Author's Post Print Risk explicit interval linear programming model for ...

Author’s Post Print Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty Simic Vladimir and Dimitrijevic Branka

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This is the author’s Post Print version of the following article: Simic, V., Dimitrijevic, B., 2013. Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty. Resources, Conservation and Recycling, 73, 197-210. http://dx.doi.org/10.1016/j.resconrec.2013.02.012 Copyright: Elsevier http://www.elsevier.com/ 1

Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty Vladimir Simic University of Belgrade, Faculty of Transport and Traffic Engineering Vojvode Stepe 305, 11000 Belgrade, Serbia Phone: +381113091322 Fax: +381113096704 E-mail address: [email protected] Branka Dimitrijevic University of Belgrade, Faculty of Transport and Traffic Engineering Vojvode Stepe 305, 11000 Belgrade, Serbia

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Abstract: With the number of vehicles expected to increase to 1.85 billion by 2030 and the scrap generated from end-of-life vehicles (ELVs) expected to be 3.71 billion tonnes, there is a strong motivation to properly process the flow of these materials. The EU Directive on end-of-life vehicles (EU ELV Directive) aims to increase recovery and recycling rates of ELVs in order to reduce waste and improve environmental performances. Long-term optimization planning of vehicle recycling is increasingly important. However, there is a lack of research of uncertainties in the vehicle recycling system, none of the previous studies analysed the linkage and trade-off’s between decision risk and system performances, and no previous research was reported on interval-based programming for vehicle recycling planning problem. In order to meet the imposed eco-efficiency quotas, maximize system profit and minimize decision risk, and at the same time fill the identified research gaps, a risk explicit interval linear programming model for optimal long-term planning in the EU vehicle recycling factories was developed. It can create optimal plans for procuring vehicle hulks, sorting of generated material fractions, allocation of sorted waste flows and allocation of sorted metals for desired value of the system aspiration level. A numerical study demonstrated the potentials and applicability of the proposed model. Vehicle recycling factories aim at reaching the highest possible level of quantity and quality of sorted metal flows. The future eco-efficiency quotas will not endanger their business. The success of the final phase of implementation of the EU ELV Directive is not jeopardised, because even the future eco-efficiency quotas were reached in all created test problems. Quantity of landfilled wastes will be radically reduced after January 1, 2015. The model results and trade-offs would be valuable for supporting the EU vehicle recycling factories in creating optimal long-term production strategies and reducing the risk for uncertain situations. Keywords: End-of-life vehicle; EU ELV Directive; Uncertainty; Risk; Vehicle recycling

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1. Introduction Waste from end-of-life vehicles (ELVs) is an issue of a world-wide concern and the maximum recovery and recycling needs to be achieved to reduce waste discharge and to enhance the image of the vehicle industry through environmentally sound management (Giannouli et al., 2007; Joung et al., 2007). At present the vehicle sector generates about 5% of the world’s industrial waste, whether from vehicles or the plants which produce them (Zorpas and Inglezakis, 2012). ELV is a specified vehicle which is discarded or is to be discarded by its registered owner as waste (Go et al., 2011). It is considered as a burning environmental problem, since this kind of waste contains many precious metals (Li and Yu, 2011). In the early 1990’s ELVs have been identified by the EU as priority waste stream (Mathieux et al., 2008). Nowadays, ELVs are a major stream of waste in the EU (ECDGE, 2012). Recycling and reuse of ELV parts and components, and metal recovery is important to governments, manufacturers, suppliers, dismantlers and vehicle recycling factories. The shortening of vehicles average life to about 10–12 years in the EU (Fiore et al., 2012), produced in the last 15 years an impressive enhancement of ELVs number. Moreover, with the number of vehicles expected to increase to 1.85 billion by 2030 and the scrap generated from ELVs expected to be 3.71 billion tonnes (Paul, 2009), there is a strong motivation to properly process the flow of these materials. The emergence of vehicle abandonment, pollution, and waste has resulted in the creation of the 2000/53/EC Directive on end-of-life vehicles (EU ELV Directive) (Edwards et al., 2006). The EU ELV Directive (EU, 2000) is designed to promote collection, reuse and recycling of ELVs (Gehin et al., 2008), and it represents the first embodiment of extended producer responsibility (EPR) in vehicle recycling (Xiang and Ming, 2011). The EU ELV Directive aims to increase recovery and recycling rates ELVs in order to reduce waste and improve environmental performances, and it has proven to be the catalyst for substantial reform within the vehicle recycling industry. The implementation of the EU ELV Directive is successful in accelerating the environmental sustainability in EU member states (Amelia et al, 2009). Moreover, this directive fundamentally changed the business philosophy of the EU vehicle recycling system, which had been used for decades and had been exclusively profit-oriented. According to the EU ELV Directive, which first took effect January 1, 2006, vehicle recovery must reach a minimum of 85% by weight per vehicle (with a maximum energy recovery of 5%), of which a minimum of 80% will have to be reusable and recyclable material. By the January 1, 2015, recovery requirements will rise to a minimum of 95% (with the maximum energy recovery raised to 10%), of which a minimum of 85% will have to be reusable and recyclable material. Automobile shredder residue (ASR) processing is essential to achieving the eco-efficiency quotas of the EU ELV Directive and represents a great concern for the EU vehicle recycling industry (Simic and Dimitrijevic, 2012). It is the finely pulverised waste (Giannouli et al., 2007), which is considered an energy source as it contains more than 7% combustible matter (Smink, 2007). In addition, the total ASR production in the EU is in the range of 1.93–2.34 million tonne per year (Vigano et al., 2010), with an estimation of 3.5 million tonnes within 2015 (Mayyas et al., 2012). In a vehicle recycling system, it is difficult to express or obtain the overall modelling data in deterministic form. Moreover, a large number of factors in real world processes are influenced by uncertainties (Wu et al., 2010). Uncertainty is the key factor influencing vehicle recycling planning. For instance, in a vehicle recycling system, sorting and transportation costs are uncertain in reality, because they can vary temporally and spatially. In addition, the costs of land-filling, municipal solid waste incinerator (MSWI) and advanced thermal treatment (ATT), i.e. gate fees, which vary among EU member states and their amounts are subject to continuous change. Furthermore, processing rates of vehicle recyclers’ sorting equipment and efficiency of ATT plants and MSWIs cannot be considered as deterministic values, because they depend on material flow composition. Finally, in long-term planning of vehicle recycling, observing scrap metal prices as deterministic values can be considered unacceptable. 4

On the other hand, the overall modelling data can be obtained as interval values and the approach to tackling such a problem is called interval linear programming (ILP). ILP method can deal with the uncertain modelling parameters expressed as intervals without any distributional information. It allows the interval information to be directly communicated into the optimization process and resulting solution (Li and Huang, 2010). Additionally, in order to reduce information costs and also to construct a real model, the use of interval linear program is fully appropriate (Ramesh and Ganesan, 2011). In this way, every modelling parameter can be expressed as interval number (lower- and upper-bounded range of real number), which assumes an extent of tolerance or a region of values that the parameter can possibly take (Sengupta et al., 2001). Hence, it is evident that effective uncertainty analysis methods must be integrated into the modelling framework to produce more reliable decision outputs and avoid inferior or simply erroneous decisions (Liu et al., 2011). To develop a model for long-term planning in the EU vehicle recycling factories, this paper uses interval approach to describe and treat imprecise and uncertain parameters. The key elements of research include: development of the ILP model for long-term planning of vehicle recycling; and development of the risk explicit interval linear programming (REILP) model for long-term planning of vehicle recycling. Therefore, the main objective of this paper is to develop a REILP model for optimal long-term planning in the EU vehicle recycling factories. A numerical case study will then be provided not only to illustrate the potentials and applicability of the proposed REILP model, but also to gain insights into profitability and eco-efficiency of the EU vehicle recycling factories. Furthermore, the results will help to identify optimal procuring, sorting, sorted waste allocation and sorted metals allocation plans with a maximized profit level and a desired decision risk. The remaining part of the paper is organised as follows: Section 2 provides an extensive literature review on vehicle recycling planning. Section 3 presents the used methodology, and developed ILP and REILP models. Section 4 presents a case study, and Section 5 presents the paper’s main conclusions.

2. Literature review The relevant literature for our contribution originates from different streams of research, but from a domain-oriented point of view only the work on vehicle recycling planning is significant. Due to the increasing importance of the subject of vehicle recycling planning, a considerable number of research papers have been published in the past decade. A detailed analysis of these papers is needed to identify the key directions for the further development of this very important and dynamic research area. A successful vehicle recycling infrastructure helps to divert materials from landfills and recycles metals from high volume consumer product. Johnson and Wang (2002) created two types of deterministic optimization models for vehicle recycling: US model, which is focused on profit only, and EU model in which optimization depends on the imposed recycling/recovery quotas. Boon et al. (2003) used the Goal Programming method and provided mathematical formulation for the recycling infrastructure to assess materials streams and process profitability for several clean vehicle cases. Sakkas and Manios (2003) applied generalized cost modelling approach to obtain a momentary snapshot of the current vehicle recycling practice in Greece. Bandivadekar et al. (2004) created a simulation model for material flows and economic exchanges (MFEE) to examine the effects of changes in vehicle material composition on the US recycling infrastructure. They noticed that the Japanese ASR recycling quota of 70% and EU recycling/recovery quotas by 2015 are unachievable without fundamental changes. Ladjouze and Rahimifard (2004) presented a cost breakdown structure with parametric cost drivers and proposed a decision support tool for the recovery of process costs. Kim et al. (2004) surveyed using some questionnaires the ELVs recycling and recovery rates, and management status in Korea to aid the establishment of policies for the management of ELVs. 5

