facility. In addition the capacities of
each facility would have to be integrated into the model and there would be the need to introduce
the real cost curves of the existing infra-structure. This approach is slightly off reality because such
a model would probably yield a solution in which the amounts of waste going through the existing
TS and DS would not represent the real amounts of waste treated by each facility (market shares).
In reality the HMW market already exists and most of the companies are still expanding their Group
III waste treatment capacities even though the overall national treatment capacity is already almost
twice the annual production. This means that in Portugal there are already companies working who
have there own market share which is insured by contracts signed between the companies and
the producers. So modelling in a partial optimization context the allocation of HMW to the existing
companies purely based on cost functions is not representative of reality and does not serve the
objective, as the operating companies have a history of contracts with the different producers.
It is necessary to say that in Portugal there are only two locations that are TS in the pure concept:
Estarreja in the Aveiro district and Pombal in the Leiria district. This means that the HMW system
layout is not very much based in TS as it should be. TS are built next to the already existing DS
and seen that it is clear by now that it is much more economical to collect Group III and IV waste
together instead of collecting each group on its own, one can argue that the company who picks
Group III waste at a certain node will also pick the Group IV waste produced at the same node.
So when studying the location of a new incinerator due to the fact that all Group IV waste goes to a
DS, with exception of the waste that goes through Estarreja or Pombal, one can say that the real
generating nodes in this case, will be the DS facilities. This tremendously simplifies the model as it
is now a two level problem with the generating nodes now being the TS/DS and the sink nodes
being the incinerators. So to reach a solution with this scenario there is only the need to know how
much Group IV is “produced” in every new generating node.
Due to the lack of data, e.g. market shares of the different infrastructure, there will be a need to
work with average values and with some simplifications. Firstly instead of considering as
production nodes the real facility locations the model will use the centroids calculated before. Also,
due to the absence of information regarding the amount of waste that goes through the TS each
year, only the DS will be considered as producers (the Aveiro node will not exist).
From the analysed data it is possible to state that the proportion of Group III and IV waste
produced at each node is constant. Assuming that each DS works with the same capacity factor
and not taking into account the Aveiro TS as a generating node, a new model can be built with
generating nodes in the locations of the current DS. The Group IV waste production at these nodes
will be equivalent to the proportion of Group III waste treated at the same node.
As an example, assuming that the overall used capacity of DS is 57%, for a DS with 6.850 ton/year
capacity there will be 57%* 6.850= 3.904,5 ton/year treated in this facility which represents 17% of
the total production, if it is assumed that 23.000 ton of Group III waste are produced yearly.
78
Therefore the production of Group IV waste for this node will be 17% of the total yearly Group IV
waste production.
The transportation costs will be the same used before – transportation cost between TS and INC,
as well as the INC treatment costs and their distribution according to the amount of waste treated.
7.4.2 Simplified model formulation
The new model objective function will be as follows:
푀푖푛푖푚푖푧푒 푐표푠푡 = 푃퐺4 ∗ 푑 ∗ 퐶푡푠 ∗ 푍
+ (푄푡퐼푁퐶 ∗ 푉푎푟퐼푁퐶 + 푌 ∗ 퐹푖푥퐼푁퐶 ) (19)
Subject to:
푍 = 1 , 푖 = 1, … ,푚 (20)
푃퐺4 ∗ 푍 ≤ 훽 ∗ 푌 , 푗 = 1, … , 푛 (21)
푄푡퐼푁퐶 ≤ 훽 ∗ 푌 , 푗 = 1, … , 푛; 푥 = 1, … , 푟 (22)
푌 ≤ 1 , 푗 = 1, … , 푛 (23)
푃퐺4 ∗ 푍 − 푄푡퐼푁퐶 = 0 , 푗 = 1, … , 푛 (24)
i, represents the set of new producing nodes equivalent to the locations of the existing DS and j, represents the possible incinerator locations. The variables are: (1) Zij, which is the binary decision
variable related to the path choice, (2) QtINCjx, which represents the amount of waste treated at
each incinerator and (3) Yjx, is the binary decision variable related to the opening of an incinerator
at a certain location.
The parameters PG4i, dij, Cts, VarINCjx, FixINCjx and β are the same as defined before in chapter
5, respectively the Group IV waste production at node i, the cost of transportation, the variable and
fixed costs of treatment and a control parameter.
The restriction (19), (20), (21), (22) and (23) are respectively equivalent to the (4), (7), (9), (11) and
(13), presented in chapter 5.
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7.4.3 Data generation
For this simplified model the previously used cost curve for the incinerator will also be used as the
variable and fixed cost for such facility. The transportation cost between DS and INC will be the
previously defined Cts, as it is assumed that the transportation conditions prevail. The generating
nodes and their total capacity are as shown in table 21, as well as the considered Group IV waste
“produced” in those nodes.
The coordinates of the node will be the ones previously calculated for the centroids. With this
information it is now possible to run the model.
Table 21 – Group IV waste “produced” at the DS
LOCATION
EIXISTING FACILITIES
D.S. Annual
Capacity (ton)
% Total Capacity
Group IV waste production (ton/year)
AVEIRO - - - -
BEJA X 5.321 12,88 334,21
BRAGA X 3.650 8,83 229,26
BRAGANÇA - - - -
CASTELO BRANCO X 17 0,04 1,07
COIMBRA - - - -
ÉVORA - - - -
FARO X 2.221 5,38 139,50
GUARDA - - - -
LEIRIA X 31 0,08 1,95
LISBOA X 11.161 27,01 701,03
PORTALEGRE - - - -
PORTO X 3.195 7,73 200,68
SANTARÉM - - - -
SETÚBAL X 15.720 38,05 987,38
VIANA DO CASTELO - - - -
VILA REAL - - - -
VISEU - - - -
7.4.4 Analysing the results
The optimal solution was found after a few seconds. It resulted in the opening of three incinerators
one big unit around the Setubal centroid and two small units, one around the Braga centroid and
the other around the Beja centroid. The Group IV waste flows are as shown in figure 18, and the
amounts eliminated by each of the incinerators are presented in table 22.
The waste flows are consistent with what was expected. At a first sight Castelo Branco DS is
misdirected but reality is that the elimination cost in Braga is far more expensive than the increase
in transportation cost to the Lisboa incinerator.
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Table 22 – Amounts of Group IV waste eliminated by each incinerator
Incinerator location
Amount of Group IV waste eliminated (ton/year)
Beja 473,71 Braga 429,94
Setubal 1.691,43
Again this application is far simpler than the one before. The results presented due optimize the
incinerator location when considering the existing facilities. But the excess in Group III waste
treatment capacity is a very important issue that is holding the HMW system cost ineffective.
The solution presented here can be considered as a short term optimal scenario. In reality the
attained layout will look more with the previous solution as the companies will try to offer a better
and more competitive service to the producers. This will result in lower treatment cost which will
reflect in fewer expenses on waste treatment by healthcare facilities. In addition the reduction in
waste treatment fees will also make the producers more compliant to a better triage of the medical
waste therefore attaining the objectives proposed by the legislation.
Figure 18 – Waste flows between DS and INC
7.5 Conclusion
Nowadays the Portuguese government is thinking about relocating the incinerator to Chamusca
(district of Santarem) and closing the Lisboa incinerator. It can be said by analysing the results
Disposal Site
Incinerator + Disposal Site
81
from both the global and the partial optimization that a less centralized distribution of the
incineration capacity would be better for two reasons.
Firstly the transportation costs would be lower which would definitely have an impact in the overall
disposing cost. Secondly it would prevent a monopolist scenario where one company controls all
the HMW incineration capacity and therefore controls the prices of incineration. If at least two
incinerators are built and operated by two different companies there will be some competition in
this sector lowering the costs of treatment thus creating a better market scenario.
In order to summarize the two studied models but also to compare the costs of the Portuguese
government solution (Chamusca), in the conditions of 7.4.1, to the solution given by the partial
optimization, table 23 presents a summary of the most relevant information. It is necessary to recall
that the partial optimization model is a two level only model, therefore only one type of facility has
to be located (the incinerators) and only one type of waste flow has to be allocated (generating
node/sink node). In the Chamusca application, presented below, the incinerator location is no
longer a variable, neither are the waste flows allocation since there is only one possible sink node.
Therefore the total costs calculi were made recurring to an excel worksheet. From table 23 it is
possible to reinforce the idea that the Chamusca option is not actually a good solution as it has a
cost associated which is 66% higher than the cost associated to the solution obtained by the partial
optimization model. Table 23 – Summary of the different models and solutions studied
No. of Variables
No. of Binary
variables
No. of Equations
No. of Non
Zeroes
No. of Iterations
CPU Time (sec)
Optimality Margin
(%)
Objective Function Value (€)
Global Optimization
Model Solution 281.035 280.962 185.939 2.022.805 51.193 1.487,2 4,59% 14.724.908
Best Solution 66.427 66.400 59.050 498.625 1.155 12,3 0,00% 14.712.062
Partial Optimization
Chamusca - - - - - - - 2.713.354
Model Solution 217 180 99 821 129 0,4 0,00% 1.634.226
By the results presented in the different approaches taken, one can present two different solutions.
The first one, given by the global optimization model, would focus in locating two big capacity
incinerators, one near the Lisbon region and the other near the Porto region. The second solution,
given by the partial optimization model, points to locating one big incinerator near the Lisbon region
and two smaller units, one near Beja and the other near Braga. Both solutions can be considered
as good approaches of the optimized HMW management system layout.
Despite the simplifications made on the partial optimization, one can conclude that the best solution
includes the installation of a big capacity incinerator near the Lisbon region and a smaller
incinerator near the Porto region. Apart from the fact that those two regions are central in terms of
the HMW management infra-structure already built, they are also the most populated regions and
the ones that have the biggest health-care infrastructure. Therefore those regions will be the ones
that produce the biggest amounts of HMW. Nonetheless the DM might need to consider other
factors than the economical point-of-view; consequently further analysis should be made in order to
understand the weight of other factor and their optimal solutions.
