Evaluating efforts to build sustainable WEEE reverse logistics network design: comparison of regulatory and non-regulatory approaches

Abstract

Many developing countries such as Turkey are still making an effort on building an infrastructure for waste of electrical and electronic equipment (WEEE) reverse logistic network design (RLND) processes. It is obvious that policies/laws/regulations related to WEEE management provide a sustainable framework for implementation in the RLND. The question is here: Does the implementation of WEEE directives make sense in terms of reducing the total cost of the network in the long term? This study aims to compare regulatory and non-regulatory situations of WEEE RLND in developing countries by formulating two models named as ‘regulatory’ and ‘non-regulatory’. Model 1 is considered as sustainable with economic, environmental and social goals, and the quotas imposed by the environmental directive are taken into consideration as the data of product return amount. In Model 2, only economic goal is considered, and product return amount is forecasted using Artificial Neural Network (ANN). A case study is conducted in a recycling company in order to evaluate performance of the proposed models. This study contributes to the relevant literature by (1) comparing the regulatory and non-regulatory situations RL models explicitly and (2) proposing ANN model to forecast EEE product return or WEEE quantity for non-regulatory situation.

Keywords:

• Artificial neural network (ANN)
• network design for sustainable development
• reverse logistics network design (RLND)
• sustainability
• waste of electrical and electronic equipment (WEEE), developing countries

1. Introduction

In the past years, firms, society and governments have increased their attention towards sustainable development. One of the most popular definitions of sustainable development is stated by the World Commission on Environment and Development (WCED) as ‘sustainability is a development that meets the needs of the present without compromising the ability of future generations to meet their needs’. In general, it includes two important key points: ‘the concept of “needs”, in particular the essential needs of the world’s poor, to which overriding priority should be given’; and ‘the idea of limitations imposed by the state of technology and social organisation on the environment’s ability to meet present and future needs’. (1987). As an industrial viewpoint, Shrivastava and Hart (1995) believe that the structures of industrial economies should be changed using energy and resources efficiently, reducing the wastes, emissions and technological dangerous effects. Sustainable development activities have been adopted in the practice of many companies. For instance, IBM, Hewlett Packard, Xerox, ReCellular promote the take-back of their products in order to recover them (Bleiwas 2001; Fleischmann, Nunen, and Gräve 2002). Recently, sustainability has begun to address the integration of not only environmental and economic responsibilities, but also social responsibilities. Compared with industrial viewpoint, the engineering viewpoint defines sustainability explicitly by incorporating social dimensions such as social equilibrium. Gończ et al. (2007) state that economic stability, ecological compatibility and social equilibrium have the same equality for sustainable development.

The definitions address that there are three main components of sustainability: economic, environmental and social. The integration of three dimensions of sustainability is also known as ‘triple bottom line approach’ which is developed by (Elkington 2004). The main focus of triple bottom line approach is to handle economic, environmental and social dimensions simultaneously and to consider environmental and social performances while measuring financial performance (Elkington 2004). The relationship between sustainability and triple bottom line is shown in Figure 1 (Carter and Rogers 2008). As Figure 1 specifies, the intersection area of three dimensions addresses sustainability.

Figure 1. The relationship between triple bottom line and sustainability.

In the last decades, one of the important managerial and engineering sustainability issues is ‘sustainable supply chain design’. It is a fairly new subject that integrates economic, environmental and societal goals in supply chain design process. The descriptions of the goals in terms of sustainable supply chain approach are discussed below.

(1)	Economic goals in supply chain are maximising the economic efficiency by providing financial benefits to owners, employees and community. In micro-economic environments, economic goals are mainly incorporated into the mathematical models as minimisation of total costs or maximisation of profit.
(2)	Environmental goals are attached more importance especially after environmental regulations come into force. Recovery activities result in environmental risks such as dangerous gas emission into the atmosphere (Chaabane et al. 2012b). The evaluation of trade-offs between economic advantages and dangerous gas emission is necessary in order to make strategic, tactical and operational sustainable decisions. The environmental regulations aim to conserve the natural resources, for instance by limiting carbon dioxide emission that is from vehicles used in logistics activities. Carbon dioxide is the most important greenhouse gas emitted through human operations, and with the impact of the Industrial Revolution which began around 1750, climate has been increasingly changed as a consequence of increase in carbon dioxide caused from human operations (EPA 2014). The main mobile sources of carbon dioxide emission are cars, vehicles, trucks, buses, aircrafts, trains and ships, construction vehicles and military vehicles and devices (Song et al. 2002). It indicates that the logistics activities have an important role in carbon dioxide emission amount. Besides decrease in carbon dioxide emission, the reduction of global warming and consumption of non-renewable energy can be achieved by recycling activities that allow obtaining high value materials from end of life products (Giacchetta, Leporini, and Marchetti 2013).
(3)	Social goals include quality-based issues, ethical-based issues, health safety issues and employment issues. Similarly, Carter and Jennings (2002) specify that social aspects consist of issues related with ethics, diversity, working conditions, human rights, safety, philanthropy and community involvement. Because social aspects are affected from governmental rules and cultural characteristics (Chaabane et al. 2012b) and they are in intangible form, it is not so easy to incorporate them into the mathematical model.

One of the most important processes that helps increase the sustainability of supply chain is recovery of the products. The stringent regulations as well as increase in environmental consciousness force companies to develop strategies on recovery of products in order to maximise their sustainability. Process of product recovery is organised by the managerial planning approach named as Reverse Logistics (RL) which is a systematic way of putting recovery activities in action effectively. One of the most widely used definitions of RL is suggested by The European Working Group on Reverse Logistics (REVLOG) as the following (De Brito and Dekker 2004); ‘The process of planning, implementing and controlling backward flows of raw materials, in process inventory, packaging and finished goods, from a manufacturing, distribution or use point, to a point of recovery or point of proper disposal’. Similarly, Dowlatshahi (2010) defines RL as ‘a process by which a manufacturing entity systematically takes back previously shipped products or parts from the point-of-consumption for possible recycling, remanufacturing or disposal’.

In many countries, the most important reason of growing interest in RL is environmental regulations. All around the world, many regulations have been developed that impose certain responsibilities on the actors of network, such as manufacturers, logistics service providers and municipalities. For instance, European Union (EU) Directives 2002/96/EC and 2002/95/EC are two of the most stringent regulations regarding waste electrical and electronic equipment (WEEE) (European Parliament and of the Council, Directive 2002/96/EC and 2002/95/EC 2002). WEEE is the fastest growing waste group in the EU and produced 8.3–9.1 million tons in 2005. It is forecasted that it will grow to 12.3 million tons by 2020. The main objective of the Directive is, (1) to prevent WEEE, (2) to impose on the recovery activities and (3) to develop the environmental performance of all actors in the chain (REC 2012). The WEEE Directive includes all electrical and electronic equipment that are commonly used in society and industry such as large household appliances; small household appliances; IT and telecommunications equipment; consumer equipment; lighting equipment; electrical and electronic tools; toys, leisure and sports equipment; medical devices; monitoring and control instruments and automatic dispensers (European Parliament and of the Council, Directive 2002/96/EC, 2002). The Directive includes strict obligations to decrease dangerous material usage and increase the recycling of electrical and electronic equipment by enforcing manufacturers to be responsible for taking back the products and reprocessing them. It also forces some operational goals such as collecting at least 4 kg of WEEE annually, ensuring the best technologies and organising and financing WEEE process.

For countries whose efforts are changing to sustainable processes, it is very prominent to figure out the results of sustainability with directives. Otherwise, it will not be possible for them to safeguard their systems against new outputs of the new sustainable systems. Especially budget constraints can limit their efforts; therefore, it is necessary to reveal the economic and strategic needs of sustainable systems. In order to declare the outputs of the sustainable WEEE RLND, regulatory-based sustainable network design and non-regulative network design should be compared. These models are general, flexible, multi-echelon (collection points, collection centres, recycling centres and disposal centres/refineries/material suppliers), multi-product, capacity constrained and one particular time period-based models. A case study is carried out in a recycling company in order to evaluate the performance of the proposed models. The proposed approaches can be used by companies to redesign their RL networks in order to balance their needs and required resources under the goals of regulatory and non-regulatory situations.

The paper is organised as follows: Section 2 reviews the relevant literature comprehensively. Section 3 reviews the main methodology of two models, and the implementation. We illustrate our method by applying it to the RL network of WEEE in a recycling company in Turkey. Section 4 presents sensitivity analysis and Section 5 presents the results and discussion.

2. Reverse logistics network design literature

In the relevant literature, it is seen that the RL topics range from strategic decisions to tactical and operational decisions (De Brito and Dekker 2004). One of the most important research topics in RL problem area is the RL network design (RLND) which has a strategic role in an effective supply chain improvement (Ramezani, Bashiri, and Tavakkoli-Moghaddam 2013). The main goal of environmental directives is to decrease the dangerous effects of products to the environment and society by designing sustainable RL networks. The strategic role of sustainable RLND comes from the ability to address costly, critical and risky decisions such as determination of quantity, location, capacity of the specified facilities and transportation modes under the dimensions of sustainability.

Based on sustainable issues, RLND studies also have become more important in recent years. In order to reveal the sustainability performance of the RLND studies, we execute a literature review on the studies relating to the period 1988–2016. The search consists of 237 papers. The results show that there are many years between 1998 and 2000 that no paper had been published in. Until 2006, the number of papers published each year was low. This result in itself shows that the importance of this research area has been increasing especially after 2006. Unfortunately, RLND models mentioned by previous studies are mostly using only the lowest cost or highest profit as its single evaluation objective. It is revealed that nearly 74% of papers use a single objective model and consider only economic goal. 21.5% of total takes into account environmental objectives besides economic ones. The comparison of number of studies with environmental objective and social objective can be seen in Figure 2. The results show that only Harraz and Galal (2011), Dehghanian and Mansour (2009), Darbari, Agarwal, and Chaudhary (2015), Kafa, Hani, and Mhamedi (2015), Govindan, Paam, and Abtahi (2016) and Zhalechian et al. (2016) state that they incorporate the social dimension into the RLND model. Harraz and Galal (2011) consider the refund amount which represents the interest of ELV owner and a major concern of network operator as a social dimension. Dehghanian and Mansour (2009) utilise Analytical Hierarchical Process (AHP) that considers four factors of social dimensions in order to assign different scores to each location alternatives. Darbari, Agarwal, and Chaudhary (2015) utilise Analytical Hierarchy Process (AHP) and the Fuzzy Technique for Order Preference by Similarity to Ideal Solutions (TOPSIS) to measure the weights for the three objectives: minimisation of the total cost, the environmental impact (in terms of CO2 emissions) and maximisation of the social impact of the network. Kafa, Hani, and Mhamedi (2015) MILP model is used to configure closed loop network by minimising the total cost of sourcing, the total greenhouse gas emissions and maximising job opportunities. Govindan, Paam, and Abtahi (2016) simultaneously consider the environmental, social and economic aspects successfully. In order to meet the needs of sustainability, they develop a mathematical model that minimises the present value of costs, as well as environmental impacts, and optimises social responsibility. Zhalechian et al. (2016) consider environmental impacts of CO2 emissions, fuel consumption, wasted energy and the social impacts of created job opportunities and economic development under uncertainty. It is clear that the existing literature is still far from combining three sustainability aspects simultaneously in RLND. Although social factors are taken into consideration as emerging subjects for the successful application of many reverse logistics practices (Sarkis 2001, Nikolaou, Konstantinos, and Allan 2012) state that recent RL models have a limited number of social dimensions that is a critical factor in the success of a firm to sustainable development. The distribution of objectives is shown in triple bottom line at Appendix 1.

Figure 2. Distribution of studies that have environmental and/or social objectives.

Furthermore, we evaluate the papers within each solution method by examining two main methodologies: exact based and heuristic. There are 148 papers using the exact methods and 89 papers using the heuristic methods (seen in Figure 3). One of the major differences between the two streams is that heuristic solution-based studies have lack of industrial case study-based implementations (as seen in Figure 4). They are mostly limited with numerical examples. This result can be caused from conservativeness of companies on sharing large amount of real data and the hardness of gathering large amount of real data in a correct and trustful manner. The distribution shows that the interest on heuristics methods has occurred 10 years later than the first exact method-based study; Gottinger (1988). Moreover, between 1998 and 2003, there was no study published using heuristic methods. After 2006, the number of papers using heuristics has grown exponentially and it has reached the highest point at 2010. In both exact- and heuristic solution-based RLND studies, mixed integer linear programming (MILP) is the most commonly used modelling type. However, in heuristics, the number of papers having non-linear programming model is more than exact method-based studies.

Figure 3. Distribution of papers relating to solution methods.

Figure 4. Distribution of implementation area quantity relating to solution methods.

The taxonomy of the literature also shows that RLND is an immature research area especially for developing and undeveloped countries. In further years, by the effect of environmental regulations’ pressures, the motivation for researches on RLND will be expected to increase in these countries.

3. The methodology and implementation

This study proposes two quantitative models: Model 1 (Regulatory approach) and Model 2 (Non-Regulatory approach).

