A Stochastic Multi-Objective Model for Optimal Design of Electronic Waste Reverse Supply Chain

Abstract

The consumption of electronic products is growing rapidly, resulting in considerable amounts of electronic waste (e-waste). In addition, economic, environmental, and social perspectives increased the need to develop an effective reverse supply chain (RSC). This study, therefore, formulates a stochastic model for a multi-objective, multi-product, multi-period RSC for electronic waste (e-waste) under uncertainty in returns’ quantity, quality, and availability to repair. Three objective functions are considered: maximizing profit, maximizing social impact, and minimizing CO2 emissions. The end-of-life (EOL) household appliance firm was considered for illustration. Results showed that selling products’ parts and generating 123.025 tons of raw materials are expected to generate profit and revenue averages of USD 547,750 and USD 220,207, respectively. The multiple-product RSC is expected to increase profit by 2.3 times that of a single-product RSC. Finally, the effects of uncertainty in model parameters on the objective functions are examined. In conclusion, the proposed RSC of e-waste can effectively enhance sustainability.

1. Introduction

A supply chain (SC) is a connected network of various entities involved in the manufacturing and delivery of finished goods or services [1]. Forward Supply Chain (FSC) transforms raw materials into finished products to fulfill customer demands [2]. Unfortunately, the growing quantities of end-of-life (EOL) products have increased negative environmental impacts and exhaustion of natural and non-renewable resources [3,4,5,6,7]. Specifically, the consumption of electronic products is growing rapidly, leading to large volumes of EOL products and, in turn, considerable e-waste [8]. Hence, growing concerns from economic, environmental, and social perspectives have increased the need to develop an effective reverse supply chain (RSC) for e-waste [9]. Moreover, the increased awareness of economic, social, and regulatory compliance-related benefits has attracted organizations and manufacturers to implement RSC [10,11].

Generally, an RSC includes various operations: collection, inspection, sorting, and recovery of returned products [11,12,13]. Mainly, e-waste recovery comprises several main stages, including collection and sorting, refurbishing and then selling to second-hand markets, a disassembly process for repairing and then selling the spare parts or recycling the extracted parts material or products’ material, and then selling to the raw material market, and finally landfill for parts or materials disposal [14,15,16,17]. From an economic perspective, the RSC reduces material consumption, adds value to recovered products and materials, and reduces costs associated with waste processing or disposal. Further, legislation and regulations have compelled organizations to take responsibility for processing returns and develop effective disposal motivated by economic incentives for remanufacturing. Furthermore, customer awareness and social responsibilities towards the environment have emphasized the need to implement RSC [18,19].

Recently, electronic and electrical waste (e-waste) has become a rapidly increasing waste stream, leading to serious environmental issues [20]. Besides its hazardous contents, e-waste typically contains valuable materials that, if recycled properly, could yield significant sustainability benefits. In addition, RSC design is a complicated process due to uncertainties in returns’ quantity and quality, market demand, various costs (transportation, handling, processing, opening, and operation), job opportunities, CO2 emissions factors, capacity, and recovery fraction. Recently, significant research has been conducted on the design of an optimal RSC of e-waste, focusing on the following: (1) the sole focus on cost minimizing, (2) dealing with certain model parameters, (3) a close focus on short-term planning design RSC over a single planning period, (4) the design of RSC for a single product, (5) lack of consideration of the availability of repair, and (6) pre-assignment of the facility locations and types of the RSC stages.

Jordan is directing significant efforts toward achieving sustainable development goals [21]. Importantly, the e-waste is evolving. The most common types of electrical and electronic equipment (EEE) are refrigerators, washing machines, and televisions, with an average of one item per household. In terms of weight representation, the most discarded EEE appliances are washing machines and kitchen equipment, with percentages of 49% and 34%, respectively. Consequently, a reliable RSC should be established to manage the recovery and recycling of e-waste processes. Stochastic modeling, also known as stochastic optimization, is a mathematical framework that supports decision-making under uncertainty [22,23,24]. The use of stochastic modeling for the optimal design of RSC supports decision-makers in obtaining reliable and valid assessments of the supply chain performance and making effective long-term decisions [25,26].

In these regards, this research aims to develop a stochastic multiple-objective mathematical model for RSC design of e-waste from multiple products over multiple periods, taking into consideration the uncertainties in the availability of repair for the collected parts, and the quality and quantity of product returns. An illustrative e-waste case study from Jordan for two electronic machines, refrigerators and dishwashers, is considered for illustration. The proposed RSC model enables decision-makers to make effective strategic and operational decisions regarding the construction or opening of different RSC facilities or stations, the physical reverse flow, and the products, parts, and materials that are attractive for collection, repair, and extraction. This research, including the introduction, is outlined as follows. Section 2 reviews relevant studies on RSC of e-waste. Section 3 outlines the development of the RSC mathematical model. Section 4 conducts computational analysis. Section 5 performs sensitivity analyses. Section 6 summarizes the concluding remarks, limitations, and future research.

2. Literature Review

The optimal design of RSC for e-waste has received significant research attention.

2.1. Deterministic and Fuzzy RSC Design on E-Waste

Wang et al. [27] proposed a two-phase fuzzy model to determine the optimal locations of treatment and transfer sites for e-wastes in RSC. The Dalian Economic-Technological Development Area in Dalian City in China was used to illustrate the proposed model. Wang et al. [28] designed a multi-echelon RSC for collecting and processing e-waste using multi-objective integer programming. The objective functions were to minimize total operation costs and disutility to people. Shanghai Xuhui District was considered to verify and validate the model. Aras et al. [29] formulated a mixed-integer model for optimal multi-period capacitated facility location-allocation under the uncertainty in the quantity of collected used products. The objective function was to minimize the maximum regret associated with the occurrence of different cases, including discarded personal computers, inkjet, and LaserJet printers in 15 major cities of Turkey. Mashhadi et al. [30] used an agent-based simulation framework to optimize e-waste recovery. The goal was to determine the optimum buy-back price proposed for a product to control the timing and quality of electronic products. Shokouhyar & Aalirezaei [31] formulated a multi-objective genetic algorithm to solve a two-stage RSC based on sustainable development objectives: economic, environmental, and social objectives. The model aimed to determine the best locations for collection stations and recycling plants in Iran. Phuc et al. [32] developed a model of optimal RSC with multiple EOL vehicles in Japan considering fuzzy model parameters. The model was transformed into linear programming with fuzzy parameters. Xu et al. [33] formulated a mixed integer model and robust optimization for the design of green RSC. The waste collection levels, associated carbon emissions, maritime transportation costs, and currency exchange rates were uncertain. Chaudhary et al. [34] examined barriers to the effective adoption of e-waste RSC in India using interpretive structural modeling. Results revealed that legal issues, lack of awareness, and poor infrastructure were the major barriers to the e-waste RSC. Guo et al. [35] established a two-echelon RSC for collecting e-waste using a game theory model. A centralized decision was made to maximize recovery price, recovery quantity, and publicity efforts. Agrawal et al. [36] explored the key strategic issues and challenges faced by an Indian electronics organization in managing RSC. They also investigated the critical success factors, outsourcing decisions, disposition decisions, and forecasting product returns. Linh et al. [37] developed a mixed-integer linear model to minimize the total e-waste cost of RSC under transportation risks and then determined the optimal locations and the amount of used products transported within the RSC network. Hashemi [38] used a multi-objective genetic algorithm and a customized bee colony algorithm to solve fuzzy mathematical programming for RSC. The model aimed to minimize the costs of facility construction, vehicle fuel, and environmental impact, and the ratio of satisfied demand over multiple periods. Cinar [39] developed a mixed-integer linear programming model for designing a sustainable RSC with multi-objective functions to minimize the system operation cost and minimize the carbon emissions related to the transportation and processing of used products. A case study from the wind turbine sector was used for model validation. Kumar Singh et al. [40] formulated a mathematical model to minimize the total cost of multi-electronic EOL products under multi-manufacturers and multi-retailers using fixed-point iteration technique. Kannan et al. [41] formulated a mixed-integer model to minimize both network cost and environmental impact resulting from transportation and processing activities in the RSC of an electronics-manufacturing firm in India. Oliveira Neto et al. [42] performed simulations and genetic algorithms for economic and environmental optimization of the RSC of e-waste in Sao Paulo, Brazil. Economic evaluations covered the reduction in fuel, drivers, insurance, and maintenance. Environmental evaluation assessed the impacts of abiotic, biotic, water, and greenhouse gases. Ali [43] proposed a multi-objective mixed-integer linear programming model to optimize e-waste management in India. The model aimed to minimize total cost, maximize resource recovery, and reduce environmental impact. A benchmark analysis against three traditional methods—Rule-Based Heuristic, Linear Programming, and Greedy Cost-Minimization. Singh et al. [44] developed a multi-manufacturer and multi-retailer framework for RSC of e-waste management, considering constrained decision-making problems, optimizing resource allocation, minimizing costs, and enhancing environmental sustainability using sequential quadratic programming and a numerical optimization technique. Sensitivity analysis and Pareto analysis were performed to demonstrate the robustness of the proposed model.