82
8. CONCLUSION AND FURTHER RESEARCH
8.1 A Summary of the work developed
In this dissertation it was possible to understand how the medical waste sector works. Firstly it is
necessary to say that generally the medical waste field is a quite regulated area in terms of the
specific care needed to handle and dispose the waste. Although there are several differences one
main aspect is common to developed countries legislations, there is always the separation between
non-hazardous and hazardous medical waste.
The work developed was focused on the HMW management problematic. As it was seen this type
of waste is dangerous for the environment and for human health. As a result it has to be made
innocuous before it can be disposed. Several countries accept different types of treatment
regarding different types of HMW. The specific requirements for disposing a certain type of waste
depend on which category the type of waste belongs to. In the European Union a general list
(EWC) was created not only containing medical waste but also other types of waste. Portugal in
1996 approved legislation concerning the current medical waste classification. From the four
groups of medical waste considered only Group III and IV are hazardous and so those are the ones
directly related to this work.
The specific requirements while storing, transporting and disposing of such waste were explained
in the first chapters of this dissertation. The main aspect to be retained is that Group III waste
needs previous decontamination before being included in the USW cycle and Group IV waste has
to be mandatorily incinerated.
In terms of the producers of such waste, it is clear that those producers are related to the human
and animal healthcare. From the producers it is necessary to distinguish the most important ones,
hospitals, which account for 70% of the total HMW production. Also it is necessary to say that by
the nature of the services that a user can get in hospitals, these can be considered as facilities to
which the users recur when in need of special care. Therefore the production of this facilities is not
associated with the surrounding resident population but with their treatment capacity. On the other
hand facilities such as public healthcare clinics, pharmacies, dental clinics, etc., are facilities with
lower complexity in the services provided. Thus it is logical that when in need, the user will use the
closest facility to its residence. The waste production of this second type of facilities is therefore
directly related to the population on its area of influence.
Regarding the production amounts, the data available is sometimes confusing and presents some
errors. Nevertheless good approximations to the real production are made by APA (2009). In terms
of the total amount of HMW treated in Portugal the available data must be very reliable as the
operating companies have to bill their clients and so need to keep track of the amounts treated.
From 2016 onwards, the predicted evolution of HMW in Portugal seems to point to a stabilization of
the amounts produced. The stabilization in production is related to the fact that once the 100%
compliance rate is attained the waste production will vary mostly with the variation of population. As
83
the INE predictions for the next 50 year point out to a slight increase of the population in the first 25
years followed by a slight decrease, it is understandable to consider the HMW production as
constant over the years to come.
This assumption, low variability of input data in the coming years, leads to the consideration of a
static deterministic model to solve the problem posed at the beginning of this dissertation. The
objective was to supply the DM with a tool that would, in a flexible and quick way, yield a solution.
The solution would be a cost optimized layout of the HMW system in Portugal.
The evolution of legislation regarding the treatment of HMW conditioned the treatment infra-
structure layout. The fact that in 1990 all hazardous waste had to be incinerated, led to the
construction of small capacity incinerators in most of the Portuguese hospitals. In 1996, the
approval of the current medical waste classification created a new HMW treatment market for the
Group III waste with alternatives treatments to the incineration, e.g. autoclave or chemical
disinfection. This opportunity led to the creation of several private held companies specialized in
Group III waste treatment. These alternative treatments soon became less expensive than
incineration resulting in the preferred way to dispose such waste. From April 1999 on several of the
hospital incinerator units were deactivated because they did not comply with the quality criteria.
Currently only one HMW incinerator is active in Portugal, more precisely in Lisboa.
The sudden deactivation of the hospital incinerator units created a new business possibility. The
Group IV waste had now to be transported form the several hospitals to Lisboa in order to be
eliminated. However the amounts of Group IV waste produced in each hospital are quite small.
This fact associated with the short timeline in which the Group IV waste has to reach the incinerator
made the direct transportation of Group IV waste from the producers to the sink nodes a very costly
solution.
Nevertheless, to the HMW management companies this generated a new business opportunity.
They could transport both waste groups to their Group III waste treatment facility and from there,
they could execute the transport to the incinerator at a lower cost taking advantage of a bigger
amount of Group IV waste to be transported (the sum of all facilities production).
This evolution of the situation and booming of the HMW market led to a HMW system layout which
jumped ahead the use of proper transfer stations and has a quite large distribution of Group III
waste treatment facilities in a uneconomical and inefficient way. Nowadays the truth is the
treatment capacity for Group III waste is almost twice its production.
From the situation exposed it can be concluded that it is necessary to have a long term planning
instead of continuously adapting the HMW system to new infra-structure. As a result the presented
tool was meant to provide the global cost optimization of the system. This means that the solutions
presented are guidelines of what the HMW system has to turn to in order to be cost efficient.
In terms of the input data to the model, there were some difficulties found to estimate certain
values. The data sets regarding the production and its distribution can be considered quite
84
accurate as the origin of the values was quite reliable. However the same cannot be said about the
costs data.
Most of these costs were taken from the available literature which sometimes was outdated. Still it
is my belief that the costs used are quite correct since they fall into the same orders of greatness
as the ones seen in the literature.
In terms of the costs functions, although the simplifications made do not invalidate the example
presented, more refined results could be attained by introducing better cost functions in the model.
Its is necessary to bear in mind that the model was constructed so as to include cost functions as
detailed as the model user wants (regarding the number of linear pieces considered).
8.2 Contributions and results
The model developed is a MILP mathematical model whose objective is to minimize the HMW
management cost in Portugal by optimizing the location of the necessary infrastructure and the
allocation of waste flows. As it could be seen this model and the problem treated are rather
innovative given that few similar examples can be found in the literature.
The main aspects where this work proved its innovation are linked to four major areas. Firstly the
field of application, in the literature only two papers concerning medical waste management were
found (Shi et al., 2009; Medaglia et al., 2009). Secondly the estimations of both costs and market
trends, which for the problem studied are very particular but also very important. Thirdly the
inclusion of cost functions associated to the located infrastructure, in fact only one paper, regarding
waste management, includes cost curves in its model formulation (Walker et al., 1974). And finally
the geographical area where it was applied, all of the examples found were related to urban areas
with a few generating nodes and possible locations for the infrastrucure, whereas this dissertation
applies an optimization model to a national scale covering all continental part of Portugal, 278
generating nodes and 3x18 (54) possible locations.
In terms of results, the model verified that the current HMW system layout is quite based on the
use of disposal sites (DS) as transfer stations (TS) for the Group IV waste. Nevertheless it seems
that the “organic” growth of this layout, which continuously adapted to the changes in the
legislation with no long term planning, is quite accurate in terms of the optimal use of TS. Because
of the high transportation costs, relatively to treatment costs, the optimal layout of the HMW system
has to be based in a rather disperse set of Group III waste treatment facilities whith low capacities
in the peripheral regions and high capacity of Group III waste treatment facilities next to the two
biggest production centres, i.e. Lisboa and Porto. Those DS serve as TS for Group IV waste as
they would do in an optimal configuration. So the only problems with the current layout, in terms of
DS, are the fact that those facilities have much higher capacities than they actually need and that
their distribution is not as balanced as it should be. This unbalanced distribution worsens the
inefficiency as there is a high number of facilities in certain districts and no facilities at all in others.
85
In terms of the location of incinerators it was made clear that, due to the higher costs associated to
the operation of such facilities, a lower number of these facilities should be constructed. The
model’s solution pointed to the construction of two facilities dividing the country into to two distinct
areas (North and South).
It was interesting to observe the influence of parameters such as the TS fixed cost and the relation
between transportation cost and treatment cost. While varying the TS fixed cost, the only type of
facility whose distribution changes was the TS itself. This leads to the conclusion that in fact TS are
the first pillar of the HMW system and the economies brought to the overall costs are associated to
the fact that these facilities are inexpensive to build. If their costs start to rise the added value
associated with TS is no longer important.
The results obtained while varying the relation between transportation costs and treatment costs
served mainly to validate the model. For the case where the transportation costs have low impact
on the total cost a more concentrated layout (fewer facilities) was observed, and in the opposite
case – which is closer to reality – a more dispersed layout popped out.
Finally to understand the effects of partial optimization versus global optimization, a simplified
model was presented in order to observe the results the DM would follow in that case.
It is necessary to bear in mind that the main issue right now is the predicted deficit of HMW
incineration capacity in Portugal and the consequent urgent need to expand such capacity due to
the auto-sufficiency principle regarding waste treatment, imposed by law. It was interesting to
observe that the partial optimization model solution included the construction of three incinerators,
one in the Lisboa area and two others in the Braga area and the Beja area.
The option of building more than one incinerator is not only related to a reduction in transportation
costs but it is also a need that is not shown in this model solution as it is not part of the costs
factors. Having a single company exploring the only mandatory way of eliminating HMW while not
regulating the fees imposed by such company makes the Group IV waste market a monopolist
market. The danger of having a monopolist market is that only one player controls the prices
practiced which are clearly inflated. This is less dangerous when the services provided are not
essential. In this case it must be said all the Group IV waste production has to be incinerated and
preferably in the Portuguese territory therefore options should be given to the Group IV waste
producers in terms of the elimination of such waste. So a multiple incinerators scenario is clearly
positive as it brings more competitive fees to the market and so the final beneficiary is the
healthcare services user who sees less money spent on HMW treatment and so more money for
direct healthcare activities.
8.3 Future developments
Regarding future research, and after having concluded this dissertation, it is possible to distinguish
between two broad areas in which improvements and additional work can be made. Firstly the
86
improvement of the model will be addressed and secondly future research on the HMW
management problematic will be dealt with.