Model 1 refers to the sustainable situation; therefore, it is built by excluding situations resulting from complying with an environmental directive. It is assumed that the environmental directive comes into force in practical successfully, and responsibilities are fulfilled by all actors in the chain. Model 1 decides on opening the collection and recycling centres, and allocation of products/materials between centres, but it does not only aim at the minimisation of the total cost of the selected network, but also minimisation of environmental risk and maximisation of social benefit. Model 1 is proposed as a multi-objective mixed integer linear programming (MILP) model which takes requirements of sustainable economy into account. Product return amount is obtained from the quotas determined by the environmental directive.

Model 2 does not consider WEEE directives and sustainable issues. It decides on opening the collection and recycling centres, and allocation of products/materials between centres by aiming at minimising the total cost of the network. In order to forecast the product return amount, a decision-making approach using Artificial Neural Network (ANN) systems is improved. The results are used in the optimisation model as return amount data.

The methodological steps and details can be seen in Figure 5.

Figure 5. The methodological steps and details.

Both the proposed models are built for a general RL network in which the returned products are gathered in collection points (CP) and then collected in existing collection centres (ECC) or potential collection centres (CC) where inspection operations are conducted. The recoverable products are shipped to the existing recovery centres (ERC) or alternative recovery centres (RC); the rest of them are sent to the disposal centres (DC). After the recoverable products are recovered at recovery centres, most of them are recycled and sold to material suppliers (MS); some of them cannot be recovered because of license permissions and sent to the refinery centres (R); the rest of them are sent to disposal centres (DC). The network is given as Figure 6.

Figure 6. General RL network structure.

Various assumptions are involved in order to decrease the complexity of the problem structures in both the models. They are shown below.

•	Locations and capacities of current and alternative centres and containers in collection points are known.
•	Costs and allocation rates of products and materials are known.
•	The changing of costs in a selected term and inventory costs are negligible.
•	Material amount rates obtained from recycling are gathered from historical data.
•	Allocation rates between centres are obtained from historical data.

Both the models are generalisable but application is conducted for Turkey as a developing country case. The models have been validated through waste of electrical and electronic (WEEE) industry to illustrate their performance. We conducted a case study in Turkey because the situation of WEEE in Turkey is challenging. The environmental regulations have been well accepted and implemented in many developed countries; however, it is still a fairly new process for many developing countries. Regional Environmental Centre (REC) Turkey (2012) forecasted that Turkish manufacturers added 812.000 tons of EEE on the market through around 20.000 distributors (2012). This high volume of EEE causes a huge volume of WEEE. Turkey tackles with 539.000 tons of WEEE annually. Average growth per year is 5%; therefore, it is expected that 894.000 tons EEE is obtained in 2020. According to analysis of REC Turkey, if the Directive comes into force successfully, 116.355 unit points of environmental risks to the ecosystem quality, to human health and to energy resources can be decreased. The WEEE Directive implementation will also provide many social benefits such as decreasing the informal sector quantity and job creation (REC (Regional Environment Center-Turkey) 2012). Because of these impacts of regulations, the successful implementation of directives has a critical impact on effectiveness of RL processes and sustainable development in Turkey.

In Turkey, with the results of the 2001 economic crisis, the unemployment rate increased to 8.4%. In further years, it increased to 10.3 and did not decline until 2005. As World Bank’s Report stated, in order to achieve EU average employment rate in 2010, Turkey has to increase job creation quantity to 10 million. Consequently, job creation has become the most significant and challenge topics of Turkish economy (Bilgin and Kilicarslan 2008). Therefore, considering the labour force increase as a job creation performance indicator is suitable for Turkey-based case in this study.

We take into consideration a recycling facility as an example to study some research questions and make some strategic decisions under triple bottom line approach necessities. Recycling centres have an important role at RL networks. They are responsible for taking out legal licenses from ministry and using appropriate technologies and techniques for recycling operations. Unless appropriate technologies and techniques are used, hazards for environment and health could increase and recycling of wastes could be done mostly by unskilled labour. Moreover, most of OEMs operate RL activities by collaborating with recycling firms. It is clear that the role of recycling centres is significant for fulfilment of an effective sustainable RL network. Therefore, in this study, case study is carried out with the data of the WEEE collection and recycling facility which operates in İzmit-Turkey.

The selected facility is the first licensed recycling firm built in Turkey. It has the highest market share as a recycling firm in this sector. The common recycled WEEE are monitors, televisions, IT and telecommunication equipment. The facility is in collaboration with municipalities, distributors and OEMs for collection of used or scrapped electrical and electronic equipment. In the network of the recycling firm, there are collection points (municipalities, OEMs and distributors), existing and alternative collection and recycling centres and disposal centres, material suppliers and refinery centres.

Strategically, the managers of the firm believe that after the WEEE Directive comes into force successfully in the following time, the product return volumes will increase rapidly. Therefore, they plan to extend its recycling operations to different locations in Turkey. Currently, it has one collection centre at İzmit () and one recovery centre at İzmit (). In order to decide on alternative centre locations, potential locations are discussed in negotiations with related entities of municipalities. The managers determined some alternative locations for collection and recycling centres. The alternative locations for collection centres determined by managers are: Tekirdağ (), Erzurum (), Antalya (), Kayseri (), Diyarbakır () and Zonguldak (). The alternative locations for recycling centres determined by managers are Ankara (), İzmir (), Adana () and Samsun (). The products of the firm can be grouped into four types: large home appliances (product group 1), IT equipment and monitors (product group 2), lighting equipment (product group 3) and small home appliances (product group 4). The products are recycled into five different materials. They can be grouped into five categories: iron (raw material 1), metals except iron (raw material 2), glass (raw material 3), plastic (raw material 4) and others (raw material 5). There are two disposal centres (DC1 and DC2), one refinery centre (R) and three material suppliers (MS) in the existing network. Currently, transportation is achieved using highways. But WEEE Directive forces firms to use more environmentally friendly transportation modes. In this case, it is believed that the railway is going to be considered as a second transportation mode. The summary of case study characteristics is shown in Table 1. The location selection decisions are made in the collection and recovery centres which are shown in Figure 7.

Table 1. Case study characteristics.

Quantity of case study characteristics
Product group	4
Raw material	5
Transportation mode	2 (for Model 1), 1 (for Model 2)
Collection points	81 (for Model 1), 219 (for Model 2)
Existing collection centres	1
Potential collection centres	6
Existing recovery centres	1
Potential recovery centres	4
Disposal centres	2
Material suppliers	3
Refinery centres	1

Figure 7. The locations of the collection and recovery centres.

Notes: White boxes refer to collection centres and grey boxes refer to recovery centres.

The resources of the data are illustrated in the following list.