2.2. Stochastic RSC Design on E-Waste

Ayvaz et al. [45] proposed a two-stage stochastic programming for multi-echelon, multi-stage, multi-product RSC design. The study considered uncertainty in the quantity and quality of returns as well as transportation cost. The objective function was to maximize the total profit from e-waste recycling. John et al. [46] constructed a mixed-integer linear model for the optimal design of a multi-stage RSC. The objective function was to maximize the total profit while varying the quantity of returns, transportation cost, and processing cost. RSC design for used refrigerators was considered for model validation. Tosarkani and Amin [47] proposed an environmental optimization model to configure a hybrid FSC and RSC under uncertainty for a multi-echelon lead acid battery network in Winnipeg, Canada. A fuzzy method and stochastic programming. The objectives were used to maximize total profit and maximize the environmental compliance of suppliers, plants, and battery recovery stations. Polat et al. [48] optimized RSC under fuzzy parameters, fuzzy sales prices, product weights, costs, and product demands, to reduce the total gain and total cost. Kuşakcı et al. [49] formulated a fuzzy mixed-integer location-allocation model for the RSC of end-of-life vehicles (ELV) at minimal total cost. The model determined the optimal locations of dismantling stations, processing, and recycling stations, in addition to determining the material flow between the network nodes. Yuchi et al. [50] proposed a bi-objective mixed-integer model to maximize profit and minimize CO2 emissions of a reverse logistics network (RLN) under uncertainty in return quality for truck tire remanufacturing. Tosarkani et al. [51] proposed a case-based possibilistic approach to optimize a multi-period, multi-echelon, multi-product, and multi-component electronic RLN. The model considered the uncertainty in the quantity and demand of returns, the quality of returned products, and costs, fixed and variable. The proposed multi-objective model aimed to maximize the environmental compliance and maximize total expected profit. Gao & Cao [52] proposed a multi-objective case-based optimization model to maximize the expected total profits, minimize total carbon emission costs, and maximize total job opportunities while considering facility reconstruction in a tire supply chain. Rau et al. [53] formulated a two-stage stochastic mixed-integer model of a multi-player RSC under uncertain demand. Disassembly, reconditioning, and reassembly strategies were developed to configure forecast and demand-driven RSC operations. The notebook computer RSC was used for illustration. Roudbari et al. [54] developed a two-stage stochastic mixed-integer programming model for optimal RSC design of the medical equipment supply chain. Their model maximized profits from returned products. The model considered uncertainty in the quality and quantity of returned products. Moslehi et al. [55] developed a bi-objective mixed-integer programming model for optimal RSC of e-waste. The focus was to minimize cost and maximize the environmental score by recovering and recycling processes while considering uncertainties in demand and return rate. The model was illustrated through a case study of an electronic equipment manufacturer in Esfahan, Iran. Karagoz et al. [56] constructed a case-based stochastic mixed-integer model to manage the ELV network in Istanbul. The objective was to determine the optimal number, locations, and material flow for network facilities that minimize total cost. Najm & Asadi-Gangraj [57] proposed a fuzzy multi-objective mixed-integer linear programming model for a sustainable RSC under uncertainty. Three objective functions were considered, including minimizing the total cost while maximizing social and environmental impacts. Finally, sensitivity analyses were conducted on key parameters to assess model robustness. Shahrabifarahani et al. [58] developed a mixed fuzzy multi-attribute decision-making approach, a multi-period, multi-objective mixed-integer possibilistic linear programming model for an optimal closed-loop chain of electronic devices under epistemic data uncertainty. The model was applied to the smartphone network in Iran. Several sensitivity analyses were carried out.

Table 1. Summary of relevant studies on stochastic RSC of e-waste.

Author Name	Paper Topic	Objective Function			Uncertainty			Multi-Product	Multi-Period	Multi-Objective	Mathematical Approach
		EN	EV	SL	Availability for Repair	Returns Quality	Returns Quantity
Ayvaz et al. [45]	Stochastic RSC design for e-waste	✓				✓	✓	✓			Two-stage stochastic programming
Li et al. [7]	RSC for multi-products and multi periods	✓				✓	✓	✓	✓		Fuzzy integer non-linear programming
Kuşakcı et al. [49]	RSC under fuzzy supply	✓					✓				Fuzzy programming approach
Yuchi et al. [50]	A bi-objective RSC under the emission trading scheme	✓	✓			✓				✓	Mixed-integer non-linear programming/genetic algorithm
Tosarkani et al. [51]	A case-based robust possibilistic model for a multi-objective RSC	✓	✓			✓		✓	✓	✓	Scenario-based robust possibilistic, Two -phase fuzzy compromise approach
Doan et al. [18]	RSC under risk and uncertainty	✓				✓		✓			Fuzzy mixed-integer linear programming
Roudbari et al. [54]	RSC under uncertainty	✓				✓	✓				Two-stage stochastic mixed-integer programming
Karagoz et al. [56]	Stochastic RSC for vehicles	✓					✓		✓		Scenario-based stochastic optimization
This study	A stochastic multi-objective RSC	✓	✓	✓	✓	✓	✓	✓	✓	✓	Multi-stage stochastic programming

presents the relevant studies on stochastic optimization of RSC for e-waste. Compared to previous studies, this research develops and applies a stochastic mathematical model for optimal RSC design of e-waste from multi-products over multiple periods. The model has three objective functions: maximizing profit, maximizing social impact, and minimizing environmental impact, with consideration of uncertainties in the quantity and quality of product returns and the availability of repair.

3. Model Development

The key elements of the proposed RSC network structure are illustrated in Figure 1, where EOL products are gathered from consumer locations and sent to waste generation points. The collected products are then transported from the waste generation point to the collection and sorting station for inspection, categorization, and sorting. After inspection, products in good condition (end-of-use products) are transferred to the refurbishment station for processing, including cleaning and refurbishing, and then sold to the secondhand market. However, products in poor condition (EOL products) are moved to the disassembly station for disassembly into good repairable parts and material extraction of poor parts. Repairable parts are then transported to the repair station, and faulty parts are moved to the material extraction station. The recyclable materials are transferred to the assigned material recycling stations, while non-recyclable materials are transported to landfills for proper disposal.

3.1. Assumptions

To facilitate model development and considering practical issues, it is assumed that (1) facility capacity is known, (2) a single mode of transportation, and (3) facility costs are known and certain.

3.2. Notations

Table 2. Nomenclature.

(a) Model indices.
Notation	Description
f ∈{1,…,F}	Index of first consumer (s)
g ∈{1,…,G}	Index of waste generation points
e ∈{1,…,E}	Index of collection and sorting centers
b ∈{1,…,B}	Index of refurbishing centers
d ∈{1,…,D}	Index of disassembly centers
i ∈{1,…,I}	Index of repairing centers
m ∈{1,…,M}	Index of material extraction centers
y ∈{1,…,Y}	Index of material recycling centers
l ∈{1,…,L}	Index of landfills
n ∈{1,…,N}	Index of secondhand markets
z ∈{1,…,Z}	Index of raw material markets
k ∈{1,…,K}	Index of spare markets
s ∈{1,…,S}	Index of scenarios
t ∈{1,…,T}	Index of time periods
j ∈{1,…,J}	Index of product
$c$	Index of part
$a$	Index of raw material
${HR}_{jca}$	Weight of raw material a in part c of product j
${\alpha }_{jc}$	Quantity of part c in product j
${\lambda }_{ja}$	Quantity of material a in product j
$P_s$	Probability of scenario s
${\tau }_{ja}$	Conversion ratio of material a in product j
${\mu }_{ts}$	Percentage of product that can be refurbished or disassembled at time t under scenario s (quality of arrivals)
${\gamma }_{ts}$	Percentage of product that can be repaired at time t under scenario s (availability for repair)
(b) Model parameters.
Notation	Description
Fixed construction cost
${FE}_e$	Fixed construction cost of the collection and sorting center e
${FB}_b$	Fixed construction cost of refurbishing center b
${FD}_d$	Fixed construction cost of dismantling center d
${FI}_i$	Fixed construction cost of repairing center i
${FM}_m$	Fixed construction cost of the material extraction center m
${FY}_y$	Fixed construction cost of the material recycling center y
Processing cost
${EC}_e$	Collection and sorting cost per unit at the collection and sorting center e
${BC}_b$	Refurbishing cost per unit at the refurbishing center b
${DC}_d$	Disassembly cost per unit at the disassembly center d
${IC}_i$	Repairing cost per unit at the repairing center i
${MC}_m$	Extraction cost per unit at the material extraction center m
${YC}_y$	Per Kg recycling cost at the material recycling center y
Transportation cost
${TRG}_{ge}$	Transportation cost per unit of product from the waste generation point g to the collection and sorting center e
${TRB}_{eb}$	Transportation cost per unit of product from the collection and sorting center e to the refurbishing center b
${TRE}_{ed}$	Transportation cost per unit of product from the collection and sorting center e to the disassembly center d
${TRI}_{di}$	Transportation cost per unit of repairable part from the disassembly center d to the repairing center i
${TRD}_{dm}$	Transportation cost per unit of faulty part from disassembly center d to material extraction center m
${TRM}_{my}$	Per kg transportation cost of material from the material extraction center m to the material recycling center y
${TRY}_{dy}$	Per kg transportation cost of material from the disassembly center d to the material recycling center y
${TRL}_{yl}$	Per kg transportation cost of non-recyclable material from the material recycling center y to landfill l
Selling price parameters
$S_{jn}$	Selling price of refurbished product j at the secondhand market n
${SC}_{jck}$	Selling price of repaired part c of product j at spare parts market k
${SA}_{jaz}$	Selling price of recycled material a of product j at the raw material market z
Capacity parameters
${CAPG}_{jg}$	Capacity of waste generation point g
${CAPE}_{je}$	Capacity of the collection and sorting center e
${CAPB}_{jb}$	Capacity of refurbishing center b
${CAPD}_{jd}$	Capacity of disassembly center d
${CAPI}_{jci}$	Capacity of the repairing center i
${CAPM}_{jcm}$	Capacity of the material extraction center m
${CAPY}_{jay}$	Capacity of the material recycling center y
${CAPL}_{jal}$	Capacity of landfill l
Parameters for carbon emissions
Processing
${CB}_{jb}$	Carbon emission from processing product j at the refurbishing center b
${CD}_{jd}$	Carbon emission from processing product j at the disassembly center d
${CI}_{jci}$	Carbon emission from the processing part c from product j at the repairing center i
${CM}_{jcm}$	Carbon emission from the processing part c of product j at the material extraction center m
${CRY}_{jay}$	Carbon emission from processing material a at material of product j at recycling center y
Transportation
${CRTG}_{ge}$	Carbon emission from transportation of the product from the waste generation point g to the collection and sorting center e
${CRTB}_{eb}$	Carbon emission from transportation of product from the collection and sorting center e to the refurbishing center b
${CRTE}_{ed}$	Carbon emission from the transportation of products from the collection and sorting center e to the disassembly center d
${CRTI}_{di}$	Carbon emission from transportation of parts from the disassembly center d to the repairing center i
${CRTD}_{dm}$	Carbon emission from the transportation of parts from the disassembly center d to the material extraction center m
${CRTM}_{my}$	Carbon emission from the transportation of material from the material extraction center m to the material recycling center y
${CRTY}_{dy}$	Carbon emission from transportation of material from the disassembly center d to the material recycling center y
${CRTL}_{yl}$	Carbon emission from transportation of material from the material recycling center y to landfill l
Social impact parameters
${JOE}_e$	Number of job opportunities created by establishing collection and sorting center e
${JOB}_b$	Number of job opportunities created by establishing refurbishing center b
${JOD}_d$	Number of job opportunities created by establishing disassembly center d
${JOI}_i$	Number of job opportunities created by establishing repairing center i
${JOM}_m$	Number of job opportunities created by establishing material extraction center m
${JOY}_y$	Number of job opportunities created by establishing material recycling center y
${WDE}_{je}$	Lost days due to work-related injuries during working at the collection and sorting center e while processing one unit of product j
${WDB}_{jb}$	Lost days due to work-related injuries while working at the refurbishing center b while processing one unit of product j
${WDD}_{jd}$	Lost days due to work-related injuries while working at the disassembly center d to process one unit of product j
${WDI}_{jci}$	Lost days due to work-related injuries during working at the repair center i to process one unit of part c of product j
${WDM}_{jcm}$	Lost days due to work-related injuries while working at the material extraction center m while processing one unit of part c of product j
${WDY}_{jay}$	Lost days due to work-related injuries while working at the material recycling center y while processing kg of material a of product j
(c) decision variables
Notation	Description
Quantity decision variables
${AR}_{jts}$	Quantity of arrivals at time t under scenario s
${QF}_{jfgts}$	Amount of product j sent from first consumer area f to waste generation point g at time t under scenario s
${QG}_{jgets}$	Quantity of end-of-life and end-of-use products that are sent from the waste generation point g to the collection and sorting center e at time t under scenario s
${QB}_{jebts}$	Quantity of end-of-use products transferred from collection and sorting center e to refurbishing center b at time t under scenario s
${QE}_{jedts}$	Quantity of end-of-life products transferred from the collection and sorting center e to the disassembly center d at time t under scenario s
${QI}_{jcdits}$	Quantity of repairable part c from product j transferred from disassembly center d to repairing center i at time t under scenario s
${QD}_{jcdmts}$	Quantity of faulty part c from product j transferred from disassembly center d to material extraction center m at time t under scenario s
${QY}_{jadyts}$	Quantity of material a from product j transferred from disassembly center d to material recycling center y at time t under scenario s
${QM}_{jamyts}$	Quantity of material a from product j transferred from material extraction center m to material recycling center y at time t under scenario s
${QL}_{jaylts}$	Quantity of non-recyclable material a from product j transferred from material recycling center m to landfill l at time t under scenario s
${QN}_{jbnts}$	Quantity of refurbished product j transferred from refurbishing center b to secondhand market n at time t under scenario s
${QK}_{jcikts}$	Quantity of repaired part c from product j transferred from repairing center i to spare market k at time t under scenario s
${QZ}_{jayzts}$	Quantity of recycled material a from product j transferred from material recycling center y to raw material market z at time t under scenario s
Binary variables
${ZE}_{et}$	Binary variable equals 1 if the collection and sorting center e is opened at time t, and 0 otherwise
${ZB}_{bt}$	Binary variable equals 1 if the refurbishing center b is opened at time t, and 0 otherwise
${ZD}_{dt}$	Binary variable equals 1 if the disassembly center d is opened at time t, and 0 otherwise
${ZI}_{it}$	Binary variable equals 1 if the repairing center i is opened at time t, and 0 otherwise
${ZM}_{mt}$	Binary variable equals 1 if material extraction center m is opened at time t, and 0 otherwise
${ZY}_{yt}$	Binary variable equals 1 if the material recycling center y is opened at time t, and 0 otherwise
${ZL}_{lt}$	Binary variable equals 1 if landfill l is opened at time t, and 0 otherwise

summarizes the notations for model indices, parameters, and decision variables.

3.3. Model Formulation

The model development of the RSC of e-waste is presented in Figure 2.

A mathematical model was constructed by developing three objective functions with their corresponding constraints, and is presented as follows:

3.3.1. Model Objectives

(a)

Maximizing the total profit gained by implementing RSC of e-waste. To construct this objective function, revenues and costs are formulated as follows:

• (i)

  Revenues

The first revenue, R₁, is gained from selling refurbished products at the secondhand market. Let S_jn denote the selling price of the refurbished product j; j = 1, …, J, at the second market, n. Let QN_jbnts represent the quantity of refurbished product j transported from refurbishing station b to secondhand market n during period t for case s. Let P_s be the probability of scenario s. R₁ is then estimated using Equation (1).

$$R_1={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{n=1}^N{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.S_{jn}.Q{N}_{jbnts}$$

(1)

The revenue, R₂, is obtained by selling repaired parts at the spare parts market. Let SC_jck, denote the selling prices of the repaired part c in product j at the spare parts market, k. Let QK_jcikts be the quantity of part c from product j transported from repairing station i to spare parts market k during period t for case s. R₂ is then mathematically expressed as

$$R_2={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{k=1}^K{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.S{C}_{jck}.Q{K}_{jcikts}}$$

(2)

Finally, the third revenue, R₃, is attained by selling recycled materials at the raw materials market. Let QZ_jayzts denote the quantity of recycled material a from product j in the material recycling station y at the raw material market, z, during period t for case s. Let SA_jaz denote the selling price of the recycled material, a, from product j at raw material market, z. Then, R₃ is estimated using Equation (3).

$$R_3={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{z=1}^Z{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.S{A}_{jaz}.Q{Z}_{jayzts}}$$

(3)

Finally, the total of revenues, TR, is obtained using Equation (4).

TR = R₁ + R₂ + R₃

(4)

• (ii)

  Total Costs

  1-

  Construction costs

Let FE_e, FD_d, FB_b, FI_i, FM_m, and FY_y denote the construction costs for a collection and sorting station e, a disassembly station d, a refurbishing station b, a repairing station i, a material extraction station m, and a recycling station y, respectively. Let ZE_et, ZD_dt, ZB_bt, ZI_it, ZM_mt, and ZY_yt be binary variables for facilities e, d, b, i, m, and y, during period t, respectively. The binary variable equals 1 if the facility is opened, and zero otherwise. Then, the total construction cost, FCC, is formulated as stated in Equation (5).

$$\begin{array}{l}FCC={\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^{T}F{E}_e}}.Z{E}_{et}+{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^{T}F{D}_d}}.Z{D}_{dt}+{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^{T}F{B}_b}}.Z{B}_{bt}+{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^{T}F{I}_i}}.Z{I}_{it}\\ +{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^{T}F{M}_m}}.Z{M}_{mt}+{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^{T}F{Y}_y}}.Z{Y}_{yt}\end{array}$$

(5)

• 2-

  Processing costs

Processing costs of products, parts, and raw materials in the RSC of e-waste are calculated as follows.

• a.

  Collection and sorting

Let EC_e denote the processing costs at the collection and sorting station e. Also, let QG_jgets be the quantity of product j transported from the waste generation point g to the collection and sorting station e during period t for case s. Then, the processing cost, PCE, of QG_jgets is calculated as follows:

$$PCE={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{g=1}^G{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.E{C}_e.Q{G}_{jgets}$$

(6)

• b.

  Refurbishing

Let BC_b denote the processing costs at the refurbishing station b. Let QB_jebts represent the quantity of product j transported from the collection and sorting station e to the refurbishing station b during period t for case s. Then, the processing cost, PCB, of QB_jebts is estimated using Equation (7).

$$PCB={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.B{C}_b.Q{B}_{jebts}$$

(7)

• c.

  Disassembly

Let DC_d denote the processing costs at the disassembly station d. Let QE_jedts denote the quantity of product j transported from the collection and sorting station e to the disassembly station d during period t for case s. Then, the total processing costs, PCD, of QE_jedts is obtained as follows:

$$PCD={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s}}}}}.D{C}_d.Q{E}_{jedts}$$

(8)

• d.

  Repair

Let IC_i denote the processing costs at the repairing station i. Let QI_jcdits represent the quantity of part c from product j transported from the disassembly station d to the repairing station i during period t for case s. Then, the processing costs, PCI, of QI_jcdits is calculated using Equation (9).

$$PCI={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.I{C}_i.Q{I}_{jcdits}}}}}}}$$

(9)

• e.

  Material extraction

Let MC_m denote the processing costs at the material extraction station m. Let QD_jcmts resemble the quantity of part c from product j transported from the disassembly station d to the material extraction station m during period t for case s. Then, the total processing costs, PCM, of QD_jcmts is estimated using Equation (10).

$$PCM={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.M{C}_m.Q{D}_{jcdmts}}}}}}}$$

(10)

• f.

  Material recycling

Let YC_y denote the recycling cost per kg at the material recycling station y. Let QM_jamyts denote the quantity of material a from product j transported from the material extraction station m to the material recycling station y during period t for case s. Then, the total processing costs, PCY₁, of the material recycling stations are estimated using Equation (11).

$$PC{Y}_1={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s. Y{C}_y. Q{M}_{jamyts}}}}}}}$$

(11)

Further, let QY_jadyts represent the quantity of material a from product j transported from the disassembly station d to the material recycling station y during period t for case s. Then, the total processing costs, PCY₂, of QY_jadyts at the material recycling stations are estimated using Equation (12).

$$PC{Y}_2={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.Y{C}_y.Q{Y}_{jadyts}}}}}}}$$

(12)

Finally, the total processing costs, TPC, are calculated as stated in Equation (13).

TPC = PCE + PCB + PCD + PCI + PCM + PCY₁ + PCY₂

(13)

• 3-

  Transportation costs

Transportation costs for different products, parts, and materials between network nodes are estimated as follows.

• (1)

  Transportation g→e

Let TRG_ge denote the transportation cost per unit moved from the waste generation point g to the collection and sorting station e. Then, the transportation costs, TPge, incurred due to moving the quantity QG_jgets from point g to e are calculated using Equation (14).

$$TPge={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{g=1}^G{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{G}_{ge}.Q{G}_{jgets}}}}}}$$

(14)

• (2)

  Transportation e→b

Let TRB_eb denote the transportation cost per unit moved from the collection and sorting station e to the refurbishing station b. Then, the transportation costs, TPeb, resulted from moving the quantity QB_jebts from point e to b can be obtained using Equation (15).

$$TPeb={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{B}_{eb}.Q{B}_{jebts}}}}}}$$

(15)

• (3)

  Transportation e→d

Let TRE_ed denote the transportation cost per unit transferred from the collection and sorting station e to the disassembly station d. Then, the transportation costs, TPed, due to moving the quantity QE_jedts from point e to d are calculated using Equation (16).

$$TPed={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{E}_{ed}.Q{E}_{jedts}}}}}}$$

(16)

• (4)

  Transportation d→i

Let TRI_di denote the transportation cost per unit moved from the disassembly station d to the repairing station i. Then, the transportation costs, TPdi, for transporting the quantity QG_jcdits from point d to i are estimated as follows:

$$TPdi={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{I}_{di}.Q{I}_{jcdits}}}}}}}$$

(17)

• (5)

  Transportation d→m

Let TRD_dm denote the transportation cost per unit moved from the disassembly station d to the material extraction station m. Then, the transportation costs, TPdm, due to moving the quantity QD_jcdmts from point d to m are calculated as given in Equations (18) and (19), respectively.

$$TPdm={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{D}_{dm}.Q{D}_{jcdmts}}}}}}}$$

(18)

• (6)

  Transportation d→y

Let TRY_dy denote the transportation cost per unit moved from the disassembly station d to the material recycling station y. Then, the transportation costs, TPdy, due to moving the quantity QY_jadyts from point d to y, are calculated as given in Equation (19).

$$TPdy={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{Y}_{dy}.Q{Y}_{jadyts}}}}}}}$$

(19)

• (7)

  Transportation m→y and y→l

Let TRM_my and TRL_yl denote the transportation cost per unit moved from material extraction station m to material recycling station y and from material recycling station y to landfill l, respectively. Let QL_jaylts represent the transported quantity of material a from product j from material recycling station y to landfill l during period t for case s. Let TPmy and TPyl denote the transportation costs by moving the quantities QM_jamyts and QL_jaylts from station m to y and from station y to l, respectively. Then, TPmy and TPyl can be estimated as stated in Equations (20) and (21), respectively.

$$TPmy={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{M}_{my}.Q{M}_{jamyts}}}}}}}$$

(20)

$$TPyl={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{l=1}^L{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.TR{L}_{yl}.Q{L}_{jaylts}}}}}}}$$

(21)

Then, the total of transportation costs, TTC, is calculated as follows:

TTC = TPge + TPeb + TPed + TPdi + TPdm + TPdy + TPyl + TPmy

(22)

Then, the objective function is to maximize the total profit as stated in Equation (23).

