Optimizing an E-Waste Reverse Supply Chain Model while Incorporating Risk Costs

Corresponding Author: Linh Thi Truc Doan School of Engineering, University of South Australia, Australia Email: linh.doan@mymail.unisa.edu.au Abstract: The rapid growth of Electronic Waste (E-waste) in recent years has created serious influences on the environment and society. The highly potential solution to mitigate this issue is the Reverse Supply Chain (RSC) which can reuse and recover E-waste materials. Risks generally derive from a RSC operation such as collection, transportation and treatment risks, but most studies ignore risk effects on the total cost of E-waste treatment in the RSC model. This paper aims to develop a mathematical model for an Ewaste RSC considering risk costs. This proposed model applied mixed integer linear programming and solved by a mathematical programming language. An illustrative example is examined to demonstrate the effectiveness of the proposed model. Sensitive analysis is also presented. The results can determine the optimal locations of facilities and the flow of materials or items in a RSC network. Furthermore, the network design decisions have been changed considerably while risk costs are incorporated.


Introduction
Due to technological advancements, customers seem to purchase the latest electronics inventions more frequently than ever. According to , the quantum of E-waste has generated around 14 million tonnes in 2014 and growing from 3 to 5% annually. Around 50 to 80% of E-waste from industrialized countries is sent to poor countries due to lower labor cost and less strict environmental regulations (Namias, 2013). For example, this would be the main reason why a number of old computers in the developing countries is forecasted to be doubled (around 600 million products) compared to the developed nations (nearly 300 million units) by 2030 (Yu et al., 2010). E-waste contains valuable materials like gold, copper, silver (Kang and Schoenung, 2005;Chancerel et al., 2009) while it also comprises hazadous substances such as lead, cadmium, mercury and hexavalent chromium (Saphores et al., 2012;Phuc et al., 2013). To mitigate the quantity of E-waste delivering to landfills and recover useful materials, manufacturers have focused on 3R approaches (Reuse, Recycle and Remanufacture) across the Reverse Supply Chain (RSC) on E-waste management (Kuik, 2013;Nagalingam et al., 2013;Kuik et al., 2011). RSC is a set of activities required to recover a returned product from a consumer and reuse or dispose it (Van Wassenhove, 2002). RSC operation can bring many advantages for companies such as the competence of enterprises, customer satisfaction and cost reduction (Choy et al., 2011;Pishvaee et al., 2010).
One of the potential solution to treat end-of-life products is RSC which has been attracted an increasing number of research activies (Sinha-Khetriwal et al., 2005;Saphores et al., 2012;Bouvier and Wagner, 2011;Li and Tee, 2012;Nagurney and Toyasaki, 2005;Kilic et al., 2015;Grunow and Gobbi, 2009;Shih, 2001;Menikpura et al., 2014;Niknejad and Petrovic, 2014;Rajagopalan and Liles, 2006;Amer et al., 2011). Most studies mainly consider the total cost for processing end-of-life products across RSC (Achillas et al., 2010;Dat et al., 2012;Phuc et al., 2013;Niknejad and Petrovic, 2014;Demirel et al., 2016;Fleischmann et al., 2001) and apply Mixed Integer Linear Programming (MILP) formulation to their models (John et al., 2017). An earlier study about the Reverse Logistic (RL) network for secondary containers using (Kroon and Vrijens, 1995). MILP is investigated by Achillas et al. (2010) suggested a RL network for E-waste and focused on the optimization of total cost. The model developed MILP and solved through A Mathematical Programming Language (AMPL). The cost elements taken into account in this model are transportation cost, operation cost and fixed cost. A real case study in Greece was obtained to validate the model. The authors suggested that incentives to consumers need to be considered to encourage a number of old products returned. This model is effective for addressing medium to small scale problems since the number of binary variables is limited. Dat et al. (2012) proposed MILP to address a multiple-echelon RL model of multiple types of E-waste. The issue is modeled by applying AMPL and then addressed by CPLEX software. This model can determine the feasible locations for constructing facilities and material flows in RL network. Mahmoudi and Fazlollahtabar (2014) suggested a multi-product RSC with considering the total costs involving shipping, fixed, operation, supply maintenance and remanufacturing costs. Kilic et al. (2015) proposed a RL system of E-waste in Turkey with 10 different scenarios of collecting rates. MILP was used to minimize total cost of RSC. Compared to the other existing researches, the model considered different categories of storage and recycling centres. Demirel et al. (2016) introduced a RSC model for end-of-life vehicles in Turkey to optimize the total cost for the recovery operation.
Based on the literature review, most studies mainly focus on transportation, fixed and operation costs and income from recovery materials to minimize the total cost of a RSC operation. Unfortunately, risks are largely not considered in the RSC models and having a significant influence on RSC costs (Sheu, 2007). Risks generally happen at treatment facilities and shipping activities because of a variety of hazardous materials contained in E-waste (Fabiano et al., 2002;Ho et al., 2009;Wilson, 2007). In addition, waste generation is uncertain which can cause risks for collecting areas (Ahluwalia and Nema, 2006). Therefore, the current models are inadequate for representing the RSC system for E-waste. Hence, this paper focuses on a comprehensive RSC model to minimize the overall cost for E-waste treatment incorporating risk costs. This proposed model can be considered as a useful tool for decision makers.
The rest of the paper is organized as follows; Section 2 presents the proposed mathematical model while a numerical example to demonstrate the possibility of the proposed model is addressed in Section 3. Results and discussion are provided in Section 4. The sensitive analysis is presented in Section 5. Finally, in Section 6 conclusions and possibilities for future research are elaborated.