In the EU, ELVs are a prioritised waste stream and are managed on the basis of economic EPR. Forslind (2005) examined how the existing Sweden’s vehicle recyclers, aimed at creating economic incentives and financing end-of-life management, are affected by EPR. Dantec (2005) created a simple technical cost model of the dismantler and shredder operations to study the recycling cost sensitivity to regional practices. Choi et al. (2005) proposed a mixed integer programming model for tactical process planning in the case of traditional US vehicle recycling factories. Muhamad Zameri and Blount (2006) provided a brief snapshot of vehicle recycling practices in EU, USA, Japan and Australia. Coates and Rahimifard (2006) presented a holistic end-of-life cost model for the vehicle recycling industry and focused on the potential applications of this model to support both high- and low-level decisions. Ferrao and Amaral (2006) developed technical cost models of vehicle dismantlers and recycling factories in order to assess the influence of the EU ELV Directive on their profitability. They identified that the main parameters affecting vehicle recycling factory economics are associated with ferrous scrap, namely its separation efficiency, the international price and the ferrous content of vehicles. Ferrao et al. (2006) used data obtained from a full scale shredding experiment to develop a technical model and access the eco-efficiency performances of several vehicle recycling strategies. They concluded that ASR mechanical separation may enable more extensive recycling and allow the achievement of the valid recycling quota. Amaral et al. (2006) developed a system dynamics model of the Portuguese ELV recycling infrastructure and concluded that mechanical separation technologies are less expensive than component/part removal by dismantlers. Coates and Rahimifard (2007) pointed out that accurate methods are required to economically assess and optimize the ELV processing activities. Joung et al. (2007) analysed status of recycling ELVs in Korea and concluded that installation of advanced sorting equipment in a vehicle recycling factory could maximize its separation efficiency and increase the attained vehicle recycling rate. Giannouli et al. (2007) developed a methodology and technical model for the evaluation of waste produced from road vehicles, both at their end-of-life and during vehicle operation. Williams et al. (2007) expanded a mixed integer programming formulation from Choi et al. (2005) in order to make short-term tactical decisions regarding to what extent to process and reprocess materials through multiple passes in eddy current sorter. Qu and Williams (2008) formulated the vehicle reverse production planning in a nonlinear programming model. They developed an approximate supply function for vehicle hulks ordering when adjacent shredders price independently and compared two pricing strategies. Coates and Rahimifard (2008) integrated several techniques, such as Activity Based Costing, regression analysis and time studies, and proposed the ELV costing framework. They framework allows various recycling operators to assess the economic consequences of their investment and processing decisions. Fuse and Kashima (2008) developed an automobile recycling input–output analysis based evaluation method to examine the appropriateness of recycling system scheme for ELVs imported from Japan. Manomaivibool (2008) explored the impacts of network management on the environmental effectiveness of the programmes for the management of ELV in the UK and in Sweden from an EPR perspective. Smith and Crotty (2008) examined the impact of the EU ELV Directive on UK vehicle component manufacturers using questionnaire tool. Miemczyk (2008) suggested that research within production and operations management is particularly needed to consider the effects of institutional environment policies on the choice of production strategy and product recovery. Kumar and Sutherland (2008) identified the following limitations of existing vehicle recycling models: inadequate description of the complex material flows and economic transactions within the infrastructure, minimal consideration of market factors, lack of consideration for government policies and limited variety of examined future scenarios. They pointed out that the long-term impact in terms of the waste that is generated by the vehicle recycling infrastructure should be at the core of any research that is undertaken in this area. Kumar and Sutherland (2009) used simulation MFEE model from Bandivadekar et al. (2004). They found that with change in vehicle design the profit of vehicle recycling factories will increase over time, due to the additional revenue from the aluminium in aluminium intensive (AI) vehicle 6

hulks. Coates and Rahimifard (2009) developed a post fragmentation separation model capable of simulating the value added processing that a piece of automated separation equipment can have on a fragmented ELV waste stream. Pehlken and Müller (2009) stated that modelling recycling processes and the uncertainty analysis needs to be simultaneously considered. They pointed out that more research concerning this matter has to be done. Mathieux and Brissaud (2010) proposed method to build an end-of-life product specific material flow analysis and applied it to aluminium coming from end-of-life commercial vehicles in EU. However, they pointed out that the implementation of the method requires a lot of field effort. Chen et al. (2010) thoroughly described principles and characteristics of the vehicle recycling system in Taiwan. They concluded that improving and optimizing the process of operational and tactical planning is necessary. Santini et al. (2010) used a Design-for-Recycling software named ProdTect® to carry out a study on the impact that pre-shredder dismantling step could have in achieving 85% recyclability rate in 2015. However, they investigated only recyclability rate, while total and energy recovery rates has not been considered. The approach of Life Cycle Assessment (LCA) was applied by Ciacci et al. (2010) to characterize and quantify environmental damage and impact resulting from different ASR management methods. Lazarevic et al. (2010) reviewed plastic waste management in the context of a European recycling society and concluded that uncertainty analysis was disregarded in available studies. Ilgin and Gupta (2010) gave an excellent overview of the literature on environmentally conscious manufacturing and product recovery and concluded that more studies are needed to better control the effects of uncertainties. Kibira and Jain (2011) used system dynamics simulation to study the impact of hybrid and electric vehicles on the profitability of the recycling infrastructure. Li et al. (2011) presented a coupled upgrading and production mathematical programming model to identify economically efficient sorting strategies and their impact on scrap usage in the case of an individual recycling firm. The model is applied to a cast/wrought alloy sorting for typical EU secondary aluminium production from four scrap types: AI vehicles, shredded extrusion, old rolled, and commingled. A review of the literature published in year 2010 on topics relating to vehicle wastes is presented in Bari et al. (2011). Go et al. (2011) presented a review on ELVs, recycling, disassemblability methods and the related fields. Simic and Dimitrijevic (2012) presented a short-term production planning problem for vehicle recycling factories in the EU legislative and global business environments. They analysed the influence of the EU ELV Directive on the vehicle recycling factories business and recommended that the control of the recycling system efficiency should be done at the system level. Passarini et al. (2012) applied LCA to estimate potential implications of waste composition evolution in vehicle recycling. They found that innovative recycling plants, modelling mechanical and chemical recycling options, achieve the lowest impacts today due to the combination of material and energy recovery, with a consequent decrease in the residual amount of waste disposed of in landfills. Blume and Walther (2012) discussed the legislative influence on the German vehicle industry and concluded that future eco-efficiency quotas are the main driving force for material flow innovations. Fiore et al. (2012) concluded that installation of post-shredding technical solutions in traditional vehicle recycling factories (so-called shredding plants) may lead to multi purposed opportunities for ASR reuse/recovery. Zorpas and Inglezakis (2012) provided an overview of the ASR problem and the options for processing this waste in order to minimize the waste directed to landfills. Mayyas et al. (2012) investigated the sustainability research within the vehicle industry, through a review of the different studies in vehicles’ life cycle, disposal and end-of-life analyses, and the different sustainability metrics and models used to quantify the environmental impact. From the review of initial literature, it is evident that there is a lack of research of uncertainties that exist in vehicle recycling planning. In addition, no previous research was reported on intervalbased programming for vehicle recycling planning problem. Finally, none of the previous studies analysed the linkage and trade-off between decision risk and system performances. Therefore, in view of the limitations in previous works and our research motivation emphasized the introduction 7

of this paper, we formulated and comprehensively tested the risk explicit interval linear programming model for long-term planning of vehicle recycling.

3. Methodology 3.1 Interval linear programming method Many methods have been developed to deal with uncertainties. One of the most popular alternatives for handling uncertainties is the ILP method. It represents an extension of the classical linear programming problem to an inexact environment (Sengupta et al., 2001). The ILP can reflect the uncertainties in the modelling system, the information requirement is low, and the solution algorithms are easy to use. A general ILP model can be defined as follows (Huang et al., 1993; Tong, 1994): Min f ± =C ± X ±

(1)

subject to:

A ± X± ≤ B ±

(2)

X± ≥ 0

(3)

where ± represents the interval number with known upper bound “+” and lower bound “−”, but m× n

unknown distribution information; f ± is objective function; A ± = {R ± } m×1

are coefficients, B ∈ {R ± }

1×n

and C± ∈ {R ± } n×1

represents the right-hand constraints, X± ∈ {R ± }

represents the

±

unknown variables, and R denotes a set of interval numbers. Eqs. (1)−(3) can be decomposed into two sub-models corresponding to the lower and upper bounds of the objective function, f − and f + respectively, and solved using standard ILP algorithms. Gray LP (Huang and Moore, 1993) and Best worst case (BWC) analysis (Chinneck and Ramadan, 2000; Tong, 1994) represent two major algorithms that are computationally efficient in obtaining interval solutions (Zhou et al., 2009).

3.2 Overview of the EU vehicle recycling system There are four actor groups involved in vehicle recycling procedure (Fig. 1). The initial participants are vehicle users, who present network sources. They are required to deliver ELVs to collection facilities (Vidovic et al., 2011). The second group is represented by collection agents and dismantling companies. Collection agents are vehicle dealers or repair shops which are required to collect ELVs and transport them to dismantling companies. Dismantlers depollute ELVs through sorting and disposing of petrol, waste oil, fluids and other noxious substances that are prohibited in landfills. In parallel, they remove selected reusable parts and some recyclable materials, while the remaining hulks are shipped to vehicle recycling factories for further recycling. The third actor’s group, the vehicle recycling factories, are responsible for hulks shredding, sorting generated material fractions, and transporting the sorted waste materials flows and sorted metal flows to the different participants of the fourth actor’s group. When the shipments arrive from dismantling companies, vehicle hulks are unloaded from trucks and stored. Hulks planned for processing are successively fed into a large rotating hammer mill, where they are broken down to smaller pieces. A heavy-duty cyclone is installed on top of the shredder to vacuum the light ASR fraction. This fraction can be further sorted or shipped to an advanced thermal treatment plant. If the first option is chosen, then the second magnetic sorter separates this material flow to ferrous metals 8

2 and non-ferrous (NF) mix fractions. The NF mix can also be further sorted to extract NF metals, and then can be sent to an ATT plant or land-filled. If the first option is chosen, then the second eddy current sorter (ECS) separates this material flow into NF metals 2 and a second fraction of non-metals, which can then be routed to the optimal destination. The heavy materials fraction passes through the first magnetic sorter, which diverts the ferrous metals 1 from the heavy ASR fraction. Market requirements dictate that both fractions of ferrous metals should be first manually treated along a conveyor for possible impurities and only then sold to the steel industry. As for the fraction of insulated copper wires, two routes are possible: export and (manual) recycling in countries with low labour costs or landfill disposal. The heavy ASR fraction is forwarded to the first ECS, which separates it into NF metals 1 and the first fraction of non-metals. The first and the second NF metals fractions are then routed to a heavy media sorter, which separates them into Alrich and Cu-rich fractions. The Al-rich fraction can be sold as is or routed to a third ECS for further refinement from the rubber, plastics and the remaining (RPR) fraction. The isolated RPR fraction can be either incinerated in a MSWI or land-filled. In an integrated EU-oriented vehicle recycling system, several waste management entities (landfills, MSWIs, ATT plants, and export to countries with low labour costs) are available for final waste processing and disposal. Along with steel, cooper and aluminium industries these entities constitute the last actor group. (insert Fig. 1)

3.3 Model A development – The ILP model for long-term planning of vehicle recycling It has been recognized that deterministic optimization techniques, such as linear programming, are not sufficient to model complex environmental engineering problems, particularly its uncertain features (Pei, 2011). Moreover, formulating a linear programming model requires specifying the values of different model coefficients that are essentially uncertain in reality and whose exact values cannot be known (Zou et al., 2010a), which is in detail commented in the Introduction. On the other hand, an interval system is defined as a system containing information presented as intervals (Wu et al., 2010). Based on the above definition, an interval model is an extension of present deterministic models. Since the vehicle recycling system is characterized with considerable, interval numbers are used to represent the uncertainty in the original linear programming framework proposed by Simic and Dimitrijevic (2012), which results in the ILP model for long-term planning in the EU vehicle recycling factories (Model A). Based on notations provided in the Appendix, the Model A is formulated as follows:

Max f ± =Total revenue (TR ) − Total cost (TC ) T

I −1

(A.1)

± ∑ Ri' i t X i' i t

(A.1.1)

TC = Hulk procurement cost (CP) + Storage cost (CI) + Sorting cost (CS) + Transportation cost of sorted materials (CT) + (Advanced) thermal treatment cost (CA) + Landfill disposal cost (CL)

(A.1.2)

TR = ∑

∑

t =1 i = I − M −1 i'∈Ωi

T

CP = ∑ CPt± Pt

(A.1.2.1)

t =1

9

T

CI = ∑ Z t± CPt± St

(A.1.2.2)

t =1

T I −I ' −2

CS = ∑

∑

t =1

i =1

T

I −1

CT = ∑

∑

CSi±t ∑ X i' i t

(A.1.2.3)

i'∈Ω i

± ∑ CTi' i t X i' i t

(A.1.2.4)

t =1 i = I − I ' i'∈Ω i T

CA = ∑ ∑ CAi±t ∑ X i' i t t =1 i∈D

(A.1.2.5)

i'∈Ω i

T

CL = ∑ CL±t ∑ X i 12 t t =1

(A.1.2.6)

i∈Ω12

subject to:

 Pt − X 01 t , if t =1 St =   Pt +St −1 − X 01 t , if t =2,...,T

(A.2)

± St ≥ S min , t = 1,...,T

(A.3)

± ∑ X i' i t ≤ Ci t , i = 1,...,I − I’ − 2; t = 1,...,T

(A.4)

∑

(A.5)

i' ∈Ω i

j'∈Ψ j

X i j' t = Ei j t ∑ X i' i t , i = 1,...,I − I’ − 2; j = Ai ; t = 1,...,T i'∈Ωi

X i j t = ∑ X i' i t , i = I − I’ − 1; j ∈ Φ i ; t = 1,...,T

(A.6)

i'∈Ωi

∑

± ∑ X i' i t + ∑ ERi ∑ X i' i t ≥ Q R X 01 t , t = 1,...,T

(A.7)

± ± ∑ X i' i t + ∑ ERi ∑ X i' i t + ∑ EEi ∑ X i' i t ≥ Q R' X 01 t , t = 1,...,T

(A.8)

i∈M i' ∈Ω i

∑

i∈F

i∈M i' ∈Ω i

i∈F

i' ∈Ω i

i' ∈Ω i

i∈D

± ∑ EEi ∑ X i' i t ≤ Q E X 01 t , t = 1,...,T

i∈D

i' ∈Ω i

(A.9)

i' ∈Ω i

Pt ≥ 0, St ≥ 0, t = 1,...,T

(A.10)

X i j t ≥ 0, i = 0,...,I − I’ − 1; j ∈ Φi ; t = 1,...,T

(A.11)

The goal of optimal planning in the EU vehicle recycling factories is to maximize profit over the planning horizon while meeting the EU ELV Directive eco-efficiency quotas. Profit is calculated by subtracting total cost (TC) from revenue (TR) (Eq. (A.1)). Revenue of the EU vehicle recycling factories is defined in Eq. (A.1.1), which computes income from the sorted metals sale. The components of TC are defined in Eq. (A.1.2). Eq. (A.1.2.1) calculates the procurement cost and Eq. (A.1.2.2) represents the storage cost of vehicle hulks that have not been assigned for recycling. Eq. (A.1.2.3) computes the cost of vehicle hulks shredding and further sorting of generated material fractions. Eq. (A.1.2.4) calculates costs associated with transportation to the final destinations. Eq. 10

(A.1.2.5) represents the cost of (advanced) thermal treatment in proper plant and Eq. (A.1.2.6) relates to landfill disposal cost of sorted waste materials. Constraints (A.2) enforce the inventory balances. Constraints (A.3) ensure the safety stock level of vehicle hulks in order to protect the shredder from starvation. Constraints (A.4) represent the processing capacity of sorting entities. Constraints (A.5) maintain material flow balances of sorting entities. The mixer has been defined in the model to combine the various waste fractions with the ASR mix fraction (constraints (A.6)). Constraints (A.7)-(A.9) represent specific eco-efficiency requirements imposed by the EU ELV Directive. More specifically, these constraints enforce that the percentage of recycling cannot be less than the prescribed recycling quota (constraints (A.7)), the percentage of recovery cannot be less than the prescribed recovery quota (constraints (A.8)), and the percentage of energy recovery cannot be larger than the prescribed energy quota (constraints (A.9)). Constraints (A.10)-(A.11) define the value domain (i.e. non-negativity) of decision variables. Model A can, obviously, deal with uncertainties in vehicle recycling problem. However, recently it has been identified that ILP solutions tend to generate unfeasible or non-optimal implementation schemes for actual decision making, i.e. schemes that violate the constraints of the model (Zhou et al., 2009). In addition, the interval ILP solutions were found to be unable to reflect the linkage and trade-off between decision risk and system performances (Liu et al., 2011), thus being ineffective in generating schemes for efficient and practical decision support.

3.4 Risk explicit interval linear programming approach Recently, Zou et al. (2010a) developed a REILP approach in order to eliminate the limitations and problems of the traditional ILP method. The novel approach overcomes both the problems of infeasibility and non-optimality of the ILP approach. In addition, it is able to obtain crisp solutions at each desired risk tolerance level providing for decision maker explicit risk reward trade-off information. This is REILP’s significant advantage over traditional ILP approach which lacks the capability of providing quantitative relationship between system performances and risk level. A REILP model can be formulated as follows (Pei, 2011; Zou et al., 2010a):

 n   n + −  Min ξ = ⊕i  ∑ λij aij+ − aij− x j + ηi bi+ − bi−  + ⊕k  ∑ λ j c +j − c −j x j + λ0 fopt − fopt   j =1   j =1 

(

)

(

(

)

)

(

)

(4)

subject to: n − + − − + − ∑  c j x j + λ j c j − c j x j  ≥ f opt + λ 0 f opt − fopt   j =1

(

)

n

n

j =1

j =1

(

(

)

(

)

)

+ − + − + − ∑ aij x j − bi ≤ ∑ λ ij aij − aij x j + ηi bi − bi , ∀i

(5)

(6)

λ 0 = λ pre

(7)

0 ≤ λij ≤ 1, ∀i,j

(8)

0 ≤ λ j ≤ 1, ∀j

(9)

x j ≥ 0, ∀j

(10)

where λ0 represents the system aspiration level; λij , λ j and ηi are real numbers; λ pre is prescribed system aspiration level; ξ is risk function of the entire system and it represents the risk 11

+ − of violating system constraints given the uncertainty in the optimization model; f opt and f opt are

the upper and the lower bound values of objective function obtained by solving traditional ILP problem (Eqs. (1)–(3)) with BWC algorithm respectively; and ⊕i and ⊕k are general arithmetic operators. The risk optimization problem (Eqs. (4)–(9)) is a nonlinear programming problem. The nonlinearity mainly originated from the introduction of unknown variables to represent the complex nonlinear interactions of uncertainties between different variables and terms in a constraint. Since, the REILP approach represents novel methodology, only few research papers have been carried out. Zou et al. (2010b) used the REILP algorithm and an inverse mapping scheme to obtain near optimal solutions of the simulation-optimization approach for a waste load allocation analysis. Zou et al. (2010a) pointed out that newly developed REILP methodology framework could be further employed to various environmental engineering decision making problems. Liu et al. (2011) developed REILP model for optimal load reduction at the watershed scale and demonstrated that, compared with ILP, the REILP model can generate solutions which explicitly relate system performance to risk level. Finally, Pei (2011) extended the REILP approach proposed by Zou et al. (2010a) in order to consider the risk of violating the original objective function.