Maximize Profit = TR − FCC − TPC − TTC

(23)

(b)

Minimizing total CO2 emissions

• CO2 emissions from refurbishing and disassembly

Let CB_jb and CD_jd denote the amount of CO2 emitted due to processing one unit of product j at refurbishing station b and disassembly station d, respectively. Let COjb denote the total CO2 emissions due to processing quantities QB_jebts and QE_jedts at stations b and d, respectively. Then, COjb is calculated as follows:

$$COjb={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{B}_{jb}.Q{B}_{jebts}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{D}_{jd}.Q{E}_{jedts}}}}}}$$

(24)

• 2.

  CO2 emissions from repair and material extraction

Let CI_jmi and CM_jci denote the amount of CO2 emitted from processing part c of product j at repairing station i and material extraction station m, respectively. Then, the total CO2 emissions, COim, from processing the quantities QI_jcdits and QD_jcdmts at stations i and m, respectively. Then, COim is estimated as stated in Equation (25).

$$COim={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}{\displaystyle \sum _{d=1}^E{\displaystyle \sum _{i=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{I}_{jci}.Q{I}_{jcdits}}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^E{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{M}_{jcm}.Q{D}_{jcdmts}}}}}}}$$

(25)

• 3.

  CO2 emissions from material recycling

Further, let CY_jay represent the total amount of CO2 emitted from processing materials a from material extraction station m and disassembly d of product j at material recycling station y in case s. Then, the total CO2 emissions, COy, resulting from quantities QM_jamyts and QY_jadyts at stations y, respectively, is calculated as given in Equation (26).

$$\mathit{COy}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{Y}_{jay}.Q{M}_{jamyts}}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.C{Y}_{jay}.Q{Y}_{jadyts}}}}}}}$$

(26)

Then, the total of CO2 emissions, TPCO2, resulting from processing products, parts, and materials at distinct stations, is calculated as follows:

TPCO2 = COjb + COim + COy

(27)

• 4.

  CO2 emissions from transportation

Let the amount of CO2 emissions resulting from moving a unit of product j between stations g→e, e→b, e→d, d→i, d→m, d→y, m→y, and y→l be denoted by CRTG_ge, CRTB_eb, CRTE_ed, CRTI_di, CRTD_dm, CRTY_dy, CRTM_my, and CRTL_yl, respectively. The total CO2 emissions, TTCO2, due to moving the quantities QG_jgets, QB_jebts, QE_jedts, QI_jcdits, QD_jcdmts, QY_jadyts, QM_jamyts, and QL_jaylts between stations g→e, e→b, e→d, d→i, d→m, d→y, m→y, and y→l, respectively, is calculated as stated in Equation (28).

TTCO2 = Cge + Ceb + Ced + Cdi + Cdm + Cdy + Cmy

(28)

where

$$\mathit{Cge}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{g=1}^G{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{G}_{ge}.Q{G}_{jgets} [\mathrm{Stations} g\to e]}}}}}$$

(29)

$$\mathit{Ceb}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{B}_{eb}.Q{B}_{jebts} [\mathrm{Stations} e\to b]}}}}}$$

(30)

$$\mathit{Ced}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{E}_{ed}.Q{E}_{jedts} [\mathrm{Stations} e\to d]}}}}}$$

(31)

$$\mathit{Cdi}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{I}_{di}.Q{I}_{jcdits} [\mathrm{Stations} d\to i]}}}}}}$$

(32)

$$\mathit{Cdm}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{D}_{dm}.Q{D}_{jcdmts} [\mathrm{Stations} d\to m]}}}}}}$$

(33)

$$\mathit{Cdy}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{Y}_{dy}.Q{Y}_{jadyts} [\mathrm{Stations} d\to y]}}}}}}$$

(34)

$$\mathit{Cmy}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{M}_{my}.Q{M}_{jamyts} [\mathrm{Stations} m\to y]}}}}}}$$

(35)

$$\mathit{COyl}={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{l=1}^L{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.CRT{L}_{yl}.Q{L}_{jaylts} [\mathrm{Stations} y\to l]}}}}}}$$

(36)

The second objective function is finally formulated to minimize the total CO2 emission, TCO2. Mathematically,

Minimize TCO2 = TPCO2 + TTCO2

(37)

(c)

Maximizing the social impact

From a labor indicators perspective, two main indicators are considered, including employment generation and occupational health. This offers a clear, simplified way to describe the trade-off between employment creation and workplace safety. The third objective function, therefore, aims to maximize social impact.

(1)

Job opportunities

Let JOEe, JOBb, JODd, JOIi, JOMm, and JOYy denote the number of job opportunities created by opening collection and sorting station e, refurbishing station b, disassembly station d, repairing station i, material extraction station m, and material recycling station y, respectively. Then, the total of job opportunities, TJOB, at various stations is calculated as stated in Equation (38).

$$\begin{array}{l}TJOB={\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^{T}JO{E}_i}}.Z{I}_{et}+{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^{T}JO{D}_d}}.Z{D}_{dt}+{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^{T}JO{I}_i}}.Z{I}_{it}+{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^{T}JO{B}_b}}.Z{E}_{bt}+\\ {\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^{T}JO{M}_m}}.Z{E}_{mt}+{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^{T}JO{Y}_y}}.Z{Y}_{yt}\end{array}$$

(38)

(2)

Lost days due to work-related injuries

Let WDE_je, WDB_jb, and WDD_jd represent the lost days due to work-related injuries while processing product j at stations e, b, and d, respectively. Similarly, let WDI_jci and WDM_jcm denote the lost days due to work-related injuries while processing part c from product j at stations i and m, respectively. Finally, let WDY_jay represent the lost days due to work-related injuries while recycling material a from product j at station y. Then, the total number of lost days, TLD, due to work-related injuries at various stations is calculated using Equation (39).

$$\begin{array}{l}TLD={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{g=1}^G{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{E}_{je}.Q{G}_{jgets}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{b=1}^B{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{B}_{jb}.Q{B}_{jebts}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{e=1}^E{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{D}_{jd}.Q{E}_{jedts}}}}}}+\\ {\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{i=1}^I{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{I}_{jci}.Q{I}_{jcdits}}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{M}_{jcm}.Q{D}_{jcdmts}}}}}}}+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{d=1}^D{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{Y}_{jay}.Q{Y}_{jadyts}}}}}}}+\\ {\displaystyle \sum _{j=1}^J{\displaystyle \sum _{a=1}^A{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{y=1}^Y{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{s=1}^S{P}_s.WD{Y}_{jay}.Q{M}_{jamyts}}}}}}}\end{array}$$

(39)

Finally, the second objective function aims to maximize the social impact (SI), which is calculated by subtracting the total lost days due to work-related injuries, TLD, from total opportunities, TJOB. Mathematically,

Maximize SI = TJOB − TLD

(40)

3.3.2. Model Constraints

The three objective functions are subject to the following constraints:

▪

The total of QF_jfgts (f→g) of product j sent from the consumer area f to the waste generation g is equal to the total QG_jgets (g→e) of product j during period t at case s. That is,

$${\displaystyle \sum _{f=1}^{F}Q{F}_{jfgts}}={\displaystyle \sum _{e=1}^{E}Q{G}_{jgets}},\forall g,t,s,j$$

(41)

▪

The total of QF_jfgts is equal to the sum of the totals of moved quantities QBjebts (e→d) and QE_jedts (e→b) during period t at each case s. Mathematically,

$${\displaystyle \sum _{e=1}^{E}Q{G}_{jgets}}={\displaystyle \sum _{b=1}^{B}Q{B}_{jebts}}+{\displaystyle \sum _{d=1}^{D}Q{E}_{jedts}},\forall e,t,s,j$$

(42)

▪

The total QB_jebts (e→b) of product j moved from station e to b is equal to the total QN_jbnts (b→n) transported from station b to secondhand market n during period t at case s, as expressed in Equation (43).

$${\displaystyle \sum _{e=1}^{E}Q{B}_{jebts}}={\displaystyle \sum _{n=1}^{N}Q{N}_{jbnts}},\forall b,t,s,j$$

(43)

▪

At each case s, the total QI_jcdits (d→i) of part c from product j transferred from disassembly station d to i is equal to the total QK_jcikts (i→k) transported from station i to spare market k during period t at case s, as stated in Equation (44).

$${\displaystyle \sum _{d=1}^{D}Q{I}_{jcdits}}={\displaystyle \sum _{k=1}^{K}Q{K}_{jcikts}},\forall c,i,t,s,j$$

(44)

▪

The sum of the totals QM_jamyts and QY_jadyts of material a in product j that is collected at both the material extraction station m and disassembly station d, respectively, and then transferred to the material recycling station y is equal to the sum of the totals QZ_jayzts and QL_jaylts sent from material recycling station y to both raw material market z and landfill l, respectively, as formulated in Equation (45).

$${\displaystyle \sum _{m=1}^{M}Q{M}_{jamyts}}+{\displaystyle \sum _{d=1}^{D}Q{Y}_{jadyts}}={\displaystyle \sum _{z=1}^{Z}Q{Z}_{jayzts}+}{\displaystyle \sum _{l=1}^{L}Q{L}_{jaylts}},\forall a,y,t,s,j$$