In terms of the improvements directly related to this model, several ideas seem interesting to
explore. The first one, and in my opinion the most important one, is to take into consideration the
cost of shifting the layout into the globally optimized one, namely by taking into account the costs of
closing facilities. It would be interesting to try to understand what would be the strategy followed by
some of the companies present in the market and the costs associated with reaching the optimized
layout – probably analyse the perspectives of two different companies (market leader vs. small
competitor), and even understand if there is space for new competitors. Thus it would be
interesting if the model could schedule the shifting, e.g. closing of certain facilities, reducing
capacity in others, non-renewing a licence for a certain facility, etc, of the HMW system layout. This
shifting would not only include the schedule for the old facilities but it would consider as well the
opening of new ones. To attain this goal some other factors such as the cost of closing facilities
had to be taken into account. The main goal of such and adaptation of the model would be to do a
mix between the concept of partial and global optimization.
Another aspect that would be interesting to develop would be the application of genetic algorithms
to optimize this model. Although not much of the literature about that subject has been included in
this thesis, it is my belief that these types of algorithm applied to a problem in which the decision
variables are binary variables could provide a faster way to reach an optimal solution. Therefore it
would be possible to make the model more complex by introducing other factors and still obtain a
quick solution.
Although not directly related to the execution of the model but more to the input data, it would be
interesting to develop work in the field of cost curves characterization as did Tsilemou and
Panagiotakopoulos (2006). It is understandable that such work is difficult as most of the companies
who possess such data want to keep it confidential. Still such cost curves would be very helpful to
develop not only this model but any other type of optimization model. Of course the interest of
obtaining such data would be to follow through with the application of this model, and replace the
used cost curves by more precise ones in order to understand what could be the biggest savings
from the current scenario to the optimized one.
Regarding the HMW management problematic but also the results presented by this model, it
would be interesting to divide the several zones around the located facilities and to develop a
model that by including other factors, such as social, environmental, political, would point out in that
specific area where would the optimal location of the facility be. This model would be a multi-
objective model which would obtain the best solution in terms of the compromise of the previously
mentioned factors.
Finally in terms of the HMW production data, it is strongly advisable that further studies are made in
order to better understand which producers are in fact complying with the obligation of special
treatment for HMW and which are not, but also to understand how much is being produced in
reality.
87
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APPENDIX I – PORTUGUESE MEDICAL WASTE CLASSIFICATION
Group I – Refuse equivalent to USW, which has no special requirements in terms of treatment:
Waste originated by general services (such as offices, meeting rooms, staff rooms, toilets, locker
rooms, etc.);
Waste originated by auxiliary services (such as workshops, gardens, warehouses and others);
Common packages and wrapping (such as paper, cardboard, and others from identical nature);
Waste originated by the catering services to patients, when not included in Group III.
Group II – Non hazardous refuse requiring no specific treatments, which can be considered equivalent to USW:
Orthopaedics’ material: splints, plasters and plaster bands not contaminated and with no signs of blood;
Disposable diapers and sheets not contaminated and with no signs of blood;
Individual protection gear used by the common and auxiliary services staff, except for the gear used to
handle the medical waste;
Empty packages of medicine or other products of medical or common use, with the exception of those
included in Group III and Group IV;
Serum flasks not contaminated, with the exception of those included in Group IV.
Group III – Biological hazardous refuse, which were contaminated or are suspicious of contamination; incineration or pre-
treatment is required prior to disposal as USW:
All waste originated by private rooms or hospital wards where there are patients that have or are
suspected to have an infectious disease, dialysis facilities, operating rooms, treatment rooms, autopsy
rooms, pathological anatomy and clinical pathology specialities, as well as by research laboratories,
with the exception of those included in Group IV;
All the material used in dialysis treatments;
Unidentified anatomical parts;
Wasted generated by blood transfusions (or blood by-products);
Material used to administer serum or other medicine, with the exception of those included in group IV;
Organic fluids collection bags and the material used for the collection;
Orthopaedics’ material: splints, plaster and plaster bands contaminated or with signs of blood; Patients’
prosthesis;
Disposable diapers and sheets contaminated or with signs of blood;
Individual protection gear used by the medical, common and auxiliary services staff, where there has
been contact with contaminated products (such as gloves, masks, aprons and others).
Group IV – Specific type of refuse whose only form of disposal is elimination:
Identified anatomical parts, foetuses and placentas (until specific legislation is approved);
Animal corpses from experiments;
Cutting and piercing material: needles, catheters and all invasive material;
Chemical products, rejected pharmaceuticals, when those are not dependent on specific legislation;
Cytostatic material and all gear and material used during its administration and handling.
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APPENDIX II – LINKAGE BETWEEN THE EWC AND THE PORTUGUESE
MEDICAL WASTE CLASSIFICATION
Code Description Portuguese Classification
18 01 Wastes from natal care, diagnosis, treatment or prevention of disease in humans
18 01 01 Sharps (except 18 01 03) Group IV
18 01 02 Body parts and organs including blood bags and preserves (except 18 01 03) Group III
18 01 03 Wastes whose collection and disposal is subject to special requirements in order to prevent infection Group III
18 01 04
Wastes whose collection and disposal is not subject to special requirements in order to
prevent infection (for example dressings, plaster casts, linen, disposable clothing, diapers)
Group II
Group III
18 01 06 Chemicals consisting of or containing dangerous substances Group IV
18 01 07 Chemicals other than those mentioned in 18 01 06 Group IV
18 01 08 Cytotoxic and cytostatic medicines Group IV
18 01 09 Medicines other than those mentioned in 18 01 08 Group IV