3.5 Model B development – The REILP model for long-term planning of vehicle recycling Long-term optimization planning for vehicle recycling system is increasingly important for the EU. In order to meet the EU ELV Directive demand of three eco-efficiency quotas, and at the same time maximize system profit and minimize decision risk, the REILP model for long-term planning of vehicle recycling is formulated. Based on the methodology presented in the previous subsection, the REILP model for long-term planning in the EU vehicle recycling factories is a further extension of Model A, and can be written as follows (Model B): (B.1) Risk function: I −1 T T + − + − Min RISK =2λ 0  ∑ ∑ ∑ Ri' i t − Ri' i t X i' i t + ∑ CPt − CPt Pt t =1 t =1 i = I − M −1 i'∈Ωi

(

T

)

(

)

T I − I ' −2

+ ∑ Zt+ CPt+ − Zt−CPt− St + ∑ t =1

I −1

T

(

∑

t =1 i =1

)

(CSi+t − CSi−t ) i'∈∑Ω X i' i t i

T

CTi'+i t − CTi'−i t ) X i' i t + ∑ ∑ ( CAi+t − CAi−t ) ∑ X i' i t ( t =1 i = I − I ' i'∈Ω t =1 i∈D i'∈Ω

+∑

∑

∑

i

T

(

+ ∑ CL+t − CL−t t =1

(

+ − + 2λ1T Smin − Smin T

(

i

)

+ −  ∑ X i 12 t + fopt − f opt  i∈Ω12 

T

)

T I − I’ − 2

− + + S min ) ( Smin ) +2 ∑

+ ∑ ∑ λ3 i ERi+ − ERi− t =1 i∈F

(

∑

t =1 i =1

)

− + fopt + f opt

(

λ 2 i t Ci+t − Ci−t

) (Ci−t + Ci+t )

∑ X i' i t X 01t

i'∈Ωi

(

)

(

)

(

)

+ ∑  ∑ λ 4 i ERi+ − ERi− ∑ X i' i t + ∑ λ5 i EEi+ − EEi− ∑ X i' i t  X 01t  t =1 i∈F i'∈Ωi i∈D i'∈Ωi  T

+ ∑ ∑ λ 6 i EEi+ − EEi− t =1 i∈D

∑ X i' i t X 01t

i'∈Ωi

subject to: 12

(B.2) Model A objective constraint:

(

)

I −1

T

(

)

− + − ∑  Ri' i t + λ 0 Ri' i t − Ri' i t  X i' i t t =1 i = I − M −1 i'∈Ω

− + − f opt + λ 0 f opt − f opt ≤ ∑

∑

i

T

(

)

− ∑ CPt+ − λ 0 CPt+ − CPt−  Pt t =1 T

(

)

− ∑  Zt+ CPt+ − λ 0 Z t+ CPt+ − Z t−CPt−  St t =1 T I − I ' −2

(

)

CS + − λ CS + − CS −  ∑ X 0 it it  i' i t  it t =1 i =1 i'∈Ω i

−∑

∑

T

I −1

(

)

+ + − ∑ CTi' i t − λ 0 CTi' i t − CTi' i t  X i' i t t =1 i = I − I ' i'∈Ω

−∑

∑

i

T

(

)

− ∑ ∑ CAi+t − λ 0 CAi+t − CAi−t  ∑ X i' i t   i'∈Ω t =1 i∈D i

T

(

)

− ∑ CL+t − λ 0 CL+t − CL−t  ∑ X i 12 t t =1

i∈Ω12

(B.3) Inventory balances equations:  Pt − X 01 t , if t =1 St =   Pt +St −1 − X 01 t , if t =2,...,T (B.4) Safety stock level:

(

)

+ + −  − λ1 Smin − Smin St −  Smin  ≥ 0, t = 1,...,T

(B.5) Capacity constraints for sorting entities: − + − ∑ X i' i t − Ci t + λ 2 i t Ci t − Ci t  ≤ 0, i = 1,...,I − I’ − 2; t = 1,...,T i' ∈Ω

(

)

i

(B.6) Material flow balances equations: ∑ X i j' t = Ei j t ∑ X i' i t , i = 1,...,I − I’ − 2; j = Ai ; t = 1,...,T j'∈Ψ j

i'∈Ωi

(B.7) Mixing operations: X i j t = ∑ X i' i t , i = I − I’ − 1; j ∈ Φ i ; t = 1,...,T i'∈Ωi

(B.8) EU ELV Directive environmental constraints: (Recycling efficiency constraints) − + − ∑ ∑ X i' i t + ∑  ERi + λ3 i ERi − ERi  ∑ X i' i t −QR X 01t ≥ 0, t = 1,...,T i∈M i'∈Ωi

i∈F

(

)

i'∈Ωi

(Recovery efficiency constraints)

13

∑

(

)

− + − ∑ X i' i t + ∑  ERi + λ 4 i ERi − ERi  ∑ X i' i t

i∈M i' ∈Ω i

i∈F

(

)

i' ∈Ω i

+ ∑  EEi− + λ 5 i EEi+ − EEi−  ∑ X i' i t − QR' X 01 t ≥ 0, t = 1,...,T i∈D

i' ∈Ω i

(Energy recovery efficiency constraints) + + − ∑  EEi − λ6 i EEi − EEi  ∑ X i' i t X 01t ≤ QE , t = 1,...,T i∈D

(

)

i'∈Ωi

(B.9) Value domains of decision variables:

Pt ≥ 0, St ≥ 0, t = 1,...,T X i j t ≥ 0, i = 0,...,I − I’ − 1; j ∈ Φi ; t = 1,...,T (B.10) Prescribed system aspiration level: λ 0 = λ pre (B.11) Value domains of risk level variables:

0 ≤ λ1 ≤ 1 0 ≤ λ 2 i t ≤ 1, i = 1,...,I − I’ − 2; t = 1,...,T 0 ≤ λ3 i , λ 4 i ≤ 1, i ∈ F 0 ≤ λ5 i , λ6 i ≤ 1, i ∈ D The proposed model tackles the strategic, long-term vehicle recycling planning problem in the EU legislative context. It provides optimal plans for procuring vehicle hulks, sorting generated material fractions, allocating sorted waste flows and allocating sorted metals for desired decision risk levels. Note that symbols used in Model B are the same as those in Model A (Appendix) and Eqs. (4)-(10). Finally, the detailed algorithmic procedure to solve the Model B can be summarized as follows: • Step 1 − Formulate Model A. + • Step 2 − Use the BWC algorithm to split Model A into two sub-models, where f opt is desired

since the objective is to maximize profit. • Step 3 − Formulate the first sub-model of Model A, which corresponds to f + . + • Step 4 − Solve the f + sub-model and obtain solution of f opt .

• Step 5 − Formulate the second sub-model of Model A, which corresponds to f − . − • Step 6 − Solve the f − sub-model and obtain solution of f opt . • Step 7 − Using solutions obtained in Steps 4 and 6 solve Model B for a series of prescribed system aspiration level values to obtain corresponding optimal solutions for the minimized risk levels. • Step 8 − Derive normalized risk levels (NRLs) based on solutions of Model B such that the most pessimistic condition has a value of 0 and the most optimistic condition has a value of 1. • Step 9 − Generate a risk-return trade-off curves. • Step 10 − Stop.

14

4. Result analysis and discussion To test the proposed model, the necessary data from a significant number of peer-reviewed papers and published scientific studies were collected (data available in Supplementary material). Having in mind specific eco-efficiency requirements imposed by the EU ELV Directive, two legislative cases were considered: • Case 1 − valid eco-efficiency quotas (valid since January 1, 2006). The vehicle recycling factories have to guarantee that recycling rate and recovery rate do not fall under 80% and 85% respectively, and that the energy recovery rate does not exceed 5%. • Case 2 − future eco-efficiency quotas (valid beginning January 1, 2015). The vehicle recycling factories have to guarantee that recycling rate and recovery rate do not fall under 85% and 95% respectively, and that the energy recovery rate does not exceed 10%. In this case study, a total planning horizon of 6 years are to be considered: 3 years sub-horizon (2012-2014) for the first legislative case, and 3 years sub-horizon (2015-2017) for the second legislative case. In addition, to account for the dynamics of various modelling parameters, both long-term planning sub-horizons are further divided into three periods, each having a time interval of 1 year. In long-term planning of vehicle recycling, observing scrap metal prices as deterministic values is completely unacceptable. On the other hand, observing them as interval values is purely natural, either on a level of day, week, month or year. However, considerable uncertainty that is constantly present on scrap metal markets, a large number of various influential factors, non-existence of adequate studies dealing with long-term estimates of scrap metal prices, and inadequacy of forming scrap metal prices based on primary metal prices (Aruga and Managi, 2011; Xiarchos and Fletcher, 2009), imposes the necessity of a detailed analysis of multiple possible scenarios for both considered legislative cases. Having in mind that the world economy has overcome the recent economic crisis and that the expected recovery of the metal markets has already begun, in this case study three possible scrap metal price trends were examined: • Scenario 1 − slight volatility trend. The market prices for sorted metals and vehicle hulks slightly change at [-2.50, 2.50] %/year value interval. • Scenario 2 − moderate growth trend. The price values increase at [2.51, 5.0] %/year value interval. • Scenario 3 − strong growth trend. The price values increase at [5.1, 15.0] %/year value interval. For all investigated scenarios we formed 22 test problems (11 per each considered legislative case) by varying the system aspiration level value 0.0−1.0 interval with 0.1 step. As a result, 66 problem instances were created and comprehensively analysed. Additionally, optimal decisions for all created test problems were solved using the LINGO 13.0 solver on a Toshiba Qosmio with an Intel Core i5-430 M mobile technology processor. The CPU times for all test problems varied from less than one second to several seconds. Profits per tonne of processed hulks and normalized risk levels of the optimal decisions for 66 test problems are given in Table 1. Analysis of these results indicates that the more favourable the trend in scrap metal prices are the more optimistic the planning will be justified. So, for example, any incremental change of the system aspiration level in scenario 1 and scenario 3 will on average bring larger profits of 24.35 and 46.48 €/tonne for processed hulks respectively. The influence of the EU ELV Directive on the vehicle recycling factories business is also analysed. The introduction of stringent eco-efficiency quotas will not endanger their profitability, especially because of the expected recovery on scrap metal markets. Besides, additional testing of 33 test problems in Case 2 under valid eco-efficiency quotas led to the conclusion that the profit could be more than 7 €/tonne of processed hulks if quotas remained at the present level even after January 1, 2015. 15

