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Resources, Conservation and Recycling 89 (2014) 52–63

Contents lists available at ScienceDirect

Resources, Conservation and Recycling

jo u r n al homep age: www.elsev ier .com/ locate / resconrec

ulti-objective optimization of waste and resource management inndustrial networks – Part I: Model description

arl Vadenboa,∗, Stefanie Hellwega, Gonzalo Guillén-Gosálbezb

ETH Zurich, Institute of Environmental Engineering, John-von-Neumann-Weg 9, CH-8093 Zurich, SwitzerlandDepartament d’Enginyeria Química, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain

r t i c l e i n f o

rticle history:eceived 2 March 2014eceived in revised form 6 May 2014ccepted 23 May 2014vailable online 17 June 2014

eywords:aterial flow analysis (MFA)

ife cycle assessment (LCA)ulti-objective optimizationaste management

ndustrial ecology

a b s t r a c t

This article presents a general multi-objective mixed-integer linear programming (MILP) optimizationmodel aimed at providing decision support for waste and resources management in industrial networks.The MILP model combines material flow analysis, process models of waste treatments and other industrialprocesses, life cycle assessment, and mathematical optimization techniques within a unified framework.The optimization is based on a simplified representation of industrial networks that makes use of lin-ear process models to describe the flows of mass and energy. Waste-specific characteristics, e.g. heatingvalue or heavy metal contamination, are considered explicitly along with potential technologies or pro-cess configurations. The systems perspective, including both provision of waste treatment and industrialproduction, enables constraints imposed upon the systems, e.g. available treatment capacities, to beexplicitly considered in the model. The model output is a set of alternative system configurations interms of distribution of waste and resources that optimize environmental and economic performance.The MILP also enables quantification of the improvement potential compared to a given reference state.Trade-offs between conflicting objectives are identified through the generation of a set of Pareto-efficient

solutions. This information supports the decision making process by revealing the quantified performanceof the efficient trade-offs without relying on weighting being expressed prior to the analysis. Key featuresof the modeling approach are illustrated in a hypothetical case. The optimization model described in thisarticle is applied in a subsequent paper (Part II) to assess and optimize the thermal treatment of sewagesludge in a region in Switzerland.

© 2014 Elsevier B.V. All rights reserved.

. Introduction

The management of municipal and industrial waste poses manyhallenges to ensure cost efficiency, environmental protection, andocial acceptance. The waste directive of the European Commis-ion prescribes that the waste hierarchy shall be applied among theember states to prioritize between different waste management

trategies, which in decreasing order of priority are prevention,reparation for reuse, recycling, other recovery, e.g. energy recov-ry, and disposal (EC, 2008/98/EC). The hierarchy approach haseen criticized, for example, for being inadequate to guide deci-

ions on combinations of waste treatments (e.g. McDougall andruska, 2000; Pearce, 1998). Complementary to the waste hier-rchy, the European waste directive also prescribes that member

∗ Corresponding author. Tel.: +41 44 633 70 66.E-mail address: vadenbo@ifu.baug.ethz.ch (C. Vadenbo).

ttp://dx.doi.org/10.1016/j.resconrec.2014.05.010921-3449/© 2014 Elsevier B.V. All rights reserved.

states “shall take measures to encourage the option that deliversthe best overall environmental outcome” (EC, 2008/98/EC). Thisimplies that the waste management options need to be consideredwith respect to the entire life cycle, including all relevant upstreamand downstream impacts.

Life cycle assessment (LCA) is a method for the environmentalassessments of products and services (ISO 14040, 2006; ISO 14044,2006). Due to its system perspective, LCA has been put forward asa suitable tool for comparing options in waste management froman energy-related and environmental perspective (Ekvall et al.,2007; Finnveden, 1999). LCA has also been identified as a toolwith potential to support the analysis, improvement, expansion,and design of industrial symbiosis (Chertow, 2000; Mattila et al.,2012). The valorization (co-processing) of wastes and by-products,i.e. the beneficial use as raw materials or as energy carriers (Nzihou

and Lifset, 2010), might improve the resources efficiency in indus-try and reduce the need for conventional waste treatments. Theenvironmental performance of valorization and other waste treat-ment options, however, often depends on the properties of the

ervation and Recycling 89 (2014) 52–63 53

mcaltDKua2aG

tEKeEcatctsin

mepatiplaiiK(biS(areofpmiiw(tWw

tstastF

Fig. 1. Simplified illustration of the optimization problem: Given the quantities ofwaste which require treatment, a set of available process inputs, and the demandfor industrial outputs, the task is to find the optimal distribution of imported inputs

C. Vadenbo et al. / Resources, Cons

aterials in question. One strategy to account for the dependen-ies between input characteristics and the resulting resource usend emissions in LCA is the use of process models to generate theife cycle inventories. This approach has for example been appliedo municipal solid waste incineration (MSWI) (Boesch et al., 2013;oka and Hischier, 2005; Harrison et al., 2000; Hellweg et al., 2001;remer et al., 1998; Riber et al., 2008), treatment of hazardous liq-id waste (Seyler et al., 2005), wastewater treatment systems (Dokand Hischier, 2005; Köhler et al., 2007), landfills (Doka and Hischier,005; Hellweg et al., 2005; Manfredi and Christensen, 2009; Nielsennd Hauschild, 1998), the production of cement (Boesch et al., 2009;äbel et al., 2004) and in ironmaking (Vadenbo et al., 2013).

Several tools have been developed for the environmen-al assessment of entire waste management systems, e.g.ASETECH/EASEWASTE (Bhander et al., 2010; Clavreul, 2013;irkeby et al., 2006), ORWARE (Dalemo et al., 1997; Erikssont al., 2002), WRATE (Thomas and McDougall, 2003, 2005; UK-nvironment-Agency, 2012); see also the review by Gentil andolleagues (2010). The system boundaries of these tools generallydhere to a waste management perspective, i.e. the required func-ionality of affected industrial product systems is only implicitlyonsidered. Most of the aforementioned models and tools restricthe analysis to the assessment of a limited number of alternativecenarios. There is, therefore, a need for a framework to systemat-cally optimize waste management and resource use in industrialetworks that will overcome the aforementioned limitations.

The combination of LCA methodology and mathematical opti-ization techniques aimed at simultaneously optimizing the

nvironmental and economic performance of a system was firstroposed in the scientific literature in the mid-1990s: Stefanisnd colleagues (1995) introduced a methodology for environmen-al impact minimization that embedded the principles of LCAn a process optimization framework. Azapagic and Clift (1995)roposed that linear programming can be used to solve the prob-

em of allocation in multi-output product systems through thenalysis of marginal or shadow values. In recent years, some stud-es have addressed the optimization of the physical exchangesn industrial networks based on life cycle metrics, e.g. Wolf andarlsson (2008), Cimren and colleagues (2011), Tan and colleagues

2009, 2012). In waste management, optimization models havee extensively applied to minimize the cost and/or environmental

mpacts of logistics and treatment of MSW, e.g. by Ljunggren (2000),alvia et al. (2002), Badran and El-Haggar (2006), Faccio et al.2011), Anghinolfi et al. (2013), Antmann et al. (2013), Minoglound Komilis (2013), Santibanez-Aguilar et al. (2013), see also theeview by Juul et al. (2013). The application of optimization mod-ls enables the systematic identification of optimal solutions basedn large sets of decision variables and consequently among manyeasible solutions which commonly characterize these types ofroblems. For a national perspective, the waste input–output (WIO)odel by Kondo and Nakamura (2005), based on the conventional

nput–output model (Leontief, 1936, 1970), explicitly considers thenterdependence between the flows of goods and waste for the

hole economy. The linear programming extension of the modelWIO-LP) enables optimal national waste management strategieso be derived. The high level of aggregation, however, makes the

IO-LP approach less suited to reflect the specific processes andaste streams on the level of a single industrial park or region.

The aim of the present paper is to describe a modeling approachhat enables waste and resource characteristics as well as con-traints imposed upon individual processes or the entire systemo be explicitly considered, and to discuss the opportunities and

dvantages offered by optimization techniques to support moreustainable regional waste and resource management. In relationo the existing body of literature, the novelty of this work is twofold:irstly, the scope is broadened to encompass both the waste

and inter-industry exchanges among the available industrial activities. Transportactivities and exchanges with nature are considered, but have been omitted fromthe figure for clarity.

management and a production perspective. Secondly, we proposea framework for the integration of a set of methods to circum-vent some of their respective short-comings. More specifically, bycombining mass/substance flow analysis (MFA/SFA), LCA and math-ematical optimization techniques, we aim (i) to capture the effectof waste characteristics on resource consumption, emission levels,and by-product recovery, (ii) to explicitly reflect the system- andprocess-specific constraints imposed upon the optimal solutions,and (iii) to facilitate the systematic identification of configurationsthat minimize the system-wide environmental impact. In a sec-ond article (Vadenbo et al., accepted for publication), we presenta case study focused on the optimal distribution of sewage sludgeamong the regionally available thermal treatment options (mono-incineration, co-incineration in MSWI, and co-processing in cementproduction) in a region in Switzerland.

2. Method – problem formulation

Without loss of generality, we consider a generic industrial net-work, including the waste treatment system (Fig. 1). The industrialactivities in a region or an eco-industrial park make up the fore-ground system of the optimization model. The background systemencompasses the supply chains associated with product inputsto the activities of the foreground system, and the product sys-tems displaced by recovered by-products which are utilized beyondthe borders of the foreground system. The benefits or the bur-dens of any displaced product system due to the recovery of theseby-products are assigned to the multi-functional process throughsubstitution by system expansion (EC, 2010).

In order to contribute to more sustainable management ofresources and waste in industrial networks, we formulate threekey research questions to be addressed:

• What is the optimal system configuration in terms of industrialresource use, by-products exchanges, and waste treatment?

• How large is the improvement potential compared to a referencecase, e.g. the business-as-usual scenario?

54 C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63

Table 1Indices and sets in optimization model.

Indices Description Sets Description

D Decision space for decision nodes (splitters) IJi,j Set defines whether a process unit j ∈ J belongs to an activity i ∈ IE Complete set of exchanges with the environment considered

in the modelINj,s Set defines whether a stream s ∈ S is an input to process unit j ∈ J

F Functionality (required) JDj,d Set defines whether a decision d ∈ D is valid for splitter node j ∈ JSPLIT

I Activities OUTj,s Set defines whether a stream s ∈ S is an output of process unit j ∈ JJ (unit) processes PRp,r Correspondence of recovered resource r ∈ R to product p ∈ PJMIX ⊂ J Subset of processes representing mixer nodes PSp,s Correspondence of product p ∈ P to stream s ∈ SJPROC ⊂ J Subset of processes for transforming process nodes REFj,s Indicates whether stream s ∈ S is a reference flow of unit process j ∈ JJSPLIT ⊂ J Subset of processes for splitter nodes SFs,f Correspondence of stream s ∈ S to required functionality f ∈ FK Substances, i.e. chemical elements and compounds SMs,m Correspondence of material m ∈ M to stream s ∈ SM Materials SWs,w Determines whether quality criteria w ∈ W is applied to stream s ∈ SN LCIA method/categoryP ProductsPINFRA ⊂ P Subset of products representing equipment and facilities

(infrastructure)PMF ⊂ P Subset of products which are considered as inputs to the mass

flow modelPTRSP ⊂ P Subset of products which represent transportation servicesPUTIL ⊂ P Subset of products which represent energy utilitiesR Recovered by-productsRMF ⊂ R Subset of recovered by-product based on mass flowsRQ ⊂ R Subset of recovered by-product based on energy flows

•

to(oaispiw

3

eTshwtonnwotTfc

3

iw

S StreamsSIMP ⊂ S Subset of streams imported into the foreground systemw ∈ W Set of quality criteria considered in the model

Which trade-offs are necessary due to conflicting object-ives?

In a more formal framework, the static (single-period) optimiza-ion problem can be defined as follows: Given (i) the quantitiesf waste to be treated, (ii) the demand for industrial outputs,iii) a set of available process feedstocks and utilities, (iv) a setf industrial activities, including both dedicated waste treatmentsnd co-processing activities, (v) the feasible exchanges within thendustrial network, and (vi) a set of system- or process-specific con-traints, the task is to find the optimal distribution of importedrocess inputs and inter-industry exchanges among the available

ndustrial activities that simultaneously minimizes the system-ide environmental impacts and/or the associated monetary cost.

. Method – mathematical model

Next, we present a mixed-integer linear program (MILP) for thefficient solution of the optimization problem described above.he nomenclature used for indices, parameters and variables isummarized in Tables 1–3, respectively. This MILP is based on aigh-level representation of the system that avoids nonlinearitieshereby each process is modeled using linear mass balance equa-

ions. Models have been proposed and extensively applied for theptimization of physical exchanges in, for example, mass-exchangeetworks (e.g. El-Halwagi and Manousiouthakis, 1989) and wateretworks (e.g. Bagajewicz, 2000; Keckler and Allen, 1999), buthich cannot be directly applied to our problem. As shown below,

ne of the main novelties of the model presented here concernshe use of multiple levels of aggregation to model the mass flows.he optimization model comprises four main blocks of equations:unctional unit and reference flows, mass balances, operationalonstraints, and objective functions.

.1. Functional unit and reference flows

The fulfillment of the required functionality of the system,.e. the functional unit, both in terms of treatment of occurring

astes and by-products as well as meeting the demand for product

outputs, represents the driving constraint for the activities in theforeground system (1):

FUf =∑

s ∈ SFs,f

MFSs , ∀f ∈ F (1)

where the parameter FUf is a constraint vector for the required func-tionality per function f ∈ F, and the variable MFS

s is the total massflow along stream s ∈ S (input or output), where S is a set of feasi-ble mass-based exchanges between the nodes of the system. Theset SFs,f describes the possible combinations (or correspondence)of a stream s ∈ S and the required functionality f ∈ F. Similarly, thereference flow of a unit process is determined according to (2):

RFj =∑

s ∈ REFj,s

MFSs , ∀j ∈ J (2)

where the variable RFj is the annual reference flow of unit processj ∈ J, and the set REFj,s defines the ingoing or outgoing streams s ∈ Sthat correspond to the reference flow of the process. The referenceflow of a co-processing activity is the output of the main product(s),e.g. the amount of clinker produced in a cement kiln. Any wastetreatment service provided through the use of waste materials asalternative feedstock is consequently considered a by-product. Thereference flow of dedicated waste treatment processes correspondsto the total amount of waste treated, whereas any energy or mate-rials recovered in the process are regarded as by-products. Thereference flow is hence a model variable that is determined by theactivity level of a unit process, whereas the required functionalityin (1) is a model constraint that has to be satisfied.

3.2. Mass balances

The mass flows in the optimization model are structured intothree levels of aggregation (Fig. 2) (Hellweg et al., 2001): The high-est level is the stream s ∈ S which may consist of one or morerelatively homogenous material fractions (e.g. metals, polymers,

etc.) m ∈ M, representing the second level. At the most detailedlevel, we consider the chemical composition in terms of ele-ments and compounds k ∈ K of a material. The three levels ofaggregation facilitate a consistent modeling of physical exchanges,

C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63 55

Table 2Input parameters of the optimization model.

Parameter Description Unit

˛Ws,m,k,w

Coefficient for substance k ∈ K in material m ∈ M along stream s ∈ S in the nominator of quality criteria w ∈ W [–]ˇW

s,m,k,wCoefficient for substance k ∈ K in material m ∈ M along stream s ∈ S in the denominator of quality criteria w ∈ W [–]

�Qjr

Specific generation rate of recovered by-product r ∈ RQ in unit process j ∈ J [Giga-Joule/Giga-Joule]BP

n,p Aggregated life cycle impact of a product p ∈ P in impact assessment category n ∈ N [unit/unit]CFe,n Characterization factor of emission e ∈ E in impact assessment category n ∈ N [unit/tonne]compMTRL

k,mComposition of material m ∈ M in terms of element/compound k ∈ K [tonne/tonne]

compPRODm,p Composition of product p ∈ P in terms of material m ∈ M [tonne/tonne]

FUf Total system-wide required functionality per function f ∈ F [unit/year]MCAPIN,L

jLower limit on total acceptable input quantity (mass basis) per year for a process unit j ∈ J [tonne/year]

MCAPIN,Uj

Upper limit on total acceptable input quantity (mass basis) per year for a process unit j ∈ J [tonne/year]

MCAPOUT,Us,p Upper limit for the output of stream s ∈ S in a process unit j ∈ J [tonne/year]

NCVm Net calorific value of a material m ∈ M [Giga-Joule/tonne]QCL

w Lower limit for quality criteria w ∈ W [tonne/tonne]QCU

w Upper limit for quality criteria w ∈ W [tonne/tonne]QCAPIN,U

jUpper limit on total acceptable input of heat (gross thermal capacity) per year for a process unit j ∈ J [Giga-Joule]

REQ P,Lj,p

Lower limit on specific input rate of product p ∈ P per unit of reference flow in process j ∈ J [unit/unit]

REQ P,Uj,p

Upper limit on specific input rate of product p ∈ P per unit of reference flow in process j ∈ J [unit/unit]

REQ Q,Lj

Lower bound on specific energy requirement per unit of reference flow in process j ∈ J [Giga-Joule/unit]

REQ S,Lj,s

Lower limit on specific input rate of stream s ∈ S per unit of reference flow in process j ∈ J [tonne/unit]

REQ S,Uj,s

Upper limit on specific input rate of stream s ∈ S per unit of reference flow in process j ∈ J [tonne/unit]supplyU

p Upper limitation in total supply of product p ∈ P [unit/year]TCMF

′ ′ ′ Transfer coefficient of mass flows of substance k′ in material m′ in input stream s′ to chemical element or [tonne/tonne]

n to st

mtmrm

vt(taadmm

TO

s ,s,m ,m,k ,kcompound k in material m in outgoing stream s

TFSPLITd,s

Transfer coefficient of decision nodes (splitter), i.e. fractio

aterial separation, and processes in which chemical reactionsake place. Note that standard models for the optimization of

ass-exchange and water networks lack this feature and for thiseason cannot be applied to our problem in a straightforwardanner.The optimization model contains two independent decision

ariables: First, Xj,p is a continuous decision variable which denoteshe amount of product p ∈ PMF which is assigned to process j ∈ Jsee Fig. 3a). Second, the binary decision variable Yd,j representshe decision to direct a given fraction of the total flow through

splitter, e.g. a decision node j ∈ JSPLIT, to the outgoing streams

ccording to the decision d ∈ D, where the set D represents theecision space (see Fig. 3c). That is, to avoid bilinear terms in theodel that would lead to non-convexities and the existence ofultiple local optima, we consider a discrete set of allowable split

able 3ptimization model variables.

Variable Description

CCj Annual capital cost per process unit j ∈ J

COj Annual operating cost per process unit j ∈ J

EMTOTj,e

Amount of emission e ∈ E arising from process unit j ∈ J

HJj,n

Environmental impact of process unit j ∈ J in impact category n ∈

HIi,n

Annual impacts per industrial activity i ∈ I in impact category n ∈HSYS

n Total annual impact of the foreground system in impact categoryMFK

s,m,kMass flow rate of substance k ∈ K in material m ∈ M along stream

MFMs,m Mass flow rate of material m ∈ M along stream s ∈ S

MFSs Total mass flow rate along stream s ∈ S

RDj,e Extraction of resource e ∈ ERD arising from process unit j ∈ J

RECMFj,r

Recovery by-product r ∈ RMF in terms of mass in unit process j ∈ JP

RECQj,r

Recovery by-product r ∈ RQ in terms of energy in unit process j ∈ J

REVFj

Annual revenue obtained from provision of functionality in F for

REVRj

Annual revenue obtained from export of recovered by-products iRFj Reference flow of unit process j ∈ J

TACJj

Annual cost per industrial activity j ∈ J

TACSYS Total annual cost of the system

Xj,p Continuous variable denoting the amount of product p ∈ P distribYd,j Binary variable representing decision for flow through decision n

the decision space d ∈ DZC Objective value for monetary cost

ZNn Objective value for environmental criteria per impact assessmen

ream s ∈ S [tonne/tonne]

ratios. Hence, the amount of material going into a splitter can bedistributed among the output streams in a fixed number of alter-natives, each entailing a given split ratio. As will be shown below,this approach leads to linear equations that can be more easilyhandled.

The import of a product which enters the mass flow model(p ∈ PMF) over the foreground system boundary expressed in Eq.(3):

MFKs′,m′,k′ = compMTRL

m′,k′ · compPRODp,m′ · Xj,p ∀j, m′, s′, p ∈ PMF ∩ SIMP

∩PS ′ ∩ SM ′ ′ ∩ IN ′ ∩ J, k′ ∈ K (3)

p,s s ,m j,s

where Xj,p is the decision variable that assigns an amount of productp ∈ PMF into unit process j ∈ J. The variable MFK

s′,m′,k′ is the result-ing mass flow rate of compound k′ ∈ K in material m′ ∈ M into the

Unit

[monetary unit/year][monetary unit/year][tonne/year]

N [unit/year] N [unit/year]

n ∈ N [unit/year]s ∈ S [tonne/year]

[tonne/year][tonne/year][tonne/year]

ROC [tonne/year]PROC [Giga-Joule/year]process j ∈ J [monetary unit/year]n R for process j ∈ J [monetary unit/year]

[unit/year][monetary unit/year][monetary unit/year]

uted to unit process j ∈ J [unit/year]ode j ∈ JSPLIT to an outgoing streams according [–]

[monetary unit/year]t category n ∈ N [unit/year]

56 C. Vadenbo et al. / Resources, Conservatio

Fra

paTpwe

c

rFpweh

3

tc

M

wi

cteoss

mf

ig. 2. Mass flows structured into three levels of aggregation, namely streams, mate-ial fractions, and elements and compounds (chemical composition). The three levelsre here illustrated by the example of municipal solid waste (MSW).

rocess along stream s′ ∈ INj,s. The sets INj,s and OUTj,s ensure that s′

nd s are ingoing and outgoing streams of process j ∈ J respectivelyhe set PSp,s describes the set of possible combinations of importedroducts p ∈ PMF and streams s′ ∈ SIMP and the set SMs′ ,m′ indicateshether a material m′ ∈ M is included in stream s′ ∈ SIMP. The param-

ter compMTRLm′,k′ contains the chemical composition of elements and

ompounds k′ ∈ K for each material m′ ∈ M, whereas compPRODp,m′ rep-

esents the material composition matrix for the products in PMF.or example, municipal solid waste (a product → one or multi-le streams) is composed of materials like plastics, paper, kitchenaste, etc. All these materials are in turn composed of chemical

lements and compounds, e.g. moisture, carbon, phosphorous, andeavy metals.

.2.1. Process nodesThe mass transfer from ingoing to outgoing streams over the

ransforming process nodes j ∈ JPROC is governed by transfer coeffi-ients as shown in Fig. 3a and expressed in Eq. (4):

Ks,m,k =

∑s′ ∈ INj,s

∑m′ ∈ SMs′,m′

∑k′ ∈ K

TCMFs′,s,m′,m,k′,k · MFK

s′,m′,k′ ,

∀j, m, s ∈ SMs,m ∩ OUTj,s ∩ JPROC, k ∈ K (4)

here incoming mass flows are indicated with prime (′) and outgo-ng without (see also Fig. 3a). The outgoing mass flows MFK

s,m,kare

alculated as the sum of the ingoing mass flows MFKs′,m′,k′ entering

he process unit multiplied with a mass transfer coefficient param-ter TCMF

s′,s,m′,m,k′,k. The transfer coefficient describes the transfer′ ′

f chemical element or compound k in material m in the ingoing

tream s′ to chemical compound k in material m in outgoing stream, where k′, k ∈ K, m′, m ∈ M and s′, s ∈ S.1

1 For example, the complete calcination of a mineral containing carbonates, e.g.agnesium carbonate (MgCO3), in a given process could be modeled using the

ollowing pair of transfer coefficients:

TCMFFeedstock,outputproduct,mineral,outputmaterial,MgCo3,MgO

= 100% · molar mass(MgO)molar mass(MgCO3)

and

TCMFFeedstock,fluegas,mineral,fluegas,MgCO3,CO2

= 100% · molar mass(CO2)molar mass(MgCO3)

.

n and Recycling 89 (2014) 52–63

The total mass flow of each material m ∈ M in stream s ∈ S, MFMs,m

and the total flow of a stream s ∈ S, MFSs , is calculated according to

(5) and (6), respectively:

MFMs,m =

∑k ∈ K

MFKs,m,k, ∀m, s ∈ SMs,m (5)

MFSs =

∑m ∈ SMs,m

MFMs,m ∀s ∈ S (6)

3.2.2. Mixer nodesIn a mixer j ∈ JMIX, several streams are combined into one single

stream (see Fig. 3b). The mass flow rate of the outgoing stream isderived via the mass balance in (7).

MFKs,m′,k′ =

∑s′ ∈ INj,s

MFKs′,m′,k′ , ∀j, m′, s ∈ SMs,m′ ∩ OUTj,s ∩ JMIX, k′ ∈ K

(7)

3.2.3. Splitter nodesThe splitters represent decision nodes, in which neither chemi-

cal reactions nor physical processes occur: the input flow is merelydivided into two or more output flows (Fig. 3c). A limited num-ber of pre-defined options are considered to distribute the inputsamong the output streams in order to reduce the computationaleffort. To model this, we define the binary variable Yd,j, which takesthe value of one if the flows over the splitter j ∈ JSPLIT are to be dis-tributed according to the decision option d ∈ D, and zero otherwise.Eq. (8) ensures that one-and-only-one decision is selected for eachsplitter node.∑

d ∈ JDj,d

Yd,j = 1, ∀j ∈ JSPLIT (8)

where the set JDj,d dictates whether the decision d ∈ D is to be con-sidered for the splitter j ∈ JSPLIT. By letting the parameter TCSPLIT

d,srepresent the fraction of the input stream s′ that leaves the nodethrough a output stream s for the decision d, the mass balance canbe written as follows:

MFKs,m′,k′ =

∑s′ ∈ INj,s

∑d ∈ D

TCSPLITd,s · Yd,j · MFs′,m′,k′ ,

∀s, m′, j ∈ SMs,m′ ∩ OUTj,s ∩ JSPLIT , k′ ∈ K, d ∈ D (9)

Eq. (9) is nonlinear due to the product between the variablesMFs′,m′,k′ and Yd,j. To overcome this limitation, we reformulatethis equation into an equivalent linear form as described in Eqs.(S.1)–(S.6) in the Supplementary material on the web. An alter-native strategy to the ‘big-M’ reformulation used in (S.3)–(S.6) isthe convex-hull reformulation (Balas, 1985). The latter approachenables the feasible region of the problem to be reduced but comesat the cost of an increase in the number of variables and conse-quently the size of the problem to be solved. There is hence atrade-off between the problem size and a tighter bound (Khuranaet al., 2005; Raman and Grossmann, 1994) and the preferableapproach therefore depends on the character and knowledge aboutthe problem in question. In the case presented in Part II (Vadenboet al., accepted for publication), it was possible to define the boundsused in the big-M reformulation quite accurately, since existing

knowledge of the problem made it possible to derive good esti-mates of the maximum flow rates that will pass through the units.These tight big-M values lead to better relaxations. For this reason,we decided to implement the big-M reformulation in our model.

C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63 57

Fig. 3. Generic representation of three types of system nodes: (a) The amount of a product which is assigned to a process node j ∈ JPROC is represented by the continuousd K ithin t MIX

a ode fm d nota

3

ostqvsmeis

e

s

ffltwas

M

M

M

wiu

twq∑

∑

infrastructure are expressed by (18) and (19) respectively

Xj,p − REQ P,Uj,p

· RFj ≤ 0, ∀j ∈ J, p ∈ P (18)

Xj,p − REQ P,Lj,p

· RFj≥0, ∀j ∈ J, p ∈ P (19)

2 For example, the lime saturation factor of clinker is calculated asmCaO/(2.8mSiO2

+ 1.18mAl2O3+ 0.65mFe2O3 ) and is commonly required to be in the

interval of 92–98% (Winter, 2005). Hence:

˛Wclinker,clinker,CaO,LSF

= 1

ˇWclinker,clinker,SiO2,LSF

= 2.8

ˇWclinker,clinker,Al2O3,LSF

= 1.18.

ecision variable Xj ,p . The dependent variables MFs′,m′,k′ represent the mass flows w

ggregated to a single outgoing stream. (c) A splitter j ∈ JSPLIT represents a decision nass flow among the available options (please refer to the main text for the detaile

.3. Operational constraints

The mathematical formulation of constraints is a key componentf the optimization model in order to adequately reflect reality. Thisection presents a selection of some key model constraints relatedo supply limitations, treatment or production capacities, productuality, and process requirements, which are likely to also be rele-ant for most industrial networks. For some of the constraints, e.g.upply or capacity limitations, analogous formulations are com-only used in the literature (e.g. Azapagic and Clift, 1999; Tan

t al., 2009). In addition, the modeling of transport requirementss described in Section S.1.2 in the Supplementary material due topace limitations.

The upper limit on the total supply, supplyUp , of product p ∈ P that

nters the foreground system is expressed in (10):

upplyUp ≥

∑j ∈ J

Xj,p, ∀p ∈ P (10)

We also consider capacity constraints for the input and outputor either products or streams and in terms of individual or totalow. For example, the upper and lower capacity constraints for theotal acceptable quantity of ingoing streams to a unit process, e.g.aste to be treated at a particular facility, are expressed by (11)

nd (12), respectively, whereas the maximum output of a producttream is expressed by (13):

CAPIN,Uj

≥∑

s′ ∈ INj,s

MSs′ , ∀j ∈ J (11)

CAPIN,Lj

≤∑

s′ ∈ INj,s

MSs′ , ∀j ∈ J (12)

CAPOUT,Uj,s

≥MSs , ∀j, s ∈ OUTj,s ∩ J (13)

here the parameters MCAPIN,Uj

and MCAPIN,Lj

represent the max-mum and minimum total acceptable input quantity for a processnit j ∈ J, and MCAPOUT,U

j,sis the upper limit for output of stream s ∈ S.

The optimization model contains a pair of constraints to ensurehat the quality of a product output, in terms of composition, is keptithin acceptable limits. Eqs. (14) and (15) ensure upper and lower

uality limits, respectively:

k ∈ K

˛Ws,m,k,w · MFK

s,m,k − QCUw ·

∑k ∈ K

ˇWs,m,k,w · MFK

s,m,k ≤ 0,

∀s, m, w ∈ SMs,m ∩ SWs,w (14)

k ∈ K

˛Ws,m,k,w · MFK

s,m,k − QCLw ·

∑k ∈ K

ˇWs,m,k,w · MFK

s,m,k≥0,

∀s, m, w ∈ SMs,m ∩ SWs,w (15)

he foreground system. (b) In the mixer nodes j ∈ J , multiple incoming streams are

or which the binary decision variable Yd ,j controls the distribution of the incomingtion).

where the set SWs,w represents whether quality criterion w ∈ Wapplies to stream s ∈ S, while ˛W

s,m,k,wand ˇW

s,m,k,ware coefficients

controlling whether an element or compound k ∈ K in materialm ∈ M and stream s ∈ S is considered for quality criteria w ∈ W. Theupper and lower acceptable weight-per-weight ratio in quality cri-teria w ∈ W are given by the parameters QCU

w and QCLw , respectively.2

Alongside the capacity and quality limitations, process require-ments in terms of input of energy and operating materials areimportant. The lower thermal energy requirement of a process isexpressed via (16):∑

s′ ∈ INj,s′

∑m′ ∈ SMs′,m′

NCVm′ · MFMs′,m′ +

∑p ∈ PUTIL

Xj,p≥REQ Q,Lj

· RFj,

∀j ∈ JPROC (16)

where NCVm′ is the net calorific value (in Giga-Joule per tonne) fora material m′ ∈ M, and REQ Q,L

jis the lower specific energy require-

ment (in Giga-Joule per unit of reference flow) for process j ∈ JPROC.The first term on the left-hand side of (16) express the total netcalorific content of the feedstock material. The second term on theleft-hand side represents the energy supplied by any utility p ∈ PUTIL.

The upper limit of the total treatment capacity of an incinerationprocess, e.g. MSWI, may be restricted by the annual gross thermalcapacity, QCAPIN,U

j, of the furnace as expressed in (17):

∑s′ ∈ INj,s′

∑m′ ∈ SMs′,m′

NCVm′ · MFMs′,m′ +

∑p ∈ PUTIL

Xj,p ≤ QCAPIN,Uj

,

∀j ∈ JPROC (17)

The upper and lower limits on the consumption of utilities and

ˇWclinker,clinker,Fe2O3,LSF

= 0.65

QCLLSF

= 0.92

QCULSF

= 0.98

5 ervatio

wlflia

M

M

3

mo

3

flsteflp

tstfeo

R

w

ptbmte

R

w

e

ata(

H

wmrpg

8 C. Vadenbo et al. / Resources, Cons

here parameters REQ P,Uj,p

and REQ P,Lj,p

denote the upper and lowerimits on the specific input rate of product p ∈ P per unit of referenceow in process j ∈ J. Similarly, the upper and lower limits on the

nput of specific streams in a process are expressed by Eqs. (20)nd (21) respectively:

FSs − REQ S,U

j,s· RFj ≤ 0, ∀j, s ∈ INj,s ∩ J (20)

FSs − REQ S,L

j,s· RFj≥0, ∀j, s ∈ INj,s ∩ J (21)

.4. Objective function calculations

The optimization of the environmental and economic perfor-ance requires two different objective functions to be defined, as

utlined in the following sections.

.4.1. Environmental assessmentIn life cycle impact assessment, the environmentally relevant

ows of mass and energy occurring throughout the entire productystem are translated into environmental impacts. The optimiza-ion model allows both input-dependent and process-specificmissions and resource extraction to be assessed based on the massows model described above (the mathematical formulations arerovided in Section S.2.1 in the Supplementary material).

Some activities might generate by-products which are allowedo be variable in the model, i.e. not part of the required functionality,uch as the amount of energy recovered from waste incinera-ion. Any burdens or benefits arising from this kind of additionalunctionality are accounted for through substitution by systemxpansion (EC, 2010). Eq. (22) provides the variable functionalityf the recovered by-products based on mass.

ECMFj,r =

∑s ∈ OUTj,s∩PSp,s∩PRp,r

MFSs , ∀j ∈ JPROC, p ∈ P, r ∈ RMF (22)

here RECMFj,r

is the quantity (tonnes per year) of recovered by-

roduct r ∈ RMF in unit process j ∈ JPROC, and PRp,r is a set whichogether with the set PSp,s links outgoing streams to exportedy-products. To ensure mass balances the recovery efficiency foraterials is expressed by the mass transfer coefficients. In con-

rast, the recovery of energy, in (23), is modeled by considering thefficiency of recovery �Q

j,rexplicitly.

ECQj,r

= �Qj,r

·∑

s′ ∈ INj,s′

∑m′ ∈ SMs′,m′

NCVm′ · MFMs′,m′ , ∀j ∈ JPROC, r ∈ RQ

(23)

here RECQj,r

is the amount of energy (Giga-Joules per year) recov-

red as by-product r ∈ RQ, e.g. heat or power, in process j ∈ JPROC.The total life cycle impact of a unit process j ∈ J is derived over

set N of environmental impact categories. Direct exchanges withhe environment, life cycle impact of imported process inputs, andny credits obtained for recovered by-products are added up in24):

Jj,n

=∑e ∈ E

CFe,n · (EMTOTj,e + RDj,e)

+∑p ∈ P

BPn,p ·

⎛⎝Xjp −

∑r ∈ PRp,r

(RECMFj,r + RECQ

j,r)

⎞⎠ , ∀j ∈ J, n ∈ N (24)

here parameter CFe,n is the characterization factor of an environ-

ental exchange e ∈ E in impact category n ∈ N, and EMTOT

j,eand RDj,e

epresent total direct emissions and depletion of natural resourceser process unit, respectively. Parameter BP

n,p represents the aggre-ated life cycle impact in n ∈ N of product p ∈ P sourced from the

n and Recycling 89 (2014) 52–63

ecoinvent database (ecoinvent Center, 2010). No upstream impactsare considered for waste imported over the system boundaries, asthese impacts are assumed to be carried by the product systemsresponsible for the waste generation. The third term on the right-hand side of (24) represents the credits obtained from recoveredby-products.

The total impacts per activity i ∈ I and for the entire system arecalculated according to (25) and (26) respectively:

HIi,n =

∑j ∈ IJi,j

HJj,n

, ∀i ∈ I, n ∈ N (25)

HSYSn =

∑i ∈ I

HIi,n, ∀n ∈ N (26)

where the set IJi,j indicates whether a unit process j ∈ J belongs to anactivity i ∈ I, and the variables HI

i,nand HSYS

n represent the impact incategory n ∈ N per activity and over the entire system, respectively.

3.4.2. Monetary costOnly a single time period (typically one year) is considered in the

optimization model, i.e. it represents a static optimization prob-lem. The investment cost associated with constructing, replacingor retrofitting equipment or facilities (referred to as infrastructurein LCA terminology) can nevertheless be accounted for by breakingit down into an annual capital cost: Departing from the approachof Brunet et al. (2012), the total annualized cost (TACj) of a unitprocess j ∈ J is calculated as the sum of the annual operating cost(COj) and the annual capital cost (CCj), and subtracting the totalrevenue from provision of required functionality (REVF

j) and by-

product recovery (REVRj

) (27). One approach to define the termson the right-hand side in (27) is described in Section S.2.2 in theSupplementary material.

TACJj

= COj + CCj − REVFj − REVR

j , ∀j ∈ J (27)

The total annual cost of the entire system is calculated accordingto (28):

TACSYS =∑j ∈ J

TACJj, ∀i ∈ I (28)

where TACSYS is the total annual cost of the system.

3.4.3. Multi-dimensional objective functionThe objective functions for environmental impact and monetary

cost are given by (29) and (30) respectively.

ZNn = HSYS

n , ∀n ∈ N (29)

ZC = TACSYS (30)

3.5. Multi-objective optimization

The overall multi-objective MILP model can be expressed incompact form as follows in (31):

minxyZ

⎧⎪⎪⎨ environmental impact in category 1

. . .(31)

⎪⎪⎩ environmental impact in category n

monetary cost

Subject to:

C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63 59

F ging dt the g

••••••••

atciamiapbof

4

4

pspcod

msgtattof

ig. 4. Superstructure of the optimization problem for the case study on glass packahe relevant disposal options. Mass flows for flue gas and internal cullet recycling in

Fulfillment of the required system functionalityAvailable supply of resourcesTreatment and production capacitiesMass balancesProcess input and output constraintsRegulatory constraintsNon-negativity of mass and energy flowsx ∈ Rn, y ∈ Y = {0, 1}

The solution to this type of optimization problem is typically set of Pareto-optimal alternatives that represent the efficientrade-off between the objectives considered (Azapagic, 1999). Theoncept of Pareto-optimality implies that it is not feasible tomprove the performance in one objective without compromisingnother objective. There are different methods available to solveulti-objective problems (Ehrgott, 2005) (see also Section S.2.3

n the Supplementary material for a brief overview of approachespplied in LCA). The MILP optimization model proposed in theresent article can accommodate a wide range of approaches toe applied. The most suitable approach is highly dependent on theptimization problem being addressed and on the target audienceor the results.

. Case study – glass packaging disposal

.1. Case description

The aim of this case study is to provide an illustrative exam-le of the modeling approach described above. The scope of casetudy encompasses a simplified system for the disposal of glassackaging (Fig. 4). The reader may refer to the work by Meylan andolleagues for a detailed analysis and environmental assessmentf future scenarios for the specific case of Swiss glass packagingisposal (Meylan et al., 2013, 2014).

The optimization problem is formulated as given a set of treat-ent options (disposal processes: glass packaging production, glass

and production, and foam glass production), the demand for newlass packaging (green, brown, and white), the production sys-ems displaced by glass sand and foam glass (natural silica sandnd extruded polystyrene, respectively), and the amounts of four

ypes of glass cullets (mixed, green, brown, white) to be treated,he goal is to both find the optimal distribution of the culletsver the available treatment options and the feedstock inputsor the production processes of new glass packaging such as the

isposal. The decision variable reflects the distribution of the four cullet types amonglass packaging production processes have been omitted for clarity.

system-wide environmental impact is minimized. The backgroundlife cycle inventory data represents average European conditionsand was sourced from the ecoinvent database v2.2 (ecoinventCenter, 2010). For this case, the environmental impacts are assessedusing an aggregated single-score indicator, ReCiPe Endpoint H/A(Goedkoop et al., 2009), v1.08. The available feedstock of primaryraw materials is assumed to only consist of silica sand, soda, lime-stone, dolomite, and feldspar for glass packaging production, andfeldspar for foam glass production. The structure of the optimiza-tion problem is illustrated in Fig. 4. The four cullet types and thecolor-sorted fractions are assumed to be eligible for treatment inthe five disposal options as follows:

• Green glass packaging production: Mixed, brown, white, andbrown cullet (up to 100% waste glass).

• Brown glass packaging production: White, and brown cullet (max70% waste glass)

• White glass packaging production: White cullet (max 60% wasteglass).

• Glass sand production: Mixed, brown, white, and brown cullet.• Foam glass production: Mixed, brown, white, and brown cullet.

The glass packaging to be treated is assumed to consist of176,000 tonnes of green cullet, 22,000 tonnes of brown cullet,22,000 tonnes of white cullet, and 90,000 tonnes of mixed cullet(50% green glass, 30% white, and 20% brown). The recycling of post-consumer glass is an integral part of packaging glass productionin Europe (EC-JRC, 2013). The production of new glass packagingis therefore assumed to also be included in the required system-wide functionality, i.e. the functional unit (equivalent quantities asin disposal are assumed), and any share of the feedstock require-ments not covered by waste glass must be compensated by theinput of primary raw materials. For the production of glass sandand foam glass, the outputs of these processes are allowed to varyin the model and the outputs (co-functions) are assumed to displacethe production of natural silica sand and extruded polystyrene(XPS), respectively (Meylan et al., 2014). The amount of insulatingmaterial that can be substituted is derived by assuming identicalthermal conductivity and adjusting for the difference in densities(110 kg/m3 and 30 kg/m3, respectively). Any differences in emis-

sions or resource use arising in the use phase are here disregardedfor simplicity, but the impacts from disposal of the insulating mate-rials are included. According to Meylan and colleagues (2014),1.5 kWh of electricity is required to optically sort 1 tonne of cullet

60 C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63

F ntal imf s have

istt

csSmadcat7bima

4

pwpcrafFlsttcotwlaoto

ig. 5. Optimal distributions of glass cullets minimizing the aggregated environmeor flue gas and internal cullet recycling in the glass packaging production processe

nto the respective color fractions, and we assume perfect (100%)orting efficiency. The life cycle inventories used in the optimiza-ion model are listed in Table S.4 in the Supplementary material onhe web.

The composition of glass packaging, which is used for both theomposition of the waste glass as well as quality criteria (con-traint) for the production of new glass packaging, is given in Table.5. Besides any CO2 generated from the calcination of calcium oragnesium carbonates, it is assumed that all mineral compounds

re completely transferred to the glass in the glass packaging pro-uction processes. It is furthermore assumed that 6% of the inputonsists of internally recycled cullet (Hischier, 2007). The avail-ble production capacity for foam glass is assumed to be limitedo 100,000 tonnes per year (equivalent to a treatment capacity of4,000 tonnes of glass cullet by assuming fixed input rate). It shoulde noticed that only technical constraints have been considered

n this simplified case study, and that a more thorough assess-ent or optimization also needs to address regulatory, financial,

nd logistical constraints (cf. Meylan et al., 2014).

.2. Case study results

The optimal distributions of the glass cullets and the input ofrimary raw materials in the glass packaging production processeshich minimize the overall aggregated environmental impact areresented in Fig. 5. It can be observed that the color-separatedullets are completely assigned to the production process of cor-esponding new glass packing. This is possible since the availablemounts of brown and white cullets do not exceed the upper limitsor the input of waste glass in the respective production processes.urthermore, the limited capacity for foam glass production is uti-ized to the maximum extent possible by assigning it the majorhare of mixed cullet (74,000 tonnes). This result is explained byhe relatively large avoided impact credited to foam glass produc-ion from displaced production of XPS, which is dominated by theontribution to global warming stemming mainly from emissionsf blowing agents. The remaining fraction of the mixed cullet (6000onnes) is assigned to the production of green glass packaging, inhich sufficient treatment capacity is available. No cullet is sent for

ow-grade down-cycling to sand substitute due to the relatively low

voided burden and the sufficient capacities of the other treatmentptions. The resulting overall net environmental impact of the sys-em is 6.9 million points, where the net avoided impact (benefit)f the foam glass production amounts to 5.5 million points and the

pact based on ReCiPe H/A (mass flows expressed in kilo-tonnes [kt]). Mass flows been omitted for clarity.

combined production of packaging glass results in a net burden of12.4 million points.

To test the sensitivity of the results to the availability of sepa-rately collected color fractions, an alternative scenario was solvedin which the entire amount of waste glass is available as mixed cul-let. The optimal distribution for this case is presented in Fig. 6. Itcan be observed that the capacity for foam glass production is againfully utilized as it receives 74,000 tonnes of mixed cullet. The mainshare of the mixed cullet (185,500 tonnes) is directly sent to theproduction of green glass packaging as this process was assumedto accept all glass fractions as inputs. The optical color sorting pro-cess is assigned 40,500 tonnes which results in 29,200 tonnes green,5100 tonnes brown, and 6200 tonnes white cullet which are furthersent for recycling in the production of new glass packaging of eachrespective color. This leads to a decrease in net impact in the pro-duction of green glass packaging (−8%), whereas the net impacts ofthe production of brown and white glass packaging increases with21% and 15%, respectively. The overall impact, however, is essen-tially unchanged compared to the aforementioned case (presentedin Fig. 5).

The case study was selected as it illustrates several key featuresof the proposed optimization model: Firstly, the benefit of structur-ing mass flows into three levels of aggregation (streams, materials,elements/compounds) is highlighted by the material sorting, basedon color of the glass (material) of the mixed cullet (stream), andthe chemical reactions (in this case calcination of the raw mate-rials) of the glass production processes. Secondly, the constraintsimposed on the solutions to the problem were explicitly consid-ered in the model. This aspect was illustrated by various technicallimitations, e.g. the upper limit on the shares of waste glass input inthe glass packaging production processes, or the quality criteria forthe composition of the finished glass packaging. Thirdly, it reflectshow product substitution and the related avoided impacts (posi-tive and/or negative opportunity costs) are linked to the definitionof the functional unit and how it can be captured in both the fore-ground system, e.g. as variable inputs of primary raw material inthe production of glass packaging, and in the background system,e.g. through the displaced production of natural sand or insulatingmaterial.

Due to its rather limited scope, this particular case couldhave been solved ‘manually’ by assessing a number of alternative

system configurations, i.e. scenarios. As demonstrated in Part II(Vadenbo et al., accepted for publication), an optimization approachis becoming increasingly attractive with growing problem com-plexity, e.g. through a large number of feasible combinations or the

C. Vadenbo et al. / Resources, Conservation and Recycling 89 (2014) 52–63 61

F izing

i packa

iasl

5

arMbmttnmitaFcpTatisSpqno

tigrthidaot

ig. 6. Case study sensitivity analysis: optimal distributions of mixed cullet minimn kilo-tonnes [kt]). Mass flows for flue gas and internal cullet recycling in the glass

nteraction of various constraints. Further opportunities anddvantages offered by optimization techniques to support moreustainable regional waste and resource management are high-ighted in the following section.

. Discussion

The constraints posed by, for example, the total productionnd/or treatment capacity of a system in a particular region arearely explicitly considered in LCA studies on waste management.FA on the other hand enables capacity constraints to be reflected

ut typically does not provide any information on the environ-ental relevance of the different flows. Mathematical optimization

echniques are able to resolve recursions of physical flows and iden-ify optimal solutions in a systematic way which eliminates theeed to pre-define treatment scenarios in the assessment of a wasteanagement system. By taking advantage of the strengths of each

ndividual method, the proposed optimization model offers oppor-unities to support decision making for more sustainable wastend resource management by addressing three crucial aspects:irstly, it facilitates the systematic identification of Pareto-optimalonfigurations in terms of industrial resource use, exchanges of by-roducts, and waste management for a wide range of objectives.he integration of process models ensures that the effects of wastend resources characteristics are reflected in the inventories ofhe foreground system. Furthermore, the consideration of life cyclempacts of products imported into the foreground system preventshifting environmental problems elsewhere in the supply chains.econdly, it enables the system-wide improvement potential com-ared to a reference case, e.g. a business-as-usual scenario, to beuantified. Thirdly, the approach enables the identification of theeed for trade-offs due to conflicting objectives and the generationf efficient trade-off solutions.

In the optimization model, the demands for industrial produc-ion and for waste treatment services are considered as equallymportant components of the total required functionality of aiven industrial network. The acceptance of the optimizationesults among the affected stakeholders, e.g. the involved indus-ries, authorities, or the local communities might, however, beighly dependent on how the required (or desired) functionality

s defined. To ensure a broad acceptance, it might be necessary to

efine this functionality in a participatory process, aimed at finding

consensus among the stakeholders. The focus of the discussionsn the optimization results can then be shifted to the priorities andhe potential trade-offs among a set of Pareto-optimal solutions

the aggregated environmental impact based on ReCiPe H/A (mass flows expressedging production processes have been omitted for clarity.

to obtain or sustain this functionality with minimal environmen-tal impacts. By explicitly reflecting the constraints and limitationsimposed on the system, the focus of the analysis may be shiftedaway from a general ranking of alternatives to the identificationof the optimal mix of the options at hand. This is particularly rele-vant in cases in which different strategies for co-processing wastein industrial production processes are available, as these treatmentcapacities are directly dependent on the demand for the productoutputs. Explicitly including the relevant constraints also brings theadditional benefit of avoiding unfeasible solutions which cannot beimplemented in practice.

The set of industrial processes, for which representative data oncommon technologies are available, on the basis of which LCA mod-els have already been developed, includes the production of clinkerand cement (Boesch et al., 2009), ironmaking in the blast furnace(Vadenbo et al., 2013), the incineration of hazardous liquid waste(Seyler et al., 2005), and MSWI (Boesch et al., 2013). In addition, LCAmodels are also available for landfills and municipal wastewatertreatment plants (Doka, 2009) and industrial wastewater treatmentplants (Köhler et al., 2007). It is important to recognize that theselinear models are approximations of the complex thermodynamicrelationships and conditions which prevail in the actual processes.The aforementioned LCA models consequently represent trade-offsbetween model complexity and data requirements on the one hand,and accuracy and precision of the model predictions on the other.In the case of modeling of MSWIs, for example, the mass transfersin various incinerators and flue gas treatment systems have beenextensively covered in the scientific literature (e.g. Abanades et al.,2002; Belevi and Moench, 2000; Brunner and Mönch, 1986; Koehleret al., 2011; Morf et al., 2000, 2013; Riber et al., 2008; Zimmermannet al., 1996). Although MSWI can generally be considered a robusttechnology with stable performance, this might not be the casefor relatively large increases in the input of some critical elements(Astrup et al., 2011).

One potential approach to further strengthen environmentalassessment and optimization of waste management or other prod-uct systems is the integration of advanced algebraic modelingand process simulation tools and LCA methodology, cf. Iosif andcolleagues (2010) and Fröhling and Rentz (2010), and Fröhlinget al. (2013). The inclusion of more detailed process models in theoptimization might, however, lead to non-linear equations, and

most likely to non-convexities. From a purely mathematical per-spective, this results in major challenges concerning the properinitialization of the non-linear models so as to ensure a goodconvergence, and the existence of multiple local optim standard

6 ervatio

amt

dapasamcetmiacMu

6

fatameuitefsaes

A

nOt1e(awma

A

i2

R

A

A

2 C. Vadenbo et al. / Resources, Cons

lgorithms may fail during the search. The continuous advance-ents in the area of optimization theory will help in addressing

hese issues.A vast amount of model parameters are required in order to

erive the resource use and emission inventories of the variousctivities of the system according to the bottom-up-approach pro-osed in the present article. All of these model parameters aressociated with uncertainty and/or variability. One procedure totructure the collection and analysis of uncertainty information,nd to systematically integrate it into the environmental assess-ent of waste management systems was proposed by Clavreul and

olleagues (2012). Although addressing these aspects was consid-red beyond the scope of the present article, it should be mentionedhat standard approaches to incorporate the uncertainty of the

odel parameters, e.g. Monte Carlo analysis, can be implementedn the optimization model. The output obtained from this type ofnalysis then represents the probability of the resulting systemsonfigurations represent the optimal solution for the problem. TheILP could also be further extended to optimize under uncertainty

sing stochastic programming techniques (Sahinidis, 2004).

. Conclusions

In present work, we have proposed and discussed a frameworkor combining LCA with material flow analysis, process modeling,nd mathematical optimization techniques in order to advancehe use of LCA as a tool for complex waste management systemsnd industrial networks. The benefits of an optimization approachight be expected to increase as the scope of the analysis is the

xpanded to more complex systems with more feasible config-rations and intricate feedback loops. Areas for further research

nclude extending the optimization model to account for the uncer-ainty and any inherent variability of the model parameters, and tonable optimization over multiple time periods in order to includeuture scenarios for demand of products and waste treatmentervices, and to better address investment decisions. A full-scalepplication of the optimization model is presented by Vadenbot al. (accepted for publication) for the thermal treatment of sewageludge in a region in Switzerland.

cknowledgements

Carl Vadenbo is grateful for the financial support of Holcim Tech-ology Ltd., Swiss Federal Office for the Environment, Swiss Federalffice of Energy, the Association of Swiss Waste Treatment Indus-

ry, voestalpine Stahl GmbH, and the Danish Research Council (no.1-116775, IRMAR project). Gonzalo Guillén-Gosálbez acknowl-dges support from the Spanish Ministry of Education and Scienceprojects DPI2012-37154-C02-02 and CTQ2012-37039-C02). Theuthors would also like to thank Grégoire Meylan for inputs onaste glass disposal, and Catherine Raptis for proofreading theanuscript. Finally, the comments of two anonymous reviewers

re gratefully acknowledged.

ppendix A. Supplementary data

Supplementary data associated with this article can be found,n the online version, at http://dx.doi.org/10.1016/j.resconrec.014.05.010.

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