(1)	The data of carbon dioxide emission amount are retrieved from United Nations Framework Convention on Climate Exchange (UNFCC) institution and carbon dioxide emission calculators for buildings.
(2)	The changing data regarding transportation mode are retrieved from Turkish State Railways reports.
(3)	The labour force data are retrieved from Turkish Statistical Institute’s databases.
(4)	The rest of data related to parameters and constraints are retrieved from the current and historical data of the recycling centre.

3.1. The implementation of model 1

Model 1 proposes an optimisation model considering all sustainable dimensions in the same design procedure in accordance with triple bottom line approach. The model includes three main objectives:

(1)	minimising total costs as an economic goal,
(2)	minimising carbon dioxide emission as an environmental goal,
(3)	increasing job creation as a social goal.

Job creation is one of the most important economic concerns. From an employment perspective, job creation can be defined as the total number of employment positions gained and job destruction can be defined as the total number of employment positions lost (Klein, Schuh, and Triest 2002). Increase in labour force as a job creation indicator is taken into account in this study. For each existing and alternative collection and recovery centre, job creation rates are calculated by considering the amount of qualified (white-collar worker) and non-qualified labour (blue-collar worker) increase that will occur when a new facility is opened, and will lose when an existing facility is closed. The values of increase and decrease in job creation when a new facility is opened or closed are obtained with the help of experts in the recycling centre. In order to define the contribution of each alternative city to job creation, these values are proportionally evaluated by the current employment rates of each alternative city which are obtained from Turkish Statistics Institute. In other words, increase (or decrease) in employment rate by the effect of opening (or closing) a facility is calculated by finding the change in percentage on employment rates of each city. Total labour amounts of collection and recycling centres are taken into consideration within this context. Assuming x refers to employment amount of alternative city and y refers to the amount of qualified/non-qualified worker amount in a potential centre, then the contribution (in percentage) can be counted as y*100/x.

As Melo, Nickel, and Saldanha-da-Gama (2009) state, although the choice of transportation mode is related to location decisions, researchers have not drawn much attention to the transportation mode selection in the relevant literature. Therefore, Model 1 also decides on the transportation mode which differs in terms of carbon dioxide emission amount.

The proposed model is general and flexible to solve larger problems. The mathematical formulation of the model is given in Appendix 2 [Equations (7)–(47)]. The following three objectives are addressed in the mathematical formulation:

(1)	Economic objective (): The economic objective is evaluated by total network cost including fixed costs, collection costs, disposal and refinery costs, processing costs, transportation costs, information costs, application costs and penalty costs [shown in Equations (7)–(14)].
(2)	Environmental objective (): The second critical objective to a successful sustainable RLND is the optimisation of the environmental dimension. Many logistics operations and industrial-based processes are added to a rise in the greenhouse effect through carbon dioxide emissions (Harris et al. 2011). Trucks’ emissions also indicate no signs of decrease and increased from 42% (1995) to 49% (2006) (Ülkü 2012). Therefore, in order to make the determination of the environmental objective general, we consider the most common environmental risk indicator ‘carbon dioxide emission amount’ as an environmental objective [shown in Equations (15) and (16)].
(3)	Social Objective (): The sustainability performance of a RL model should be evaluated based on social benefits besides economic and environmental benefits. In order to make the determination of the social objective general, we consider one of the most common social benefit considerations ‘increase in labour force’ as a job creation indicator. With the help of the social objective, the model evaluates the trade-offs between objectives under various constraints, and makes decision on location selection by considering how the labour force is affected when a centre is opened or closed. The aim is to incorporate ‘increase in labour force’ factor into the decision process. [shown in Equations (17) and (18)].

The decision variables in this mathematical formulation are:

(1)	Decision variables for opening a set of centres or closing existing ones.
(2)	Logical decisions that refer to the connections between centres.
(3)	Flow quantities between centres.

The problem is subject to the following constraints:

(1)	Balance constraints which determine the equality between inputs and outputs of the centres. These constraints make assignment of products to the centres in proportion to their known rate amounts [shown in Equations (19)–(30)].
(2)	Capacity constraints which prevent to transport more products to a centre than its capacity [shown in Equations (31)–(34)].
(3)	Logic constraints which eliminate the possibility of irrational decisions such as sending a container to more than one centre. Furthermore, logical constraints guarantee to send products and/or materials to the centre if it is open. The minimum distribution amounts that are shown by , , and are calculated using break-even point analysis [shown in Equations (35)–(47)].

Multi-objective model is a specific form of mathematical programming models. In the proposed multi-objective model, the method of global criterion (MGC) is utilised. Using the help of MGC, it is easier to reduce all objective functions into one function (Marler and Arora 2004). If the decision-makers state that the importance of all objectives is same and if they believe that results should be evaluated independently from their ideas, the utilisation of MGC will be meaningful under these conditions. MGC is a compromising method that makes all decisions content with less than their best. It is easy to use and flexible (Kuruüzüm 1998). According to the method, optimal vector is a vector which makes total criteria minimum. The optimal solution is the total square of relative deviations of objective functions from feasible values. Assume that the optimum solution of m number problems separately is, . Then, the model is shown as (Evren and Ülengin 1992):(1) (2)

The following model should be solved.(3) (4)

For various parameters of a, many trials can be done. Boychuk and Ovchinnikov (1973) propose ‘1’ for the value of a (1971). If all objective functions and all constraints are linear and the value of a is 1, then the model will be a classical linear programming model. If a is chosen as 2, problem will have a quadratic form. The basic form of the model is:

Objective function

  Minimum Cost (

  Minimum Carbon Dioxide Emission (

  Maximum Social Benefit (

Constraints

  Balance constraints

  Capacity constraints

  Logic constraints

First of all, the multi-objective model is solved by considering each objective separately. The optimum results of each objective function ( are placed into the other objective function as known parameters. That retrieves other objective functions’ optimum values when optimal values of one objective function are considered as known parameters in the other model. The results can be shown as: All alternatives of objective functions ( are shown in the following trade-off matrix:(5)

The maximum values of each objective function are shown as ,, and the minimum values of each objective function are shown as , , . The normalised model for minimisation of relative deviation of objective function values from feasible values can be shown as:

Objective function:(6)

Constraints

  Balance constraints

  Capacity constraints

  Logic constraints

In this case, the value of a is given as ‘1’ because of the linearity of the proposed model.