(insert Table 1) Speaking of risk in general terms, the more distant the time period is for which the planning is done, the more considerable the uncertainty will be in terms of values of all model parameters (i.e. larger widths of corresponding interval numbers). Therefore, it is expected, but also justified, for the risk function to have a larger value in Case 2, because it covers period 2015-2017, than in Case 1 (2012-2014) (Fig. 2). In addition, risk analysis in the vehicle recycling system is additionally complicated by a considerable uncertainty on scrap metal markets. Interval widths of analysed trends have, in certain scenarios, direct influence on the values of the risk. Specifically, if the trend width is larger, the risk curve will move upwards, and vice versa. For this particular reason, the system risk is the greatest in scenario 3, followed by scenario 1 and scenario 2, because the interval widths of considered trends are 10%, 5% and 2.5% respectively. Illustratively speaking, a pessimistically oriented decision making (the system aspiration level has value close to 0) brings smaller value of risk function and substantial probability that the created plans will be thoroughly fulfilled. It is based on the following assumptions: the sorting equipment works at less capacity, more expensive sorting of generated material fractions, holding higher safety inventory level, greater inventory holding costs, lower recycling and/or energy efficiency of the optimal destinations, more expensive vehicle hulks procurement, smaller revenue from metals sales, more expensive transport to the optimal destinations, more expensive land-filling, incineration and advanced thermal treatment. Unused sorting capacities can be considered a major disadvantage causing smaller revenue from what was originally possible. On the other hand, optimistically oriented decision making (the system aspiration level has value close to 1) brings larger value of risk function and small probability that the created plans will be fulfilled at all. It is based on the assumptions contrary to the above mentioned, and a major disadvantage is a possibility of piling up inventories, because everything that has been procured cannot always be processed. Owing to the above mentioned, the obtained results (Tables 1 and 2) are helpful for production managers not only in making decisions about vehicle recycling planning, but also in gaining insight into the trade-offs between economic and system-risk objectives. For instance, the model’s sensitivity to variation of system aspiration level in scenario 1 is presented in Fig. 2. Large slope of both NRL curves is the consequence of considerable uncertainty (i.e. large number of influential factors) in the investigated system, which only additionally confirms that development of described model and detailed insight into obtained results are justified. For instance, supposing that with a generally hesitant decision maker, the value of normalized risk level 0.4 presents a turning point, i.e. the value above which he will not be willing to take any risks, it is clear that the system aspiration level will be up to 0.3 and 0.2 for Case 1 and Case 2 respectively. However, such an approach could result in the decrease of revenue for even 43.45 €/tonne, i.e. from 115.05 €/tonne in Case 1 with system aspiration level 0.3 to 71.60 €/tonne in Case 2 with system aspiration level 0.2. Such a result could be considered unacceptable, and taking more risks is considered justified especially if noted that the average profit in Case 2 is bigger than in Case 1 for approximately 4 €/tonne. Therefore, it is obvious that the obtained numerical results and the trade-offs between economic and system-risk objectives are valuable for supporting the EU vehicle recycling factories in creating optimal long-term production strategies, because they can provide a lot of valuable information for decision makers who understand the modelling approach and have specific aspiration levels when making their vehicle recycling decisions. (insert Fig. 2) Regarding the eco-efficiency, even the future quotas were reached in all corresponding test problems, so we are led to conclusion that the success of the final phase of implementation of the EU ELV Directive is not jeopardised. However, eco-efficiency quotas are attainable but only if vehicle recycling factories have a possibility to forward sorted waste fractions to MSWIs and/or 16

ATT plants for further processing. In addition, the number of ATT plants will undoubtedly grow after January 1, 2015, because their availability is the necessary requirement for the ultimate success of the already mentioned directive. The influence of decision risks on vehicle hulks procurement planning is identified in all analysed scenarios. The conducted testing showed that shredding rates, whose bounds were in [61.1, 81.3] tonne/h interval (supplementary Table S3), were the basis for creating the vehicle hulks procurement plan. Specifically, quantity of procured vehicle hulks was during each of the 6 considered planning periods (3 per each legislative case) in [158860, 211380] tonne interval; from the risk perspective , the lower-bound and the upper-bound values represent the optimal quantities in the most pessimistic (system aspiration level is 0) and the most optimistic (system aspiration level is 1) situations respectively. Therefore, it is evident that during every planning period the quantity of procured vehicle hulks was exactly the same as the maximum capacity of shredding. The exceptions to the above mentioned occur when there are big fluctuations in hulk costs. In that case, if hulk costs are expected to increase substantially and storage costs of vehicle hulks that have not been assigned for recycling are expected to be smaller than procurement in the next period (or periods), it would be possible to procure quantities larger than those that can be processed. As for the inventory management, their level was during entire testing equal to the safety inventory level. Safety inventories can be used only if the supply is suddenly terminated, most frequently because of bad traffic conditions. Safety inventories are planned in quantities that can supply at least a week of shredding. Finally, it has been identified that vehicle recycling factories favour the approach of ordering the exact quantities of hulks that can be processed, which clearly indicates their intention to avoid unnecessary costs for storing excess hulks. Table 2 presents, under different system aspiration levels, the values of the sorted waste flows allocated to ATT plants, MSWIs and landfills with the 3-year planning sub-horizon. Comparative analysis of the examined scenarios revealed that waste allocation schemes are just slightly influenced by the changes in scrap metal prices. Exceptions occur only when the prices on scrap metal markets are so unfavourable (i.e. low) that vehicle recycling factories decide to cease further production. Therefore, trade-off’s between sending various waste flows to ATT plants, MSWIs and/or landfills is under the dominant influence of the corresponding gate fees (supplementary Table S6) and eco-efficiency quotas. Comparative analysis of the examined legislative cases verifies that the EU ELV Directive has crucial influence on decision making about sorted waste flow allocation. In case of valid ecoefficiency quotas, i.e. Case 1, owing to generally higher costs of advanced thermal treatment compared to the costs of incineration in MSWIs, and the possibility to reach imposed eco-efficiency quotas even when ATT plants are excluded from the vehicle recycling process, routing of sorted waste materials to ATT plants was not identified in any of the three scenarios. Therefore, the entire quantity of sorted waste materials is allocated between landfills (from 59.55% in scenario 3, when system aspiration level is 0.1, to 87.42% in most optimistic instances) and MSWIs (from 12.58% in most optimistic instances to 40.45% in scenario 3, when system aspiration level is 0.1). In reference to Case 2, the biggest share of sorted waste materials is routed to MSWIs (from 46.29% in most pessimistic instances to 54.39% in scenario 1, when system aspiration level is 0.1), a somewhat smaller share is forwarded to ATT plants (from 35.67% in scenario 1, when system aspiration level is 0.1, to 43.44% in most pessimistic instances). Presently preferred entities for sending sorted waste materials, i.e. landfills, will in the second implementation phase of the EU ELV Directive be lowered to the third place. Specifically, [9.94, 12.63]% of sorted waste is shipped to the landfills, where the lower-bound and the upper-bound values represent the optimal waste allocation plan with the system aspiration level from 0.1-0.8 and 0.9-1 respectively. (insert Table 2) 17

Analysis of waste flow allocation in the considered legislative cases (Fig. 3) led to the conclusion that the introduction of the stringent eco-efficiency quotas will radically reduce the quantity of land-filled wastes fraction. Particularly, waste quantities routed to the landfills will be reduced from 3.5 times (when system aspiration level is 0 and 1 in Cases 1 and 2 respectively) to 11.0 times (when system aspiration level is 1 and 0 in Cases 1 and 2 respectively). On the other hand, the planned 10% and 5% increase of recovery and recycling quotas respectively, will dictate that one share sorted waste flows which from January 1, 2015 will not be able to be routed to the landfills is forwarded to MSWIs and/or ATT plants. The corresponding gate fees in particular will have the crucial influence in reallocation of “excess” waste flows between these two network entities. In addition, it should be emphasized that their entire forwarding to MSWIs will not be possible, because the energy recovery constraint stays in force, with increase to 10%. Introducing stringent recovery/recycling quotas, waste combustion in MSWIs will increase up to 4.4 times, while the highest increase was noted when the system aspiration level was equal to 0.8 in Case 2 of scenario 1, and was equal to 1 in Case 1. The waste shipped to the ATT plants would be larger in quantities than the waste shipped to the landfills. In detail, waste transported to the ATT plants would be [31776, 38773] tonnes in Case 2, where the lower-bound and the upper-bound values represent the optimal sorted waste allocation plan with the system aspiration level 0.1 (scenario 2) and 1 respectively. Finally, it should be highlighted that the above conclusions are fully in compliance with expectations of the EU policy makers and their intent to create a sustainable EU vehicle recycling system. (insert Fig. 3) The influence of decision risks on sorted waste flow allocation is clearly identified in all analysed scenarios. For instance, Fig. 4 displays the REILP model’s sensitivity to a variation of system aspiration level in scenario 3. It is noticeable in Fig. 4 that the risk growth influences the increase of the total quantity of sorted waste flows. A practical question can immediately be asked: Why should more risk be taken if it leads to larger waste quantities in both observed legislative cases? The answer might be in the opportunity to increase the level of made profit by processing more vehicle hulks. Specifically, the revenue from the sales of excess quantities of sorted metal flows surpasses the costs of sending the resulting waste to selected optimal destinations. On the other hand, the increase of the system aspiration level did not have a more significant influence on the quantity of sorted waste flows allocated to MSWIs, ATT plants and landfills (Fig. 4). However, three exceptions to this rule can be clearly identified in Fig. 4. The first exception occurs when the aspiration level is increased from 0 to 0.1 in Case 1, when approximately 4,800 tonne from the additional 9,100 tonne of sorted waste is routed to MSWIs. Then, the share of incinerated waste reaches its maximum value of 40.45%. This decision results from assigning value 1 to the risk level variable of MSWI energy recovery efficiency, instead of 0 that it originally had. The second exception also occurs in Case 1. Specifically, increasing the system aspiration level from 0.9 to 1 results in sending almost 30,000 tonne more of sorted waste to landfills than what was previously routed to ATT plants. This comes as the result of risk level variables of manual recycling efficiency in countries with low labour costs and energy recovery efficiency in MSWIs, λ 4 16 and

λ5 11 respectively, taking values 1 instead of 0 that they have previously used. Therefore, this reallocation is based on expectations that the energy and recycling efficiency of MSWIs and export entities will be equal to the corresponding upper-bound values (supplementary Table S7). Finally, the last exception was identified in Case 2 where the system aspiration level’s value was greater than 0.8. The land-filling then grows to for approximately 2,900 tonnes as a consequence of the standpoint that it can be compensated by more efficient manual recycling and advanced thermal treatment, as well as larger energy efficiency of the MSWIs. Particularly, risk level variables λ 4 16 and λ5 11 , and risk level variables of ATT plant recycling efficiency, λ5 10 , increase from 0.273, 18

0.02 and 0.03 to 1 respectively. Reallocation of sorted waste to landfills in Case 2 (exception 3) is over ten times less than in Case 1 (exception 2), which is a direct consequence of introducing the stringent recycling/recovery quotas, meaning significantly less flexibility of the recycling system. (insert Fig. 4) Creating the sorted metals allocation plan is much simpler than creating the waste allocation plan, because ecological requirements of the EU ELV Directive have no influence over it. Moreover, each sorted metal has its natural destination (Fig. 1); for instance, Cu-rich and final Fe metals fractions are always sold to copper and steel production plants respectively. Alternatively, it is recognized that export possibilities of insulated copper wire have primacy over land-filling. Such a decision is fully expected because its export can be useful for two reasons: the recycling rate and the level of profits reached will grow. However, it should be mentioned that the implementation of this decision is primarily influenced by the demand of the international scrap market. Regarding the sorting decisions, it has been clearly identified that the vehicle recycling factories aim at reaching the highest possible level of quantity and quality of sorted metal flows, regardless of the level of eco-efficiency quotas. Both ASR fractions are always mechanically recycled, primarily in order to isolate valuable NF metals. The Al-rich fraction is always additionally purified, because the additional income always exceeds the costs of its sorting. That is why none of the test problems identify sales of the Al-rich fraction to aluminium production plants, but exclusively Al fraction.

5. Conclusions A risk explicit interval linear programming model for optimal long-term planning in the EU vehicle recycling factories has been developed in this paper. The proposed model has been applied to a case study in which three scrap metal price trends under two EU ELV Directive legislative cases were examined. The merit of the presented numerical study is manifold. Firstly, the potentials and applicability of the developed model are fully illustrated. Secondly, the influences of the EU ELV Directive and the system risk level on the procuring, sorting, sorted waste allocation and sorted metals allocation decisions were thoroughly examined. Thirdly, detailed insights on the profitability and eco-efficiency of the EU vehicle recycling factories were presented. Lastly, the numerical results can help quantify the relationships between system performances and risk levels, and thus desired decision schemes were provided. The developed model can create the optimal plans for procuring vehicle hulks, sorting generated material fractions, allocating sorted waste flows and allocating sorted metals for the desired value of the system aspiration level. Testing the proposed model proved that the vehicle recycling factories aim at reaching the highest possible level of quantity and quality of sorted metal flows, regardless of the level of eco-efficiency quotas. The influence of decision risks on vehicle hulks procurement planning is recognized in all created test problems, since the starting point for the creation of the vehicle hulks procurement plan are shredding rates. With regard to inventory management, it has been identified that a more favourite approach is the one of procuring the exact quantities of vehicle hulks that can be processed. Ecological requirements of the EU ELV Directive do not influence the creation of sorted metals allocation plan, because each sorted metal has its own natural destination. On the other hand, comparative analysis of examined scenarios revealed that waste allocation schemes are only slightly influenced by the changes in the scrap metal prices and that the trade-off between sending various waste flows to ATT plants, MSWIs and/or landfills is under the dominant influence of the corresponding gate fees and eco-efficiency quotas. Analyzing the waste flow allocation in two analysed legislative cases led to conclusion that introduction of the stringent ecoefficiency quotas will radically reduce the quantity of land-filled wastes; waste quantities routed to the landfills will be reduced from 3.5 to 11.0 times, the waste shipped to the ATT plants will be larger in quantity than the waste shipped to the landfills, while the waste combustion in MSWIs will 19

increase to up to 4.4 times. The influence of the EU ELV Directive on the vehicle recycling factories business is thoroughly analysed. The introduction of stringent eco-efficiency quotas will not endanger their profitability, but it was noticed that the revenue could exceed 7 €/tonne of processed hulks if quotas remained at present level even after January 1, 2015. Regarding ecoefficiency, even the future quotas were reached in all created test problems, so we are led to conclude that the success of the final phase of implementation of the EU ELV Directive is not jeopardised. Finally, it is obvious that the presented numerical results and the trade-offs are valuable for supporting the EU vehicle recycling factories in creating optimal long-term production strategies and to reduce the risk of uncertain situations, because they could provide a lot of valuable information for recycling managers who understand the modelling approach and have specific aspiration levels in making their decisions. The proposed model is applicable only in the EU legislative context. However, having in mind that there are countries with modern ELV legislation around the world, such as China, Korea and Japan, adapting this model in order to comply also with characteristics of some other vehicle recycling systems and their eco-requirements can certainly be considered a field of future interest. On the other hand, it should be noted that vehicle recycling problem is characterized by substantial uncertainty and that it won’t always be justified for certain reasons to observe all modelling data as interval values. For instance, the processing rates of sorting equipment may fluctuate unintentionally in the considered planning horizon caused by the variations of material flow composition and equipment conditions. A potential approach for overcoming this problem could be sought in the implementation of the concept of dual intervals in the proposed modelling framework. This novel concept of dual interval (being the interval-boundary interval) should preferably be used when highly uncertain information exists in the boundaries of some interval parameters, and its implementation in the vehicle recycling planning could present another direction for further research.

Appendix: Notation Indices and sets: i index of entity (i.e. sorting equipment and manual processes, storage, mixer and destinations); i∈{0,…,I-1} j index of material flow; j∈{1,…,J} t index of time period; t∈{1,…,T} Ai set of material flows isolated with sorting entity i; i∈{1,…,I-I’-2}

Ψj

set of entities on which material flow j is forwarded; j∈{2,…,J}

Ωi

set of entities that route materials to entity i; i∈{1,…,I-1}

Φi

set of entities on which materials are routed from entity i; i∈{0,…,I-I’-1} set of destinations where material recycling take place set of various metal producers in EU member state set of destinations where energy recovery takes place

F M D

Parameters: I number of entities J number of material flows T number of analysed time periods I’ number of destinations ± S min

safety inventory level

Ci±t

processing capacity in the case of entity i and period t 20

ERi±

recycling efficiency of destination i in percentages

EEi±

energy efficiency of destination i in percentages

Ei jt

efficiency of sorting entity i in the case of material flow j and period t in percentages

QR QR’ QE

EU recycling quota EU recovery quota EU energy quota

Ri'±i t

revenue from each unit weight of metal fraction sorted on entity i and sold to destination i’ in time period t

CAi±t

(advanced) thermal treatment cost in destination plant i and period t per weight unit

CL±t

land-filling cost per weight unit in period t

CPt±

procurement cost per weight unit in period t

Zt±

percentage of capital cost for inventory in period t

CSi±t

sorting cost per weight unit in the case of entity i and period t

CTi'±i t transportation cost from entity i’ to i in period t per weight unit

Variables: St weight of vehicle hulks in storage at the end of period t

Pt weight of incoming procurement in period t X i i' t weight of material flow routed from entity i to i’ in period t

Acknowledgment This work was partially supported by Ministry of Science and Technological Development of the Republic of Serbia through the project TR 36006 for the period 2011-2014.

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Figure captions Fig. 1. Flow diagram of the EU vehicle recycling system. Fig. 2. Profit per tonne of hulks processed under different normalized risk levels, with corresponding aspiration levels in scenario 1. Fig. 3. Waste flow allocation in planning horizon. Fig. 4. Comparison of optimal waste allocation decisions in scenario 3.

Table captions Table 1 Case study profits in €/tonne and normalized risk levels. Table 2 Optimal allocation of sorted waste flows under different system aspiration levels (1,000 tonne).

25

Vehicle users

Heavy materials (j=2)

Hulks shipment

Last owners

Collection agents

Ferrous metals 1 (j=4)

Storage (i=0) Hulks (j=1)

ELVs

Dismantling companies Sale prices

Vehicles

Hulks cost

Shredding/ Air suction (i=1)

Nonmetals 1 (j=9)

Light ASR (j=3)

Eddy current sorter 1 (i=4) NF metals 1(j=8)

Parts

Usable parts market

ELVs

New vehicle buyers

Heavy ASR (j=5)

ELVs

Vehicles

Secondhand vehicle buyers

Magnetic sorter 1 (i=2)

Magnetic sorter 2 (i=3)

Ferrous metals 2 (j=6)

NF mix (j=7)

NF metals 2 (j=10)

Heavy media sorter (i=6)

Cu-rich fraction (j=13)

Al-rich fraction (j=12)

Metals

Scrap metal market The second actor’s group

Manual separation (i=8)

Cu wires (j=17)

Final Fe metals (j=16)

Eddy current sorter 3 (i=7)

Al fraction (j=14)

RPR (j=15)

Eddy current sorter 2 (i=5) Flow of materials

Non-metals 2 (j=11)

Flow of money

Mixer (i=9) Vehicle recycling factory

ASR mix (j=18)

Sale prices

ATT cost

ATT plant (i=10)

MSWI cost

MSWI (i=11)

LD cost

The fourth actor’s group Landfill (i=12)

Copper production (i=13)

Aluminium production (i=14)

Steel production (i=15)

Export (i=16)

Fig. 1. Flow diagram of the EU vehicle recycling system.

26

1.0 0.9 0.8

250

0.7 200 0.6 0.5

150

0.4

Profit (€/tonne)

Normalized risk level

300

Risk (case 1) Risk (case 2) Profit (case 1) Profit (case 2)

100

0.3 0.2

50 0.1 0.0

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

System aspiration level

Fig. 2. Profit per tonne of processed hulks under different normalized risk levels, with corresponding aspiration levels in scenario 1.

