Supply Chain Management of E-Waste for End-of-Life Electronic Products with Reverse Logistics

: Sustainable development and environmental pollution have become valuable stimulating factors for the resource recovery of end-of-life products through reverse logistics. E-waste is considered in reverse logistics. Electronic waste is solely responsible for environmental hazards and contains valuable raw materials that can be recycled/repaired, so reverse logistics is essential to minimizing their inappropriate disposal. This paper presents the mathematical model for multi-electronic products, considering multi-manufacturers and multi-retailers. After the end-of-life product, the reverse logistics network collects the e-waste in return processors where testing, sorting, and disassembling are carried out and then sent to the repair and recycling units. Components that are not repaired/recycled are shipped to the secondary manufacturer as raw materials. An electronic product’s reverse supply chain is employed to incorporate the idea of e-waste nulliﬁcation. The ﬁxed point iteration technique is used to solve the proposed model. A numerical example is analyzed to demonstrate the model’s efﬁcacy where the total cost is minimized. The model’s validity and usefulness in reducing e-waste are validated through managerial insights into the model and sensitivity analysis of the key factors. The proposed policy suggests that the e-waste nulliﬁcation strategy might be a useful apparatus for managers in ensuring long-term sustainability.


Introduction
The notion of reverse logistics (RL) in a supply chain (SC) has been extensively used in businesses around the world due to environmental requirements, the recovery of potentially valuable materials for secondary manufacturers, and sustainable businesses [1,2]. Many governments worldwide require manufacturers to follow the "extended producer responsibility (EPR)" principle because waste creation by diverse industries is rising exponentially. On the other side, a customer's quest for a better way of life results in a diminished product life run [3,4], particularly for electronic and electrical items, which quickly boosts the production of e-waste. Since 2005, the generation of e-waste has increased annually by about 5% [5], which is about three times more than the growth of other garbage [6]. Due to a lack of organized recycling and recovery mechanisms, the rapid development of e-waste origination has become a grave issue [7,8]. As a result, more effort should be made to give decision-makers guidance and support systems to enhance systematic recycling facilities for sustainable management of e-waste [9]. This will enable more e-waste to be recycled and treated in economically, environmentally, and socially effective ways. Real-world organizations are adopting reverse logistics to retrieve electronics products from the market, for example, waste mobile phones in China [10], electrical and electronic equipment in Australia [11], and so on. Consistently, only 8-9 million tons of EOL vehicles are produced, five times fewer than the e-waste generation [12].
RL is a concept that is acknowledged and extensively applied in the global manufacturing sector [13]. RL actions in a waste management paradigm enable more thorough perspectives on resource patronage and recycling for EOL products. An RL system is different from the generic form when e-waste is considered. Manufacturers must create sustainable reverse supply chains (RSCs) in addition to traditional forward SCs, as waste output by many industries continues to grow [14]. E-waste (waste electronic equipment) is significant among the waste generated by various industries. E-waste is currently one of the branches with the strongest development rates because of its shorter product life cycle and fast-shifting consumer attitudes regarding its disposal. E-waste has a more complicated material structure than other EOL products, and it contains valuable (and vital) raw materials, such as gold and copper. Environmentally harmful compounds include lead, mercury, chromium, and ozone-depleting chemicals, such as CFC [15]. The Organisation for Economic Co-operation and Development claims that "EPR is a policy approach under which producers are given a significant responsibility-financially or physically-for the treatment or disposal of post-consumer products" [16].
The complex process of RSC starts with the disposal of EOL electronic products. E-waste return management, however, involves several variables and a higher level of uncertainty, including quality, quantity, and timing [17]. First, there are three separate sources of the enormous generation: households, governments and institutions, and companies. When it comes to collecting locations, e-waste collection differs greatly, for instance: (a) at the municipality pickup points, (b) curbside collection points, (c) delivered to special occasions, and (d) returned to the store or point of sale. The return processor unit collects this e-waste, where e-waste goes through inspection, testing, sorting, and dissembling into several product categories before transferring it for treatment. Next, depending on the value proposition and material content, repair, and recycling exists [18], the scraps are sent to the secondary manufacturer as raw material [19]. For instance, 6000 collection locations were established in Switzerland through three take-back programs, "SWICO, SENS, and Swiss Lighting Recycling Foundation (SLRS)", allowing for the recycling and collection of 95% of the country's electronic trash [20]. The network design that is optimized for efficient and profitable RL procedures plays an essential role. This study considers the multi-manufacturers and multi-retailers for multi-electronic products. After the EOL of the electronic products, the return processor units collect these products, which are inspected, tested, sorted, and disassembled. This study incorporates the repair and recycling of all e-waste, which nullifies e-waste. The scraps are sent to the secondary manufacturer as raw materials to generate some revenue. The proposed framework of the forward and reverse SCs of electronic products is displayed in Figure 1.
The rest of the paper is arranged as follows. Section 2 presents the literature on e-waste and the RL system domain; Section 3 presents the notations and assumptions. Section 4 presents the mathematical model for e-waste nullification. Section 5 describes the solution methodology. A numerical experiment is presented in Section 6 to show how the proposed framework might be used. Section 7 provides sensitivity analyses of key parameters to validate the model. The managerial implications of this study are discussed in Section 8. The paper concludes in Section 9, where we also make some recommendations for further investigation.

Literature Review
Kannan et al. [21] created "a mathematical model for material procurement, distribution, recycling, and disposal of waste batteries based on mixed-integer linear programming". Shokohyar and Mansour [22] created an optimization-and simulation-based multi-objective model for the sustainable design of the RSC of e-waste. Yu and Solvang [23] developed two objective functions for sustainable RSC of e-waste. The model was created by Capraz et al. [24] for decision-makers of e-waste recycling organizations and solved using a mixed linear programming approach. A general reverse logistics network design model was put forth by Ayvaz et al. [25] under sorting ratio, return quantity, and transportation cost uncertainty. Kilic et al. [26] studied "ten scenarios with different collection requirements of e-waste and developed mixed integer programming for designing the optimal RSC structure". A quality-based price competition model is put forth by Liu et al. [27] to assess the effectiveness of legal and informal e-waste recycling pathways. In an e-waste RSC network in Iran, Sajjad and Armin [28] discovered the most appropriate locations for recycling plants and collecting centers. Using the system dynamics technique, the Ghisolfi et al. [29] model calculated the sustainability of SCs in terms of raw material use due to recycling, collection, disposal fees, and return of some items from PCs and laptops. Xu et al. [30] developed a global RSC for solid waste, which included uncertainties about garbage collection levels and constraints provided by the SC's global aspect, and was verified in an e-waste management case study. According to Caiado et al. [31], in developing nations e-waste is a growing waste branch; developing nations may provide infrastructures for the disposal and recycling of e-waste. According to Jafari et al. [32], several factors influence how residents in Iran behave when returning e-waste and taking part in RL activities. The current circumstances surrounding e-waste globally, its management, and the most recent technological advancements in metal recovery from diverse e-waste streams were covered by Işldar et al. [33]. Tasbirul and Nazmul [34] "reviewed numerous research papers published on RL and electrical and electronic equipment/e-waste". Ilankoon et al. [35] analyzed articles, gave an outline of the global supply of e-waste, and identified the industry's main concerns regarding waste management techniques, generation, and international trade. Goswami et al. [36] examined the relationships between the measures of sustainable freight transport performance with the associated externalities and intrinsic characteristics when information exchange occurs between logistics firms and the auto manufacturer. Mondal et al. [37] discussed a hybrid closed-loop supply chain management in cooperation with a hybrid production system and restricted the vendor's carbon missions from the entire hybrid production system. A comprehensive analysis of initiatives to address problems related to improper recycling practices for e-waste and their harmful impacts on humanity, flora, and fauna was presented by Rautela et al. [38]. Ahirwar et al. [39] discussed a few techniques that can be employed to improve e-waste recycling, a more effective and secure procedure. Xavier et al. [40] conducted "an exploratory analysis of the management of e-waste at various scales in the American continent and emphasized the regulatory frameworks in Brazil and Canada to identify how e-waste management options are driven by specific legal, economic, and environmental criteria". To examine the profitable buyback strategy, Ray et al. [41] considered two supply chain models for original equipment manufacturers who produce both new and remanufactured items as well as independent remanufacturers who produce remanufactured products. Mogale et al. [42] developed a sustainable freight transportation network considering capacitated cross-docks for minimizing the total supply chain costs and carbon emission costs. Sarkar et al. [43] created a two-SC model with food waste, waste redirection to the secondary chain, and waste nullification. De et al. [44] addressed the Norwegian salmon food supply chain network by aiming to minimize the fuel cost components from various transportation modes and considered carbon emission-related restrictions. Mogale et al. [45] developed a multi-objective optimization model for a sustainable closed-loop SC considering price-sensitive demand.