(45)

▪

Let ZG_gt be a binary variable that indicates whether or not the waste generation point g is opened, where a value of one indicates that waste generation g is opened and 0 otherwise. Let CAPG_jg denote the capacity of waste generation g for product j. Inequality (46) guarantees that the capacity of waste generation station g for product j cannot be exceeded during period t at case s.

$${\displaystyle \sum _{f=1}^{F}Q{F}_{jfgts}}\le CAP{G}_{jg}.Z{G}_{gt},\forall j,g,t,s$$

(46)

▪

The total transferred QG_jgets (g→e) should not exceed the capacity, CAPE_je, of the collection and sorting station e for product j during period t at case s. Mathematically,

$${\displaystyle \sum _{g=1}^{G}Q{G}_{jgets}}\le CAP{E}_{je}.Z{E}_{et},\forall j,g,t,s$$

(47)

▪

The total QB_jebts (e→b) will not exceed the capacity, CAPB_jb, of refurbishing station b during period t for case s as stated in Inequality (48).

$${\displaystyle \sum _{e=1}^{E}Q{B}_{jebts}}\le CAP{B}_{jb}.Z{B}_{bt},\forall j,b,t,s$$

(48)

▪

The total QE_jedts (e→d) will not exceed the capacity, CAPD_jd, of the disassembly station d during period t at case s. That is,

$${\displaystyle \sum _{e=1}^{E}Q{E}_{jedts}}\le CAP{D}_{jd}.Z{D}_{dt},\forall j,d,t,s$$

(49)

▪

Inequality (50) ensures that the total QI_jcdits (d→i) will not exceed the capacity, CAPD_jci, of the repairing station i during period t at case s.

$${\displaystyle \sum _{d=1}^{D}Q{I}_{jcdits}}\le CAP{I}_{jci}.Z{I}_{it},\forall j,c,i,t,s$$

(50)

▪

Inequality (51) guarantees that the total QD_jcdmts (d→m) will not exceed the capacity, CAPM_jcm, of the material extraction station m during period t at case s.

$${\displaystyle \sum _{d=1}^{D}Q{D}_{jcdmts}}\le CAP{M}_{jcm}.Z{M}_{mt},\forall j,c,m,t,s$$

(51)

▪

Inequality (52) ensures that the total QD_jcdmts will not exceed capacity, CAPY_jay, of material recycling station y during period t at case s.

$${\displaystyle \sum _{d=1}^{D}Q{Y}_{jadyts}}+{\displaystyle \sum _{m=1}^{M}Q{M}_{jamyts}}\le CAP{Y}_{jay}.Z{Y}_{yt},\forall j,a,y,t,s$$

(52)

▪

Let ZL_lt be a binary variable that decides whether or not landfill location l is opened during period t, where a value of 1 indicates that landfill location l is open and 0 otherwise. Let CAPL_jal denote the capacity of landfill l for material a from product j. Then, the total QL_jaylts should not exceed CAPL_jal during period t at case s as shown in Inequality (53).

$${\displaystyle \sum _{y=1}^{Y}Q{L}_{jaylts}}\le CAP{L}_{jal}.Z{L}_{lt},\forall j,a,l,t,s$$

(53)

▪

Let AR_jts denote the quantity of returns (return rate) of product j during period t at case s. Inequality (54) ensures that the total QF_jfgts will not exceed AR_jts.

$${\displaystyle \sum _{f=1}^F{\displaystyle \sum _{g=1}^{G}Q{F}_{jfgts}}}\le A{R}_{jts},\forall j,t,s$$

(54)

▪

Products sent from the consumer area f to the waste generation station g have distinct quality levels, depending on the product’s condition. Let μ_ts denote the percentage of product or quality of returns that can be refurbished from QG_jgets during period t for case s. Accordingly, the total QB_jebts (e→b) with a high-quality level is calculated as stated in Equation (55).

$${\displaystyle \sum _{b=1}^{B}Q{B}_{jebts}}={\displaystyle \sum _{g=1}^{G}Q{G}_{jgets}}.{\mu }_{ts},\forall j,e,t,s$$

(55)

▪

Products with poor quality levels are sent to station e for disassembling into different parts and extracted materials. The total QE_jedts (e→d) of non-refurbished products that are sent from station e to d is estimated as given in Equation (56).

$${\displaystyle \sum _{b=1}^{B}Q{E}_{jedts}}={\displaystyle \sum _{g=1}^{G}Q{G}_{jgets}}.(1-{\mu }_{ts}),\forall j,e,t,s$$

(56)

▪

Let α_jc and γ_ts denote the quantity of part c from product j and repair possibility of part c during period t at case s, respectively. The quantity of repairable parts, QI_jcdits (d→i) that are sent from disassembly station d to repairing station i during period t at case s is calculated as:

$${\displaystyle \sum _{i=1}^{I}Q{I}_{jcdits}}={\displaystyle \sum _{e=1}^{E}Q{E}_{jedts}}.{\alpha }_{jc}.{\gamma }_{ts},\forall j,c,d,t,s$$

(57)

▪

The total quantity of faulty parts, QD_jcdmts (d→m), transferred from disassembly station d to material extraction m during period t at case s is obtained as stated in Equation (58).

$${\displaystyle \sum _{y=1}^{Y}Q{D}_{jcdmts}}={\displaystyle \sum _{e=1}^{E}Q{E}_{jedts}}.{\alpha }_{jc}.(1-{\gamma }_{ts}),\forall j,c,d,t,s$$

(58)

▪

The total amount, QY_jadyts (d→y), of material a from product j moved from disassembly station d to material recycling station y at each case s can be estimated using Equation (59).

$${\displaystyle \sum _{y=1}^{Y}Q{Y}_{jadyts}}={\displaystyle \sum _{e=1}^{E}Q{E}_{jedts}}.{\lambda }_{ja},\forall j,a,d,t,s$$

(59)

▪

Let τ_ja and HR_jac denote conversion ratio (recycling ratio) of material a in part c and the weight of material a in part c from product j, respectively. The recyclable material, QM_jamyts (m→y), of faulty part c from product j transferred from material extraction station m to material recycling station y can be estimated for during period t at case s as stated in Equation (60).

$${\displaystyle \sum _{y=1}^{Y}Q{M}_{jamyts}}={\displaystyle \sum _{c=1}^C{\displaystyle \sum _{d=1}^{D}Q{D}_{jcdmts}}}.{\tau }_{ja}.H{R}_{jac},\forall j,a,y,t,s$$

(60)

▪

The non-recyclable material, QL_jaylts (y→l), from product j moved from material recycling station y to landfill l for proper disposal during period t at case s is estimated using Equation (61).

$${\displaystyle \sum _{l=1}^{L}Q{L}_{jaylts}}={\displaystyle \sum _{d=1}^{D}Q{Y}_{jadyts}}.(1-{\tau }_{ja}),\forall j,a,y,t,s$$

(61)

▪

The decision variables that indicate whether or not to open distinct facilities are binary variables as stated in Equation (62).

$$\mathit{ZGet} ,\mathit{ZEet} ,\mathit{ZDdt} ,\mathit{ZBbt} ,\mathit{ZIit} ,\mathit{ZMmt} ,\mathit{ZLLt} \mathit{and} \mathit{ZYyt} \in \left\{1,0\right\}$$

(62)

▪

Non-negativity constraints for quantities are stated in Equation (63).

$$\begin{array}{l}A{R}_{jfts}, Q{F}_{jfgts}, Q{G}_{jgets}, Q{B}_{jebts}, Q{E}_{jedts}, Q{I}_{jcdits}, Q{D}_{jcdmts}, Q{Y}_{jadyts}, Q{M}_{jamyts}, Q{N}_{jbnts}\\ Q{K}_{jcikts}, Q{Z}_{jayzts}, Q{L}_{jaylts}\ge 0,\forall a,i,j,f,g,c,t,s,b,e,d,m,n,k,z,l,y\end{array}$$

(63)

▪

AR_jts is a stochastic parameter that is normally distributed with a mean and standard deviation of (μ, σ²).

▪

μ_ts and γ_ts are probabilistic parameters that have outcomes associated with probabilities.

4. Computational Analysis

A household appliance manufacturing company specialized in producing several types of household appliances was considered for model illustration. The company produces refrigerators, freezers, washing machines, dishwashers, televisions, microwaves, and air conditioners. Two types (J = 2) of household appliances, refrigerators (j = 1 or R) and washing machines (j = 2 or W), were considered. The products consist of several components and precious raw materials. Figure 3 illustrates the facilities developed in the RSC of e-waste under study.

Table 3. Products’ weight and price.

Product Type	Weight (kg)	Price (USD)
Refrigerator	87	$S_{1n}=$ 200
Washing machine	65	$S_{2n}=$ 173

lists the weight (kg) and price (USD) of each product on the reverse supply chain.

Table 4. List of materials and parts.

(a) Refrigerator (j = 1)
Part name	Part index	Quantity of parts/materials in product	Raw Material	Weight of raw material in part (kg)	Price (USD)
Parts
Compressor	$c_1$	${\mathsf{\alpha }}_1$ = 1	Steel Copper	${HR}_{111}=$ 8 ${HR}_{112}=$ 1	50
Evaporator	$c_2$	${\mathsf{\alpha }}_2$ = 1	Aluminum	${HR}_{124}=$ 2	16
Condenser	$c_3$	${\mathsf{\alpha }}_3$ = 2	Steel	${HR}_{131}=$ 4	17
Materials
Metal sheets	$a_1$	${\lambda }_1=$4	Steel	-	-
Connecting pipe	$a_2$	${\lambda }_2=$4	Copper	-	-
Plastic parts	$a_3$	${\lambda }_3=$ 10	Plastic	-	-
Electrical wires	$a_2$	${\lambda }_2=$ 1	Copper	-	-
(b) Washing machine (j = 2)
Part name	Part index	Quantity of parts/materials in product	Raw material	Weight of raw material in part (kg)	Price (USD)
Parts
Motor	$c_1$	${\mathsf{\alpha }}_1$ = 1	Steel Copper	${HR}_{211}=$3.6 ${HR}_{212}=$3.4	40
Pump	$c_2$	${\mathsf{\alpha }}_2$ = 1	Steel Copper Plastic	${HR}_{221}=$0.4 ${HR}_{222}=$0.3 ${HR}_{223}=$0.3	20
Door	$c_3$	${\mathsf{\alpha }}_3$ = 1	Glass	${HR}_{233}=$3.0	20
Materials
Metal sheets	$a_1$	${\lambda }_1=$15	Steel	-	-
Electrical wires	$a_2$	${\lambda }_2=$1	Copper	-	-
Plastic parts	$a_3$	${\lambda }_3=$ 14	Plastic	-	-

and

Table 5. Selling price and conversion ratio of raw material.