The proposed model is optimised with mixed integer linear programming (MILP). It is coded in GAMS (general algebraic modelling system) CPLEX solver. As stated before, it is assumed that the data of r_kp which refers to annual returns of products from collection points (containers) to collection centres are retrieved from WEEE Directive Regulation. The regulation forces all actors collect 4 kg e-wastes per person with the proportion of their market share. Therefore, returns of 81 collection points are calculated by multiplying the total population by 4 and getting the proportion of 10% that indicates the market share of the company. The results of the multi-objective model indicate that the optimum value of the network is 206,691,800 monetary units under the given conditions. The carbon dioxide emission amount will be 270,132,000,000 grams and the relative increase in labour force rate of the selected locations will be 0.000246. There exist capacity excess problems in the centres. That increases penalty costs and it causes high total cost of the network.

According to the optimum results, the existing collection and recovery centres at İzmit are not closed. Additionally, collection centres at Kayseri, Tekirdağ, Antalya and Diyarbakır and recovery centres at Ankara, İzmir, Adana and Samsun are opened. In this case, there are two different transportation modes between collection centres and recovery centres: highways and railways. The allocations between centres with various transportation modes are shown in Figure 8.

Figure 8. Allocation amounts in ton for Model 1.

Due to limited space, the details cannot be shown in the figure. The detailed information about allocation results can be summarised as:

(1)	The optimum results address that product group 1 and product group 3 should be sent from the existing collection centre at İzmit () to potential collection centre Samsun () using different combinations of highways and railways. The rest of allocations between collection centres and recovery centres should be made using highways.
(2)	The unrecoverable products at collection centres should be sent to disposal centre DC 2.
(3)	The raw material 2 and raw material 5 which are retrieved from the existing recovery centre İzmit () should be sent to material supplier MS 2. The rest of them should be sent to material supplier MC 1. The disposed product group 2 and product group 4 should be sent to disposal centre DC 1.
(4)	The retrieved raw materials from Ankara (): raw material 1, raw material 4 and raw material 5 should be sent to MS 1, the rest should be sent to MS 2.
(5)	All raw materials that are retrieved from İzmir () should be sent to material supplier MS 3.
(6)	The retrieved raw materials from Adana (): raw material 1, raw material 2 and raw material 3 should be sent to MS 1, the rest should be sent to MS 2.
(7)	The retrieved raw materials from Samsun (): raw material 1, raw material 2 and raw material 5 should be sent to MS 1, the rest should be sent to MS 2.
(8)	The unrecoverable and disposed products at Ankara (): product group 1 and product group 3 should be sent to DC 2, the rest should be sent to DC 1. The products which do not have any license to recover are sent to refinery centres.
(9)	The unrecoverable and disposed products at İzmir (): product group 1 and product group 2 should be sent to DC 1, the rest should be sent to DC 2. The products which do not have any license to recover are sent to refinery centres.
(10)	The unrecoverable and disposed products at Samsun (): product group 1 and product group 3 should be sent to DC 1, the rest should be sent to DC 2.

3.2. The implementation of model 2

The studies utilising neural network approaches give more satisfactory results compared to traditional statistical methods in many cases (Mukta & Kumar, 2009). Therefore, an ANN approach which is a system that simulates biological neural networks to get solution for hard, mathematically ill-defined, non-linear or stochastic problems (Graupe 2007) is used for forecasting product return amount of Model 2. A general ANN structure includes three kinds of layer: input layer, hidden layer and output layer. The principle of ANN depends on carrying out many trials in order to find the best layer and processing element quantity for the relevant problem. The value of mean square error (MSE), as a performance indicator, shows the reasonability of each trial. If a trial gives MSE value equal or less than 0.01, it is mostly considered as highly satisfactory.

For Model 2, it is assumed that the factors such as take-back price (Klausner and Hendrickson 2000; Guide and Van Wassenhove 2001), population density (WEEE Directive; Hanafi, Kara, and Kaebernick 2007), income (WEEE Directive), product category (Hess and Mayhew 1997; Rogers and Tibben-Lembke 1999), investment on environmental protection, number of households (Ikhlayel 2016) and electricity consumptions have an impact on product return amount. That means the input layer consists of these seven factors. The general structure of the proposed ANN model is given in Figure 9.

Figure 9. The general structure of the proposed ANN model for product return rate forecasting.

It is necessary to train many networks with different hidden layers and neuron combinations to find the best structure which has the minimum MSE value. It is assumed that existing 200 collection points’ return amount is known. The ANN system is run only for forecasting product return of 19 alternative cities which have high potential to collect high amount of end of life products after the directive comes into force. Therefore, in total there will be 219 collection points in Model 2.

Experiment results show that in the network structure with minimum MSE values (MSE = 0.01) and maximum correlation value on test results (0.74), there are two hidden layers, and four neurons take place at first hidden layer and four neurons at second one. Neuro Solutions for Excel Software is utilised for ANN development process. The product amounts are given in Table 2.

Table 2. ANN results: return amount of alternative locations (in kg).

New locations	Product group 1	Product group 2	Product group 3	Product group 4	New locations	Product group 1	Product group 2	Product group 3	Product group 4
Location 1	2579	30315	2456	2502	Location 11	2575	36470	2456	2453
Location 2	2468	2642	2451	2456	Location 12	2459	2537	2451	2065
Location 3	2653	2725	2451	2499	Location 13	2726	57647	2455	2569
Location 4	2469	2672	2451	2466	Location 14	2468	2555	2451	2455
Location 5	2711	78272	2454	2562	Location 15	3606	14289	2455	2876
Location 6	2454	11400	2452	2474	Location 16	3084	109972	2455	2709
Location 7	2459	3664	2451	2463	Location 17	2469	2564	2451	2463
Location 8	2456	2516	2451	2451	Location 18	7857	13512	2452	5353
Location 9	2456	8456	2451	2467	Location 19	2478	26629	2451	2499
Location 10	2498	10957	2451	2490

The mathematical model is a one-objective version of Model 1 that is given in Appendix 2. The environmental and social parameters and environmental and social objectives are excluded. The objective is to minimise total cost of the network as sum of annualised fixed costs, information costs, transportation costs, processing costs, disposal and refinery costs, collection costs and penalty costs (that is unit variable cost of non-used capacity of collection centres to each product). Balance constraints make sure that incoming and outgoing flows of the centres are balanced. Capacity equations make the incoming flow to each centre not exceed the maximum capacity of the centre, ensure that one container is sent to only one collection centre and reflect the limitations in minimum product amount required for moving into profit. Others represent the binary variables and the non-negativity of decision variables. Data of (product return amount) are gathered at the end of ANN development process.

The results indicate that the cost of the network is 55.434.247 monetary units under the given conditions. The existing collection and recovery centres at İzmit are not closed. Additionally, one collection centre at Kayseri and recovery centre at Ankara should be opened. The allocations between centres with various transportation modes are shown in Figure 10.

Figure 10. Allocation amounts in ton for Model 2.

The detailed information about allocation results can be summarised as:

(1)	At the existing collection recovery centre (İzmit ()) and newly opened centre (Kayseri ()), the unrecoverable products should be sent to disposal centre DC 1 and DC 2.
(2)	At the existing recovery centre (İzmit ()) the unrecoverable product group 1, product group 2 and group 4 should be sent to disposal centre DC 2. The rest should be sent to DC 1.
(3)	At the newly opened recovery centre (Ankara ()), the unrecoverable product group 1 and product group 3 should be sent to disposal centre DC 1. The product group 2 should be sent to DC 2.
(4)	The raw materials which are retrieved from the existing recovery centre İzmit () or newly opened recovery centre (Ankara ()) should be sent to material supplier MS 3.

The brief information about the model results is shown in Table 3.

Table 3. Results of Model 1 and Model 2.

	Model 1	Model 2
Results of modelling
Total cost	206,691,800 monetary unit	55,434,247 monetary units
Total carbon dioxide emission	270,132 ton	–
The increase in labour force	0.000246	–
Closed centres	–	–
Opened collection centres	Tekirdağ, Antalya, Kayseri, Diyarbakır	Kayseri
Opened recovery centres	Ankara, İzmir, Adana, Samsun	Ankara
Transportation mode – railway	From İzmit to Samsun	All transportations
Transportation mode – highway	All transportations except between İzmit and Samsun	–
Results of sensitivity analysis
The effect of capacity decrease (to 40%)	Decrease in cost: 25%	Decrease in cost: 5.6%
	Decrease in carbon dioxide emission:
	3.5%	–
	Decrease in job creation: 40%	–
The effect of product returns amount increase (to 70 %)	Increase in cost: 26%	Increase in cost: 1.8%
	Increase in carbon dioxide emission:
	15%	–
	Increase in job creation: 70%	–

4. Sensitivity analysis

In order to explore the effect of changing capacities and product return amount, two sensitivity analyses are proposed for both the models.

4.1. Sensitivity analysis for model 1

4.1.1. The effect of capacity changing

In the first sensitivity analysis, it is aimed to explore if the optimum centres are opened and their capacities are decreased, they will be successful to meet the product return amount or not. Because of that reason, the model is run for decreasing capacities of all collection and recovery centres by keeping the rest of the parameters constant. It is evident that the total cost converges with decreasing volume. It is seen that if their capacities are decreased more than 40%, the solution becomes infeasible. That means the capacity amounts can be reviewed again by managers because there is a capacity excess and that results in high penalty costs. It is necessary to look over the initial capacities for potential centres. The impact of decrease in capacities on the total cost can be seen in Figure 11. Moreover, it is worth mentioning that the amount of qualified and non-qualified workers linearly changes according to increase or decrease in capacity. Therefore, the effect of capacity on labour force is equal to the percentage change in capacity. But in actual, as a social responsibility, rather than laying off, the company should attach more importance on training the workers to increase their multi-functionalities, and thus new job opportunities can be created for excess labour within the company, such as automation-oriented operations and organising awareness raising activities.

Figure 11. The impact of decrease in capacities on total cost.

The impact of decrease in capacities on the total carbon dioxide emission can be seen in Figure 12. As Figure 12 specifies, if the capacities are decreased by 40%, besides increase in cost by 25%, the carbon dioxide emission will be decreased by 3.5%.

Figure 12. The impact of decrease in capacities on the total carbon dioxide emission.

4.1.2. The effect of product returns amount changing

In the future, it is expected that the return quantity of WEEE will increase when the consciousness of consumer increases. In order to explore the effect of return amounts on the results, a sensitivity analysis is proposed by keeping the rest of the parameters constant. It is evident that the total cost converges with increasing volume. Also, when the amounts are increased more than 70% for each collection point, the model gives infeasible solution. That means if the return amount is increased by 70%, new centres should be open for recycling of total products. Increase in total cost with increasing return amounts can be seen in Figure 13.

Figure 13. The impact of increase in product return amount on the total cost (Model 1).

The impact of increase in product return amount on the total carbon dioxide emission can be seen in Figure 14. As Figure 14 specifies, if the product return amount is increased by 70%, the carbon dioxide emission will be increased by 15%.

Figure 14. The impact of increase in product return amount on the total carbon dioxide emission (Model 1).

4.2. Sensitivity analysis for model 2

4.2.1. The effect of capacity changing

The model is performed for decreasing capacities of all collection and recovery centres from 1% to 7% by keeping the rest of the parameters constant. As seen in Figure 15, the total cost converges with decreasing volume. Also, when the capacities decreased more than 7%, the model gives infeasible solution. That means if the capacities decreased to 7%, it is advised to open new centres for recycling of existing products.

Figure 15. Decrease in total cost with decreasing capacities (Model 2).

4.2.2. The effect of product returns amount changing

The model is performed for increasing return amounts of all collection points from 5 to 10% by keeping the rest of the parameters constant. As seen in Figure 16, it is explicit that the total cost converges with increasing volume. Also, when the amounts increased more than 10%, the model gives infeasible solution. That means if the return amount is increased to 10%, it advised to open new centres for recycling of total products.^{Table 4}

Figure 16. Increase in total cost with increasing return amounts (Model 2).

Table 4. Yearly product return amount retrieved from trend analysis.

Years	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024	2025
Yearly product return amount (kg per person)	0.5	1	1.5	1.75	2	3	4	4.24	4.81	5.38	5.95	6.52	7.09	7.66

According to sensitivity analysis results, it is clear that the given capacity values are high for existing conditions of the firm. That means firms should analyse capacity requirements with decision-making tools before making strategic decisions and high investments. Moreover, firms should follow yearly changing on return amounts in order to see their requirements on opening extra facilities (Figure 17).

Figure 17. Change in the profit when return amount is increased.

5. Results and discussion

This study presents a methodology that gives efficient solutions for all important actors of the system: companies, environment and society. The proposed models enable governments and managers to evaluate their strategic decisions from both sustainable regulative and non-regulative perspectives. There are some important discussion points and managerial insights that should be considered by the company:

•	In the sustainable network, it is revealed that it is not easily possible for a company in a developing country to have profit from RL activities. As Srivastava (2008b) figures out, in developing countries in which directives comes into force, new, recovery options cannot give economic advantages in a short time.
•	In the sensitivity analysis, it is figured out that if the return amount is increased by 70%, new centres should be open for recycling of total products. By considering the Ministry of Environment and Urban Planning’s quotas between 2012 and 2018 (Ministry of Environment and Urban Planning 2008), we conducted a trend analysis in order to forecast how long the capacities will be appropriate for the company. As Table 4 specifies, if the Directive comes into force successfully, in 2024, the company will have 7.09 kg e-wastes that refers to 70% increase on 4 kg e-waste quotas. These results indicate that in 2024, the company will have to review their capacities.
•	In order to clarify the total profit gained by RL activities in Model 2, break-even analysis is conducted. The revenue obtained from each material that is taken by recovery options is approximately 2.121 monetary units/ton. The 64% of total product returns are transformed to the materials such as plastic, glass, iron and aluminium. Under the light of these, looking up the relationship between marginal costs and revenue shows that the profit relatively decreases across time (as seen in Figure 14). That shows although companies believe that establishment of a sustainable structure is highly expensive, non-regulative network design also offers no profitable advantage in the length of time.
•	In a sustainable environment, the given capacity values are high for existing conditions of the firm. That means firms should review capacity requirements by utilising decision-making tools before making strategic decisions that need high investments.
•	In a non-regulatory situation, if the return amount is increased to 10%, it advised to open new centres for recycling of total products. Therefore, managers should carefully track the increases in the product return amount in order to safeguard themselves against enlargement needs.
•	Unfavourable results indicate that it is not realistic to make the amount of product return goal as 4 kg for the year of 2018. Turkish Ministry of Environment and Urban Planning should review the product return quotas again, and rather than accepting the EU’s environmental regulation’s quotas directly, they should improve a unique system that considers Turkey’s conditions and characteristics.

6. Conclusions and further researches

In the uncertain and complex nature of RL networks of developing countries, developing a methodology that compares the RL design model with regulative and non-regulative dimensions becomes a significant task. Although developing countries are familiar with non-regulative RL networks, due to the difficulty in incorporating environmental and social benefit into RLND models, there is a lack of RLND studies that fully achieves sustainability by taking into account triple bottom line approach necessities. In the light of these, this study aims to reveal the regulatory and non-regulatory situations of WEEE RLND in developing countries in which individual sustainable WEEE RLND efforts are still unorganised and informal. With this aim, we present two MILP models; one refers to the current conditions of a developing country including economical goal, and one refers to the future conditions of a developing country including three objectives: minimising total cost, minimising environmental risk and maximising labour force. Both the models are multi-echelon, multi-product, capacity constrained, particular time period facility location allocation models. Model 1 contributes to the relevant literature by generating multi-objective sustainable RL model for WEEE industry of developing countries. Model 2 contributes by proposing an ANN-based process for forecasting product returns. A case study is conducted in a recycling company in order to evaluate and validate performance of the proposed models. This comparative methodology can help the managers take decisions on facility selection by contributing to the industrial sustainable development and allow governments review their regulatory initiatives in terms of return amount expectations. The results reveal that in the adoption process managers should be aware of enormous investment costs that they have been charged at the beginning of the RL network design processes because in the beginning of the adoption process, product return amount is not enough to satisfy and meet the quotas identified by regulations. That also indicates that the ministry should immediately review the lower limits of WEEE collection amounts because it is not possible for a developing system to make society aware of the benefits of WEEE collection in a short time. Profit analysis indicates that even if managers are not likely to invest on sustainable networks because of its high costs, non-regulative systems offer no satisfactory profit advantage across time as it is expected. Therefore, they should not ignore the effect of economies of scale in WEEE collection and make effort on collecting more and more e-wastes that will also increase the profits after a while.

Directions for further researches include: (1) new issues can also be added into the methodology, such as lot sizing, vehicle routing and inventory management, (2) generalising the model to a multi-period programming model that can handle time-based changing on capacities, product returns, etc. and (3) allowing some parameters such as product returns, costs, capacities etc. uncertain. Furthermore, considering the lack of recorded data for the recycling facility employment, labour productivity and compensation costs, it should be highlighted that investigation of capacity and product return quantity impacts on job creation is a comprehensive evaluation focusing on recruiting decisions for future studies.

Notes on contributors

Gül Tekin Temur is an associate professor of Management Engineering at Bahçeşehir University, Turkey. Her main research interests are in supply chain management, reverse logistics, decision-making and artificial ıntelligence. Previous publications have appeared in Applied Soft Computing, International Journal of Computational Intelligence Systems, and Enterprise Information Management.

Bersam Bolat is an associate professor of Management Engineering at İstanbul Technical University, Turkey. Her main research interests are in production and operations management, production planning and control and project management. Previous publications have appeared in Resources, Conservation and Recycling, Enterprise Information Management, Computers & Industrial Engineering.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This study was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) (Project No: 115M551).

Acknowledgement

The authors are thankful to TÜBİTAK for supporting their project numbered as 115M551.

Appendix 1.

Triple bottom line graph for grouping RLND studies according to their goals

Appendix 2.

Indices and parameters of model 1

The following notations are used in the formulation of the model.

Sets:

k ∈ K:	=	set of collection point (CP) locations
l ∈ L:	=	set of potential collection centre (CC) locations
i ∈ İ:	=	set of existing collection centre (ECC) locations
m ∈ M:	=	set of potential recycling centre (RC) locations
j ∈ J:	=	set of existing recycling centre (ERC) locations
d ∈ D:	=	set of disposal centre (DC) locations
s ∈ S:	=	set of material supplier (MS) locations
r ∈ R:	=	set of refinery centre (RC) locations
p ∈ P:	=	set of product type
h ∈ H:	=	set of material type
t ∈ T:	=	set of transportation mode

Model parameters:

Costs:

Fixed costs (in monetary unit):

:	=	annualised fixed costs for opening l
:	=	annualised fixed costs for closing i
:	=	annualised fixed costs for opening m
:	=	annualised fixed costs for closing j
:	=	annual information cost at l
:	=	annual information cost at i
:	=	annual information cost at m
:	=	annual information cost at j
:	=	annual application cost at l
:	=	annual application cost at i
:	=	annual application cost at m
:	=	annual application cost at j

Transportation costs (in monetary unit/ton-km):

:	=	unit variable cost serving p from k to l by transportation mode t
:	=	unit variable cost serving p from k to i by transportation mode t
:	=	unit variable cost serving p from l to d by transportation mode t
:	=	unit variable cost serving p from i to d by transportation mode t
:	=	unit variable cost serving p from l to m by transportation mode t
:	=	unit variable cost serving p from l to j by transportation mode t
:	=	unit variable cost serving p from i to m by transportation mode t
:	=	unit variable cost serving p from i to j by transportation mode t
:	=	unit disposal cost for p served from m to d by transportation mode t
:	=	unit disposal cost for p served from j to d by transportation mode t
:	=	unit variable cost serving h from m to s by transportation mode t
:	=	unit variable cost serving h from j to s by transportation mode t
:	=	unit disposal cost for h served from m to r unit disposal cost for h served from j to r by transportation mode t
:	=	unit disposal cost for h served from j to r unit disposal cost for h served from j to r by transportation mode t