18 01 10 Amalgam waste from dental care -
18 02 Wastes from research, diagnosis, treatment or prevention of disease involving animals
18 02 01 Sharps except (18 02 02) Group IV
18 02 02 Wastes whose collection and disposal is subject to special requirements in order to prevent infection Group III
18 02 03 Wastes whose collection and disposal is not subject to special requirements in order to prevent infection Group II
18 02 05 Chemicals consisting of or containing dangerous substances Group IV
18 02 06 Chemicals other than those mentioned in 18 02 05 Group IV
18 02 07 Cytotoxic and cytostatic medicines Group IV
18 02 08 Medicines other than those mentioned in 18 02 07 Group IV
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APPENDIX III - HMW PRODUCTION PER TYPE AND PER NODE
District Municipality Population (INE 2008)
Numb. of hospital
beds (Anuário
Estatisticos da Região)
Annual Production (day-to-day) (ton)
Annual Production - Hospitals
(necessity) (ton)
Total Annual Production (ton)
Group III
Group IV Group III Group
IV Group III Group IV
AVEIRO Águeda 49857 101 35,371 3,869 61,478 6,725 96,849 10,595 AVEIRO Albergaria-a-Velha 26279 0 18,643 2,039 0,000 0,000 18,643 2,039 AVEIRO Anadia 31422 44 22,292 2,439 26,782 2,930 49,075 5,368 AVEIRO Arouca 23663 0 16,788 1,836 0,000 0,000 16,788 1,836 AVEIRO Aveiro 73100 402 51,860 5,673 244,694 26,768 296,554 32,441 AVEIRO Castelo de Paiva 16785 0 11,908 1,303 0,000 0,000 11,908 1,303 AVEIRO Espinho 29481 37 20,915 2,288 22,522 2,464 43,437 4,752 AVEIRO Estarreja 28195 51 20,003 2,188 31,043 3,396 51,046 5,584 AVEIRO Ílhavo 41271 0 29,279 3,203 0,000 0,000 29,279 3,203 AVEIRO Mealhada 22215 0 15,760 1,724 0,000 0,000 15,760 1,724 AVEIRO Murtosa 9847 0 6,986 0,764 0,000 0,000 6,986 0,764 AVEIRO Oliveira de Azeméis 71210 97 50,519 5,526 59,043 6,459 109,562 11,985 AVEIRO Oliveira do Bairro 23504 0 16,675 1,824 0,000 0,000 16,675 1,824 AVEIRO Ovar 57983 79 41,136 4,500 48,087 5,260 89,222 9,760 AVEIRO Santa Maria da Feira 147406 317 104,576 11,440 192,955 21,108 297,531 32,548 AVEIRO São João da Madeira 21762 132 15,439 1,689 80,347 8,789 95,786 10,478 AVEIRO Sever do Vouga 12643 0 8,969 0,981 0,000 0,000 8,969 0,981 AVEIRO Vagos 24107 0 17,103 1,871 0,000 0,000 17,103 1,871 AVEIRO Vale de Cambra 24360 0 17,282 1,891 0,000 0,000 17,282 1,891
BEJA Aljustrel 9460 0 6,711 0,734 0,000 0,000 6,711 0,734 BEJA Almodôvar 7163 0 5,082 0,556 0,000 0,000 5,082 0,556 BEJA Alvito 2720 0 1,930 0,211 0,000 0,000 1,930 0,211 BEJA Barrancos 1697 0 1,204 0,132 0,000 0,000 1,204 0,132 BEJA Beja 34387 249 24,396 2,669 151,564 16,580 175,960 19,249 BEJA Castro Verde 7782 0 5,521 0,604 0,000 0,000 5,521 0,604 BEJA Cuba 4674 0 3,316 0,363 0,000 0,000 3,316 0,363 BEJA Ferreira do Alentejo 8132 0 5,769 0,631 0,000 0,000 5,769 0,631 BEJA Mértola 7332 0 5,202 0,569 0,000 0,000 5,202 0,569 BEJA Moura 16120 0 11,436 1,251 0,000 0,000 11,436 1,251 BEJA Odemira 25365 0 17,995 1,969 0,000 0,000 17,995 1,969 BEJA Ourique 5426 0 3,849 0,421 0,000 0,000 3,849 0,421 BEJA Serpa 15455 0 10,964 1,199 0,000 0,000 10,964 1,199 BEJA Vidigueira 5886 0 4,176 0,457 0,000 0,000 4,176 0,457
BRAGA Amares 19853 0 14,085 1,541 0,000 0,000 14,085 1,541 BRAGA Barcelos 124555 730 88,365 9,666 444,345 48,608 532,710 58,275 BRAGA Braga 176154 967 124,971 13,671 588,605 64,389 713,576 78,060 BRAGA Cabeceiras de Basto 17635 0 12,511 1,369 0,000 0,000 12,511 1,369 BRAGA Celorico de Basto 19767 0 14,024 1,534 0,000 0,000 14,024 1,534 BRAGA Esposende 35552 0 25,222 2,759 0,000 0,000 25,222 2,759 BRAGA Fafe 53600 93 38,026 4,160 56,608 6,193 94,634 10,352 BRAGA Guimarães 162636 0 115,381 12,622 0,000 0,000 115,381 12,622 BRAGA Póvoa de Lanhoso 24230 0 17,190 1,880 0,000 0,000 17,190 1,880 BRAGA Terras de Bouro 7506 0 5,325 0,583 0,000 0,000 5,325 0,583 BRAGA Vieira do Minho 14077 0 9,987 1,092 0,000 0,000 9,987 1,092 BRAGA Vila Nova de Famalicão 134969 0 95,753 10,475 0,000 0,000 95,753 10,475 BRAGA Vila Verde 49171 0 34,884 3,816 0,000 0,000 34,884 3,816 BRAGA Vizela 24477 0 17,365 1,900 0,000 0,000 17,365 1,900
BRAGANÇA Alfândega da Fé 5368 0 3,808 0,417 0,000 0,000 3,808 0,417 BRAGANÇA Bragança 34375 432 24,387 2,668 262,955 28,765 287,342 31,433 BRAGANÇA Carrazeda de Ansiães 6744 0 4,784 0,523 0,000 0,000 4,784 0,523 BRAGANÇA Freixo de Espada à Cinta 3834 0 2,720 0,298 0,000 0,000 2,720 0,298 BRAGANÇA Macedo de Cavaleiros 16766 0 11,895 1,301 0,000 0,000 11,895 1,301 BRAGANÇA Miranda do Douro 7295 0 5,175 0,566 0,000 0,000 5,175 0,566 BRAGANÇA Mirandela 25458 0 18,061 1,976 0,000 0,000 18,061 1,976 BRAGANÇA Mogadouro 10289 0 7,299 0,799 0,000 0,000 7,299 0,799 BRAGANÇA Torre de Moncorvo 8829 0 6,264 0,685 0,000 0,000 6,264 0,685 BRAGANÇA Vila Flôr 7432 0 5,273 0,577 0,000 0,000 5,273 0,577 BRAGANÇA Vimioso 4857 0 3,446 0,377 0,000 0,000 3,446 0,377 BRAGANÇA Vinhais 9388 0 6,660 0,729 0,000 0,000 6,660 0,729 C. BRANCO Belmonte 7733 0 5,486 0,600 0,000 0,000 5,486 0,600 C. BRANCO Castelo Branco 53909 308 38,245 4,184 187,477 20,509 225,722 24,692 C. BRANCO Covilhã 52101 351 36,963 4,043 213,651 23,372 250,613 27,415 C. BRANCO Fundão 30867 0 21,898 2,396 0,000 0,000 21,898 2,396
93
District Municipality Population (INE 2008)
Numb. of hospital
beds (Anuário
Estatisticos da Região)
Annual Production (day-to-day) (ton)
Annual Production - Hospitals
(necessity) (ton)
Total Annual Production (ton)
Group III
Group IV Group III Group
IV Group III Group IV
C. BRANCO Idanha-a-Nova 10147 0 7,199 0,787 0,000 0,000 7,199 0,787 C. BRANCO Oleiros 5754 0 4,082 0,447 0,000 0,000 4,082 0,447 C. BRANCO Penamacor 5632 0 3,996 0,437 0,000 0,000 3,996 0,437 C. BRANCO Proença-a-Nova 8849 0 6,278 0,687 0,000 0,000 6,278 0,687 C. BRANCO Sertã 15663 0 11,112 1,216 0,000 0,000 11,112 1,216 C. BRANCO Vila de Rei 3080 0 2,185 0,239 0,000 0,000 2,185 0,239 C. BRANCO Vila Velha de Ródão 3450 0 2,448 0,268 0,000 0,000 2,448 0,268 COIMBRA Arganil 12667 0 8,987 0,983 0,000 0,000 8,987 0,983 COIMBRA Cantanhede 38920 68 27,611 3,021 41,391 4,528 69,003 7,548 COIMBRA Coimbra 135314 2828 95,997 10,501 1721,381 188,307 1817,378 198,808 COIMBRA Condeixa-a-Nova 17737 0 12,583 1,377 0,000 0,000 12,583 1,377 COIMBRA Figueira da Foz 63135 157 44,791 4,900 95,565 10,454 140,355 15,354 COIMBRA Góis 4380 0 3,107 0,340 0,000 0,000 3,107 0,340 COIMBRA Lousã 19245 0 13,653 1,494 0,000 0,000 13,653 1,494 COIMBRA Mira 13295 0 9,432 1,032 0,000 0,000 9,432 1,032 COIMBRA Miranda do Corvo 13755 0 9,758 1,067 0,000 0,000 9,758 1,067 COIMBRA Montemor-o-Velho 24766 0 17,570 1,922 0,000 0,000 17,570 1,922 COIMBRA Oliveira do Hospital 21627 60 15,343 1,678 36,522 3,995 51,865 5,674 COIMBRA Pampilhosa da Serra 4283 0 3,039 0,332 0,000 0,000 3,039 0,332 COIMBRA Penacova 16857 211 11,959 1,308 128,434 14,050 140,393 15,358 COIMBRA Penela 6235 0 4,423 0,484 0,000 0,000 4,423 0,484 COIMBRA Soure 20470 107 14,522 1,589 65,130 7,125 79,652 8,713 COIMBRA Tábua 12307 0 8,731 0,955 0,000 0,000 8,731 0,955 COIMBRA Vila Nova de Poiares 7562 0 5,365 0,587 0,000 0,000 5,365 0,587