(a) Refrigerator (j = 1).
Raw material	Index of raw materials	Selling price per kg (JD)	Availability for recycling	Conversion ratio
Steel	$a_1$	0.88	85%	0.85
Copper	$a_2$	5.28	100%	1
Plastic	$a_3$	1.00	30%	0.30
Aluminum	$a_4$	1.54	60%	0.60
(b) Washing machine (j = 2).
Raw material	Index of raw materials	Selling price per kg (JD)	Availability for recycling	Conversion ratio
Steel	$a_1$	0.88	85%	0.85
Copper	$a_2$	5.28	100%	1
Plastic	$a_3$	1.00	30%	0.30
Glass	$a_4$	0.40	100%	1

summarize the parts and the amount of raw materials, respectively, in the refrigerator (R) and washing machine (W).

Relevant information on model parameters was obtained from production engineers and technical reports, as shown in

Table 6. Parameters of RSC facilities for the refrigerator and washing machines.

Waste generation point (s)	$g_1$	$g_2$	$g_3$	$g_4$
Capacity (product/year)
Refrigerator Washing machine	${CAPG}_1$ = 6000	${CAPG}_2$ = 6500	${CAPG}_3$ = 6500	${CAPG}_4$ = 6500
	${CAPG}_1$ = 7000	${CAPG}_2$ = 7500	${CAPG}_3$ = 6000	${CAPG}_4$ = 6350
Collection and sorting station (e)	$e_1$	$e_2$
Fixed construction cost (USD)	${FE}_1$ = 90,000	${FE}_2$ = 95,000
Capacity (product/year)	${CAPE}_1$ = 6000	${CAPE}_2$ = 6500	Refrigerator
	${CAPE}_1$ = 6500	${CAPE}_2$ = 7000	Washing machine
Processing cost (USD/product)	${EC}_1$ = 0.12	${EC}_2$ = 0.12
Refurbishing station	$b_1$	Refrigerator	Washing machine
Fixed construction cost (USD)	${FB}_1$	100	500
Capacity	${CAPB}_1$	1400	2000
Processing cost (USD/product)	${BC}_1$	2.1	2.1
Disassembly station (d)	$d_1$	$d_2$
Fixed construction cost (USD)	${FD}_1$ = 100,000	${FD}_2$ = 95,000
Capacity (product/year)	${CAPD}_1$ = 6200	${CAPD}_2$ = 5400	Refrigerator
	${CAPD}_1$ = 6000	${CAPD}_1$ = 5500	Washing machine
Processing cost (USD/product)	${DC}_1$ = 2.5	${DC}_2$ = 2.5
Repairing station	$i_1$	Refrigerator	Washing machine
Fixed construction cost (USD)	${FR}_1$ = 200,000
Capacity (product/year)	${CAPI}_{11}$	20,000	25,000
	${CAPI}_{21}$	20,800	25,000
	${CAPI}_{31}$	20,600	20,000
Processing cost (USD/part)	${IC}_1$= 1.2
Material extraction station	$m_1$	Refrigerator	Washing machine
Fixed construction cost (USD)	${FM}_1$ = 188,000
Capacity (kg/year)	${CAPM}_{11}$	20,000	25,000
	${CAPM}_{21}$	25,000	25,000
	${CAPM}_{31}$	20,000	25,000
Processing cost (USD/part)	${MC}_1$= 0.15
Material recycling station (y)	$y_1$	$y_2$
Fixed construction cost (USD)	${Fy}_1$ = 250,000	${Fy}_2$ = 250,000
Capacity (kg/year)	${CAPY}_{11}$ = 30,000	${CAPY}_{12}$ = 35,000	Refrigerator
	${CAPY}_{21}$ = 45,000	${CAPY}_{22}$ = 40,000
	${CAPY}_{31}$ = 30,000	${CAPY}_{32}$ = 30,000
	${CAPY}_{41}$ = 30,000	${CAPY}_{42}$ = 30,000
	${CAPY}_{11}$ = 40,000	${CAPY}_{12}$ = 45,000	Washing machine
	${CAPY}_{21}$ = 50,000	${CAPY}_{22}$ = 50,000
	${CAPY}_{31}$ = 35,000	${CAPY}_{32}$ = 40,000
	${CAPY}_{41}$ = 35,000	${CAPY}_{42}$ = 35,000
Processing cost (USD/part)	${YC}_1$ = 1.2	${YC}_2$ = 1.2
Landfill (l)	$l_1$	$l_2$
Capacity (Kg/year)	${CAPL}_{11}$ = 25,000	${CAPL}_{12} =$ 20,000	Refrigerator
	${CAPL}_{21}$ = 20,000	${CAPL}_{22} =$ 25,000
	${CAPL}_{31}$ = 20,000	${CAPL}_{32} =$ 20,000
	${CAPL}_{41}$ = 20,000	${CAPL}_{42} =$20,000
	${CAPL}_{11}$ = 25,000	${CAPL}_{12} =$20,000	Washing machine
	${CAPL}_{21}$ = 20,000	${CAPL}_{22} =$25,000
	${CAPL}_{31}=$ 20,000	${CAPL}_{32} =$20,000
	${CAPL}_{41}$ = 20,000	${CAPL}_{42} =$20,000

.

The transfer of different components between facilities is performed using a heavy-duty truck with a capacity of 5 tons. The fuel consumption of the truck is 0.11 Liter/km at a fuel price of 0.79 USD/Liter. Moreover, burning one liter of diesel results in 2.62 kg of CO2 emissions.

Table 7. Average transportation cost (USD/unit).

	g1	g2	g3	g4	b1	e1	e2	d1	d2	m1	y1	y2
e1	0.46	0.31	0.01	0.07
e2	0.68	0.02	0.33	0.29
b1						0.03	0.28
d1						0.001	0.32
d2						0.29	0.04
i1								0.01	0.28
m1								0.05	0.24
y1								0.05	0.22	0.23
y2								0.28	0.03	0.42
l1											0.46	0.64
l2											0.23	0.03

and

Table 8. CO2 emissions from transportation (kg/unit).

	g1	g2	g3	g4	b1	e1	e2	i1	m1	y1	y2
e1	1.52	1.03	0.003	0.22	0.1
e2	2.24	0.005	1.07	0.94	0.9
b1						0.005	1.04	0.02	0.15
d1						0.94	0.12	1.04	0.79	0.16	0.74
d2										0.95	0.11
y1									0.77
y2									1.4
l1										1.49	2.14
l2										0.78	0.10

display the average transportation cost and the amount of CO2 emissions from the transportation of units between different facilities, respectively.

Table 9. CO2 emissions from processing.

Description	Parameter
CO2 emission from refurbishing one unit of product (kg/unit) for both products	${CB}_1$ = 0.05
CO2 emission from disassembling one unit of product (kg/unit) for both products	${\mathrm{C}\mathrm{D}}_1$ = 0.03${\mathrm{C}\mathrm{D}}_2$ = 0.02
CO2 emission from repairing one unit of the part (kg/unit) for both products	${\mathrm{C}\mathrm{I}}_{11}=$ 0.10${\mathrm{C}\mathrm{I}}_{21}=$ 0.08${\mathrm{C}\mathrm{I}}_{31}=$ 0.10
CO2 emission from processing one unit of part (kg/unit) for both products	${\mathrm{C}\mathrm{M}}_{11}=$ 0.01${\mathrm{C}\mathrm{M}}_{21}=$ 0.02${\mathrm{C}\mathrm{M}}_{31}=$ 0.02
	${\mathrm{C}\mathrm{M}}_{11}=$ 0.02${\mathrm{C}\mathrm{M}}_{21}=$ 0.02${\mathrm{C}\mathrm{M}}_{31}=$ 0.02
CO2 emission from recycling one Kg of material (kg/unit) for both products	${\mathrm{C}\mathrm{Y}}_{11}=$ 0.30	${\mathrm{C}\mathrm{Y}}_{12}=$ 0.20
	${\mathrm{C}\mathrm{Y}}_{21}=$ 0.20	${\mathrm{C}\mathrm{Y}}_{22}=$ 0.15
	${\mathrm{C}\mathrm{Y}}_{31}=$ 0.20	${\mathrm{C}\mathrm{Y}}_{32}=$ 0.15
	${\mathrm{C}\mathrm{Y}}_{41}=$ 0.30	${\mathrm{C}\mathrm{Y}}_{42}=$ 0.20

presents the CO2 emissions incurred by processing products, parts, and materials at different facilities. The parameters related to the social impact objective function are displayed in

Table 10. Social impact parameters for both products.

Station	Number of Job Opportunities Created	Lost Days Due to Work-Related Injuries (Day/Product)
Collection and sorting station	${JOE}_1=$ 20${JOE}_2=$ 20	${WDE}_1=$ 0.01${WDE}_2=$ 0.01
Refurbishing station	${JOB}_1=$ 19	${WDB}_1=$ 0.01
Disassembly station	${JOD}_1=$ 20${JOD}_2=$ 20	${WDD}_1 =$ 0.01 ${\mathrm{W}\mathrm{D}\mathrm{D}}_2=$ 0.01
Repairing station	${JOI}_1 =$30	${WDI}_{11} =$0.02${WDI}_{21} =$0.02${ WDI}_{31} =$0.02
Material extraction station	${JOM}_1 =$25	${WDM}_{11} =$0.025 ${ WDM}_{21} =$0.025${WDMR}_{31} =$0.025
Material recycling station	${JOY}_1 =$30${ JOY}_2 =$35	${WDY}_{11} =$0.02${WDY}_{12} =$0.02 ${WDY}_{21}=$ 0.02${WDY}_{22}=$ 0.02 ${WDY}_{31}=$ 0.02${ WDY}_{32} =$0.02 ${WDY}_{41} =$0.02 ${WDY}_{42} =$0.02

.

Moreover, the number of returns (return rate), quality of returns, and availability for repair are assumed to be stochastic (uncertain) variables as presented in

Table 11. Uncertainties in the proposed RSC.

Random Variable		Mode	Value	Probability
Quality of returns		Good conditions	0.55	0.45
		Bad conditions	0.45	0.55
Availability for repair		Repairable	0.55	0.45
		Faulty	0.30	0.55
Random variable		Distribution	Mean	Sigma
Quantity of returns (return rate)	${AR}_{1ts}$	Normal distribution	1700	30
	${AR}_{2ts}$		1300	30

.

LINGO 18.0 software on a personal computer with an Intel Core i7-1065G 1.5 GHz (7 CPU) processor and 16 GB memory under the Windows 10 operating system was used to solve the optimization model. Monte Carlo sampling technique was used to generate cases for the uncertain variables. The sample size was set to two, resulting in two samples being created at each stage. This resulted in four stages; the total number of cases for stages one through four is $2^4$ = 16. The problem is defined as a multi-stage, multi-period stochastic programming problem. The total number of scenarios is 16, and the total number of random variables is 16. The total numbers of variables, constraints, non-zeroes are 963, 1793, and 6887, respectively. The elapsed time for solving this problem was 146.14 s, and the total number of iterations was 259,421. The optimal values of decision variables at stage zero are presented in

Table 12. Optimal values of decision variables at stage zero.

Decision Variable	Value	Decision Variable	Value	Decision Variable	Value	Decision Variable	Value
ZG(2,$t_1$)	1	ZG(2,$t_2$)	1	ZG(2, $t_3$ )	1	ZG(2,$t_4$)	1
ZE(1,$t_1$)	1	ZE(1,$t_2$)	1	ZE(1,$t_3$)	1	ZE(1,$t_4$)	1
ZB(1,$t_1$)	1	ZB(1,$t_2$)	1	ZB(1,$t_3$)	1	ZB(1,$t_4$)	1
ZD(2,$t_1$)	1	ZD(2,$t_2$)	1	ZD(2,$t_3$)	1	ZD(2,$t_4$)	1
ZI(1,$t_1$)	1	ZI(1,$t_2$)	1	ZI(1,$t_3$)	1	ZI(1,$t_4$)	1
ZM(1,$t_1$)	1	ZM(1,$t_2$)	1	ZM(1,$t_3$)	1	ZM(1,$t_4$)	1
ZY(2,$t_1$)	1	ZY(2,$t_2$)	1	ZY(2,$t_3$)	1	ZY(2,$t_4$)	1
ZL(2,$t_1$)	1	ZL(2,$t_2$)	1	ZL(2,$t_3$)	1	ZL(2,$t_4$)	1

. Accordingly, the second waste generation point g₂, the collection and sorting station e₁, the refurbishing station b₁, the disassembly station d₁, the repairing station i₁, the material extraction station m₁, material recycling station y₁, and landfill location l₂ were decided to be opened at period 1 and still opened until the end of the planning horizon to achieve the optimal solution.

The optimal values of the objective functions under different cases are presented in

Table 13. Set of cases and optimal values of objective functions.

Scenario Number	Economic	Environmental Impact	Social Impact
	Profit (USD)	Carbon Emissions (KgCO2)
1	388,277	157,227.92	214
2	499,361	142,309.72	241
⁝	⁝	⁝	⁝
7	304,670	157,692.42	197
8	415,754	142,724.22	224
9	436,666	157,447.46	222
10	547,750	142,479.26	249
11	400,663	158,142.91	212
⁝	⁝	⁝	⁝
15	353,059	157,861.96	205
16	464,144	142,893.66	231

, where cases 10 and 7 are the best and worst cases, respectively. However, according to the optimal values of the objective functions, from an economic perspective, the best case has the maximum profit with a value of USD 547,750, while the worst case has the minimum profit value of USD 304,670. Furthermore, from an environmental perspective, the best case has the minimum emissions with a value of 142,479.26 kgCO2, while the worst case has the maximum emissions with a value of 157,692.42 kgCO2. Finally, from a social perspective, the job opportunities created are the same in all cases; due to their connection with the opening of facilities at stage zero, which means that there are no random variables affecting them, whereas the number of days lost due to work-related injuries varies from one case to another depending on the quantities of products, parts, and materials entering the network.

Figure 4 illustrates the distribution paths between RSC’s different facilities and the optimal flow of quantities of products, all its parts, and materials for each period over the planning horizon. The optimal values of the decision variables for each period are shown in

Table 14. Decision variables under best (worst) case for R and W products.

Time	${AR}_{1t}$	${QR}_{1fgts}$	${QR}_{1gets}$	${QB}_{1ebts}$	${QN}_{1bnts}$	${QE}_{1edts}$	${QI}_{1cdits}$				${QK}_{1cikts}$	${QD}_{1cmts}$
							$c_3$	$c_2$	$c_1$	∑		$c_3$	$c_2$	$c_1$	∑
$t_1$	1710 (1692)	1710 (1692)	1710 (1692)	941 (761)	941 (761)	770 (931)	462 (1024)	231 (512)	231 (512)	923 (2047)	923 (2047)	1077 (838)	539 (419)	539 (419)	2155 (1675)
$t_2$	1688 (1724)	1688 (1724)	1688 (1724)	928 (776)	928 (776)	760 (948)	456 (1043)	228 (522)	228 (522)	912 (2086)	912 (2086)	1063 (853)	532 (427)	532 (427)	2127 (1707)
$t_3$	1696 (1728)	1696 (1728)	1696 (1728)	933 (778)	933 (778)	763 (950)	458 (1045)	229 (523)	229 (523)	916 (2091)	916 (2091)	1068 (855)	534 (428)	534 (428)	2137 (1711)
$t_4$	1662 (1712)	1662 (1712)	1662 (1712)	914 (770)	914 (770)	748 (942)	823 (565)	411 (282)	411 (282)	1645 (1130)	1645 (1130)	673 (1318)	337 (659)	337 (659)	1346 (2636)
Time	${AR}_{2t}$	${QR}_{2fgts}$	${QR}_{2gets}$	${QB}_{2ebts}$	${QN}_{2bnts}$	${QE}_{2edts}$	${QI}_{2cdits}$				${QK}_{2cikts}$	${QD}_{2cmts}$
							${\mathit{c}}_3$	${\mathit{c}}_2$	${\mathit{c}}_1$	∑		${\mathit{c}}_3$	${\mathit{c}}_2$	${\mathit{c}}_1$	∑
$t_1$	1287 (1313)	1287 (1313)	1287 (1313)	708 (761)	708 (761)	579 (931)	174 (397)	174 (397)	174 (397)	521 (1192)	521 (1192)	405 (325)	405 (325)	405 (325)	1216 (975)
$t_2$	1342 (1298)	1342 (1298)	1342 (1298)	738 (776)	738 (776)	604 (984)	181 (393)	181 (393)	181 (393)	544 (1178)	544 (1178)	423 (321)	423 (321)	423 (321)	1268 (964)
$t_3$	1275 (1320)	1275 (1320)	1275 (1320)	701 (778)	701 (778)	574 (950)	172 (399)	172 (399)	172 (399)	516 (1198)	516 (1198)	402 (327)	402 (327)	402 (327)	1205 (980)
$t_4$	1344 (1279)	1344 (1279)	1344 (1279)	739 (770)	739 (770)	605 (942)	333 (211)	333 (211)	333 (210)	998 (633)	998 (633)	272 (492)	272 (492)	272 (492)	816 (1477)
Time	${QM}_{1amyts}$					${QY}_{1adyts}$					${QL}_{1aylts}$
	$a_4$	$a_2$	$a_2$	$a_1$	∑	$a_4$	$a_2$	$a_2$	$a_1$	∑	$a_4$	$a_2$	$a_2$	$a_1$	∑
$t_1$	646 (503)	-	539 (419)	7326 (5695)	8511 (6617)	-	7695 (9306)	3848 (4653)	3078 (3722)	14,621 (17,681)	-	5387 (6514)	-	462 (558)	5848 (7073)
$t_2$	638 (512)	-	532 (427)	7231 (5803)	8401 (6742)	-	7596 (9482)	3798 (4741)	3038 (3793)	14,432 (18,016)	-	5317 (6637)	-	456 (569)	5773 (7206)
$t_3$	641 (513)	-	534 (428)	7266 (5816)	8441 (6757)	-	7632 (9504)	3816 (4752)	3053 (3802)	14,501 (18,058)	-	5342 (6653)	-	458 (570)	5800 (7223)
$t_4$	404 (791)	-	337 (659)	4577 (8964)	5318 (10,414)	-	7479 (9416)	3740 (4708)	2992 (3766)	14,210 (17,890)	-	5235 (6591)	-	449 (565)	5684 (7156)
Time	${QM}_{2amyts}$					${QY}_{2adyts}$					${QL}_{2aylts}$
	${\mathit{a}}_4$	${\mathit{a}}_2$	${\mathit{a}}_2$	${\mathit{a}}_1$	∑	${\mathit{a}}_4$	${\mathit{a}}_2$	${\mathit{a}}_2$	${\mathit{a}}_1$	∑	${\mathit{a}}_4$	${\mathit{a}}_2$	${\mathit{a}}_2$	${\mathit{a}}_1$	∑
$t_1$	1216 (975)	36 (29)	1500 (1202)	1378 (1105)	4131 (3311)	-	8108 (10,110)	579 (722)	8687 (10,832)	17,375 (21,665)	-	5676 (7077)	-	1303 (1625)	6979 (8702)
$t_2$	1268 (964)	38 (29)	1564 (1189)	1437 (1092)	4308 (3274)	-	8455 (9995)	604 (714)	9059 (10,709)	18,117 (21,417)	-	5918 (6996)	-	1359 (1606)	7277 (8602)
$t_3$	1205 (980)	36 (29)	1486 (1209)	1366 (1111)	4093 (3329)	-	8033 (10,164)	574 (726)	8606 (10,890)	17,213 (21,780)	-	5623 (7115)	-	1291 (1634)	6914 (8748)
$t_4$	816 (1477)	24 (44)	1007 (1822)	925 (1674)	2773 (5018)	-	8467 (9848)	605 (703)	9072 (10,552)	18,144 (21,104)	-	5927 (6894)	-	1361 (1583)	7288 (8477)
Time	${QZ}_{1ayzts}$							${QZ}_{2ayzts}$
	${\mathit{a}}_4$	${\mathit{a}}_2$	${\mathit{a}}_2$	${\mathit{a}}_1$	∑			${\mathit{a}}_4$	${\mathit{a}}_2$	${\mathit{a}}_2$	${\mathit{a}}_1$	∑
$t_1$	646 (503)	2309 (2792)	4386 (5072)	9942 (8859)	17,283 (17,225)			1216 (975)	2469 (3062)	2079 (1925)	8763 (10,312)	14,527 (16,274)
$t_2$	638 (512)	2279 (2845)	4330 (5168)	9814 (9027)	17,061 (17,551)			1268 (964)	2574 (3027)	2168 (1903)	9137 (10,194)	15,148 (16,088)
$t_3$	641 (513)	2290 (2851)	4350 (5180)	9861 (9048)	17,141 (17,592)			1205 (980)	2446 (3079)	2060 (1935)	8681 (10,367)	14,391 (16,361)
$t_4$	404 (791)	2244 (2825)	4076 (5367)	7120 (12,165)	13,844 (21,148)			816 (1477)	2565 (2999)	1612 (2525)	8637 (10,643)	13,629 (17,645)

.