Collecting and processing costs (in monetary unit/ton):

:	=	unit collecting cost of p from k to l by transportation mode t
:	=	unit processing cost of p at l
:	=	unit processing cost of p at i
:	=	unit processing cost of p at m
:	=	unit processing cost of p at j

Disposing and refinery costs (in monetary unit/ton):

:	=	unit disposing cost for p served from l or i to d
:	=	unit disposing cost for p served from m j to d
:	=	unit refinery cost for p served from m or j to r

Penalty costs (in monetary unit/ton):

:	=	opportunity costs caused from not collecting p at l
:	=	opportunity costs caused from not collecting p at i

Carbon dioxide emission amount (ton):

:	=	carbon dioxide emission amount caused from opening l
:	=	carbon dioxide emission amount caused from closing i
:	=	carbon dioxide emission amount caused from opening m
:	=	carbon dioxide emission amount caused from closing j
:	=	carbon dioxide emission amount caused serving p from k to l by transportation mode t
:	=	carbon dioxide emission amount caused serving p from k to i by transportation mode t
:	=	carbon dioxide emission amount caused serving p from l to d by transportation mode t
:	=	carbon dioxide emission amount caused serving p from i to d by transportation mode t
:	=	carbon dioxide emission amount caused serving p from l to m by transportation mode t
:	=	carbon dioxide emission amount caused serving p from l to j by transportation mode t
:	=	carbon dioxide emission amount caused serving p from i to m by transportation mode t
:	=	carbon dioxide emission amount caused serving p from i to j by transportation mode t
:	=	carbon dioxide emission amount caused serving p from m to d by transportation mode t
:	=	carbon dioxide emission amount caused serving p from j to d by transportation mode t
:	=	carbon dioxide emission amount caused serving h from m to s by transportation mode t
:	=	carbon dioxide emission amount caused serving h from j to s by transportation mode t
:	=	carbon dioxide emission amount caused serving p from m to r by transportation mode t
:	=	carbon dioxide emission amount caused serving p from j to r by transportation mode t

Distances (km):

:	=	distance k to l by transportation mode t
:	=	distance k to i by transportation mode t
:	=	distance l to d by transportation mode t
:	=	distance i to d by transportation mode t
:	=	distance l to m by transportation mode t
:	=	distance l to j by transportation mode t
:	=	distance i to m by transportation mode t
:	=	distance i to j by transportation mode t
:	=	distance m to d by transportation mode t
:	=	distance j to d by transportation mode t
:	=	distance m to s by transportation mode t
:	=	distance j to s by transportation mode t

Capacities (in ton):

:	=	capacity of potential collection centre l for p
:	=	capacity of existing collection centre i for p
:	=	capacity of potential recycling centre m for p
:	=	capacity of existing recycling centre j for p

Allocation rates:

:	=	average rate of p sent from l to d
:	=	average rate of p sent from l to m and j
:	=	average rate of h sent from m to s
:	=	average rate of p sent from m to r
:	=	average rate of p sent from m to d
:	=	average rate of p sent from i to d
:	=	average rate of p sent from i to m and j
:	=	average rate of h sent from j to s
:	=	average rate of p sent from j to r
:	=	average rate of p sent from j to d

Annual return amount (in ton):

:

=

annual returns of product p from k

Minimum required product amount (in ton):

:	=	min. product for moving into profit at l
:	=	min. product for moving into profit at m
:	=	min. product for moving into profit at i
:	=	min. product for moving into profit at j

Material rate:

:

=

rate of material h for each product

Social benefit amounts:

:	=	increase in non-qualified labour force when l is opened
:	=	increase in qualified labour force when l is opened
:	=	increase in non-qualified labour force when m is opened
:	=	increase in qualified labour force when m is opened
:	=	decrease in non-qualified labour force when i is closed
:	=	decrease in qualified labour force when i is closed
:	=	decrease in non-qualified labour force when j is closed
:	=	decrease in qualified labour force when j is closed

Decision variables

Decisions related to centre location:

:	=	Indicator opening l (1 if opened; 0 otherwise)
:	=	Indicator closing i (1 if closed; 0 otherwise)
:	=	Indicator opening m (1 if opened; 0 otherwise)
:	=	Indicator closing j (1 if closed; 0 otherwise)

Logical decisions:

:	=	Indicator connecting k to l (1 if connected; 0 otherwise)
:	=	Indicator of connecting k to i (1 if connected; 0 otherwise)

Decisions related to production units:

:	=	flow p from k to l by transportation mode t
:	=	flow p from k to i by transportation mode t
:	=	flow p from l to m by transportation mode t
:	=	flow p from i to m by transportation mode t
:	=	flow p from l to j by transportation mode t
:	=	flow p from i to j by transportation mode t
:	=	flow p from l to d by transportation mode t
:	=	flow p from i to d by transportation mode t
:	=	flow h from m to s by transportation mode t
:	=	flow h from j to s by transportation mode t
:	=	flow p from m to r by transportation mode t
:	=	flow p from j to r by transportation mode t
:	=	flow p from m to d by transportation mode t
:	=	flow p from j to d by transportation mode t

Model formulation

Objective function

1. Economic objective (

Fixed costs: are the costs to open potential centres in different locations or close the existing ones.(7)

Collection costs: are the costs to collect the returned products, such as take-back payments and costs of container placement.(8)

Disposal and refinery costs: are the costs to dispose unrecoverable products and make some special products recover in licensed firms.(9)

Processing costs: are the costs to process operations to recover the recoverable products.(10)

Transportation costs: are the costs to distribute or transport the products and materials.(11)

Information costs: are the costs to increase the consciousness of the actors on RL activities in the chain. The consciousness raising studies are organised by municipalities, OEMs or logistics service provides.(12)

Application costs: are the costs to improve the technical adjustment of the RL systems into the existing systems.(13)

Penalty costs: are the costs not able to make the centres process in full capacity. Excess capacity addresses that capacity utilisation is low and that makes the firm put up with the cost of missing the opportunity for gaining more.(14)

2. Environmental objective (f₂(x)):

Carbon dioxide emission amount caused from transportation:(15)

Carbon dioxide emission amount caused from opening/closing centres:(16)

3. Social objective (f₃(x)):

Increase in labour force when a centre is opened:(17)

Decrease in labour force when a centre is closed:(18)

Constraints:

Balance constraints:(19) (20)

(21) (22) (23) (24) (25) (26) (27) (28)

(29) (30)

Capacity constraints:(31)

(32)

(33)

(34)

Logic constraints:(35)

(36)

(37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47)

Other constraints: