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
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
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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
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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.
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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
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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.
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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 6
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.
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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.
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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
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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
Quantity (ton) Group 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
2006 (ton)
Group SNS P.H.C. Hospitals
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
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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
2006 Group Hospitals P.H.C. Companies (t) (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
SNS hospital Total Production Group Year production Ratio estimative (ton) (ton)
Group III 20.741 13.639 (a) 66% Group IV 2001 2.269 2.942 (a) 130% Total 23.010 16.581 72%
Source: (Levy, Teles, Madeira, & Pinela, 2002), (a) (A.P.A., 2009)
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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. 12
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
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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
2016 (ton) Group 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 14
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.
1,6
1,4
1,2
1
0,8 Group I + II Group III 0,6 Group IV
% of production in 2001 in productionof % 0,4
0,2
0 2001 2002 2003 2004 2005 2006
Years
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 15
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)
2009 2016 Cesur estimates Years 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 16
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 C.P.I. relatively to period (%) 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.
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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
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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
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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.
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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
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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.
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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
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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.
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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 25
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.
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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).
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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
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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;
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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
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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,
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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.
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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
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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)
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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.
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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.
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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).
Real world problem
IMPROVEMENT
APPLICATION of Definition of the SOLUTION CONSTRAINTS and and OBJECTIVES CONCLUSIONS
Mathematical SOLVING model method FORMULATION
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.
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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
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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. GIV-1
TRANSFER STATION 1 GIV-2 GIV-2
GIV-3 GENERATING TRANSFER GIV-3 INCINERATOR NODE GIII-1 STATION 2
GIII-2 GIII-1 Group III Flow
DISPOSAL Group IV Flow SITE 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
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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 ∗ ( + 2 ). This represents a lower cost alternative to path 1 which can be represented by ∗ ( + 10 ).
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.
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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.
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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.
100 90 80 70 60 50 40 Piece-wise linear 30 % of total costtotal of % cost function 20 Concave cost 10 function 0 0 20 40 60 80 100 % of total capacity used
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}
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Parameters Cost per ton*Km of transporting Group IV waste from a generating node to a transfer Cs station or incinerator individually in a small capacity vehicle
Cost per ton*Km of transporting Group IV together with Group III from a generating Ct 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
Cost per ton*Km of transporting all types of waste from the transfer station to its a Cts 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 Fixed cost of using/opening a DS at a specific location k, associated to a specific cost FixDS kx curve x Fixed cost of using/opening a INC at a specific location l, associated to a specific cost FixINC lx 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 Control parameter equal to the highest ratio "Group IV waste produced at node i divided δ by Group III waste produced at the same node" plus 1 Control parameter which has to be greater or equal than the total amount of HMW in the β system dij dik dil Euclidean distances between the different sets of nodes (km) djk djl
Positive variables
QtDSkx Quantity of waste being treated at a certain DS (k) associated to a certain cost curve (x) Quantity of waste being eliminated at a certain INC (l) associated to a certain cost curve QtINC lx (x)
Binary variables = 1 If Group IV waste is transported from node i to incinerator l Z1il GIV-1 (figure 5) = 0 Otherwise If Group IV waste is transported individually from node i to TS j, and = 1 then to INC l Z2sijl GIV-2 (figure 5) = 0 Otherwise
If Group IV waste is transported together with Group III from node i to = 1 TS j, and then to INC l Z2tijl GIV-3 (figure 5) = 0 Otherwise
= 1 If Group III waste is transported from node i to DS k Z3ik GIII-2 (figure 5) = 0 Otherwise = 1 If Group III waste is transported from node i to TS j, and then to DS k Z4ijk GIII-1 (figure 5) = 0 Otherwise 43
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: