An environmentally sustainable decision model for urban solid waste management

An environmentally sustainable decision model for urban solid waste management

Waste Management 24 (2004) 277–295 www.elsevier.com/locate/wasman An environmentally sustainable decision model for urban solid waste management P. C...

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Waste Management 24 (2004) 277–295 www.elsevier.com/locate/wasman

An environmentally sustainable decision model for urban solid waste management P. Costia, R. Minciardia,b, M. Robbaa,*, M. Rovattib,c, R. Sacilea,b a

DIST, Department of Communication, Computer and System Sciences, University of Genova, Via Opera Pia 13, 16145 Genova, Italy b CIMA, Interuniversity Research Center in Environmental Monitoring, Via Cadorna 7, 17100 Savona, Italy c DICHEP, Department of Chemical and Process Engineering, University of Genova, Via Opera Pia 15, 16145 Genova, Italy Accepted 4 April 2003

Abstract The aim of this work is to present the structure and the application of a decision support system (DSS) designed to help decision makers of a municipality in the development of incineration, disposal, treatment and recycling integrated programs. Specifically, within a MSW management system, several treatment plants and facilities can generally be found: separators, plants for production of refuse derived fuel (RDF), incinerators with energy recovery, plants for treatment of organic material, and sanitary landfills. The main goal of the DSS is to plan the MSW management, defining the refuse flows that have to be sent to recycling or to different treatment or disposal plants, and suggesting the optimal number, the kinds, and the localization of the plants that have to be active. The DSS is based on a decision model that requires the solution of a constrained non-linear optimization problem, where some decision variables are binary and other ones are continuous. The objective function takes into account all possible economic costs, whereas constraints arise from technical, normative, and environmental issues. Specifically, pollution and impacts, induced by the overall solid waste management system, are considered through the formalization of constraints on incineration emissions and on negative effects produced by disposal or other particular treatments. # 2003 Elsevier Ltd. All rights reserved.

1. Introduction Waste management is one of the priority issues concerning protection of the environment and conservation of natural resources. Actually, there is an increasing attention by managers and planners to follow a sustainable approach to waste management and to integrate strategies that will produce the best practicable option. That is a quite hard task, as it is necessary to properly take into account economic, technical, and normative aspects, paying particular attention to environmental issues. The aim of this work is to present the structure of a decision support system (DSS) designed

§

DOI of original article: 10.1016/S0361-3682(02)00026-0 * Corresponding author. Tel.: +39-010-3532804; fax: +39-0103532154. E-mail addresses: [email protected] (P. Costi), riccardo. [email protected] (R. Minciardi), [email protected] (M. Robba), [email protected] (M. Rovatti), [email protected] unige.it (R. Sacile). 0956-053X/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0956-053X(03)00126-0

to help decision makers of a municipality in the development of incineration, disposal, treatment and recycling integrated programs. A case study, relevant to the municipality of Genova, in northern Italy, is presented. Generally speaking, the main alternatives to treat collected municipal solid waste (MSW) are represented by recycling, treatment in specific plants, and sanitary landfill disposal. Namely, within a MSW management system, several treatment plants and facilities can generally be found: separators, plants for production of refuse derived fuel (RDF), incinerators with energy recovery, plants for treatment of organic material, and sanitary landfills. The main goal of the DSS, whose structure is described in the paper, is to plan the MSW management, defining the refuse flows that have to be sent to recycling or to different treatment or disposal plants. To this end, it is necessary to define the decision variables of the problem, and to determine how the various performance indexes of the system can be expressed as functions of such variables. Such indexes will refer to economic costs as well as to pollution indicators.

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The definition of a decision model concerning the design of a urban solid waste management system would require the use of multi-objective decision concepts and techniques. However, since the model developed in this paper is specifically oriented to real-world applications, the multi-objective nature of the decision problem is taken into account simply by considering a single optimization objective consisting of the overall economic cost, and transforming all other objectives (pollution containment, impact minimization, etc.) into constraints. This is also in accordance with reality, as regulations specify strict bounds as regards the release of pollutants and other negative effects on the environment. As concerns environmental impacts, this approach has been mainly applied to incineration process and emissions, and chemical composition of RDF and SOM. However, dioxin emission and polycyclic aromatic hydrocarbons production have not been taken into account, due to the complexity of the chemical process involved in the formation of such compounds, which can be hardly integrated in the overall decision model proposed in this paper. The organization of the paper is the following. In Section 2, a brief survey is presented of the main approaches proposed in the literature as regards solid waste management in urban areas. Section 3 presents a general description of the model on which the DSS is based, and the definition of the decision variables. In Section 4, the various terms of the function to be optimized are presented. In Section 5, normative and technical constraints are introduced, whereas constraints concerning the containment of the environment impact of the overall system are discussed in Section 6. Then, in Section 7, the application of the proposed decision model is presented with reference to a specific case study relevant to the municipality of Genova.

2. Solid waste management in urban areas In recent years, many works have been presented with the aim of providing useful and comprehensive decision models, which should be both significantly close to reality and computationally tractable in order to help planners in managing solid waste disposal and treatment in urban areas, taking into account multidisciplinary aspects involving economic, technical, normative, and environmental sustainability issues. Specifically, in the past two decades, considerable research efforts have been directed towards the development of economic-based optimization models for MSW flow allocation. A model has been recently presented (Chang and Chang, 1998), which is based on the minimization of an overall cost (taking into account energy and material recovery requirements), which takes place through the solution of a constrained non-linear

optimization problem. This model is formalized through the definition of a set of continuous decision variables, which express the material flows to the various plants, whereas the cost function includes transportation, treatment, maintenance, and recycling costs, and takes into account possible benefits due to the sale of electric energy. The problem constraints are relevant to mass balance, plant capabilities, and the required minimum energy recovery. However, the model does not take into account normative, environmental and technical aspects. Some of the authors of the present paper have recently presented a decision model (Fiorucci et al., 2003), based on the same approach as Chang and Chang (1998), but within a more general modeling framework, both as regards the system representation and the decision variables considered. However, an approach merely based on economic considerations cannot be considered as completely satisfactory in connection with waste management problems. In fact, a wide set of possible developments can be pursued. Above all, modeling the environmental impact of solid waste management requires the modeling and analysis of a quite heterogeneous set of subsystems, which are affected by the decisions concerning solid waste management. For instance, among such subsystems, one can mention the atmospheric pollution model, the city traffic system, the sanitary landfill, etc. In this connection, some suggestions may come from recent works. For instance, Tsiliyannis (1999) has discussed the main environmental problems related to MSW management, and in particular those concerning pollutant releases. Chang and Wang (1997a) have proposed a fuzzy goal programming approach for optimal planning of MSW systems, in which they consider four objectives: economic costs, noise control, air pollution control, and traffic congestion limitations. Another possible approach is based on life cycle assessment (Finnveden, 1999; Barton et al., 1998). Specifically, Finnveden (1999) has discussed some methodological issues that arise in connection with such an approach. Moreover, the waste reduction problem could be studied at a more general level, taking into account issues concerning the design of production processes (Young et al., 1996). Actually, planning a MSW management system is a very complex task, because it is necessary to simultaneously consider conflicting objectives; in addition, such problems are generally characterized by an intrinsic uncertainty as regards the estimates of costs and environmental impacts. Such reasons have led several authors (Chang and Wang, 1997a,b; Hokkanen and Salminem, 1997; Karagiannidis and Moussiopoulus, 1997) to introduce and apply multi-criteria decision techniques. As regards the detailed treatment of the dynamics of pollution processes deriving from MSW management,

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many authors have developed models aiming at representing chemical processes and reactions that take place in the various plants used in a MSW management system. Specifically, a crucial issue is that concerning the modeling of the formation of pollutants deriving from combustion or from specific processes. A recent work (Chang et al., 1998) has paid a great attention to the impact of solid waste presorting on incineration facilities, through the evaluation of the comparative effects of burning MSW and RDF in the same incinerator. Specific issues comparatively analyzed are heat balance, ash properties, and the quality of flue gas in the incineration process. Morf et al. (2000) have paid particular attention to material balances and to the determination of coefficients expressing the input/output fraction. Moreover, they have used statistical techniques to analyze the uncertainty arising from variations in input waste variations and process conditions. Bjo¨rklund et al. (1999) have used a substance-flow simulation model, namely the organic waste research model (ORWARE), to evaluate economic aspects and environmental impacts, and comparing three scenarios: incineration with heat recovery, composting, anaerobic digestion. The results are then evaluated by using a life cycle assessment (LCA) methodology. In this framework, the purpose of the present paper is that of considering a quite general model, which is comprehensive of all technical, economic, normative, and environmental aspects concerning the management of MSW. Specifically, the proposed system can help decision makers in choosing the size and the typology (i.e. separators, incinerators, etc. . .) of the various treatment plants, on the basis of a careful analysis of the chemical composition of the produced refuse. The number and the possible locations for each kind of plant, are assumed to have been fixed a priori. However, for any of such plants, the actual existence is a matter of the decision problem, whose formalization thus requires the introduction of binary decision variables. Then, the problem to be solved is a non-linear mixed integer mathematical programming problem. In this way, the optimal configuration of the system (from the physical and technological point of view) can be determined, as well as the optimal flows among the various plants in the system. Environmental impacts are carefully represented, with specific attention paid to incinerator emissions and RDF chemical composition.