27

Quantity (1,000 tonne)

100

92.07

80 58.42

60 48.21 41.05

38.77

37.60

40

31.78

20

13.65 8.34

13.25

0 Landfill

MSWI

ATT plant

Valid eco-efficiency quotas (2011-2014)

Landfill

MSWI

ATT plant

Future eco-efficiency quotas (2015-2017)

Fig. 3. Waste flow allocation in planning horizon.

28

1.0 100

0.9

80

0.7 0.6

60 0.5 0.4

40

0.3 0.2

Quantity (1,000 tonne)

Normalized risk level

0.8

20

0.1 0.0

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

System aspiration level Risk (case 1) MSWIs (case 1) Landfills (case 1) ATT plants (case 1) Total (case 1)

Risk (case 2) MSWIs (case 2) Landfills (case 2) ATT plants (case 2) Total (case 2)

Fig. 4. Comparison of optimal waste allocation decisions in scenario 3.

29

Table 1 Case study profits in €/tonne and normalized risk levels. Scenario Case 1

1 2

2

1 2

3

1 2

Measure System aspiration level 0 0.1 0.2 Profit 55.44 76.31 95.78 NRL 0.0 0.1581 0.2884 Profit 11.97 43.18 71.60 NRL 0.0 0.2465 0.3812 Profit 86.62 104.56 122.33 NRL 0.0 0.1438 0.2594 Profit 90.33 115.93 140.63 NRL 0.0 0.1516 0.2722 Profit 68.83 98.10 127.68 NRL 0.0 0.1849 0.3044 Profit 22.30 88.56 152.40 NRL 0.0 0.3319 0.4565

0.3 115.05 0.3930 100.18 0.4671 139.86 0.3582 165.14 0.3718 157.15 0.3962 216.53 0.5403

0.4 134.22 0.4817 128.91 0.5366 157.43 0.4447 189.57 0.4578 186.16 0.4780 280.41 0.6147

0.5 153.68 0.5581 157.77 0.5992 174.76 0.5245 213.66 0.5368 214.82 0.5529 344.18 0.6844

0.6 173.36 0.6256 186.62 0.6584 191.98 0.5985 237.71 0.6092 243.32 0.6224 407.88 0.7514

0.7 192.89 0.6893 215.45 0.7160 209.16 0.6676 261.71 0.6767 271.69 0.6878 471.54 0.8167

0.8 212.37 0.7503 244.27 0.7726 226.31 0.7328 285.69 0.7405 299.98 0.7503 535.18 0.8809

0.9 231.80 0.8091 273.11 0.8283 243.44 0.7950 309.68 0.8014 328.21 0.8105 598.83 0.9442

1 252.14 1.0 302.31 1.0 261.54 1.0 334.14 1.0 357.56 1.0 663.09 1.0

30

Table 2 Optimal allocation of sorted waste flows under different system aspiration levels (1,000 tonne). Scenario

Case

Entity

1

1

Landfill MSWI ATT Landfill MSWI ATT Landfill MSWI ATT Landfill MSWI ATT Landfill MSWI ATT Landfill MSWI ATT

2

2

1

2

3

1

2

System aspiration level 0 0.1 0.2 48.21 51.51 54.81 30.95 34.98 37.22 0.00 0.00 0.00 8.34 9.53 10.15 37.60 52.14 55.45 35.29 34.20 36.50 48.21 50.93 53.64 30.95 34.49 36.32 0.00 0.00 0.00 8.34 8.76 9.26 37.60 47.64 50.31 35.29 31.78 33.61 48.21 52.58 55.58 30.95 35.71 37.63 0.00 0.00 0.00 8.34 9.87 10.30 37.60 53.98 56.05 35.29 35.43 37.26

0.3 57.10 38.77 0.00 10.40 56.77 37.46 56.97 36.52 0.00 9.62 52.27 34.91 58.64 37.59 0.00 10.45 56.94 37.79

0.4 60.09 38.61 0.00 10.53 57.44 37.94 58.62 37.58 0.00 9.89 53.74 35.88 60.04 38.50 0.00 10.55 57.47 38.11

0.5 61.32 39.36 0.00 10.60 57.77 38.29 60.01 38.48 0.00 10.11 55.00 36.63 61.15 39.23 0.00 10.61 57.83 38.33

0.6 62.18 39.89 0.00 10.65 58.05 38.46 61.18 39.24 0.00 10.29 56.02 37.24 62.05 39.81 0.00 10.66 58.08 38.48

0.7 62.87 40.35 0.00 10.69 58.26 38.58 62.17 39.89 0.00 10.44 56.86 37.74 62.78 40.29 0.00 10.69 58.28 38.59

0.8 63.45 40.73 0.00 10.72 58.42 38.68 63.01 40.44 0.00 10.56 57.56 38.17 63.39 40.68 0.00 10.72 58.42 38.68

0.9 63.95 41.05 0.00 13.65 55.64 38.76 63.74 40.92 0.00 13.56 55.27 38.52 63.91 41.02 0.00 13.64 55.63 38.75

1 92.07 13.25 0.00 13.65 55.67 38.77 92.07 13.25 0.00 13.65 55.67 38.77 92.07 13.25 0.00 13.65 55.67 38.77

31

HIGHLIGHTS: > A REILP model for optimal long-term planning in the EU vehicle recycling factories is proposed. > The model creates optimal plans for procuring, sorting and allocating waste and metals for the desired risk levels. > A numerical study demonstrated the potentials and applicability of the developed model. > Detailed insights on the profitability and eco-efficiency are presented. > Quantity of land-filled wastes will be radically reduced after January 1, 2015.

32

Supplementary material – Data collection

This supplement contains the data used in the case study presented in the accompanying article. According to the EU ELV Directive, vehicle is defined as any vehicle designated as class M1 (passenger vehicles with less than eight seats in addition to the driver's seat) or N1 (vehicles used for the carriage of goods whose maximum weight does not exceed 3.5 tonnes), and three-wheel motor vehicles (Vidovic et al., 2011). In this case study, the inventory lists of M1 and N1 vehicle classes are based on data reported in Cheah et al. (2007), Davis et al. (2010), Jody et al. (2010). In addition, data regarding what and to what extent dismantlers take apart certain components, as well as their material composition is taken into consideration (Eurostat, 2012b; IDIS, 2011). The material composition of the light and heavy automobile shredder residue (ASR) fraction is in accordance with Gaillot and McCormack (2010). Finally, the values of sorting entities efficiency are simulated using the post-fragmentation separation model (SMART, 2006), and they are given in Table S1. Table S1 Efficiency of sorting entities in percentages. Entity

Material fraction

Shredder

Heavy materials Light ASR Magnetic sorter Ferrous metals 1 Heavy ASR Ferrous metals 2 NF mix Eddy current sorter NF metals 1 Non-metals 1 NF metals 2 Non-metals 2 Al fraction RPR Heavy media sorter Al-rich fraction Cu-rich fraction Manual separation Final Fe metals Cu wires

t=1 79.08 20.92 90.41 9.59 4.37 95.63 53.32 46.68 38.23 61.77 95.52 5.48 87.02 12.98 99.65 0.35

Case 1 t=2 78.72 21.28 90.16 9.84 4.28 95.72 53.93 46.07 38.73 61.27 94.68 5.32 87.58 12.42 99.65 0.35

t=3 78.36 21.64 89.90 10.10 4.20 95.80 54.54 45.46 39.24 60.76 94.83 5.17 88.12 11.88 99.64 0.36

t=1 78.0 22.0 89.65 10.35 4.12 95.88 55.16 44.84 39.74 60.26 94.98 5.02 88.65 11.35 99.64 0.36

Case 2 t=2 77.64 22.36 89.38 10.62 4.02 95.98 55.76 44.24 40.24 59.76 95.11 4.89 89.17 10.83 99.63 0.37

t=3 77.28 22.72 89.12 10.88 3.94 96.06 56.37 43.63 40.74 59.26 95.23 4.77 89.68 10.32 99.62 0.38

NF, non-ferrous; RPR, rubber, plastics and the remaining fraction

When performing long-term planning for the vehicle recycling system, particular attention should be paid to the processing workflow. Because the analysed sorting process is continuous (Fig. 1 of the accompanying article), the processing rates of magnetic sorters, heavy media sorter and manual separations are calculated based on the processing rates of shredder and eddy current sorters, and the processing efficiencies from Table S1. The obtained values and the corresponding sorting costs are summarised in Tables S2 and S3 respectively. Table S2 Processing rates of sorting entities (tonne/h). Entity Shreddera Magnetic sorter Eddy current sorterb Heavy media sorter Manual separation

t=1 [61.1, 81.3] [47.55, 65.33] [18.3, 30.5] [18.3, 30.5] [43.06, 60.48]

Case 1 t=2

t=3

t=1

Case 2 t=2

t=3

[47.33, 65.04]

[47.11, 64.74]

[46.89, 64.45]

[46.67, 64.15]

[46.45, 63.86]

[42.74, 60.06]

[42.41, 59.63]

[42.09, 59.21]

[41.76, 58.77]

[41.44, 58.34]

a

Based on data from Harris (2012) and Simic and Dimitrijevic (2012). b According to Kumar and Sutherland (2008) and Simic and Dimitrijevic (2012).