Research Gaps and Contributions
In electronic product supply chain models, research has been conducted to obtain zero waste concepts. Different research studies were conducted in the field of e-waste. The following research gaps have been found: • No work has been conducted on integrating SC management and RL under the concept of repairing, recycling, and raw-material conservation. • No concept has been realized regarding the nullification of e-waste without any closed-loop SCs, where raw material can be restored in the system.
The proposed study deals with research gaps and makes the following novel contribution to advancing the knowledge in the field of e-waste: • The proposed research has incorporated the integration of SC management and RL under the concept of repair and recycling. The e-waste generated after the EOL of electronic products is redirected to the return processor units. • The proposed study is based on the e-waste nullification concept. The e-waste is repaired and recycled. A scrap of e-waste is directly sent to the second manufacturer as a raw material. This shows the e-waste nullification and raw-material conservation at the same time. It helps to reduce the disposal.

Assumptions and Notation
For convenience, Table 1 lists all of the input parameters, indices, and decision variables used in this research. This section contains the proposed model's underlying assumptions.

•
In this model, m-type electronic products are considered. After the EOL of electronic products, all electronic products are returned to the return processor units. • This study considers the recycling, repairing, and scraping of returned electronic products, which nullifies e-waste. The parts of EOL electronic products that have been 'scarred' are sold as raw materials to secondary manufacturers. • All retailers in the forward SC have the same ordering and holding costs. • Based on the previous studies, the demand for electronic products in each demand zone is deterministic, i.e., constant.

Parameters
CT m manufacturing cost of product m ($/unit) CTC pr transportation cost from manufacturer to the retailer ($/unit-km) CT r ordering cost of the retailer ($/unit) CTC rd m transportation cost from the retailer to the market ($/unit-km) h rm holding cost of the retailer ($/unit/year) CT i testing and inspection costs at the return processor ($/unit) CT s sorting cost at the return processor ($/unit) CT d disassemble cost at the return processor ($/unit) CTC kl transportation cost from the return processor to the repair unit ($/unit-km) CT rp repairing cost per item ($/unit) CTC kn transportation cost from the return processor to the recycling unit ($/unit-km) CT rc recycling cost per item ($/unit) P s selling price of scrap ($/unit)

Decision variables
Q m production quantity of product m Q pr amount transferred from the manufacturer to the retailer of product m Q rd m amount transferred from the retailer to the market Q kl amount transferred from the return processor unit to the repairing unit Q kn amount transferred from the return processor unit to the recycling unit

Mathematical Model
The mathematical model's primary objective is to minimize the total supply chain cost (TSC) and nullify e-waste. The four echelons exist in forward SC (a) manufacturer (P), (b) retailer (R), (c) demand zones of electronic products (D m ), and (d) return processor unit (K). After EOL electronic products, the return processor units do the testing/inspecting, sorting, and disassembling of returned electronic products. The return process sends the equipment of EOL electronic products for the nullification of e-waste (according to the analysis in return processor units) to the (a) repairing unit (L), (b) recycling unit (N), (c) scrap. The scraps of EOL electronic products that cannot be repaired/recycled are sent to the secondary manufacturer as raw materials. Objective (12) is determined as the TSC of the intended SC for electronic products and e-waste nullification.

Manufacturing Costs
Firstly, electronic products are manufactured by different industries. Electronic product production quantities must satisfy the demand for electronic products. Thus, the optimal production quantity of electronic products is essential to optimize production costs. The per unit production cost of the electronic product m at the manufacturer p is given as (1)

Retailer's Cost
Retailers order electronic products m from manufacturers p, so the ordering costs are associated with retailers. All retailers are expected to carry the same amount of inventory of electronic products.

Ordering Cost
The ordering costs of electronic products m from manufacturers p at retailers r follows

Inventory Holding Cost
All retailers adhere to the model of economic order quantity. After receiving the manufacturer's shipments, all retailers have part of the electronic products in inventory. The per-unit inventory holding costs of electronic products m at retailers r are as follows

Return Processor's Cost
All electronic products are collected back to the return processor units following the EOL of those products. Electronic products acquired by EOL are tested and inspected in the return processor. After which, these products are sorted and disassembled. The costs of testing/inspecting, sorting, and disassembling electronic products m at the return processor units k are given as (4)

Repairing Cost
When the return processor units discover that x% of the electronic products are damaged, vandalized, or destroyed, these parts are sent to the repairing unit. The x% of EOL electronic products m are repaired at the repairing unit l, and the cost of the repair is as follows

Recycling Cost
Recycling is a key component of modern e-waste reduction, i.e., the return processor units discover that y% of the electronic products are waste that could be recycled to create new products and resources. So, these parts are sent to the recycling unit. The y% of the EOL electronic products m are recycled at the recycling units n, and the cost of the recycling is as follows

Scrap Material
Scraps are leftover bits of electronic products that cannot be repaired/recycled. When the return processor units discover that z% of the electronic products were scrapped, these scraps are sent to the secondary manufacturer as raw materials, which provides some financial help for the industries. The z% of EOL electronic products m are sent to the secondary manufacturer o, and the profit from the scrap material is as follows

Transportation Cost
The manufacturer transports the electronic product m to the retailer r, and the retailer fulfills the market's demand. In RSC, the return processor unit sends x% of electronic products to the repair unit l for repairing, and y% of electronic products to the recycling unit n for recycling. The transportation costs among these SC echelons are given as

Mass Balance
Electronic products m delivered to all retailers r must be less than the electronic products manufactured at the manufacturer p, according to constraint (9)

Demand Constraint
The demand of each demand zone D m of the electronic product m must be fulfilled by the retailers r (10).

Non-Negative Constraint
All the decision variables are non-negative constraints.

Total Cost
The main objective focuses on minimizing the total cost of the SC and the profits from the scraps that are generated by EOL electronic products.

Solution Methodology
The solution methodology for this designed model requires an approach that can manage a range of variables. It is a time-consuming effort to manage a large number of variables using a classical approach. Several techniques can be employed to obtain an optimal result. This model aims to minimize the total SC cost by allocating the quantity from the manufacturer to the retailer of product m, from the retailer to the market, from the return processor unit to the repairing unit, and from the return processor unit to the recycling unit. To obtain a closed-form solution to this mathematical model, the fundamental operation of non-linear programming, called a fixed point iteration technique, is performed [46].

Numerical Example
One numerical discussion with the optimal TSC was developed to validate the model where several parameters from Sarkar et al. [43] are referenced. The numerical information is shown in Table 2. The main objective is the nullification of e-waste that minimizes the TSC. For the RSC of electronic products, the three types of electronic products (m = 1, 2, 3), two manufacturers (P1 and P2), three retailers (R1, R2, and R3), two return processors (K1 and K2), two repair units (L1 and L2), two recycling units (N1 and N2), and four market zones (D1, D2, D3, and D4) for electronic products are considered.

Results
The results reveal that the optimal cost for the given SC network is $7.475654 × 10 8 . The optimal quantity of electronic products (m) transferring at distinct stages of the forward SC is given in Figure 2. The return processor units send x% of EOL electronic products for repair to the repair units, and y% of EOL electronic products for recycling to the recycling units, as presented in Figure 3. The outcomes of the aforementioned case demonstrate that, to meet the demand of the markets, the manufactured products are as follows: A    Table 3 compares the cost capacity and the effects of changing various limits on various factors. The following percentages vary the parameters: (±50%, ±40%, ±30%, ±20%, ±10%).

•
The testing and inspection costs at the return processor have similar behavior of positive and negative alterations in the total costs. The extremely substantial discovery is that the disassembly cost at the return processor is the most sensitive metric. • Figure 4 demonstrates how the total cost increases along with the rising repair costs and recycling costs. If the CT rp increases by 10% to 50% and the CT rc increases by 10% to 50%, then the total SC cost increases linearly. • A large or low change in the amount of the demand parameter for all markets of electronic products results in a sizable change in the total cost that is demonstrated in Figure 5.

Managerial Insights
The minimization of TSC and e-waste nullification are the two main focuses of this research. The results mentioned above provide strategic and critical insights for organizations involved in the electronic products of SC networks.
• Landfills must be kept to a minimum for sustainability. Any reason-related e-waste produced in retail establishments could be diverted away from landfills and used for another purpose. The e-waste nullification approach is the suggested policy in the research study and it may be a crucial instrument for management to maintain sustainability. • The repair and recycling costs of EOL electronic products have been the most sensitive metrics among all costs. Management can reduce the burdens of these costs by generating revenue from scraps sold as raw materials to secondary manufacturers. • Management can optimize the quantity and order period, which can optimize the rate of the creation of e-waste, using the recommended policy in the current study.

Conclusions
The idea of waste nullification was subjected to the SC for electronic products in this study. The multi-electronic products were manufactured at multi-manufacturing units, finished electronic products were sent to the retailers, and the retailers fulfilled the demand for electronic products. The e-waste was generated after the EOL-electronic product was collected. The e-waste was collected at the return processor unit for testing/inspection, sorting, and disassembly. Products that could be repaired were transferred to the repair units, and those that could be recycled were sent to recycled units. The scrapes were shipped to the secondary manufacturer as raw material for nullifying e-waste. The fixed point iteration technique was implemented to solve the developed model.
The study produced insightful management information that can help firms and decision-makers create SC designs for electronic products. Electronic products could be manufactured to profit from this reverse supply chain, where the increment of e-waste was diminished to tackle the current environmental concerns. The organization may optimize the quantity and ordering time, which can optimize the waste production amount, using the recommended policy in the present study. This research enhances the body of literature by acknowledging managerial, policy, and realistic challenges in the electronic product's SC and e-waste nullification. This model can be efficient and find the solution in a reasonable time for large problems, as seen in the real-world scenario.
The model can be extended as the conceptualization of the triple bottom line (economic, social, and environmental aspects), and carbon tax policy. The environmental aspect and carbon tax policies can be implemented in the transportation sector and at manufacturers, recycling units, and repair units. The social aspects refer to the number of jobs provided in the transportation sector and at manufacturers, recycling units, repair units, and retailers. Some of the major concerns that need to be addressed in the future include the type of e-waste items disposed of, the average lifetime of the disposed product, the disposal rate, and customer awareness. It would significantly increase the value and significance of the paper.