Modelling of WEEE recycling operation planning under uncertainty
Introduction
Due to rapid technology changes and fashion-driven demand, like many other product types, electrical and electronic equipment (EEE) may become waste within a few months to a few years (Ikhlayel, 2018). Therefore, the quantity of waste electrical and electronic equipment (WEEE) has been progressively increasing all over the world. Predictions made in recent years show that 20–50 million tons of WEEE are generated annually worldwide, and this quantity increases by at least 3%–5% every year (Robinson, 2009, UNEP, 2006). WEEE may consist of more than 1000 different substances of various sizes and shapes. Due to the hazardous materials contained in WEEE, such as lead, mercury, and cadmium, many countries have imposed regulations on their manufacturers and consumers to recover WEEE (EU, 2003a, EU, 2003b, EU, 2011, EU, 2012). Since WEEE also contains considerable amounts of valuable materials, such as gold, palladium and copper (Widmer et al., 2005), recovery of WEEE offers a potential economic gain (Cesaro et al., 2017). Please refer to a literature review conducted by Pérez-Belis et al. (2015) to find out the main research areas in the field of WEEE.
Today, there are various recovery options for WEEE including reuse, repair, recycling, remanufacturing and disposal. Recycling is the process of retrieving the material content of used and nonfunctioning products through a series of operations, including sorting, disassembly and bulk recycling. Determining the process methods and types and quantities of WEEE to be recycled using related processes is an important operational-level decision for the planning of recycling systems (Gungor and Gupta, 1999, Ilgin and Gupta, 2010). However, operational level decisions need to be made under the complex and mostly unknown nature of WEEE whose material content may vary based on its age and type (Robinson, 2009). Due to this structural complexity, a high level of variability and uncertainty is expected in recycling operations of WEEE and resulting outcomes (Musee et al., 2008a, Musee et al., 2008b). For instance, recycling processing times and the amounts of retrieved materials and components from WEEE may fluctuate even in the group of same type of products. Similarly, other internal and external aspects of WEEE recycling bring additional uncertainties, such as the quantity and the content of WEEE to be processed, demand for the output of WEEE recycling systems and operational capacities of resources. One can handle these issues using stochastic modelling approaches if there are sufficient historical data for uncertain parameters. However, for the case of recently developing areas like WEEE recycling, it is difficult to generate actual and exact random distributions due to the lack of reliable historical data. In these cases, a powerful alternative is to use fuzzy set theory (Bellman and Zadeh, 1970), which provides a framework to handle different kinds of uncertainty issues.
Therefore, the main objective of this paper is to contribute to the enhancement of uncertainty-focused studies in the WEEE recycling literature. In order to achieve this, a mathematical model for the multi-period operation planning problem considering fuzzy parameters in the WEEE recycling environment is provided. In order to solve the model, the ranking method of fuzzy numbers through the comparison of their expected intervals (Jiménez, 1996, Jiménez et al., 2007, Parra et al., 2005, Pishvaee and Torabi, 2010) was utilized. This method a computationally efficient method because it aims to compare fuzzy parameters to solve linear problems by preserving its linearity. Therefore, the method can be conveniently used to solve large models such as the proposed model in this study. The solution of the model determines the process methods and types and quantities of WEEE to be recycled in order to maximize the total profit by considering all related cost and benefit terms associated with WEEE recycling operations. Additionally, in order to enhance the decision maker's flexibility, scenario analysis was carried out for different membership degrees of fuzzy parameters by applying a full factorial design.
The remainder of this paper is structured as follows. In Section 2, related literature is provided and the contribution of the study is clearly identified. Section 3 describes the problem environment and the LP model of the problem with fuzzy parameters is formulated. Section 4 presents a way to transform the fuzzy model into a crisp model. An illustrative example is presented in Section 5. Numerical results are given and alternative scenarios analyzed in Section 6. Finally, the last section contains conclusions and remarks about possible future developments.
Section snippets
Literature review
In the literature, there are several papers addressing the planning of WEEE recycling operations. Their contributions are briefly given as follows in a chronological order. Sodhi et al. (1999) and Sodhi and Reimer (2001) presented mathematical models for planning of recycling operations, including disassembly, bulk recycling and smelting. Ploog and Spengler (2002) and Spengler et al. (2003) developed a mixed-integer linear programming model for integrated planning of acquisition, disassembly
Problem formulation
The proposed LP model is detailed in this section. Assumptions, sets of indices, parameters and decision variables of the model are defined as follows:
The following assumptions were made to simplify the problem:
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All parameters are known beforehand.
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Selling prices for each output are fixed during the planning period.
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Processing times are described with the same fuzzy function for products within the same WEEE category.
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The amount of output obtained from WEEE are described with the same fuzzy
Transformation of the model
The parameters are represented by fuzzy numbers reflecting more efficient and practical real-world applications. In the fuzzy model, fuzzy numbers may be transformed into their crisp equivalents by using defuzzification according to satisfying membership functions at a defined degree (Carlsson and Korhonen, 1986). There are several methods available in the literature to transform fuzzy models with imprecise coefficients into equivalent crisp models (Chen and Chen, 2003, Inuiguchi and Ramı́k,
The case study
An overview of the proposed LP modeling environment and the case study is depicted in Fig. 1. In the case study, there are five products, i.e. e = {1, 2, 3, 4, 5} and f = {1, 2, 3, 4, 5}, and ten fractions, f = {6, 7, 8, …, 15}. There are three types of resources, i.e., direct sales, manual disassembly workstations and bulk recycling units, represented by r = {1, 2, 3}. There are also four activities, i.e., l = {1, 2, 3, 4}, which are SR, CD, BR and CDB. More specifically, after a recycler gets
Numerical results and analysis
The proposed LP model was solved using IBM ILOG CPLEX Optimization Studio V12.7.1 for the case study. In this study, different α values were considered to show how the model output changes in order to enhance the decision maker's flexibility. The model was validated with the help of an expert in the field using the numerical results of a base model. Then, experimental results were obtained for different α values between 0 and 1, where α = 0 reflects the unrealistic and α = 1 reflects the fully
Conclusions and implications
Recycling is one of the recovery strategies used to retrieve recyclable materials and reusable parts from WEEE. Common recycling operations include sorting, disassembly and bulk recycling, whose levels of utilization are important for profitability. In this study, an LP model was presented to determine the best recycling strategies and types and quantities of WEEE to maximize the total profit. The model was developed in a fuzzy environment since, as stated in the earlier studies in the
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