ÉVORA Alandroal 6039 0 4,284 0,469 0,000 0,000 4,284 0,469 ÉVORA Arraiolos 7182 0 5,095 0,557 0,000 0,000 5,095 0,557 ÉVORA Borba 7380 0 5,236 0,573 0,000 0,000 5,236 0,573 ÉVORA Estremoz 14500 0 10,287 1,125 0,000 0,000 10,287 1,125 ÉVORA Évora 54780 414 38,863 4,251 251,998 27,567 290,862 31,818 ÉVORA Montemor-o-Novo 18407 0 13,059 1,429 0,000 0,000 13,059 1,429 ÉVORA Mora 5231 0 3,711 0,406 0,000 0,000 3,711 0,406 ÉVORA Mourão 3387 0 2,403 0,263 0,000 0,000 2,403 0,263 ÉVORA Portel 7108 0 5,043 0,552 0,000 0,000 5,043 0,552 ÉVORA Redondo 6676 0 4,736 0,518 0,000 0,000 4,736 0,518 ÉVORA Reguengos de Monsaraz 11557 0 8,199 0,897 0,000 0,000 8,199 0,897 ÉVORA Vendas Novas 12288 0 8,718 0,954 0,000 0,000 8,718 0,954 ÉVORA Viana do Alentejo 5702 0 4,045 0,443 0,000 0,000 4,045 0,443 ÉVORA Vila Viçosa 8656 0 6,141 0,672 0,000 0,000 6,141 0,672 FARO Albufeira 38966 0 27,644 3,024 0,000 0,000 27,644 3,024 FARO Alcoutim 3104 0 2,202 0,241 0,000 0,000 2,202 0,241 FARO Aljezur 5323 0 3,776 0,413 0,000 0,000 3,776 0,413 FARO Castro Marim 6472 0 4,592 0,502 0,000 0,000 4,592 0,502 FARO Faro 58698 513 41,643 4,555 312,259 34,159 353,902 38,714 FARO Lagoa 24875 0 17,647 1,930 0,000 0,000 17,647 1,930 FARO Lagos 28890 0 20,496 2,242 0,000 0,000 20,496 2,242 FARO Loulé 65444 0 46,429 5,079 0,000 0,000 46,429 5,079 FARO Monchique 6024 0 4,274 0,468 0,000 0,000 4,274 0,468 FARO Olhão 44319 7 31,442 3,440 4,261 0,466 35,703 3,906 FARO Portimão 49881 309 35,388 3,871 188,086 20,575 223,473 24,446 FARO São Brás de Alportel 12569 0 8,917 0,975 0,000 0,000 8,917 0,975 FARO Silves 36165 15 25,657 2,807 9,130 0,999 34,787 3,805 FARO Tavira 25394 0 18,016 1,971 0,000 0,000 18,016 1,971 FARO Vila do Bispo 5421 0 3,846 0,421 0,000 0,000 3,846 0,421 FARO Vila Real de Santo António 18539 0 13,152 1,439 0,000 0,000 13,152 1,439
GUARDA Aguiar da Beira 6161 0 4,371 0,478 0,000 0,000 4,371 0,478 GUARDA Almeida 7015 0 4,977 0,544 0,000 0,000 4,977 0,544 GUARDA Celorico da Beira 8572 0 6,081 0,665 0,000 0,000 6,081 0,665 GUARDA Figueira de Castelo Rodrigo 6542 0 4,641 0,508 0,000 0,000 4,641 0,508 GUARDA Fornos de Algodres 5237 0 3,715 0,406 0,000 0,000 3,715 0,406 GUARDA Gouveia 15334 0 10,879 1,190 0,000 0,000 10,879 1,190 GUARDA Guarda 44121 0 31,301 3,424 0,000 0,000 31,301 3,424 GUARDA Manteigas 3650 0 2,589 0,283 0,000 0,000 2,589 0,283 GUARDA Meda 5712 0 4,052 0,443 0,000 0,000 4,052 0,443 GUARDA Pinhel 9840 0 6,981 0,764 0,000 0,000 6,981 0,764 GUARDA Sabugal 13261 0 9,408 1,029 0,000 0,000 9,408 1,029 GUARDA Seia 26844 60 19,044 2,083 36,522 3,995 55,566 6,079 GUARDA Trancoso 10338 0 7,334 0,802 0,000 0,000 7,334 0,802
94
District Municipality Population (INE 2008)
Numb. of hospital
beds (Anuário
Estatisticos da Região)
Annual Production (day-to-day) (ton)
Annual Production - Hospitals
(necessity) (ton)
Total Annual Production (ton)
Group III
Group IV Group III Group
IV Group III Group IV
GUARDA Vila Nova de Foz Côa 7905 0 5,608 0,613 0,000 0,000 5,608 0,613 LEIRIA Alcobaça 55641 63 39,474 4,318 38,348 4,195 77,822 8,513 LEIRIA Alvaiázere 7716 26 5,474 0,599 15,826 1,731 21,300 2,330 LEIRIA Ansião 13495 49 9,574 1,047 29,826 3,263 39,400 4,310 LEIRIA Batalha 15993 0 11,346 1,241 0,000 0,000 11,346 1,241 LEIRIA Bombarral 13809 0 9,797 1,072 0,000 0,000 9,797 1,072 LEIRIA Caldas da Rainha 52823 0 37,475 4,099 0,000 0,000 37,475 4,099 LEIRIA Castanheira de Pêra 3176 0 2,253 0,246 0,000 0,000 2,253 0,246 LEIRIA Figueiró dos Vinhos 6824 0 4,841 0,530 0,000 0,000 4,841 0,530 LEIRIA Leiria 128537 0 91,190 9,976 0,000 0,000 91,190 9,976 LEIRIA Marinha Grande 38599 0 27,384 2,996 0,000 0,000 27,384 2,996 LEIRIA Nazaré 14480 0 10,273 1,124 0,000 0,000 10,273 1,124 LEIRIA Óbidos 11377 0 8,071 0,883 0,000 0,000 8,071 0,883 LEIRIA Pedrógão Grande 4069 0 2,887 0,316 0,000 0,000 2,887 0,316 LEIRIA Peniche 28615 53 20,301 2,221 32,261 3,529 52,561 5,750 LEIRIA Pombal 59858 59 42,466 4,645 35,913 3,929 78,379 8,574 LEIRIA Porto de Mós 25153 0 17,845 1,952 0,000 0,000 17,845 1,952 LISBOA Alenquer 46536 0 33,015 3,612 0,000 0,000 33,015 3,612 LISBOA Amadora 172110 0 122,102 13,357 0,000 0,000 122,102 13,357 LISBOA Arruda dos Vinhos 12314 0 8,736 0,956 0,000 0,000 8,736 0,956 LISBOA Azambuja 21841 0 15,495 1,695 0,000 0,000 15,495 1,695 LISBOA Cadaval 14638 0 10,385 1,136 0,000 0,000 10,385 1,136 LISBOA Cascais 188244 443 133,548 14,609 269,650 29,498 403,199 44,107 LISBOA Lisboa 489562 7271 347,316 37,994 4425,798 484,151 4773,114 522,145 LISBOA Loures 195035 0 138,366 15,136 0,000 0,000 138,366 15,136 LISBOA Lourinhã 25616 0 18,173 1,988 0,000 0,000 18,173 1,988 LISBOA Mafra 70867 0 50,276 5,500 0,000 0,000 50,276 5,500 LISBOA Odivelas 153584 0 108,959 11,919 0,000 0,000 108,959 11,919 LISBOA Oeiras 172021 0 122,039 13,350 0,000 0,000 122,039 13,350 LISBOA Sintra 445872 1087 316,320 34,603 661,648 72,380 977,968 106,983 LISBOA Sobral de Monte Agraço 10525 0 7,467 0,817 0,000 0,000 7,467 0,817 LISBOA Torres Vedras 77556 265 55,022 6,019 161,303 17,645 216,325 23,664 LISBOA Vila Franca de Xira 142163 211 100,856 11,033 128,434 14,050 229,290 25,083
PORTALEGRE Alter do Chão 3442 0 2,442 0,267 0,000 0,000 2,442 0,267 PORTALEGRE Arronches 3211 0 2,278 0,249 0,000 0,000 2,278 0,249 PORTALEGRE Avis 4931 0 3,498 0,383 0,000 0,000 3,498 0,383 PORTALEGRE Campo Maior 8295 0 5,885 0,644 0,000 0,000 5,885 0,644 PORTALEGRE Castelo de Vide 3701 0 2,626 0,287 0,000 0,000 2,626 0,287 PORTALEGRE Crato 3707 0 2,630 0,288 0,000 0,000 2,630 0,288 PORTALEGRE Elvas 22118 99 15,691 1,717 60,260 6,592 75,952 8,309 PORTALEGRE Fronteira 3160 0 2,242 0,245 0,000 0,000 2,242 0,245 PORTALEGRE Gavião 4027 0 2,857 0,313 0,000 0,000 2,857 0,313 PORTALEGRE Marvão 3489 0 2,475 0,271 0,000 0,000 2,475 0,271 PORTALEGRE Monforte 3087 0 2,190 0,240 0,000 0,000 2,190 0,240 PORTALEGRE Nisa 7536 0 5,346 0,585 0,000 0,000 5,346 0,585 PORTALEGRE Ponte de Sôr 17078 0 12,116 1,325 0,000 0,000 12,116 1,325 PORTALEGRE Portalegre 23731 272 16,836 1,842 165,564 18,112 182,400 19,953 PORTALEGRE Sousel 5317 0 3,772 0,413 0,000 0,000 3,772 0,413
PORTO Amarante 61582 170 43,689 4,779 103,478 11,320 147,166 16,099 PORTO Baião 20686 0 14,676 1,605 0,000 0,000 14,676 1,605 PORTO Felgueiras 58976 0 41,840 4,577 0,000 0,000 41,840 4,577 PORTO Gondomar 173910 0 123,379 13,497 0,000 0,000 123,379 13,497 PORTO Lousada 47723 0 33,857 3,704 0,000 0,000 33,857 3,704 PORTO Maia 140859 0 99,931 10,932 0,000 0,000 99,931 10,932 PORTO Marco de Canaveses 55275 0 39,214 4,290 0,000 0,000 39,214 4,290 PORTO Matosinhos 169261 445 120,081 13,136 270,868 29,631 390,949 42,767 PORTO Paços de Ferreira 56333 0 39,965 4,372 0,000 0,000 39,965 4,372 PORTO Paredes 87142 0 61,822 6,763 0,000 0,000 61,822 6,763 PORTO Penafiel 71841 295 50,967 5,575 179,564 19,643 230,531 25,218 PORTO Porto 216080 3813 153,296 16,770 2320,942 253,895 2474,238 270,664 PORTO Póvoa de Varzim 66655 0 47,288 5,173 0,000 0,000 47,288 5,173 PORTO Santo Tirso 69920 133 49,604 5,426 80,956 8,856 130,560 14,282 PORTO Trofa 40680 0 28,860 3,157 0,000 0,000 28,860 3,157 PORTO Valongo 97138 74 68,914 7,539 45,043 4,927 113,957 12,466 PORTO Vila do Conde 77320 0 54,854 6,001 0,000 0,000 54,854 6,001 PORTO Vila Nova de Gaia 312742 0 221,872 24,271 0,000 0,000 221,872 24,271
SANTARÉM Abrantes 39987 0 28,368 3,103 0,000 0,000 28,368 3,103
95
District Municipality Population (INE 2008)
Numb. of hospital
beds (Anuário
Estatisticos da Região)
Annual Production (day-to-day) (ton)
Annual Production - Hospitals
(necessity) (ton)
Total Annual Production (ton)
Group III
Group IV Group III Group
IV Group III Group IV
SANTARÉM Alcanena 14657 0 10,398 1,138 0,000 0,000 10,398 1,138 SANTARÉM Almeirim 22937 0 16,272 1,780 0,000 0,000 16,272 1,780 SANTARÉM Alpiarça 8266 0 5,864 0,642 0,000 0,000 5,864 0,642 SANTARÉM Benavente 28312 0 20,086 2,197 0,000 0,000 20,086 2,197 SANTARÉM Cartaxo 25156 0 17,847 1,952 0,000 0,000 17,847 1,952 SANTARÉM Chamusca 10976 0 7,787 0,852 0,000 0,000 7,787 0,852 SANTARÉM Constância 3751 21 2,661 0,291 12,783 1,398 15,444 1,689 SANTARÉM Coruche 19624 0 13,922 1,523 0,000 0,000 13,922 1,523 SANTARÉM Entroncamento 21751 0 15,431 1,688 0,000 0,000 15,431 1,688 SANTARÉM Ferreira do Zêzere 9126 0 6,474 0,708 0,000 0,000 6,474 0,708 SANTARÉM Golegã 5533 0 3,925 0,429 0,000 0,000 3,925 0,429 SANTARÉM Mação 7061 0 5,009 0,548 0,000 0,000 5,009 0,548 SANTARÉM Ourém 50890 0 36,104 3,949 0,000 0,000 36,104 3,949 SANTARÉM Rio Maior 21822 0 15,481 1,694 0,000 0,000 15,481 1,694 SANTARÉM Salvaterra de Magos 21491 0 15,247 1,668 0,000 0,000 15,247 1,668 SANTARÉM Santarém 63630 394 45,142 4,938 239,825 26,235 284,966 31,173 SANTARÉM Sardoal 3808 0 2,702 0,296 0,000 0,000 2,702 0,296 SANTARÉM Tomar 41951 437 29,762 3,256 265,998 29,098 295,760 32,354 SANTARÉM Torres Novas 36968 0 26,227 2,869 0,000 0,000 26,227 2,869 SANTARÉM Vila Nova da Barquinha 8170 0 5,796 0,634 0,000 0,000 5,796 0,634 SETÚBAL Alcácer do Sal 13017 0 9,235 1,010 0,000 0,000 9,235 1,010 SETÚBAL Alcochete 17464 0 12,390 1,355 0,000 0,000 12,390 1,355 SETÚBAL Almada 166103 497 117,840 12,891 302,520 33,094 420,360 45,984 SETÚBAL Barreiro 77893 0 55,261 6,045 0,000 0,000 55,261 6,045 SETÚBAL Grândola 13979 0 9,917 1,085 0,000 0,000 9,917 1,085 SETÚBAL Moita 71596 0 50,793 5,556 0,000 0,000 50,793 5,556 SETÚBAL Montijo 41432 80 29,394 3,215 48,695 5,327 78,089 8,542 SETÚBAL Palmela 62820 0 44,567 4,875 0,000 0,000 44,567 4,875 SETÚBAL Santiago do Cacém 29482 97 20,916 2,288 59,043 6,459 79,959 8,747 SETÚBAL Seixal 175837 0 124,746 13,646 0,000 0,000 124,746 13,646 SETÚBAL Sesimbra 52371 0 37,154 4,064 0,000 0,000 37,154 4,064 SETÚBAL Setúbal 124459 421 88,296 9,659 256,259 28,033 344,556 37,692 SETÚBAL Sines 13681 0 9,706 1,062 0,000 0,000 9,706 1,062
V. D. CASTELO Arcos de Valdevez 24251 0 17,205 1,882 0,000 0,000 17,205 1,882 V. D. CASTELO Caminha 16630 0 11,798 1,291 0,000 0,000 11,798 1,291 V. D. CASTELO Melgaço 9396 0 6,666 0,729 0,000 0,000 6,666 0,729 V. D. CASTELO Monção 19530 0 13,855 1,516 0,000 0,000 13,855 1,516 V. D. CASTELO Paredes de Coura 9257 0 6,567 0,718 0,000 0,000 6,567 0,718 V. D. CASTELO Ponte da Barca 13004 0 9,226 1,009 0,000 0,000 9,226 1,009 V. D. CASTELO Ponte de Lima 44527 0 31,589 3,456 0,000 0,000 31,589 3,456 V. D. CASTELO Valença 14308 0 10,151 1,110 0,000 0,000 10,151 1,110 V. D. CASTELO Viana do Castelo 91362 478 64,816 7,090 290,955 31,828 355,771 38,919 V. D. CASTELO Vila Nova de Cerveira 8686 0 6,162 0,674 0,000 0,000 6,162 0,674
VILA REAL Alijó 13453 0 9,544 1,044 0,000 0,000 9,544 1,044 VILA REAL Boticas 5736 0 4,069 0,445 0,000 0,000 4,069 0,445 VILA REAL Chaves 44039 216 31,243 3,418 131,477 14,383 162,721 17,800 VILA REAL Mesão Frio 4357 0 3,091 0,338 0,000 0,000 3,091 0,338 VILA REAL Mondim de Basto 8229 0 5,838 0,639 0,000 0,000 5,838 0,639 VILA REAL Montalegre 11402 0 8,089 0,885 0,000 0,000 8,089 0,885 VILA REAL Murça 6109 0 4,334 0,474 0,000 0,000 4,334 0,474 VILA REAL Peso da Régua 16992 0 12,055 1,319 0,000 0,000 12,055 1,319 VILA REAL Ribeira de Pena 7049 0 5,001 0,547 0,000 0,000 5,001 0,547 VILA REAL Sabrosa 6571 0 4,662 0,510 0,000 0,000 4,662 0,510 VILA REAL Santa Marta de Penaguião 8075 0 5,729 0,627 0,000 0,000 5,729 0,627 VILA REAL Valpaços 18541 0 13,154 1,439 0,000 0,000 13,154 1,439 VILA REAL Vila Pouca de Aguiar 14837 0 10,526 1,151 0,000 0,000 10,526 1,151 VILA REAL Vila Real 50131 349 35,565 3,891 212,433 23,239 247,999 27,129
VISEU Armamar 7071 0 5,016 0,549 0,000 0,000 5,016 0,549 VISEU Carregal do Sal 10599 0 7,519 0,823 0,000 0,000 7,519 0,823 VISEU Castro Daire 16503 0 11,708 1,281 0,000 0,000 11,708 1,281 VISEU Cinfães 20198 0 14,329 1,568 0,000 0,000 14,329 1,568 VISEU Lamego 25863 139 18,348 2,007 84,608 9,256 102,956 11,263 VISEU Mangualde 21155 0 15,008 1,642 0,000 0,000 15,008 1,642 VISEU Moimenta da Beira 10941 0 7,762 0,849 0,000 0,000 7,762 0,849 VISEU Mortágua 10153 0 7,203 0,788 0,000 0,000 7,203 0,788 VISEU Nelas 14740 0 10,457 1,144 0,000 0,000 10,457 1,144 VISEU Oliveira de Frades 10640 0 7,548 0,826 0,000 0,000 7,548 0,826
96
District Municipality Population (INE 2008)
Numb. of hospital
beds (Anuário
Estatisticos da Região)
Annual Production (day-to-day) (ton)
Annual Production - Hospitals
(necessity) (ton)
Total Annual Production (ton)
Group III
Group IV Group III Group
IV Group III Group IV
VISEU Penalva do Castelo 8482 0 6,017 0,658 0,000 0,000 6,017 0,658 VISEU Penedono 3286 0 2,331 0,255 0,000 0,000 2,331 0,255 VISEU Resende 11561 0 8,202 0,897 0,000 0,000 8,202 0,897 VISEU Santa Comba Dão 12263 0 8,700 0,952 0,000 0,000 8,700 0,952 VISEU São João da Pesqueira 7997 0 5,673 0,621 0,000 0,000 5,673 0,621 VISEU São Pedro do Sul 19188 0 13,613 1,489 0,000 0,000 13,613 1,489 VISEU Sátão 13528 0 9,597 1,050 0,000 0,000 9,597 1,050 VISEU Sernancelhe 6011 0 4,264 0,467 0,000 0,000 4,264 0,467 VISEU Tabuaço 6204 0 4,401 0,481 0,000 0,000 4,401 0,481 VISEU Tarouca 8323 0 5,905 0,646 0,000 0,000 5,905 0,646 VISEU Tondela 30698 64 21,778 2,382 38,956 4,262 60,735 6,644 VISEU Vila Nova de Paiva 6399 0 4,540 0,497 0,000 0,000 4,540 0,497 VISEU Viseu 99016 0 70,246 7,684 0,000 0,000 70,246 7,684 VISEU Vouzela 11660 0 8,272 0,905 0,000 0,000 8,272 0,905
97
APPENDIX IV - OPTIMIZED HMW FLOWS
District Municipality Waste Destination Total Annual Production (ton)
Transfer Station Disposal Site Incinerator Group III Group IV
AVEIRO Águeda Aveiro Aveiro Porto 96,849 10,595 AVEIRO Albergaria-a-Velha Aveiro Aveiro Porto 18,643 2,039 AVEIRO Anadia Coimbra Coimbra Porto 49,075 5,368 AVEIRO Arouca Porto Porto Porto 16,788 1,836 AVEIRO Aveiro Aveiro Aveiro Porto 296,554 32,441 AVEIRO Castelo de Paiva Porto Porto Porto 11,908 1,303 AVEIRO Espinho Porto Porto Porto 43,437 4,752 AVEIRO Estarreja Aveiro Aveiro Porto 51,046 5,584 AVEIRO Ílhavo Aveiro Aveiro Porto 29,279 3,203 AVEIRO Mealhada Coimbra Coimbra Porto 15,760 1,724 AVEIRO Murtosa Aveiro Aveiro Porto 6,986 0,764 AVEIRO Oliveira de Azeméis Aveiro Aveiro Porto 109,562 11,985 AVEIRO Oliveira do Bairro Aveiro Aveiro Porto 16,675 1,824 AVEIRO Ovar Aveiro Aveiro Porto 89,222 9,760 AVEIRO Santa Maria da Feira Aveiro Aveiro Porto 297,531 32,548 AVEIRO São João da Madeira Aveiro Aveiro Porto 95,786 10,478 AVEIRO Sever do Vouga Aveiro Aveiro Porto 8,969 0,981 AVEIRO Vagos Aveiro Aveiro Porto 17,103 1,871 AVEIRO Vale de Cambra Aveiro Aveiro Porto 17,282 1,891
BEJA Aljustrel Beja Évora Lisboa 6,711 0,734 BEJA Almodôvar Faro Faro Lisboa 5,082 0,556 BEJA Alvito Évora Évora Lisboa 1,930 0,211 BEJA Barrancos Évora Évora Lisboa 1,204 0,132 BEJA Beja Beja Évora Lisboa 175,960 19,249 BEJA Castro Verde Beja Évora Lisboa 5,521 0,604 BEJA Cuba Beja Évora Lisboa 3,316 0,363 BEJA Ferreira do Alentejo Beja Évora Lisboa 5,769 0,631 BEJA Mértola Beja Évora Lisboa 5,202 0,569 BEJA Moura Évora Évora Lisboa 11,436 1,251 BEJA Odemira Faro Faro Lisboa 17,995 1,969 BEJA Ourique Faro Faro Lisboa 3,849 0,421 BEJA Serpa Beja Évora Lisboa 10,964 1,199 BEJA Vidigueira Évora Évora Lisboa 4,176 0,457
BRAGA Amares Braga Braga Porto 14,085 1,541 BRAGA Barcelos Braga Braga Porto 532,710 58,275 BRAGA Braga Braga Braga Porto 713,576 78,060 BRAGA Cabeceiras de Basto Vila Real Vila Real Porto 12,511 1,369 BRAGA Celorico de Basto Vila Real Vila Real Porto 14,024 1,534 BRAGA Esposende Braga Braga Porto 25,222 2,759 BRAGA Fafe Braga Braga Porto 94,634 10,352 BRAGA Guimarães Braga Braga Porto 115,381 12,622 BRAGA Póvoa de Lanhoso Braga Braga Porto 17,190 1,880 BRAGA Terras de Bouro Braga Braga Porto 5,325 0,583 BRAGA Vieira do Minho Braga Braga Porto 9,987 1,092 BRAGA Vila Nova de Famalicão Braga Braga Porto 95,753 10,475 BRAGA Vila Verde Braga Braga Porto 34,884 3,816 BRAGA Vizela Braga Braga Porto 17,365 1,900
BRAGANÇA Alfândega da Fé Bragança Bragança Porto 3,808 0,417 BRAGANÇA Bragança Bragança Bragança Porto 287,342 31,433 BRAGANÇA Carrazeda de Ansiães Vila Real Vila Real Porto 4,784 0,523 BRAGANÇA Freixo de Espada à Cinta Bragança Bragança Porto 2,720 0,298 BRAGANÇA Macedo de Cavaleiros Bragança Bragança Porto 11,895 1,301 BRAGANÇA Miranda do Douro Bragança Bragança Porto 5,175 0,566 BRAGANÇA Mirandela Vila Real Vila Real Porto 18,061 1,976 BRAGANÇA Mogadouro Bragança Bragança Porto 7,299 0,799 BRAGANÇA Torre de Moncorvo Vila Real Vila Real Porto 6,264 0,685 BRAGANÇA Vila Flôr Vila Real Vila Real Porto 5,273 0,577 BRAGANÇA Vimioso Bragança Bragança Porto 3,446 0,377 BRAGANÇA Vinhais Bragança Bragança Porto 6,660 0,729 C. BRANCO Belmonte Castelo Branco Castelo Branco Porto 5,486 0,600 C. BRANCO Castelo Branco Castelo Branco Castelo Branco Porto 225,722 24,692 C. BRANCO Covilhã Castelo Branco Castelo Branco Porto 250,613 27,415 C. BRANCO Fundão Castelo Branco Castelo Branco Porto 21,898 2,396 C. BRANCO Idanha-a-Nova Castelo Branco Castelo Branco Porto 7,199 0,787 C. BRANCO Oleiros Castelo Branco Castelo Branco Porto 4,082 0,447
98
District Municipality Waste Destination Total Annual Production (ton)
Transfer Station Disposal Site Incinerator Group III Group IV
C. BRANCO Penamacor Castelo Branco Castelo Branco Porto 3,996 0,437 C. BRANCO Proença-a-Nova Castelo Branco Castelo Branco Porto 6,278 0,687 C. BRANCO Sertã Coimbra Coimbra Porto 11,112 1,216 C. BRANCO Vila de Rei Santarém Santarém Lisboa 2,185 0,239 C. BRANCO Vila Velha de Ródão Castelo Branco Castelo Branco Porto 2,448 0,268 COIMBRA Arganil Coimbra Coimbra Porto 8,987 0,983 COIMBRA Cantanhede Coimbra Coimbra Porto 69,003 7,548 COIMBRA Coimbra Coimbra Coimbra Porto 1817,378 198,808 COIMBRA Condeixa-a-Nova Coimbra Coimbra Porto 12,583 1,377 COIMBRA Figueira da Foz Coimbra Coimbra Porto 140,355 15,354 COIMBRA Góis Coimbra Coimbra Porto 3,107 0,340 COIMBRA Lousã Coimbra Coimbra Porto 13,653 1,494 COIMBRA Mira Coimbra Coimbra Porto 9,432 1,032 COIMBRA Miranda do Corvo Coimbra Coimbra Porto 9,758 1,067 COIMBRA Montemor-o-Velho Coimbra Coimbra Porto 17,570 1,922 COIMBRA Oliveira do Hospital Castelo Branco Castelo Branco Porto 51,865 5,674 COIMBRA Pampilhosa da Serra Castelo Branco Castelo Branco Porto 3,039 0,332 COIMBRA Penacova Coimbra Coimbra Porto 140,393 15,358 COIMBRA Penela Coimbra Coimbra Porto 4,423 0,484 COIMBRA Soure Coimbra Coimbra Porto 79,652 8,713 COIMBRA Tábua Coimbra Coimbra Porto 8,731 0,955 COIMBRA Vila Nova de Poiares Coimbra Coimbra Porto 5,365 0,587
ÉVORA Alandroal Évora Évora Lisboa 4,284 0,469 ÉVORA Arraiolos Évora Évora Lisboa 5,095 0,557 ÉVORA Borba Évora Évora Lisboa 5,236 0,573 ÉVORA Estremoz Évora Évora Lisboa 10,287 1,125 ÉVORA Évora Évora Évora Lisboa 290,862 31,818 ÉVORA Montemor-o-Novo Évora Évora Lisboa 13,059 1,429 ÉVORA Mora Évora Évora Lisboa 3,711 0,406 ÉVORA Mourão Évora Évora Lisboa 2,403 0,263 ÉVORA Portel Évora Évora Lisboa 5,043 0,552 ÉVORA Redondo Évora Évora Lisboa 4,736 0,518 ÉVORA Reguengos de Monsaraz Évora Évora Lisboa 8,199 0,897 ÉVORA Vendas Novas Setubal Lisboa Lisboa 8,718 0,954 ÉVORA Viana do Alentejo Évora Évora Lisboa 4,045 0,443 ÉVORA Vila Viçosa Évora Évora Lisboa 6,141 0,672 FARO Albufeira Faro Faro Lisboa 27,644 3,024 FARO Alcoutim Faro Faro Lisboa 2,202 0,241 FARO Aljezur Faro Faro Lisboa 3,776 0,413 FARO Castro Marim Faro Faro Lisboa 4,592 0,502 FARO Faro Faro Faro Lisboa 353,902 38,714 FARO Lagoa Faro Faro Lisboa 17,647 1,930 FARO Lagos Faro Faro Lisboa 20,496 2,242 FARO Loulé Faro Faro Lisboa 46,429 5,079 FARO Monchique Faro Faro Lisboa 4,274 0,468 FARO Olhão Faro Faro Lisboa 35,703 3,906 FARO Portimão Faro Faro Lisboa 223,473 24,446 FARO São Brás de Alportel Faro Faro Lisboa 8,917 0,975 FARO Silves Faro Faro Lisboa 34,787 3,805 FARO Tavira Faro Faro Lisboa 18,016 1,971 FARO Vila do Bispo Faro Faro Lisboa 3,846 0,421 FARO Vila Real de Santo António Faro Faro Lisboa 13,152 1,439
GUARDA Aguiar da Beira Vila Real Vila Real Porto 4,371 0,478 GUARDA Almeida Castelo Branco Castelo Branco Porto 4,977 0,544 GUARDA Celorico da Beira Castelo Branco Castelo Branco Porto 6,081 0,665 GUARDA Figueira de Castelo Rodrigo Vila Real Vila Real Porto 4,641 0,508 GUARDA Fornos de Algodres Castelo Branco Castelo Branco Porto 3,715 0,406 GUARDA Gouveia Castelo Branco Castelo Branco Porto 10,879 1,190 GUARDA Guarda Castelo Branco Castelo Branco Porto 31,301 3,424 GUARDA Manteigas Castelo Branco Castelo Branco Porto 2,589 0,283 GUARDA Meda Vila Real Vila Real Porto 4,052 0,443 GUARDA Pinhel Vila Real Vila Real Porto 6,981 0,764 GUARDA Sabugal Castelo Branco Castelo Branco Porto 9,408 1,029 GUARDA Seia Castelo Branco Castelo Branco Porto 55,566 6,079 GUARDA Trancoso Vila Real Vila Real Porto 7,334 0,802 GUARDA Vila Nova de Foz Côa Vila Real Vila Real Porto 5,608 0,613
LEIRIA Alcobaça Santarém Santarém Lisboa 77,822 8,513 LEIRIA Alvaiázere Coimbra Coimbra Porto 21,300 2,330
99
District Municipality Waste Destination Total Annual Production (ton)
Transfer Station Disposal Site Incinerator Group III Group IV
LEIRIA Ansião Coimbra Coimbra Porto 39,400 4,310 LEIRIA Batalha Santarém Santarém Lisboa 11,346 1,241 LEIRIA Bombarral Lisboa Lisboa Lisboa 9,797 1,072 LEIRIA Caldas da Rainha Santarém Santarém Lisboa 37,475 4,099 LEIRIA Castanheira de Pêra Coimbra Coimbra Porto 2,253 0,246 LEIRIA Figueiró dos Vinhos Coimbra Coimbra Porto 4,841 0,530 LEIRIA Leiria Santarém Santarém Lisboa 91,190 9,976 LEIRIA Marinha Grande Santarém Santarém Lisboa 27,384 2,996 LEIRIA Nazaré Santarém Santarém Lisboa 10,273 1,124 LEIRIA Óbidos Santarém Santarém Lisboa 8,071 0,883 LEIRIA Pedrógão Grande Coimbra Coimbra Porto 2,887 0,316 LEIRIA Peniche Lisboa Lisboa Lisboa 52,561 5,750 LEIRIA Pombal Coimbra Coimbra Porto 78,379 8,574 LEIRIA Porto de Mós Santarém Santarém Lisboa 17,845 1,952 LISBOA Alenquer Lisboa Lisboa Lisboa 33,015 3,612 LISBOA Amadora Lisboa Lisboa Lisboa 122,102 13,357 LISBOA Arruda dos Vinhos Lisboa Lisboa Lisboa 8,736 0,956 LISBOA Azambuja Lisboa Lisboa Lisboa 15,495 1,695 LISBOA Cadaval Lisboa Lisboa Lisboa 10,385 1,136 LISBOA Cascais Lisboa Lisboa Lisboa 403,199 44,107 LISBOA Lisboa Lisboa Lisboa Lisboa 4773,114 522,145 LISBOA Loures Lisboa Lisboa Lisboa 138,366 15,136 LISBOA Lourinhã Lisboa Lisboa Lisboa 18,173 1,988 LISBOA Mafra Lisboa Lisboa Lisboa 50,276 5,500 LISBOA Odivelas Lisboa Lisboa Lisboa 108,959 11,919 LISBOA Oeiras Lisboa Lisboa Lisboa 122,039 13,350 LISBOA Sintra Lisboa Lisboa Lisboa 977,968 106,983 LISBOA Sobral de Monte Agraço Lisboa Lisboa Lisboa 7,467 0,817 LISBOA Torres Vedras Lisboa Lisboa Lisboa 216,325 23,664 LISBOA Vila Franca de Xira Lisboa Lisboa Lisboa 229,290 25,083
PORTALEGRE Alter do Chão Portalegre Évora Lisboa 2,442 0,267 PORTALEGRE Arronches Portalegre Évora Lisboa 2,278 0,249 PORTALEGRE Avis Évora Évora Lisboa 3,498 0,383 PORTALEGRE Campo Maior Portalegre Évora Lisboa 5,885 0,644 PORTALEGRE Castelo de Vide Portalegre Évora Lisboa 2,626 0,287 PORTALEGRE Crato Portalegre Évora Lisboa 2,630 0,288 PORTALEGRE Elvas Portalegre Évora Lisboa 75,952 8,309 PORTALEGRE Fronteira Portalegre Évora Lisboa 2,242 0,245 PORTALEGRE Gavião Santarém Santarém Lisboa 2,857 0,313 PORTALEGRE Marvão Portalegre Évora Lisboa 2,475 0,271 PORTALEGRE Monforte Portalegre Évora Lisboa 2,190 0,240 PORTALEGRE Nisa Castelo Branco Castelo Branco Porto 5,346 0,585 PORTALEGRE Ponte de Sôr Santarém Santarém Lisboa 12,116 1,325 PORTALEGRE Portalegre Portalegre Évora Lisboa 182,400 19,953 PORTALEGRE Sousel Évora Évora Lisboa 3,772 0,413
PORTO Amarante Porto Porto Porto 147,166 16,099 PORTO Baião Porto Porto Porto 14,676 1,605 PORTO Felgueiras Braga Braga Porto 41,840 4,577 PORTO Gondomar Porto Porto Porto 123,379 13,497 PORTO Lousada Porto Porto Porto 33,857 3,704 PORTO Maia Porto Porto Porto 99,931 10,932 PORTO Marco de Canaveses Porto Porto Porto 39,214 4,290 PORTO Matosinhos Porto Porto Porto 390,949 42,767 PORTO Paços de Ferreira Porto Porto Porto 39,965 4,372 PORTO Paredes Porto Porto Porto 61,822 6,763 PORTO Penafiel Porto Porto Porto 230,531 25,218 PORTO Porto Porto Porto Porto 2474,238 270,664 PORTO Póvoa de Varzim Porto Porto Porto 47,288 5,173 PORTO Santo Tirso Porto Porto Porto 130,560 14,282 PORTO Trofa Porto Porto Porto 28,860 3,157 PORTO Valongo Porto Porto Porto 113,957 12,466 PORTO Vila do Conde Porto Porto Porto 54,854 6,001 PORTO Vila Nova de Gaia Porto Porto Porto 221,872 24,271
SANTARÉM Abrantes Santarém Santarém Lisboa 28,368 3,103 SANTARÉM Alcanena Santarém Santarém Lisboa 10,398 1,138 SANTARÉM Almeirim Santarém Santarém Lisboa 16,272 1,780 SANTARÉM Alpiarça Santarém Santarém Lisboa 5,864 0,642 SANTARÉM Benavente Lisboa Lisboa Lisboa 20,086 2,197
100
District Municipality Waste Destination Total Annual Production (ton)
Transfer Station Disposal Site Incinerator Group III Group IV
SANTARÉM Cartaxo Santarém Santarém Lisboa 17,847 1,952 SANTARÉM Chamusca Santarém Santarém Lisboa 7,787 0,852 SANTARÉM Constância Santarém Santarém Lisboa 15,444 1,689 SANTARÉM Coruche Santarém Santarém Lisboa 13,922 1,523 SANTARÉM Entroncamento Santarém Santarém Lisboa 15,431 1,688 SANTARÉM Ferreira do Zêzere Santarém Santarém Lisboa 6,474 0,708 SANTARÉM Golegã Santarém Santarém Lisboa 3,925 0,429 SANTARÉM Mação Santarém Santarém Lisboa 5,009 0,548 SANTARÉM Ourém Santarém Santarém Lisboa 36,104 3,949 SANTARÉM Rio Maior Santarém Santarém Lisboa 15,481 1,694 SANTARÉM Salvaterra de Magos Lisboa Lisboa Lisboa 15,247 1,668 SANTARÉM Santarém Santarém Santarém Lisboa 284,966 31,173 SANTARÉM Sardoal Santarém Santarém Lisboa 2,702 0,296 SANTARÉM Tomar Santarém Santarém Lisboa 295,760 32,354 SANTARÉM Torres Novas Santarém Santarém Lisboa 26,227 2,869 SANTARÉM Vila Nova da Barquinha Santarém Santarém Lisboa 5,796 0,634 SETÚBAL Alcácer do Sal Setubal Lisboa Lisboa 9,235 1,010 SETÚBAL Alcochete Lisboa Lisboa Lisboa 12,390 1,355 SETÚBAL Almada Lisboa Lisboa Lisboa 420,360 45,984 SETÚBAL Barreiro Lisboa Lisboa Lisboa 55,261 6,045 SETÚBAL Grândola Setubal Lisboa Lisboa 9,917 1,085 SETÚBAL Moita Setubal Lisboa Lisboa 50,793 5,556 SETÚBAL Montijo Lisboa Lisboa Lisboa 78,089 8,542 SETÚBAL Palmela Setubal Lisboa Lisboa 44,567 4,875 SETÚBAL Santiago do Cacém Setubal Lisboa Lisboa 79,959 8,747 SETÚBAL Seixal Lisboa Lisboa Lisboa 124,746 13,646 SETÚBAL Sesimbra Setubal Lisboa Lisboa 37,154 4,064 SETÚBAL Setúbal Setubal Lisboa Lisboa 344,556 37,692 SETÚBAL Sines Setubal Lisboa Lisboa 9,706 1,062
V. DO CASTELO Arcos de Valdevez Braga Braga Porto 17,205 1,882 V. DO CASTELO Caminha V. do Castelo Braga Porto 11,798 1,291 V. DO CASTELO Melgaço Braga Braga Porto 6,666 0,729 V. DO CASTELO Monção V. do Castelo Braga Porto 13,855 1,516 V. DO CASTELO Paredes de Coura V. do Castelo Braga Porto 6,567 0,718 V. DO CASTELO Ponte da Barca Braga Braga Porto 9,226 1,009 V. DO CASTELO Ponte de Lima V. do Castelo Braga Porto 31,589 3,456 V. DO CASTELO Valença V. do Castelo Braga Porto 10,151 1,110 V. DO CASTELO Viana do Castelo V. do Castelo Braga Porto 355,771 38,919 V. DO CASTELO Vila Nova de Cerveira V. do Castelo Braga Porto 6,162 0,674
VILA REAL Alijó Vila Real Vila Real Porto 9,544 1,044 VILA REAL Boticas Vila Real Vila Real Porto 4,069 0,445 VILA REAL Chaves Vila Real Vila Real Porto 162,721 17,800 VILA REAL Mesão Frio Vila Real Vila Real Porto 3,091 0,338 VILA REAL Mondim de Basto Vila Real Vila Real Porto 5,838 0,639 VILA REAL Montalegre Vila Real Vila Real Porto 8,089 0,885 VILA REAL Murça Vila Real Vila Real Porto 4,334 0,474 VILA REAL Peso da Régua Vila Real Vila Real Porto 12,055 1,319 VILA REAL Ribeira de Pena Vila Real Vila Real Porto 5,001 0,547 VILA REAL Sabrosa Vila Real Vila Real Porto 4,662 0,510 VILA REAL Santa Marta de Penaguião Vila Real Vila Real Porto 5,729 0,627 VILA REAL Valpaços Vila Real Vila Real Porto 13,154 1,439 VILA REAL Vila Pouca de Aguiar Vila Real Vila Real Porto 10,526 1,151 VILA REAL Vila Real Vila Real Vila Real Porto 247,999 27,129
VISEU Armamar Vila Real Vila Real Porto 5,016 0,549 VISEU Carregal do Sal Coimbra Coimbra Porto 7,519 0,823 VISEU Castro Daire Porto Porto Porto 11,708 1,281 VISEU Cinfães Porto Porto Porto 14,329 1,568 VISEU Lamego Vila Real Vila Real Porto 102,956 11,263 VISEU Mangualde Castelo Branco Castelo Branco Porto 15,008 1,642 VISEU Moimenta da Beira Vila Real Vila Real Porto 7,762 0,849 VISEU Mortágua Coimbra Coimbra Porto 7,203 0,788 VISEU Nelas Coimbra Coimbra Porto 10,457 1,144 VISEU Oliveira de Frades Aveiro Aveiro Porto 7,548 0,826 VISEU Penalva do Castelo Aveiro Aveiro Porto 6,017 0,658 VISEU Penedono Vila Real Vila Real Porto 2,331 0,255 VISEU Resende Porto Porto Porto 8,202 0,897 VISEU Santa Comba Dão Coimbra Coimbra Porto 8,700 0,952 VISEU São João da Pesqueira Vila Real Vila Real Porto 5,673 0,621
101
District Municipality Waste Destination Total Annual Production (ton)
Transfer Station Disposal Site Incinerator Group III Group IV
VISEU São Pedro do Sul Aveiro Aveiro Porto 13,613 1,489 VISEU Sátão Aveiro Aveiro Porto 9,597 1,050 VISEU Sernancelhe Vila Real Vila Real Porto 4,264 0,467 VISEU Tabuaço Vila Real Vila Real Porto 4,401 0,481 VISEU Tarouca Vila Real Vila Real Porto 5,905 0,646 VISEU Tondela Coimbra Coimbra Porto 60,735 6,644 VISEU Vila Nova de Paiva Aveiro Aveiro Porto 4,540 0,497 VISEU Viseu Aveiro Aveiro Porto 70,246 7,684 VISEU Vouzela Aveiro Aveiro Porto 8,272 0,905