# Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors
## 1 Introduction  
The latest technological advances have considerably shortened the lifetime of electronic products. Currently, obsolete or old electronics are rapidly being replaced by new models with more advanced functions and attractive designs [1]. This has led to electronic waste (e-waste) being one of the world's fastest-growing wastes and it is estimated to increase to 52.2 million tonnes (mt) of e-waste in 2021 [2]. Current statistics show that China is the world's top e-waste producer, having generated 10.1 million tonness of e-waste in 2019. These numbers for Africa, America, Asia, and Europe are 2.9 mt, 13.1 mt, 24.9 mt, and 12.9 mt, respectively. Values of raw materials which can be extracted from e-waste are 3.2 billion, 14.2 billion, 26.4 billion, and 12.9 billion regarding Africa, America, Asia, and Europe, respectively. The data have shown that e-waste is a valuable resource and has a crucial impact on the economy [3]. The mismanagement of e-waste can lead to serious effects for the environment and humans [4, 5]. For instance, a large amount of e-waste in Guiyu, China, which is normally processed with manual methods and improper techniques, resulted in significant impacts on soil, water, and human health [6]. However, e-waste also comprises approximately 60 different types of metals including some valuable metals such as gold, copper, aluminum, silver, steel, and iron [7]. To diminish the significant impact of e-waste and recover valuable raw materials, a reverse supply chain (RSC) operation is considered as an effective approach [8, 9]. RSC is a set of different activities which aims to reuse or recycle a returned/used product from end-users or dispose of it suitably [10]. Competitive advantages, customer loyalty, environmental regulations compliance, and cost reduction can be achieved through RSC operation [11, 12, 13, 14, 15]. RSC has been investigated by many scholars [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. However, most research considers parameters in RSC that are deterministic or known in advance, whereas the RSCsystem is normally known as a dynamic operation with a high level of uncertain data such as return rate, relevant costs, capacity, etc. [23; 29; 30; 31; 32; 33]. To handle these imprecise data, stochastic techniques have been utilized [34; 35; 36; 37]. However, using a stochastic method normally causes two main issues. Firstly, in some practical situations, collecting historical data is not enough to be used for uncertain parameters so it is quite a challenge to obtain the exact random distributions for these parameters. Secondly, a stochastic approach, used in previous studies, is normally used through different scenarios for modelling the uncertainties which might cause heavy computational burdens [38]. In this regard, to cope with the difficulties of stochastic methods, the fuzzy approach has been considered as a potential solution since it can solve imprecise data and different types of uncertainties at the same time with high computational efficiency [39]. A few studies [40; 41; 42; 43; 44; 45] applied the fuzzy method to cope with supply chain management problems. [PERSON] [42] proposed an interactive fuzzy multi-objective linear programming (FMOLP) to solve transportation problems with the minimization of the total distribution costs as well as the delivery time. FMOLP is the method that was developed to solve the multiple fuzzy linear programming by integrating the satisfaction of the decision-maker through the auxiliary variable L. If the solution is L = 1, then each objective is fully satisfied; if 0 < L < 1, then all of the objectives are satisfied at the level of L, and if L = 0, then none of the objectives are satisfied. Furthermore, a supply chain system involves various activities across many organizations including suppliers, producers, retailers, and customers and due to this fact, there might be a high degree of risks involved across the supply chain [46; 47]. According to [PERSON] et al.