3. The model and the decision variables To build a complete model of a MSW management system, a wide knowledge and a deep analysis of the available treatment processes of the materials composing the refuse is needed. In addition the model proposed in this paper has been formulated taking in mind European

279

legislation guidelines for MSW management concerning reduction of waste production, recycling, energy and material recovery, and final disposal in sanitary landfill. In this model, MSW is supposed to be composed by 11 kinds of materials (1—paper, 2—heavy plastic, 3—plastic bags, 4—plastic bottles, 5—glass, 6—organic, 7—wood, 8—metals, 9—scraps, 10—inert matter, and 11—textiles). The waste composition, the waste heating value before and after any treatment plant, the incinerator emissions, are computed in this work taking into account chemical waste composition. The daily MSW production R is partly gathered by separate collection and then sent to recycling. Note that recycling is possible for nine kinds of materials: paper, heavy plastic, plastic bottles, plastic bags, organic material, metals, textiles, wood, and glass; these materials can be separately collected by different methods. The remaining fraction of MSW is collected without separating the various materials, and then sent to three kinds of treatment plants: separators, incinerators and landfills. Three flows may come out from a separator plant: 1. The metals recovered in the refuse pre-selection in the first stage of the separation process and that can be sent to recycling. 2. The organic material sent to treatment plants (humid material). 3. A fraction of material, with low humidity and high heating value (dry material), that can be burnt, or sent to plants for RDF production, or disposed in a sanitary landfill. A RDF plant produces fuel, that can be sold to industries or burnt in an incinerator, and scraps, which can be sent either to an incinerator or to a landfill. The organic material collected for recycling can be directly sent to a composting plant because it is pure enough to produce compost for agricultural use. The humid material is treated in an organic material treatment plant, which produces stabilized organic material (SOM) and scraps. SOM can be sold, burnt in an incinerator, or sent to a landfill, while scraps are directly sent to landfill. Clearly, recovery takes place not only through recycling but also through the various treatment plants which provide SOM, RDF and metals. Also energy recovery by MSW combustion has to be taken into account. As recycling modifies the composition of the refuse sent to incineration, it influences the heating value of the refuse that has to be burnt, and hence energy recovery. The proposed model includes also the possibility of disposal in sanitary landfills. Such a disposal may be constrained by a maximum amount of MSW flow that can be sent to the landfill, or equivalently by a minimum number of years for the complete filling of the landfill.

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Finally, issues concerning the environmental impacts of the overall MSW management system are considered with specific attention to incineration processes and emissions, and to the chemical characteristics of the RDF and SOM produced. Since many aspects and possibilities have been taken into account in this work, the definition of several decision variables and of a great number of parameters was necessary. All notations used to indicate those entities are reported in the Appendix. Let R be the total daily MSW production in the considered municipal area, and ri the daily quantity of material of type i, expressed in ton/day. A conceptual representation of the model is reported in Fig. 1. Some kinds of materials present in the refuse can be recycled by separate collection. Let i represent the percentage of material of type i directly sent to recycling through separate collection (i=1,. . .,11). Such percentages are among the decision variables (throughout the whole paper, for the sake of clarity, the primary decision variables will be represented in bold character). Note that  9 ¼  10 ¼ 0 because scraps and inert matter are not recyclable. The remaining refuse (mass) flow (which is not collected separately) is taken to the generic collecting site denoted as Pd (d=1. . .D). Let Pd ;i be the fraction of ri which is collected at collection site Pd. As already specified in the previous section, the number and possible locations of such sites are fixed a priori. As regards the other kinds of plants, technological characteristics and possible locations are fixed too, but their size and actual existence are matter of the decision problem. More specifically:  Sp indicates the pth separator (p=1,. . .,P)  Cq indicates the qth RDF-plant (q=1,. . .,Q)  Ts indicates the sth organic material treatment plant (s=1,. . .,S)  In indicates the nth incinerator plant (n=1,. . .,N)  Lm represents the mth landfill (m=1,. . .,M) From a collecting site, the refuse can be sent either to a separator, or to an incinerator, or to a landfill. Then, it is necessary to introduce the decision variables Pd ;Lm , Pd ;Sp , Pd ;In , which correspond to the percentages of the untreated waste coming from collecting site Pd and sent, respectively, to landfill Lm, to separator Sp, and to incinerator In. Such percentages are the same for all kinds of materials, and thus they do not depend on index i. A separator divides the refuse in three parts: metals sent to recycling, humid material sent to specific organic material treatment plants, and a remaining quantity of dry waste, which can be sent to RDF-plants, or to incinerators, or to landfills. Let k8 be the fraction of the metals entering the separator which is sent to recycling. Similarly, for the sake of generality, let ki=0,

i=1,. . .,11, i6¼8 (this assumption is important since it states that in the separator, before dividing refuse in humid and dry material, only metals are recovered). Moreover let i be the fraction of the overall material of kind i, which is not sent to recycling after separation, which remains in the humid material. As a consequence, (1  i ) is the fraction of the material of kind i which remains in the dry material. Note that coefficient i is assumed independent of the particular separator plant, as it is reasonable to consider all such plants technologically similar. The decision variables Sp ;Cq , Sp ;In , Sp ;Lm correspond to the fractions of dry material coming from separator Sp and sent, respectively, to RDF-plant Cq, to incinerator In, and to landfill Lm. The decision variable SP ;Ts represents the fraction of the humid material produced in separator Sp and sent to the organic material treatment plant Ts. A RDF-plant separates entering refuse in two parts: RDF that can be sold or sent to any incinerator, and scraps that can be sent to incinerators and to landfills. Variables Cq ;Lm and Cq ;In represent the fraction of scraps, coming from RDF-plant Cq, and sent, respectively, to landfill Lm and to incinerator In. Variables Cq ;M and Cq ;In represent fractions of RDF produced in RDF-plant Cq that can be sold or sent to incinerator In, respectively. Let ^ i be the fraction of material of kind i entering any RDF plant Cq which becomes scraps. As a consequence, (1  ^ i ) is the fraction of the same material entering the plant that becomes RDF. Note that, even in this case, coefficient ^ i is assumed independent of the particular RDF plant. Ashes produced by incinerators In are sent to landfills; let In ;Lm be the fraction of ashes coming from incinerator In and sent to landfill Lm. The organic material treatment plants that treat humid material coming from separators produce SOM and scraps. Scraps are sent to landfills while SOM can be sent to landfills, to incinerators, or can be sold. Variables Ts ;Lm , Ts ;In and Ts ;M represent the SOM fraction coming from organic material treatment plant Ts and sent to landfill Lm, to incinerator In, or sold, respectively. Variables Ts ;Lm represent the fractions of scraps coming from organic material treatment plant and sent to landfill Lm. Let ~ i be the fraction of the overall material entering the organic material treatment plant Ts that is transformed in SOM. As a consequence, (1  ~ i ) is the fraction of the material of kind i which remains in the scraps. Here again, coefficient ~ i is assumed independent of the particular organic material treatment plant. Binary decision variables are associated to all separators, RDF plants, incinerators, organic material treatment plants and landfills, to indicate, through their value, the presence/absence of such plants: Sp , Cq , In ,

Ts , Lm . Namely, each of such variables has to be equal

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281

Fig. 1. Conceptual representation of the model.

to 1 if the plant actually exists in the solution that is determined for the optimization problem, and 0 otherwise. Thus, binary as well as continuous variables are needed in this model.

4. The cost function To write the overall cost function (to be minimized), it is necessary to take into account recycling, transportation,

and plant costs, along with possible economic benefits (all costs and benefits will be considered per year). More specifically:  recycling costs result from the balance of separate collection costs and economic benefits resulting from the sale of collected material and/ or possible contributions; separate collection costs in general depend on the way such a collection is actually carried out (ecological islands,

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direct collection at home, different types of containers positioned on the road, etc.);  transportation costs depend on the number of vehicles involved, on personnel costs, and on the distances among the various plants; note that collection costs relevant to waste gathering at the various collection sites are not considered in our model, as they are assumed independent from the decision variables of the problem;  plant costs take into account installation and maintenance costs;  economic benefits include money gained through the sale of electric energy, RDF, and the metals obtained through the separators. 4.1. Recycling costs Recycling can take place through different techniques j=1,. . .,4 (1 is referred to collection directly at home, 2 through ecological island, 3 through special holders and 4 using small holders). A fixed parameter !ij represents the fraction of material i collected through separate collection which takes place through method j. The fact that such fractions are viewed as fixed parameters may be justified by assuming that the most economical separate collection method is in any case selected as far as compatible with the urban structure, the socio-economic characteristics of the population, etc. Let Cijr be the unit cost, per ton of refuse, of separate collection of material i through method j and Ci the unit benefit from the sale of material of kind i. Then the overall annual recycling cost is: ! ! 11 4 X X r r C ¼ n Cij ri  i !ij  Coni ri  i ð1Þ i¼1

j¼1

where n is the number of days in a year. 4.2. Transportation costs Transportation costs include:  personnel costs, which depend on the number of trips necessary to transport waste and on the number of trips that a single driver can perform during his work-day;  vehicle costs (including fuel costs);  possible tolls to be paid. Let  X be the set of the possible plant-to-plant connections;  (s,d) be a generic plant-to-plant connection;

 Q s;d be the annual mass flow corresponding to connection (s,d);  s;d be the density corresponding to the flow relevant to connection (s,d);  Q^ s;d be the annual volume flow corresponding to connection (s,d), provided by Q s;d =s;d ;  Vs;d be the capacity of a single vehicle relevant to connection (s,d);  Cs;d be the cost of a trip relevant to connection (s,d). Then, the overall transportation cost (per year) can be evaluated as: Ct ¼

X Q^ s;d Cs;d Vs;d ðs;dÞ2X

Note that the number of necessary trips, for each connection, is considered as a real value, although the number of trips, according to real application, should be an integer. This is actually an approximation, but it can be justified by taking into account that the considered time horizon is equal to a year, and thus the number of necessary trips is certainly very large. For example, consider the annual volume flow from a specific collecting site Pd to a specific landfill Lm; the annual waste volume sent from collecting site Pd to landfill Lm (having density Pd ;Lm ) is given by (case A in Table 1): Q^ Pd ;Lm ¼ n

11 X ð1   i Þri Pd ;i Pd ;Lm =Pd ;Lm

ð2Þ

i¼1

and thus the overall transportation cost from collecting sites to landfills is D X M ^ X QP d¼1 m¼1

CPd ;Lm VPd ;Lm

d ;Lm

For each possible plant-to-plant connection, similar considerations may be repeated. More specifically, the following flows, in addition to those already considered, can be expressed as in Table 1: (B) from collecting sites to incinerators (C) from separators to RDF plants (D) from separators to organic material treatment plants (E) from separators to landfills (F) from separators to incinerators (G) scraps from RDF plants to landfills (H) scraps from RDF plants to incinerators (I) RDF from RDF plants to incinerators

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P. Costi et al. / Waste Management 24 (2004) 277–295 Table 1 Annual volume flow expressed in terms of the primary decision variables Flow type

Volume transported (per year)

A

P Q^ Pd Lm ¼ n 11 i¼1 ð1   i Þri Pd ;i Pd ;Lm =Pd ;Lm

B

Q^ Pd ;In ¼ n

C

Q^ Sp ;Cq ¼ n

D

P P11 Q^ Sp ;Ts ¼ n D d¼1 i¼1 ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þi Sp ;Ts =Sp ;Ts

E

Q^ Sp ;Lm ¼ n

F

Q^ Sp ;In ¼ n

G

P P P11 Q^ Cq ;Lm ¼ n Pp¼1 D d¼1 i¼1 ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

H

Q^ Cq ;In ¼ n

I

Q^ RDFq ;In ¼ n

L

P Q^ Pd ;Sp ¼ n 11 i¼1 ð1   i Þri Pd ;i Pd ;Sp =Pd ;Sp

M

Q^ Ts ;Lm ¼ n

N

Q^ SOMs ;In ¼ n

O

P P P11 Q^ SOMs ;Lm ¼ n Pp¼1 D ~ i Ts ;Lm =SOMs ;Lm d¼1 i¼1 ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þi Sp ;Ts 

P

P11

i¼1 ð1

  i Þri Pd ;i Pd ;In =Pd ;In

PD P11

i¼1 ð1

d¼1

PD P11

i¼1 ð1

d¼1

PD P11 d¼1

i¼1 ð1

 i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

  i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

 i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

PP PD P11 p¼1

d¼1

i¼1 ð1

i¼1 ð1

d¼1

PP PD P11 p¼1

d¼1

i¼1 ð1

PP PD P11 p¼1

d¼1

SP ;Lm =Sp ;Lm

SP ;In =Sp ;In

 i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

PP PD P11 p¼1

SP ;Cq =Sp ;Cq

^ i Cq ;Lm =Cq ;Lm SP ;Cq 

^ i Cq ;In =Cq ;In SP ;Cq 

  i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

SP ;Cq ð1

 ^ i ÞCq ;In =RDFq ;In

  i Þri Pd ;i Pd ;Sp ð1  ki Þi Sp ;Ts ð1  ~ i Þ Ts ;Lm =Ts ;Lm

i¼1 ð1

  i Þri Pd ;i Pd ;Sp ð1  ki Þi Sp ;Ts ~ i Ts ;In =SOMs ;In

nXD X11   ð1  i Þri Pd ;i Ashi Pd ;In =Pd ;In Q^ In ;Lm ¼ nIn ;Lm d¼1 i¼1 XP  þ p¼1 Pd ;Sp ð1  ki Þð1  i Þ SP ;In =Sp ;In XQ   þ q¼1 SP ;Cq ^ i Cq ;In =Cq ;In þ ð1  ^ i ÞCq ;In =RDFq ;In io XP XS þ p¼1 s¼1 Pd ;Sp ð1  ki Þi Sp ;Ts ~ i Ts ;In Ashfi =SOMs ;In

where Ashi is the ash content of material i and Ashfi is the ash content of material i after stabilization

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(L) from collecting sites to separators (M) scraps from organic material treatment plants to landfills (N) SOM from organic material treatment plants to incinerators (O) SOM from organic material treatment plants to landfills (P) from incinerators to landfills.

Cm ¼

P X D X Q P

CSP þ d ;Sp

P X CF;Sp SP

p¼1 d¼1

þ

p¼1

Q P X X

Q X CF;Cq Cq

p¼1 q¼1

q¼1

Q Cq ;Sp CCq þ

S X P S X P X X þ Q Sp ;Ts CTs þ CF;Ts Ts s¼1 p¼1

Note that we have two differentiate flows (H) and (I), which have the same source and destination pair, but refer to scraps and RDF, respectively. Thus, we will use the symbol Q^ Cq ;In to designate the first kind of flows and the symbol Q^ RDFq ;In to designate the second one. Similar considerations hold even for flows (M) and (O), for which we will use the symbols Q^ Ts ;Lm and Q^ SOMs ;Lm , respectively. Thus the overall expression of the transportation costs is the following: Ct ¼

D X M ^ X QP d¼1 m¼1

þ

þ þ

þ

VSp ;Lm VCq ;Lm VCq ;In

d ;In

n¼1

þ

þ

þ

þ

þ

VSp ;Ts VSp ;In

D X

P X

Q X Q Cq ;Lm

m¼1

d¼1

p¼1

q¼1

Q Sp ;Lm þ

s¼1

M X

n¼1

CF;Lm Lm

4.4. The overall objective function Finally, it is necessary to take into account the possible benefits deriving from the sale of RDF and metals obtained by the separators, as well as from electric energy production. Assume that every kg of RDF can be sold at a price PRDF. Then the annual economic benefit is:

VCq ;In VPd ;Sp

BRDF ¼

Q X PRDF RDFCq

ð5Þ

q¼1

S X M X

Q^ SOMs ;Lm CTs ;Lm VTs ;Lm s¼1 m¼1

Q^ In ;Lm CIn ;Lm VIn ;Lm n¼1 m¼1

n¼1

M X

Q Pd ;Lm þ

ð4Þ

where the annual mass flow can be expressed as Q s;d ¼ Q^ s;d s;d , using again the relations in Table 1.

S X M ^ S X N ^ X QTs ;Lm CTs ;Lm X QSOMs ;In CTs ;In þ VTp ;Lm VTs ;In s¼1 m¼1 s¼1 n¼1

N X M X

N X CF;In In CIn þ

m¼1

D X P ^ X Q Pd ;Sp CPd ;Sp d¼1 p¼1

Q Cq ;In

q¼1

q¼1

s¼1

Q X N ^ X QCq ;In CCq ;In q¼1 n¼1

Q SOMs ;In þ

!

Q X

! S S N X X X þ Q Ts ;Lm þ Q SOMs ;Lm þ Q In ;Lm CLm

CPd ;In

P X N ^ X QSp ;In CSp ;In p¼1 n¼1

p¼1

d¼1

s¼1

S X P ^ X QSp ;Ts CSp ;Ts

þ

Q N D P X X X X Q Pd ;In þ Q Sp ;In þ Q RDFq ;In

S X

VPd ;In

s¼1 p¼1

Q X N ^ X QRDFq ;In CCq ;In q¼1 n¼1

þ

VSp ;Cq

D X N ^ X QP d¼1 n¼1

Q X M ^ X QCq ;Lm CCq ;Lm q¼1 m¼1

þ

VPd ;Lm

þ

P X M ^ X QSp ;Lm CSp ;Lm p¼1 m¼1

þ

CPd ;Lm

Q ^ P X X QSp ;Cq CSp ;Cq p¼1 q¼1

þ

d ;Lm

þ

s¼1 p¼1

where ð3Þ

where it has to be remembered that terms Q^ s;d are actually functions of the primary decision variables through the expressions in Table 1. 4.3. Plant costs Plant costs are related to maintenance, management and installation. For a given plant z, the fixed cost CF;z is multiplied by the integer decision variable relative to that plant, whereas the variable cost is proportional to mass yearly entering the plant through the coefficient Cz. The following expression represents the overall plant cost in the system.

RDFCq ¼ n

P X D X 11 X ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þ p¼1 d¼1 i¼1

ð 1  i Þ

SP ;Cq ð1

 ^ i Þ SP ;Cq

ð6Þ

is the overall yearly mass quantity of RDF produced in the system. The evaluation of benefits coming from the sale of electric energy requires some specific attention. In fact, energy production depends on the heating value and the refuse flow entering the incinerator plants. The annual energy economic benefit deriving from the production of electric energy can be computed as

N X E HVIn n  Ec;n BE ¼ c~e ð7Þ f n¼1

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where:  c~e is the unit price [E/kWh] for the sale of energy;  Ec,n is the annual energy consumption [kWh/ year] of the nth incinerator;  E is efficiency concerning energy production with respect to heat produced by combustion;  f is a conversion factor equal to 3.6 MJ/kWh;  HVIn [MJ/d] is the overall daily thermal energy of the refuse entering the incinerator In. The value of HVIn is given by HVIn ¼

P X D X 11 X ð1  i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ p¼1 d¼1 i¼1 SP ;In HVi þ

D X 11 X ð1   i Þri Pd ;i Pd ;In HVi þ d¼1 i¼1

Q X P X D X 11 X ð1  i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ

system (such constraints will be thoroughly examined in Section 6), some other kinds of constraints are taken into account: normative constraint concerning separate collection, constraints on the plant possible sizes, mass balance equations, and constraints necessary to impose the actual presence of a plant whenever the flow entering is non-zero. 5.1. Normative constraint Italian legislation requires that waste recycling is no less than 35% of the total produced waste in mass. Thus, (materials recovered by separate collection) +(materials present in the MSW sent to the separators and recovered with efficiency ki)+(stabilized organic material)+(produced RDF)535% of the total refuse, i.e. 11 D X P X 11 X X  i ri þ ki ð1   i Þri Pd ;i Pd ;Sp i¼1

q¼1 p¼1 d¼1 i¼1 SP ;Cq ð1

 ^ i ÞCq ;In HVi þ

þ

Q X P X D X 11 X ð1  i Þri Pd ;i Pd ;Sp ð1  ki Þð1  i Þ q¼1 p¼1 d¼1 i¼1 SP ;Cq ð1

S X P X D X 11 X ð1  i Þri Pd ;i Pd ;Sp ð1  ki Þ

i Sp ;Ts ~ i Ts ;In HVf;i

ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þi ~ i Ts ;M

s¼1 d¼1 p¼1 i¼1

þ

Q X D X P X 11 X ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þ d¼1 p¼1 q¼1 i¼1

 ^ i ÞCq ;In HVi þ

s¼1 p¼1 d¼1 i¼1

d¼1 p¼1 i¼1 S X D X P X 11 X

ð1  i Þ

Sp ;Cq ð1

 ^ i ÞCq ;M 5 0:35

11 X ri i¼1



ð11Þ where ð8Þ

where HVi and HVfi represent the heating values [MJ/ kg], for every material i, before and after stabilization, respectively, and can be expressed as (Perry et al., 1997): HVi ¼ 34:8Ci þ 93:8Hi þ 10:46Si  10:8Oi  2:4Ui

ð9aÞ

HVfi ¼ 34; 8Cf;i þ 93:8Hf;i þ 10:46Sf;i  10:8Of;i  2:4Uf;i

ð9bÞ

where Ci ; Hi ; Si ; Oi ; Ui (Cf;i ; Hf;i ; Sf;i ; Of;i ; Uf;i ) represent carbon, hydrogen, sulfur, oxygen, and water content, respectively, expressed in kg/kg, before (after) stabilization. All such parameters have known values. Then, on the basis of the above definitions, the overall cost function to be minimized may be written as C ¼ C r þ C t þ C m  ðBE þ BRDF Þ

ð10Þ

 ki is the fraction of material i sent to recycling after separation;  i is the fraction of material i, with respect to the overall material not recycled after separation, which is sent (as humid material) to an organic material treatment plant;  ~ i is a parameter that represents the fraction of material i, entering an organic material treatment plant, which remains included in the stabilized organic material; note that such a fraction depends on index i because clearing operations to eliminate scraps take place in the organic material treatment plant, with an efficiency which depends on index i;  ^ i is the fraction of material i, entering a RDF plant, which remains as a constituent of RDF produced at that plant; here again, this fraction depends on index i.

5. Normative and technical constraints

5.2. Constraints on the flows entering the various plants

Besides to constraints which arise from the need of limiting the environmental impacts of the MSW management

For every incinerator, daily mass entering must lie between two fixed values, namely

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MIn ;a In 4 Q In 4 MIn ;b In

n ¼ 1; . . . ; N

ð12Þ

Cq ;M þ

q ¼ 1; . . . ; Q

ð20Þ

n¼1

where Q In ¼

N X Cq ;In ¼ Cq

Q D P S X X X X Q Pd ;In þ Q Sp ;In þ Q RDF;In þ Q SOM;In q¼1

p¼1

d¼1

s¼1

Q X þ Q Cq ;In

M X

M X

q¼1

In ;Lm ¼ In

n ¼ 1; . . . ; N

ð21Þ

Ts ;Lm ¼ Ts

s ¼ 1; . . . ; S

ð22Þ

m¼1

m¼1 M X

Similarly, for every separator SP

Ts ;Lm þ

m¼1

D X MSP ;a Sp 4 Q Pd ;Sp 4 MSP ;b Sp

ð13Þ

d¼1

p ¼ 1; . . . ; P

N X Ts ;In þ Ts ;M ¼ Ts

ð23Þ

n¼1

s ¼ 1; . . . ; S 5.4. Constraints imposing the presence of plants

whereas, for every RDF-plant P X MCq ;a Cq 4 Q Sp ;Cq 4 MCq ;b Cq

ð14Þ

p¼1

q ¼ 1; . . . ; Q and, for every organic material treatment plant MTs ;a Ts 4

P X Q Sp ;Ts 4 MTs ;b Ts

ð15Þ

p¼1

Note that constraints (12), (13), (14) and (15) allow a nonzero refuse flow to a plant, only when such a plant is actually existing (i.e., the corresponding variable ‘‘ ” ¼ 1). 5.3. Mass balance equations

Pd ;Lm

N P X X þ Pd ;In þ Pd ;Sp ¼ 1 n¼1

p¼1

ð16Þ

d ¼ 1; . . . ; D M X Sp ;Lm

þ

m¼1

p ¼ 1; . . . ; P

ð24Þ

Sp ;Cq

Sp ;In

þ

Q X Sp ;Cq

¼ S p

q¼1

 C q  4 0

q ¼ 1; . . . ; Q

ð25Þ

p¼1 D P X X Pd ;In þ

Sp ;In

þ

Q Q X X Cq ;In þ Cq ;In q¼1

p¼1

q¼1

ð26Þ

 In  4 0 n ¼ 1; . . . ; N D P X X Pd ;Lm þ

Sp ;Lm

p¼1

d¼1

þ

N X n¼1

P X

d¼1

Mass conservation equations are needed for each branching point at which a flow can be split. Such equations are:

m¼1

D X Pd ;Sp  Sp  4 0 d¼1

s ¼ 1; . . . ; S

M X

A constraint must be introduced for every plant whose presence/absence is a matter of the decision problem. This constraint must impose that if the flow entering such a plant is greater than zero, then the plant must actually exist. In our model, such constraints must be introduced for every separator, any RDF-plant, any incinerator, and any landfill. In summary, we have:

Q N X X Cq ;Lm þ In ;Lm q¼1

S X

S X

s¼1

s¼1

Ts ;Lm þ

þ

n¼1

ð27Þ

Ts ;Lm  Lm  4 0

m ¼ 1; . . . ; M ð17Þ

p ¼ 1; . . . ; P

P X Sp ;Ts  Ts  4 0

s ¼ 1; . . . ; S

ð28Þ

p¼1 S X Sp ;Ts ¼ Sp

p ¼ 1; . . . ; P

ð18Þ

s¼1 M X

Cq ;Lm þ

m¼1

N X Cq ;In ¼ Cq n¼1

q ¼ 1; . . . ; Q

ð19Þ

where ! is a very great number with respect to values that can be assumed by every decision variable. Of course, in the proposed model, it is also possible to impose the existence of a certain plant. This may be due to the fact that such a plant is actually already built, or to political or technical reasons which impose

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the presence of that plant. In this case, the corresponding variable ‘‘ ’’ has to be set as equal to 1 (or, equivalently, it may be removed at all), and only the material flows related to such a plant are a matter to be considered in the decision problem (within the bounds specified as in Section 5.2).

 ð0:25  Ui Þ for the constraint which prescribes that humidity content in produced RDF must be less than 0.25%. In fact, considering for instance the constraint relevant to the chlorine content, (29), is equivalent to ðthe RDF daily produced in RDF plant Cq Þ 0:0009

6. Environmental constraints

11 X ðdaily mass flow relevant to material i in the RDF

The introduction of environmental constraints is necessary in order to avoid a too heavy impact of the overall MSW management system. To this end, constraints on incineration emissions, and on the RDF and SOM chemical contents have to be introduced, aiming at limiting the presence of specific noxious substances. In addition, constraints concerning combustion process as well as landfill saturation limitations have to be introduced.

i¼1

6.1. RDF constraints Produced RDF must have specific chemical characteristics, fixed by regulations, in order to limit pollution derived from its combustion. Specifically, Cl, S, ashes, humidity content and heating value have to be taken into account. These contents can be calculated by summing the quantity present in every material i composing the produced RDF. Besides, the unitary heating value (kcal/kg) of the produced RDF must be greater than or equal to a minimum specified value. Such constraints may be expressed via the following general structure P X D X 11 X ð1   i Þri Pd ;i Pd ;Sp ð1  ki Þ p¼1 d¼1 i¼1

ð 1  i Þ

ð29Þ SP ;Cq ð1

 ^ i ÞAi 5 0

q ¼ 1; . . . ; Q where Ai is given by:  gHVi—3600 kcal/kg for the constraint relevant to the heating value, where HVi [MJ/kg] represents the heating value for the ith kind of material and g is a conversion factor from MJ to kcal, equal to 238.9 kcal/MJ;  0.009—Cli for the constraint which prescribes that chlorine content in produced RDF must be less than 0.9%; Cli is the chlorine content for i th kind of material;  0.006—Si for the constraint which prescribes that sulfur content in produced RDF must be less than i is the 0.6%; SAsh  sulfur content for ith kind of material; i  0:2  1U for the constraint which prescribes i that ashes content in produced RDF must be less than 0.2%; Ashi is the ash content for i th kind of material and Ui is humidity of material i;

produced in plant Cq Þ Cli 5 0 which, in turn, is equivalent to the unitary content of chlorine in the RDF plant produced in plant Cq 4 0:09. Similar considerations hold for the other constraints, which can be represented under the general form (29). Of course, (29) represents Q.5 constraints to be taken into account in the optimization problem. Besides, a maximum daily production (determined on the basis of marketing considerations) of RDF must not be overcome, that is Q X P X D X 11 X ð1   i Þ ri Pd ;i Pd ;Sp ð1  ki Þ q¼1 p¼1 d¼1 i¼1

ð1  i Þ

SP ;Cq

ð1  ^ i Þ 4 RDFS

ð30Þ

where RDFS is a fixed parameter. 6.2. SOM constraints Stabilized organic material is obtained from the treatment of humid material coming from separators. Usually, this sequence of processes produces a SOM with many impurities, for which European normative fixes specific limits. In fact, these materials can be noxious for the environment when SOM is re-used in land. Then, constraints are necessary to guarantee a good quality of the product obtained through stabilization. Such constraints specify the minimum content of organic material and the maximum content of glass, plastic and C/N. In fact, fraction C/N must not be too much high because, in such a case, it may give problems as regards N content, pH, and emissions of bad odors. A generic structure can be used to represent such constraints: ( ) ( P X D P X D X 11 X X Pd ;Sp Sp ;Ts K  H

ð1   i Þ ri p¼1 d¼1

p¼1 d¼1 i¼1

)

Pd ;Sp ð1  ki Þ i Sp ;Ts ~ i ð1  hi Þ 4 0 s ¼ 1; . . . ; S

ð31Þ

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where  hi is the humidity content of material i present in SOM after stabilization;  constants K and H are so specified:  K=  ð1   6 Þr6 ð1  k6 Þ6 ~ 6 , and H=0.4, for the constraint relevant to the organic material content, that must be greater than 40% with respect to the total SOM without humidity (dry material);  K=ð1   5 Þr5 ð1  k5 Þ5 ~ 5 , and H=0.03, for the constraint relevant to the glass content, that must be less than 3% with respect to totalP SOM without humidity;  K= 4i¼2 ð1   i Þri ð1  ki Þi ~ i , and H=0.01, for the constraint relevant to the plastic content, that must be less than 1% with respect  P to total SOM without humidity; ~ i 0:3 Nf;i  Cf;i  K= 11 i¼1 ð1   i Þri ð1  ki Þi  and H=0, for the constraint relevant to the C/N content, that must be less than 30%; Cf,i and Nf,i represent, respectively, C and N content in SOM for every material i (the values of Cf,i and Nf,i are known for the specific process considered).

aspects of the incineration process. For example, considering SO2 emission, it is first necessary to remind that the chemical reaction that takes place in the incinerator plant and produces SO2 is: S þ O2 ! SO2 Then, the relation between the overall amount of sulfur MS,n entering daily the incinerator plant In and the daily overall emission [kg/day] MSO2 ;n of SO2 is MSO2 ;n ¼ 2 MS;n because 2 is the fraction between SO2 and S molecular weights. Besides, MS,n can be evaluated taking into account the various flows entering each incinerator, namely D X 11 X P X MS;n ¼ ð1 i Þri Pd ;i Pd ;Sp d¼1 i¼1 p¼1

ð1ki Þð1i Þ þ

S X P X D X 11 X ð1  i Þri Pd ;Sp ð1  ki Þi Sp ;Ts ~ i 4 SOMS

ð1   i Þri Pd ;i Pd ;In Si

d¼1 i¼1

þ Finally, it is necessary to introduce a constraint limiting the quantity of material that can be sold.

SP ;In Si

D X 11 X

Q X P X D X 11 X ð1   i Þri Pd ;i Pd ;Sp q¼1 p¼1 d¼1 i¼1

^ i Cq ;In Si SP ;Cq 

ð1  ki Þð1  i Þ þ

s¼1 p¼1 d¼1 i¼1

ð34Þ

Q X P X D X 11 X

ð1   i Þri Pd ;i Pd ;Sp

q¼1 p¼1 d¼1 i¼1

ð32Þ where SOMS is a fixed parameter, determined on the basis of marketing considerations.