Proposed Model for E-Waste Reverse Supply Chain
To overcome the literature gap presnted in Section 1, the proposed model aims to develop a mathematical model for an e-waste RSC model to minimize the total cost. The key difference of the proposed model to other existing models is that risk costs are included across RSC. Risks generally stem from factors such as supply risks, transportation disruptions, or technological issues in RSC (Sharma et al., 2012;Gu and Gao, 2012) and might affect the flow of materials in the RSC network. In this model, risks are considered at collection and treatment facilities and transportation between sites in the proposed E-waste RSC. The proposed model focuses on the development of a multi-layer RSC network for multi-products which include four stages as shown in Fig. 1. Firstly, returned products are collected from collection areas (A in Fig. 1) such as stores selling the appliances and designed collection sites by classified groups. They are then sent to dismantling facilities (B). Secondly, after receiving the returned products from collection areas, the main task of this stage is to separate these products into fractions and determine which items (or parts) should be transported to the right centers. For example, toxic materials or hazardous items are then transported to landfill sites (G). Some damaged or broken components are transported to refurbishing facilities (C). The rest of components in need of further treatment are sent to recycling facilities (D). The third stage involves recycling and refurbishing facilities receiving components from dismantling facilities. Damaged components will be treated at refurbishing facilities. In recycling facilities, certain parts such as plastic, ferrous metals and non-ferrous metals will be recycled while toxic substances such as mercury, lead, mercury and barium will be delivered to landfills. The fourth layer consists of landfill sites, material and secondary markets. The recycled materials will be sent to material markets while the secondary markets include directly reusable components and upgraded items. The dangerous or nonrecyclable materials will be sent to landfill sites.
Based on this four stage RSC, a mathematical model is developed to find the total cost across the entire RSC, some assumptions are necessary to be made and listed in the below: • The locations of collecting returned products, landfill sites, material and secondary markets are decided in advance • The capacities of facilities are limited • The unit transportation cost is related to the distance traveled • The likelihood of accidents happening and the loss of such accidents are predetermined  The loss of occurrence of an accident of collecting returned product h at collection area a I2 hb The loss of occurrence of an accident of processing returned product h at dismantling facility b

I3 jc
The loss of occurrence of an accident of processing reusable item j at refurbishing facility c I4 id The loss of occurrence of an accident of processing recycling material i at recycling facility d I5 ab The loss of occurrence of an accident of shipping from a to b I6 bc The loss of occurrence of an accident of shipping from b to c I7 bd The loss of occurrence of an accident of shipping from b to d I8 bg The loss of occurrence of an accident of shipping from b to g I9 ce The loss of occurrence of an accident of shipping from c to e I10 df The loss of occurrence of an accident of shipping from d to f I11 dg The loss of occurrence of an accident of shipping from d to g Total cost = collection cost (C 1 ) +constructing cost (C 2 ) +operating cost (C 3 ) + shipping cost (C 4 ) + disposal cost (C 5 )+ risk costs (C 6 ) -income from selling recovery materials and renew items (I).
Cost of collecting returned products at collection areas is given as follow: Cost of constructing treatment facilities (dismantling, recycling and refurbishing facilities) is described below: Cost of operation at treatment facilities can be calculated as following: Shipping cost from one facility to another facility is presented as below: Disposal cost for discarding non-recyclable and toxic materials can be calculated as: Risk costs (C 6 ) are the cost happening from the probability of any disruptive appearance that might affect a part of the collection, shipping and operation costs at facilities. According to (Sohani and Chaurasia, 2016), the risk qualification can be calculated by multiplying the likelihood of occurrence and the loss. In this research, for instance, the first component of risk costs in Equation 6 presents the risk arising from the collection activity such as uncertain quality of product returns and having an influence on collection cost. Similarly, the second, third and fourth components of risk costs might arise from the undesirable event like less 22 manpower or technological issues during the processing product returns at dismantling, refurbishing and recycling facilities. The rest parts indicate the shipping risks during RSC network.
In the proposed model, the main objective is to minimize the total cost from (1)-(7). Constraint (8) ensures all returned products are collected from collection areas. The outcomes of dismantling facilities are presented by constraints (9)-(11). Constraints (12)-(14) make sure the flow equivalence at different kinds of facilities. Constraints (15)-(18) require that the total quantity of items or components at dismantling, refurbishing, recycling facilities and landfill sites do not exceed the maximum capacity of these facilities.  guarantee that the amount of items do not exceed the maximum demand of material and secondary markets. Constraints (21)-(22) represent the binary and non-negative variables.

Numerical Example
This section presents a numerical example to verify the proposed model. In most situation, the size of the reality issue is usually enormous so the process of calculating seems to be difficult to verify the proposed model. Therefore, the size of the suggested problem is considerably chosen to help the readers to simplify the proposed model easily. This model considers two types of returned products. The size of the proposed model and relevant parameters are shown in Table 1-15 adopted from (Dat et al., 2012;Phuc et al., 2013) with a small adjustment to suit the suggested model. The likelihood score and the loss score of accident occurrence are generated with a scale of 1 (lowest) to 10 (highest) adopted from (El Dabee et al., 2014).        Recycling materials items

Results and Discussion
The proposed mathematical model is solved by using AMPL with processor Intel ® Core i5-3.3 GHz and 8 GB RAM. The optimal total cost is equal to $65727 with risk costs while the total cost is $57453 without risk costs. The result indicates that risk costs in the RSC operation have a remarkable impact, accounting for 14.4% of the total cost. In consideration of risk costs, the opening facilities and the flow of materials and items in the network have been changed. The noticeable difference between the model without considering risk costs and the one with integrating risk costs is the opening of recycling facilities in the network. Without incorporating risk costs, only d1 should be opened while d1 and d2 should be built in the model that risk costs are incorporated (Table 16). As a result, this can lead to the differences in the flow of items (V3 ibd , V6 idf , V7 ndg ) transported in the network in the two situations (Table 17-18).

Sensitivity Analysis
In this proposed model, all parameters are assumed constant over time. However, these parameters might change due to unexpected elements in the real world and consequently might affect the solution of the model. To mitigate this issue, a sensitivity analysis is utilised to investigate the variation of the result and the model. The sensitivity analysis is conducted by changing the value of one parameter in a range from −20 to +20% while the remaining parameters are unchanged.
Comparison between parameters only showing the value of the highest level (+20%) and the lowest level (−20%) are presented in Table 19. Furthermore, a new total cost is obtained by optimizing the model with the modified parameters. The model sensitivity is shown in Table 19 (Columns a-c) with the proportion of change between the new and current total cost. Generally, as can be seen in Column c of Table 19, the total cost is slightly sensitive to the majority parameters changed. It is also shown that the fluctuation of the parameters by 20% lead to changes in the total cost by less than 2.5% only. However, the variation of demand and shipping cost strongly affect the overall cost. Determining the number of opening facilities in the RSC network is not really affected by the changes of most input parameters by 20%, except for the demand changed (Column d, Table 19).

Conclusion
This paper suggests a comprehensive E-waste reverse supply chain model integrating risk costs during collection, shipping and treatment of returned products in RSC activities. Multi-product and multi-layer RSC model consisting of many recycling processes for different types of electronics waste are considered. The suggested model is addressed by using AMPL which can provide exact solutions and handle large-scale optimization. From the numerical test, it is illustrated that risk costs regarding the RSC operation have a vital effect on the overall cost. The flow of materials or items have significantly changed in the RSC network in consideration of risk costs. This proposed model is able to assist decision makers in designing RSC network for E-waste.
For future research, a case study in which the proposed model is applied for a particular industry should be conducted to validate the practical application of this study. This proposed model has not considered the way to reduce risks. Therefore, this model can be extended to trade-off between risks and cost. Furthermore, one of the main issues related to establishing RSC activities is the level of uncertainty in terms of the amount of returned products, cost and risk factors and this problem may be addressed in future work.

Ethics
This manuscript is original. The corresponding author would like confirm that all authors have approved the manuscript and no ethical issues involved.