33

Table S3 Sorting costs (€/tonne). Entity a

Shredder a Magnetic sorter a Eddy current sorter a Heavy media sorter b Manual separation

t=1 [53.73, 71.49] [3.36, 4.61] [2.07, 3.45] [76.67, 85.88] [1.21, 1.71]

Case 1 t=2 [54.92, 73.08] [3.45, 4.74] [2.11, 3.52] [78.37, 87.78] [1.22, 1.73]

t=3 [56.01, 74.52] [3.53, 4.85] [2.15, 3.59] [79.92, 89.52] [1.23, 1.74]

t=1 [57.01, 75.85] [3.61, 4.96] [2.19, 3.66] [81.35, 91.12] [1.23, 1.76]

Case 2 t=2 [57.93, 77.09] [3.69, 5.07] [2.23, 3.71] [82.67, 92.60] [1.23, 1.76]

t=3 [58.80, 78.25] [3.76, 5.17] [2.26, 3.77] [83.91, 93.99] [1.23, 1.77]

a

Forecasted by considering the electricity prices for medium size industrial consumers in the EU (Eurostat, 2012a) and data from Simic and Dimitrijevic (2012) b Forecasted by considering the hourly labour costs in the EU waste management industry (Eurostat, 2012e) and data from Williams et al. (2007) and Simic and Dimitrijevic (2012)

Transportation cost intervals are forecasted by considering the annual average indices for transport prices in the EU (Eurostat, 2012c), the specific densities of individual shipments, the maximum weight and volume per truckload, and the corresponding transportation distances (Table S4). Table S4 Transportation costs (€/tonne). Material Destination Case 1 Case 2 fraction t=1 t=2 t=3 t=1 t=2 t=3 Non-ferrous mix Landfilla [6.66, 10.39] [6.78, 10.66] [6.90, 10.93] [7.01, 11.22] [7.13, 11.51] [7.25, 11.82] Non-metals 1 Landfill [8.79, 16.80] [8.95, 17.23] [9.10, 17.67] [9.26, 18.30] [9.41, 18.61] [9.56, 19.10] Non-metals 2 Landfill or MSWIa [11.23, 19.46] [11.43, 19.96] [11.63, 20.48] [11.82, 21.01] [12.02, 21.56] [12.22, 22.13] RPR Landfill or MSWI [12.76, 21.30] [12.98, 21.84] [13.21, 22.41] [13.43, 22.99] [13.66, 23.59] [13.88, 24.22] Insulated copper Landfill [6.66, 10.0] [6.78, 10.25] [6.90, 10.52] [7.01, 10.79] [7.13, 11.07] [7.25, 11.37] wires Exportb [100.0, 150.0][101.76, 153.83][103.51, 157.80] [105.27, 161.91][107.02, 166.16][108.78, 170.55] Cu-rich Cupper productionc [13.34, 20.0] [13.57, 20.51] [13.80, 21.04] [14.04, 21.59] [14.27, 22.16] [14.51, 22.74] Al-rich Aluminium productionc Aluminium Final Fe metals Steel productionc ASR mix ATT plantd [10.18, 10.25] [10.36, 10.51] [10.54, 10.79] [10.71, 11.07] [10.89, 11.36] [11.07, 11.66]

MSWI, municipal solid waste incinerator; RPR, rubber, plastics and the remaining fraction; ATT, advanced thermal treatment a The closest landfill and municipal solid waste incinerator (MSWI) are approximately twice as close as metal production plants (i.e. the truckload cost is €[200.0, 300.0]) b The high cost is inevitable because intercontinental transportation must have multimodal character c All sorted metals are transported over the same distances and the cost per truckload is €[400.0, 600.0] d Based on recommendations and data from Ciacci et al. (2010) and Simic and Dimitrijevic (2012)

In the case study presented in the accompanying article, several trends of change in scrap metal prices were analysed in the long run. The lower- and upper-bound values of vehicle hulk costs and sorted metal prices in 2011 were used as a basis for creating the three possible scrap metal price trends for a six-year planning horizon (Table S5). The land-filling and MSWI costs are forecasted by considering the harmonised indices of consumer prices (HICPs) for corresponding EU member state (Eurostat, 2012d), due to recommendation from CEWEP (2012). On the other side, the adjustment of ATT cost intervals is performed in accordance with HICP values for the EU (Eurostat, 2012d). The obtained values are given in Table S6.

34

Table S5 Vehicle hulk costs and sorted metal prices (€/tonne). Trend Slight volatility

Moderate grow

Strong growth

Scrap metal type Vehicle hulk Ferrous metal Al-rich fraction Aluminium fraction Cu-rich fraction Insulated copper wires Vehicle hulk Ferrous metal Al-rich fraction Aluminium fraction Cu-rich fraction Insulated copper wires Vehicle hulk Ferrous metal Al-rich fraction Aluminium fraction Cu-rich fraction Insulated copper wires

Year 2011 a

[156.76, 208.43] b [304.61, 327.78] [1352.01, 1434.43]c [1487.21, 1721.32]d [2074.99, 2633.64]e [1289.30, 3192.29]f

t=1 [152.85, 213.64] [296.99, 335.97] [1318.21, 1470.29] [1450.03, 1764.35] [2023.12, 2699.48] [1257.06, 3272.10] [160.70, 218.85] [312.25, 344.17] [1385.95, 1506.15] [1524.54, 1807.39] [2127.07, 2765.32] [1321.66, 3351.91] [164.76, 239.69] [320.14, 376.95] [1420.96, 1649.59] [1563.06, 1979.52] [2180.82, 3028.69] [1355.05, 3671.14]

Case 1 t=2 [149.02, 218.98] [289.57, 344.37] [1285.25, 1507.04] [1413.78, 1808.46] [1972.54, 2766.97] [1225.64, 3353.90] [164.73, 229.79] [320.09, 361.38] [1420.73, 1581.46] [1562.80, 1897.76] [2180.46, 2903.59] [1354.83, 3519.50] [173.16, 275.64] [336.47, 433.49] [1493.43, 1897.03] [1642.77, 2276.45] [2292.04, 3482.99] [1424.16, 4221.81]

t=3 [145.30, 224.45] [282.33, 352.98] [1253.12, 1544.72] [1378.43, 1853.67] [1923.22, 2836.14] [1195.0, 3437.75] [168.87, 241.28] [328.13, 379.45] [1456.39, 1660.53] [1602.03, 1992.64] [2235.19, 3048.77] [1388.84, 3695.48] [181.99, 316.99] [353.63, 498.51] [1569.60, 2181.58] [1726.56, 2617.91] [2408.93, 4005.44] [1496.79, 4855.08]

t=1 [141.67, 230.06] [275.27, 361.81] [1221.80, 1583.34] [1343.97, 1900.02] [1875.14, 2907.05] [1165.12, 3523.69] [173.11, 253.34] [336.36, 398.42] [1492.95, 1743.55] [1642.24, 2092.28] [2291.30, 3201.21] [1423.70, 3880.25] [191.28, 364.54] [371.67, 573.29] [1649.65, 2508.82] [1814.61, 3010.60] [2531.79, 4606.26] [1573.13, 5583.34]

Case 2 t=2 [138.12, 235.81] [268.39, 370.85] [1191.25, 1622.92] [1310.37, 1947.52] [1828.27, 2979.27] [1135.99, 3611.79] [177.45, 266.01] [344.80, 418.34] [1530.42, 1830.73] [1683.46, 2196.89] [2348.81, 3361.27] [1459.43, 4074.27] [201.03, 419.22] [390.62, 659.28] [1733.78, 2885.14] [1907.15, 3462.19] [2660.91, 5297.20] [1653.36, 6420.84]

t=3 [134.67, 241.71] [261.68, 380.12] [1161.47, 1663.50] [1277.61, 1996.20] [1782.56, 3054.22] [1107.59, 3702.08] [181.91, 279.31] [353.46, 439.26] [1568.84, 1922.27] [1725.72, 2306.73] [2407.76, 3529.33] [1496.06, 4277.98] [211.28, 482.10] [410.54, 758.18] [1822.20, 3317.92] [2004.42, 3981.52] [2796.61, 6091.77] [1737.68, 7383.97]

a

The price for a “vehicle auto body” obtained from 5 US export yards (AMM, 2012) Determined as the selling price for “ferrous shredded auto scrap” from the Birmingham metal market AMM (2012) c Determined as a price for “nonferrous auto shred (90% aluminium) for secondary smelters” (AMM, 2012) d Priced as 110-120% of Al-rich fraction price e The price for “mixed yellow brass turnings, borings copper scrap” from 14 US and 2 Canadian dealers (AMM, 2012) f Based on individual buy-sell agreements from Recycler’s World (2012) for waste flow labelled as “Druid” (ISRI, 2012) b

Table S6 Land-filling, MSWI and advanced thermal treatment costs (€/tonne). Cost Land-fillinga MSWIb ATTc

t=1 [22.72, 196.72] [33.77, 147.04] [121.20, 207.40]

Case 1 t=2 [22.84, 203.41] [33.94, 152.77] [122.41, 215.07]

t=3 [22.95, 210.32] [34.11, 158.73] [123.64, 223.03]

t=1 [23.07, 217.47] [34.28, 164.92] [124.87, 231.28]

Case 2 t=2 [23.18, 224.87] [34.45, 171.35] [126.12, 239.84]

t=3 [23.30, 232.51] [34.62, 178.04] [127.38, 248.72]

ATT, advanced thermal treatment a According to costs in 14 EU member countries that provided data about land-filling to Confederation of European waste-to-energy plants (CEWEP), where lower-bound and upperbound values correspond to the lowest cost in Czech Republic and the highest cost in Norway (CEWEP, 2012) b According to costs in 11 EU member countries that made available data to CEWEP, where lower-bound and upper-bound values correspond to the lowest cost in Portugal and the highest cost in Finland (CEWEP, 2011) c Based on data from GHK/BioIS (2006), Warner and Brown (2008) and Simic and Dimitrijevic (2012), and recommendation from Vigano et al. (2010)

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The remaining modelling parameters are provided in Table S7. Table S7 Additional modelling parameters. Description Planning sub-horizon Safety inventory level Percentage of capital cost for inventory Energy recovery efficiency of a MSWI Recycling efficiency of an ATT plant Energy recovery efficiency of an ATT plant Efficiency of (manual) recycling in countries with low labour costs

Unit 7800 ha [3055, 4065] tonneb [0.48, 0.75] %/weekc [74.5, 77.0]%d [32.5, 33.5]%e [51.0, 53.0]%e [95.0, 100.0]%

ATT, advanced thermal treatment a Three-year production plan with three one-year plan periods b The maximum weekly capacity of shredder c Based on costs from Williams et al. (2007) and Simic and Dimitrijevic (2012) d The case of incinerating the mixture of ASR/MSW (Ciacci et al., 2010; Simic and Dimitrijevic, 2012) e Based on data from GHK/BioIS (2006), Vigano et al. (2010), and Simic and Dimitrijevic (2012)

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