ð1  ki Þð1  i Þ þ

SP ;Cq ð1

 ^ i ÞCq ;In Si

S X P X D X 11 X

ð1   i Þri Pd ;i Pd ;Sp

s¼1 p¼1 d¼1 i¼1

ð1  ki Þi Sp ;Ts ~ i Ts ;In Sf;i

6.3. Incineration process constraints Italian regulations state that the minimum power for plants burning RDF must be 10 MW; then the following constraints must be introduced fHVIn  In 10 MW 5 0

n ¼ 1; . . . ; N

ð33Þ

where HVIn is given by (8) and represents the heating value of refuse entering the incinerator plant In expressed in [MJ/day], and f is a conversion factor equal to 1.16 105 MW/MJ/day. 6.4. Incineration emissions constraints The introduction of constraints on the emissions (in terms of concentration) from incinerators is necessary for the following substances: SOx, HCl, HF, NOx, heavy metals and dust emissions. To formalize such constraints, it is necessary to focus on the technical

n ¼ 1; . . . ; N where:  Si is the sulfur content (kg/kg) of the ith material present in the refuse  Sf,i is the sulfur content (kg/kg) of the ith material present in the refuse after stabilization process. Both Si and Sfi have known values. The various terms of expression (34) refer respectively to:  dry material coming from the various separators and sent to the generic incinerator In;  untreated waste coming from collection sites and sent to the generic incinerator In;

P. Costi et al. / Waste Management 24 (2004) 277–295

 scraps coming from RDF plants and sent to the generic incinerator In;  RDF coming from RDF plants and sent to the generic incinerator In;  SOM coming from stabilized organic material treatment plants and sent to the generic incinerator In. SO2 daily emission, expressed in kg/day, must be less or equal to a limit arising from regulations and from a safety coefficient SF. The general form of such constraints is MSO2 ;n SO2 ;n 4 SF Claw;SO2 Vn

n ¼ 1; . . . ; N

ð35Þ

289

6.5. Landfill saturation Solutions for MSW management problems that are heavily based on sanitary landfill exploitation are not environmentally sustainable over a long time horizon. For this reason, it is necessary to introduce in our model specific constraints, which have the function of preventing a too rapid saturation of the available sanitary landfills. Such constraints may be expressed in terms of the minimum filling time for each sanitary landfill. Q^ In ;Lm þ Q^ Pd ;Lm þ Q^ Sp ;Lm þ Q^ SOM;Lm þ Q^ Ts ;Lm V Lm þ Q^ Cq ;Lm 4 TLm

ð37Þ

where: where:  SO2 ;n is the depuration efficiency for SO2 for the considered incinerator (such coefficient is considered as a given parameter);  Claw;SO2 is the normative limit, expressed in kg/ m3, for SO2 (hereafter all gas concentrations will be expressed referring to standard conditions as regards pressure and temperature, that is, 1 atm and 25 C, respectively);  Vn is the volume flow of dry fumes expressed in Nm3/day, which is given by

Vn ¼

Vt;n 21=100 ¼ 2:1 Vt;n ; 21=100  PO2

n ¼ 1; . . . ; N

ð36Þ

where PO2 ¼ 11=100 is the percentage of oxygen (in volume) in dry fumes produced by the considered process, and Vt,n is the theoretical volume of fumes (i.e. the volume obtained without considering oxygen in excess) produced by incinerator In. Actually, Vt,n is itself a function of the decision variables. In fact, it can be evaluated through an expression similar to (34) but substituting Si and Sf,i with Vt,i and Vft,i, respectively, where: Vt;i ¼ 8:887Ci þ 3:3174Si þ 20:9597Hi  2:6408Oi þ 0:8Ni þ þ0:038Cli þ 0:07Fi Vft;i ¼ 8:887Cf;i þ 3:317Sf;i þ 20:96Hf;i  2:641Of;i þ 0:8Nf;i þ 0:038Clf;i þ 0:07Ff;i where all symbols have been defined above, apart from Fi and Ffi, which refer to the fluorine content before and after stabilization, respectively. Thus, substituting (34) and (36) in (35) provides the constraints on SO2 emission. In a similar way, emission constraints relevant to HCl, HF, NOx, heavy metals and dust can be obtained. All such constraints have been taken into account in this work.

 VLm is the (volume) quantity of waste that saturates landfill Lm [m3]  TLm is the minimum allowed time to saturate landfill Lm [years]

7. Case study The model proposed has been applied to the case study concerning the municipality of Genova where refuse disposal is a very critical problem. With a daily waste production of 1355 t, of which only 18% is presently recycled, the current solution is disposal in one landfill, whose residual capacity is rapidly decreasing. In passing, Italian regulations require that the percentage of recycled waste must reach 35% within 2003, and strongly discourages disposal of untreated refuse in landfills. In Genova City, waste management is a very critic problem not only because the landfill is rapidly filling, but also because, due to the local geographic characteristics, there are only few suitable areas in which the plants or the new landfills could be built. In fact, Genova City overlooks the sea and, because in this region the mountains are very close to the sea, its extension is mainly along the coast. The proposed model has been applied to this specific case study according to local decision makers and exigencies. Specifically, only two plants whose existence is a matter of decision are considered. Presently, the possible alternative solutions that can be designed and evaluated are based on a set of already existing plants and on a set of ‘‘potential plants’’, namely:  two collecting sites (D=2), already existing;  one separator (P=1), already existing; it can recover only metals (k8=0.9; ki=0, i=1. . .11, i6¼8);

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Table 2 Results obtained by solving the optimization problem

1 (%paper) 2 (%plastic) 3 (%plastic bags) 4 (%plastic bottles) 5 (% glass) 6 (%organic material) 7 (%wood) 8 (%metals) 11 (%textiles) C I L

I M L I M I L

1 (RDF plant)

2 (incinerator) Cost (ME) Separate collection (t/day) HV kcal/kg Produced RDF (t/day) HCl emission (mg/Nm3)

Case 1a TR=15

Case 1b TR=15 RDFS =100

Case 2a TR=15

Case 2b TR=15 RDFS =100

15 67.3 0 85 90 0 8 2 65 0.7 0.3 0 0 1 0 0 1 0.6 0.4 1 1 43 504 3421 325 10

15 47.3 0 85 90 0 8 2 65 0.2 0.8 0 0 1 0 0 1 0.5 0.5 1 1 44 492 3601 100 10

15 0 0 51.1 90 28.2 8 2 65 0.8 0.2 0 0 1 0 0 1 1 0 1 1 38 474 3954 415 8,3

22.4 0 0 30.4 90 0 8 2 65 0.24 0.76 0 0 1 0 0 1 1 0 1 1 39 474 3983 100 6

 one possible incinerator (N=1), whose existence is a matter of the decision problem;  one landfill (M=1), already existing;  one possible RDF plant (Q=1), whose existence is a matter of the decision problem;  one plant for organic material treatment (S=1), already existing.

Fig. 2. Sensitivity analysis for Case 2b (overall cost versus upper bound of HCl emission).

Fig. 3. Sensitivity analysis for Case 2b (separate collection versus upper bound of HCl emission).

As there are only two plants whose existence is a matter of decision, there are only 2 integer decision variables. Moreover, the (primary) continuous decision variables are 21: eleven variables , three , two , two , and three . Note that it is neither necessary to introduce variables  and , as there is only one landfill, nor , as there is only one organic material treatment plant. Specifically, in the model corresponding to this case study, the following decision variables are to be considered:          

that corresponds to SP ;Cq that corresponds to SP ;Lm I that corresponds to SP ;In I that corresponds to Cq ;In L that corresponds to Cq ;Lm I that corresponds to Cq ;In M that corresponds to Cq ;M I that corresponds to Ts ;In L that corresponds to Ts ;Lm M that corresponds to Ts ;M C L

The decision variables representing the percentages of untreated waste coming from collecting site Pd and sent to landfill Lm and to incinerator In are imposed to be zero in the considered case study. The optimization problem has been solved on a PentiumIII 600 MHz computer by use of the optimization software Lingo 6.0 (LINDO Systems, Inc., http:// www.lindo.com) requiring less then one minute of computation. To simplify its use, this software, although at prototypal stage, is already provided with an input/ output communication with a spreadsheet file, which allows the decision maker to use it as a ‘‘black box’’, thus hiding the complexity of the formulation. The optimization problem has been solved considering various scenarios, with the aim of underlining the most crucial

P. Costi et al. / Waste Management 24 (2004) 277–295

aspects of the MSW management problem in the city of Genova. Specifically, the following aspects have been considered:  landfill filling time; of course the solution of the optimization problem is sensitive to the parameter specifying the minimum filling time of the landfill TL; in the following, in all cases, such a parameter has been set equal to 15 years;  depuration technology; two different kinds of technologies have been considered for depuration in the incinerators, namely gas absorber and wet scrubber (the first one is based on absorption of acid gases through solid reagents, while the second one uses removing by liquid–gas contact); the choice of a particular technology determines the values of the depuration coefficient like the one in (35), and may be more or less suitable depending on the chemical characteristics of material entering the incinerator plant; of course, incinerators based on different technologies are characterized by different values of the coefficients appearing in the maintenance cost function in (4);  RDF quantity that can be sold; variations of the allowed RDF quantity to be sold can influence the solution of the overall problem. Thus, four different cases have been considered:  Case 1a—the depuration system for the incinerator plant is the gas absorber one; constraint (30) is not taken into account (i.e. the quantity of the RDF that can be accepted by the market is unlimited);  Case 1b—as Case1a with the only difference that constraint (30) is taken into account (setting RDFS=100 ton/day);  Case 2a—as Case 1a but using wet scrubber depuration system;  Case 2b—as Case 2a, but with constraint (30) taken into account, with the same value of RDFS as above; Table 2 shows a summary of the optimal solution obtained for the four cases. For the sake of brevity, only the HCl emissions are reported, since they are the closest to the normative limit. In all cases the optimal solution requires the actual presence of the incinerator and the RDF plant. It turns out that in Case 1a most of the dry material is sent from the separator to the RDF plant ( C ¼ 0:7) and the remaining part to incinerator ( I ¼ 0:3). The produced RDF is entirely sold (M ¼ 1). In Case 2b, i.e. when imposing a constraint on the maximum amount of RDF that can be sold, the production of RDF attains such a value. Similar considerations can be made as regards Cases 2a and 2b.

291

Moreover, when comparing Cases 1a and 1b with Cases 2a and 2b, the overall costs are lower in Cases 2a and 2b. This arises from the fact that, in Cases 1a and 1b, the overall waste, separately collected, is higher than in Cases 2a and 2b. This, in turn, derives from the higher efficiency of the wet scrubber depuration technology ( HCl ¼ 0:004) with respect to gas absorber depuration technology ( HCl ¼ 0:012). Owing to this higher depuration efficiency, it is possible to plan a lower separate collection, and thus a corresponding reduction in the overall cost. To be more specific, when using a gas absorber, the abatement of HCl emissions is not too efficient; then, in order to fulfill the law limit, it is necessary to increase separate collection and specifically plastic and plastic bottles (in fact they contain high percentages of Cl). Instead, using a wet scrubber, the law limit is respected also with lower percentage of separately collected plastic and plastic bottles. Finally, a sensitivity analysis has been carried out with respect to the upper bound for the HCl concentration in the incinerator emissions. In Fig. 2 the cost corresponding to the optimal solution for Case 2b is reported when such an upper bound is reduced. Of course, a reduction in this upper bound determines an increase in the cost of the optimal solution. Instead, in Fig. 3, the values of parameters  1 ,  2 ,  4 , in the optimal solution, are reported as functions of the same upper bound. Clearly, the more restrictive the bound about HCl emissions, the higher the percentage of plastic and plastic bottles that have to be separately collected. Of course, the developed DSS allows to perform sensitivity analyses with respect to any parameter and to evaluate different possible system configurations.

8. Conclusions and future developments The proposed DSS allows the planning of the treatment plants that must be used in an optimal MSW management system and defines how to size recycling and waste disposal in an integrated approach. The DSS is based on the formalization of a constrained nonlinear optimization problem, where some decision variables are binary and other ones are continuous. The objective function includes all possible economic costs, whereas constraints arise from technical, normative, and environmental issues. On the whole, the proposed approach allows taking into account the multiplicity of aspects and issues that play an important role in planning MSW management systems. A careful attention has been paid to provide a proper characterization of the system, as regards chemical waste composition, heating value, material recovery, and possible treatments. Particular attention is focused on environmental impacts with specific

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attention to incinerator process and emissions, and chemical composition of RDF and SOM.1 As concern the actual use of the DSS, the decision makers can specify their problem inserting data in a spreadsheet file, running the optimization and finding the results in tables and graphics in the same spreadsheet file. The obtained results show the optimal organization for their waste management system, taking into account all the aspects mentioned in the cost function and in the constraints of the model. Further aspects that are not present in the current version of the optimization problem (such as dioxin emissions or produced leachate in the landfills) can be computed, deriving them from the obtained configuration. Another aspect to be considered is that concerning biogas and leachate production in landfills. In the literature (Wreford et al., 2000), an analysis of the variations in landfill gas production and composition, in response to precipitation variations, was carried out, highlighting the relationships between leachate formation and gas production. Another development of the model proposed in this paper could refer to the minimization of effects of bad odors. A recent study (Hobbs et al., 2000) has been developed to assess the dispersion of odor from a waste transfer station in the North London area, UK, making use of two models to analyze the extent of dispersions, taking into account meteorological issues. Other future developments of this work may regard the refinement of the analysis of recycling, transportation and maintenance costs; for example, the simplifying assumption that such costs are linear in the flows could be realistically removed. In this connection, a deeper correlation with the territorial system should be taken into account. For instance, separate collection costs may depend not only on the different kinds of materials, but also on the different areas of the considered municipality. In such a case, separate collection should be carefully sized for the different areas. Another possibility would be that of formalizing the decision problem in a dynamical setting, i.e. considering time-varying (over years) input refuse flows, and a timevarying configuration of the MSW management system. In such a way, it would be possible to determine optimal sequence of interventions (capacity expansions, building 1 Dioxin emission and polycyclic aromatic hydrocarbons production have not been considered, due to the complexity of modeling the chemical processes involved in their formation. In fact, in the literature some contribution by Chang and Chen (2000) has recently appeared concerning the formation of such noxious substances in an incinerator. More specifically, they showed that without accurate prediction of PCDD/PCDF emissions, reasonable assessment of the health risk and essential appraisal of the combustion criteria cannot be achieved. In particular, they developed a process model based on genetic programming and neural network modeling.

of new plants, etc.), over a given time horizon, capable of optimally driving the MSW management system from the present configuration to a final one.

Acknowledgements The authors would like to thank AMIU (Azienda Multiservizi di Igiene Urbana), the company managing MSW in Genova municipality, Italy, for the precious contributions to the development of this work. The LINGO sources and sample data stored in a spreadsheet file are available by contacting the corresponding author by e-mail.

Appendix List of notations (a) Decision variables  1: percentage of recycled paper  2: percentage of recycled heavy plastic  3: percentage of recycled plastic bags  4: percentage of recycled plastic bottles  5: percentage of recycled glass  6: percentage of recycled organic material  7: percentage of recycled wood  8: percentage of recycled metals  9: 0; percentage of scraps sent to recycling 10: 0; percentage of inert matter sent to recycling 11: percentage of recycled textiles Pd ;Lm : fraction of untreated waste coming from collecting site Pd (d=1. . .D) and sent to landfill Lm (m=1. . .M) Pd ;Sp : fraction of untreated waste coming from collecting site Pd (d=1. . .D) and sent to separator Sp (p=1. . .P) Pd ;In : fraction of untreated waste coming from collecting site Pd (d=1. . .D) and sent to incinerator In (n=1. . .N) fraction of dry material coming from Sp ;Cq : separator Sp (p=1. . .P) and sent to RDFplant Cq (q=1. . .Q) fraction of dry material coming from Sp ;In : separator Sp (p=1. . .P) and sent to incinerator In (n=1. . .N) fraction of dry material coming from Sp ;Lm : separator Sp (p=1. . .P) and sent to landfill Lm (m=1. . .M) Cq ;Lm : fraction of scraps coming from RDF-plant Cq (q=1. . .Q) and sent to landfill Lm (m=1. . .M) Cq ;In : fraction of scraps coming from RDF-plant Cq (q=1. . .Q) and sent to incinerator In (n=1. . .N) Cq ;In : fraction of RDF produced in the RDF-plant

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Cq ;M : Sp ;Ts :

Ts ;Lm :

Ts ;In :

Ts ;M : Ts ;Lm :

In ;Lm :

Sp :

C q :

I n :

L m :

T s :

(b) Other P: D: Q: N: M: S: Pd ;i : i :

^ i :

~ i :

ki: ri: Cijr :

Cq (q=1. . .Q) and sent to incinerator In (n=1. . .N) fraction of RDF produced in the RDF-plant Cq (q=1,. . .,Q) that is sold fraction of humid material produced in the separator plant Sp (p=1,. . .,P) and sent to organic material plant Ts (s=1. . .S) fraction of SOM produced in the organic material plant Ts (s=1. . .S) and sent to landfill Lm (m=1,. . ..,M) fraction of SOM produced in the organic material plant Ts (s=1,. . .,S) and sent to incinerator In (n=1. . ..N) fraction of SOM produced in the organic material plant Ts (s=1,. . .,S) that is sold fraction of scraps produced in the organic material plant Ts (s=1,. . .,S) and sent to landfill Lm (m=1,. . .,M) fraction of ashes coming from incinerator In (n=1,. . .,N) and sent to landfill Lm (m=1,. . .,M) binary decision variable related to separator Sp (p=1,. . .,P) binary decision variable related to RDF plant Cq (q=1,. . .,Q) binary decision variable related to incinerator In (n=1,. . .,N) binary decision variable related to landfill Lm (m=1,. . .,M) binary decision variable related to organic material plant Ts (s=1,. . .,S)

notations number of separators number of collecting sites number of RDF-plants number of incinerators number of landfills number of organic material plants percentage of material i sent to collection site Pd separation efficiency for material i in a separator (for simplicity, supposed independent from separator Sp) separation efficiency for material i in a RDF plant (for simplicity, supposed independent from RDF plant Cq) separation efficiency for material i in an organic material plant (for simplicity, supposed independent from the organic plant Ts) fraction of material i sent to recycling after separation daily refuse production for every component unit costs (E/t) for the jth method of collection and for the ith material

!i;j :

293

fraction of material i collected through method j Coni : contributions for recycling the ith material [E/t] n: number of days in a year X: the set of the possible plant-to-plant connections; (s,d): the generic plant-to-plant connection; Q s;d : the mass flow corresponding to connection (s,d); s;d : the density corresponding to the flow relevant to connection (s,d); Q^ s;d : the volume flow corresponding to connection (s,d), provided by Q s;d =s;d Vs;d : the capacity of a single vehicle relevant to connection (s,d); Cs;d : the cost of a trip relevant to connection (s,d) RDFCq : annual quantity of produced RDF in Cq Q^ Pd ;Lm : annual refuse volume transported from collecting site Pd to landfill Lm Q^ Pd ;In : annual refuse volume transported from collecting site Pd to incinerator In Q^ Sp ;Cq : annual refuse volume transported from separator Sp to RDF plant Cq Q^ Sp ;Ts : annual refuse volume transported from separator Sp to the plant for organic material Ts Q^ Sp ;Lm : annual refuse volume transported from separator Sp to landfill Lm Q^ Sp ;In : annual refuse volume transported from separator Sp to incinerator In Q^ Cq ;Lm : annual refuse volume of scraps transported from RDF plant Cq to landfill Lm Q^ Cq ;In : annual refuse volume of scraps transported from RDF plant Cq to incinerator In Q^ RDF;In : annual produced RDF transported from RDF plant Cq to incinerator In Q^ In ;Lm : annual refuse volume transported from incinerator In to landfill Lm Q^ Pd ;Sp : annual refuse volume transported from collecting site Pd to separator Sp Q^ Ts ;Lm : annual refuse volume transported from organic material plant Ts to landfill Lm Q^ SOMs ;Lm : annual refuse volume of SOM, transported from organic material plant Ts to landfill Lm Q^ SOMs ;In : annual refuse volume of SOM, transported from organic material plant Ts to incinerator In Q Pd ;Sp : annual mass flow of material coming from collecting site Pd treated in the separator Sp Q Cq ;Sp : annual mass flow of refuse coming from separator SP and treated in the RDF plant Cq Q Sp ;Ts : annual mass flow of material coming from the separator and treated in the plant for organic material Ts Q Pd ;In , Q Sp ;In ,Q RDFq ;In and Q Cq ;In : annual refuse flows sent to incinerator plant In coming from, respectively, collection site

294

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Pd, separator Sp and RDF plant (RDF and scraps, respectively) Cq Q Pd ;Lm , Q Sp ;Lm and Q Cq ;Lm : annual refuse flows sent to landfill Lm coming from, respectively, collection site Pd, separator Sp and RDF plant Cq Q SOMs ;In , Q SOMs ;Lm : annual mass flow of SOM coming from organic material plant Ts and sent, respectively, to the incinerator In and to the landfill Lm Q In ;Lm : annual mass flow of ashes coming from incinerator In and sent to landfill Lm Q Ts ;Lm : annual mass flow of scraps coming from organic material plant Ts and sent to landfill Lm CPd ;Lm : cost of a trip from collection site Pd to landfill Lm VPd ;Lm : capacity of the vehicle used for the trip from collection site Pd to landfill Lm CPd ;In : cost of a trip from collection site Pd to incinerator In VPd ;In : capacity of the vehicle used for the trip from collection site Pd to incinerator In CSp ;Ts : cost of a trip from collection separator Sp to the organic material plant Ts VSp ;Ts : capacity of the vehicle used for the trip from separator Sp to the organic material plant Ts CSp ;Lm : cost of a trip from separator Sp to landfill Lm VSp ;Lm : capacity of the vehicle used for the trip from separator Sp to landfill Lm CSp ;Cq : cost of a trip from separator Sp to RDFplant Cq VSp ;Cq : capacity of the vehicle used for the trip from separator Sp to RDF plant Cq CSp ;In : cost of a trip from separator Sp to incinerator In VSp ;In : capacity of the vehicle used for the trip from separator Sp to incinerator In CCq ;Lm : cost of a trip from RDF-plant Cq to landfill Lm VCq ;Lm : capacity of the vehicle used for the trip from RDF-plant Cq to landfill Lm CIn ;Lm : cost of a trip from incinerator In to landfill Lm VIn ;Lm : capacity of the vehicle used for the trip from incinerator In to landfill Lm CPd ;Sp : cost of a trip from collection site Pd to separator Sp VPd ;Sp : capacity of the vehicle used for the trip from collection site Pd to separator Sp CCq ;In : cost of a trip from RDF-plant Cq to incinerator In VCq ;In : capacity of the vehicle used for the trip from RDF-plant Cq to incinerator In CTs ;Lm : cost of a trip from organic material plant Ts to landfill Lm

VTs ;Lm :

capacity of the vehicle used for the trip from organic material plant Ts to landfill Lm CTs ;In : cost of a trip from organic material plant Ts to incinerator In VTs ;In : capacity of the vehicle used for the trip from organic material plant Ts to incinerator In CSp : unit cost for separator Sp, comprehensive of installation, maintenance and management costs CCq : unit cost for RDF plant Cq, comprehensive of installation, maintenance and management costs C Ts : unit cost for the organic material plant Ts, comprehensive of installation, maintenance and management costs CIn : unit cost for incinerator In, comprehensive of installation, maintenance and management costs C Lm : unit cost for landfill Lm, comprehensive of installation, maintenance and management costs CF;Sp : fixed cost for separator Sp, comprehensive of installation, maintenance and management costs CF;Cq : fixed cost for RDF plant Cq, comprehensive of installation, maintenance and management costs CF;Ts : fixed cost for organic plant Ts, comprehensive of installation, maintenance and management costs CF;In : fixed cost for incinerator In, comprehensive of installation, maintenance and management costs CF;Lm : fixed costs for landfill Lm, comprehensive of installation, maintenance and management costs PRDF: unit price for the sale of RDF c~e : unit cost [E/kWh] for the sale of energy Ec,n: annual energy consumption [kWh/year] of the nth incinerator E : efficiency concerning energy production with respect to heat produced by combustion f: conversion factor equal to 3.6 MJ/kWh f: conversion factor equal to 1.16 105 MW/ (MJ/day) g: conversion factor from MJ to kcal, equal to 238.9 kcal/MJ HVIn [MJ/day]: the overall daily thermal energy of the refuse entering the incinerator In HVi and HVfi: the heating values [MJ/kg], for every material i, before and after stabilization, respectively Ci ; Hi ; Si ; Oi ; Ui (Cf;i ; Hf;i ; Sf;i ; Of;i ; Uf;i ): carbon, hydrogen, sulfur, oxygen, and water

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content, respectively, expressed in kg/kg, before (after) stabilization MIn ;a : lower bound for the size of the incinerators MIn ;b : upper bound for the size of the incinerators MSp ;a : lower bound for the size of the separators MSp ;b : upper bound for the size of the separators MCq ;a : lower bound for the size of the RDF plants MCq ;b : upper bound for the size of the RDF plants MTs ;a : lower bound for the size of the organic material plants MTs ;b : upper bound for the size of the organic material plants !: very great number Ashi: the ash content of material i Ui: the humidity of material i hi : the humidity content of material i present in SOM after stabilization;

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