Table 15. Optimal flow of parts and materials.

Refrigerator
	Part/Material	Period 1	Period 2	Period 3	Period 4	Revenues (USD)
Quantity of parts (part/year)	Compressor	231 (512)	228 (522)	229 (523)	411 (282)	54,950 (91,927)
	Evaporator	231 (512)	228 (522)	229 (523)	411 (282)	17,584 (29,417)
	Condenser	462 (1024)	456 (1043)	458 (1045)	823 (565)	37,383 (62,510)
	Total	924 (2048)	912 (2087)	916 (2091)	1645 (1129)	109,917 (183,854)
Quantity of materials (kg/year)	Steel	9942 (8859)	9814 (9027)	9861 (9048)	7120 (12,165)	32,329 (34,408)
	Copper	4386 (5072)	4330 (5168)	4350 (5180)	4076 (5367)	90,510 (109,751)
	Plastic	2309 (2792)	2279 (2845)	2290 (2851)	2244 (2852)	9122 (11,312)
	Aluminum	646 (503)	638 (512)	641 (513)	404 (719)	3587 (3571)
	Total	17,283 (17,226)	17,061 (17,552)	17,142 (17,529)	13,844 (21,148)	135,547 (159,042)
Washing machine
	Part/Material	Period 1	Period 2	Period 3	Period 4	Revenues (USD)
Quantity of parts (part/year)	Motor	173 (397)	181 (393)	172 (399)	333 (211)	34,360 (56,007)
	Pump	174 (398)	181 (393)	172 (399)	333 (211)	17,200 (28,003)
	Door	174 (398)	181 (393)	172 (399)	332 (210)	17,180 (27,983)
	Total	521 (1193)	543 (1178)	516 (1198)	998 (664)	68,740 (111,993)
Quantity of materials (kg/year)	Steel	8763 (10,321)	9137 (10,194)	8681 (10,367)	8637 (10,643)	30,992 (36,535)
	Copper	2079 (1925)	2168 (1903)	2060 (1935)	1612 (2525)	41,812 (43,757)
	Plastic	2469 (3062)	2575 (3027)	2446 (3079)	2564 (2999)	10,054 (12,167)
	Glass	1216 (975)	1268 (964)	1204 (980)	816 (1477)	1,802 (1,758)
	Total	14,527 (16,274)	15,148 (16,088)	14,391 (16,361)	13,629 (17,645)	84,660 (94,217)

demonstrates the flow of parts and materials across network facilities regarding the best (worst) case for each period, as well as the expected revenues from selling these parts and materials in the markets. A refrigerator, as illustrated in Table 15, is composed of three major parts: a compressor, a condenser, and an evaporator, and four major materials: steel, copper, plastic, and aluminum. A washing machine contains three major parts: a motor, a pump, and a door, and four major materials: steel, copper, plastic, and glass. The total revenues (USD) that may be obtained from selling the repaired parts from refrigerators and washing machines are calculated as 109,917 and 68,740, respectively. The total revenues (USD) resulting from selling the recycled materials of refrigerators and washing machines are 135,547 and 84,660, respectively.

Figure 5 shows the distribution of revenues for the refrigerator and washing machine parts, where it is noticed that the compressor is the most valuable part of a refrigerator, which represents 50% of the total revenues gained from selling the refrigerator parts, followed by the condenser and the evaporator with percentages of 34% and 16%, respectively. However, the washing machine’s motor is the most valuable part, representing 50% of the total revenues. Figure 6 depicts the distribution of the revenues from the collected product materials, where it is noticed that for both products, the most valuable material is copper, followed by steel, plastic, aluminum, and glass.

For refrigerators, the copper material contributed the highest percentage (=66.8%) from the total revenues gained by selling the recycled materials, followed by steel, plastic, and aluminum, contributions of 23.9%, 6.7%, and 2.6%, respectively. While for washing machines, copper material also accounts for the highest percentage (=49.4%) of the total revenues gained from selling recycled materials, followed by steel, plastic, and glass with contributions of 36.6%, 11.9%, and 2.1%, respectively. Consequently, to decrease the network’s total processing cost resulting from recycling activities and their corresponding emissions, the main focus should be placed on recycling copper and steel, which were identified as the most valuable recycled materials. The details of the total costs and profit for the generated cases are presented in

Table 16. Cost details and profit for all generated cases.

Scenario Number	Processing Cost (USD)	Transportation Cost (USD)	Construction Cost (USD)	Profit (USD)
1	221,732	34,915	1,640,000	388,277
2	208,417	31,246	1,640,000	499,361
⁝	⁝	⁝	⁝	⁝
7	236,131	34,270	1,640,000	304,670
8	222,815	30,603	1,640,000	415,754
9	214,919	35,328	1,640,000	436,666
10	201,603	31,659	1,640,000	547,750
⁝	⁝	⁝	⁝	⁝
14	207,965	31,236	1,640,000	500,146
15	229,318	34,683	1,640,000	353,059
16	216,002	31,015	1,640,000	464,144

.

Figure 7 displays the totals of costs and revenues under the best case, where it is noticed that the total construction cost represents around 88% of the total network cost, while processing cost and transportation cost represent 11% and 2% of the total network cost, respectively. The network cost comprises three major costs: construction costs associated with facility opening, transportation costs, and processing costs are USD 31,659 and USD 201,603, respectively. The total incurred costs (USD) and profit (USD) from resulting revenues from selling refurbished products, repaired parts, and recycled materials are 1,873,263 and 547,750, respectively.

The environmental objective is concerned with the CO2 emissions resulting from processing and transportation activities in the network. The total of carbon emissions resulting from the processing of different quantities of products, parts, raw materials, and transportation is presented in

Table 17. Carbon emissions of the network.

Scenario Number	From Processing (kg CO2)	From Transportation (kg CO2)	Total Emissions (kg CO2)
1	39,287.32	117,940.6	157,227.92
2	36,491.92	105,817.8	142,309.72
⁝	⁝	⁝	⁝
6	37,360.07	104,668.7	142,028.77
7	41,313.92	116,378.5	157,692.42
8	38,518.52	104,205.7	142,724.22
9	38,344.16	119,103.3	157,447.46
10	35,548.76	106,930.5	142,479.26
⁝	⁝	⁝	⁝
15	40,370.76	117,491.2	157,861.96
16	37,575.36	105,318.3	142,893.66

.

In Table 17, the CO2 emissions resulting from transportation and processing represent 74% and 26% of the total network emissions, respectively. Moreover, the amounts of CO2 emissions from processing quantities and transportation at each stage in the RSC for each period are listed in

Table 18. CO2 emissions resulting from RSC.

Stage	T	CO2 Source (kg CO2)	Stage	T	CO2 Source (kg CO2)	Stage	T	CO2 Source (kg CO2)	Stage	T	CO2 Source (kg CO2)
Collection and sorting station		Processing	Disassembly station		Processing	Material extraction station		Processing	Landfill		Processing
	$t_1$	-		$t_1$	40.46 (604.83)		$t_1$	62.0 (48.8)		$t_1$	-
	$t_2$	-		$t_2$	40.91 (609.23)		$t_2$	62.6 (49.1)		$t_2$	-
	$t_3$	-		$t_3$	40.11 (620.99)		$t_3$	61.5 (49.5)		$t_3$	-
	$t_4$	-		$t_4$	40.58 (596.13)		$t_4$	39.9 (75.7)		$t_4$	-
		Transportation			Transportation			Transportation			Transportation
	$t_1$	3086.9 (3095.2)		$t_1$	1267.7 (1553.6)		$t_1$	2662.9 (2093.5)		$t_1$	1282.7 (1577.4)
	$t_2$	3120.9 (3112.7)		$t_2$	1281.7 (1562.4)		$t_2$	2682.1 (2109.7)		$t_2$	1305.0 (1580.9)
	$t_3$	3060.1 (3139.4)		$t_3$	1256.7 (1575.8)		$t_3$	2640.0 (2125.7)		$t_3$	1271.4 (1597.1)
	$t_4$	3096.2 (3080.7)		$t_4$	1271.5 (1546.3)		$t_4$	1708.5 (3249.8)		$t_4$	1297.2 (1563.3)
Refurbishing station		Processing	Repairing station		Processing	Material recycling station		Processing
	$t_1$	82.4 (67.6)		$t_1$	136.4 (305.7)		$t_1$	6253.8 (7143.2)
	$t_2$	83.3 (68.0)		$t_2$	137.3 (308.1)		$t_2$	6353.5 (7153.6)
	$t_3$	81.7 (68.6)		$t_3$	135.2 (310.4)		$t_3$	6206.2 (7223.8)
	$t_4$	82.7 (67.3)		$t_4$	249.5 (166.4)		$t_4$	6322.5 (7078.6)
		Transportation			Transportation			Transportation
	$t_1$	164.8 (135.2)		$t_1$	1502.4 (3368.4)		$t_1$	18,271.0 (15,295.3)
	$t_2$	166.7 (136.0)		$t_2$	1513.2 (3394.5)		$t_2$	18,425.9 (15,427.1)
	$t_3$	163.4 (137.2)		$t_3$	1489.5 (3420.3)		$t_3$	18,088.6 (15,571.2)
	$t_4$	165.3 (134.6)		$t_4$	2749.0 (1833.5)		$t_4$	11,939.3 (22,961.9)

. It is noted that the material recycling station contributes the largest CO2 emissions due to the processing and transportation of large amounts of materials entering the material recycling station from the disassembly and material extraction stations, which require advanced processing activities.

Figure 8 conducts a comparison of the environmental objective between the worst and best cases, where the best and worst cases in total carbon emissions are 142,479.26 kg CO2 and 157,692.42 kg CO2, respectively.

5. Results and Sensitivity Analysis

5.1. Optimization Results

The analysis of the objective functions was conducted over four periods. Regarding the economic objective function, which represents the profit of the network, a comparison between the best- and worst-case profits over four periods is illustrated in Figure 9, where the total profit under the best case in period four is expected to increase by about 22% with a value of USD 153,820. In contrast, the total profit from the worst case increases slightly from period one to three and then drops sharply at period four by 43% of the total profit in period one because of the quantity and quality of returns that enter the network during this year.

Further, Figure 10 shows a comparison of the expected revenues between the RSC networks with refrigerators only (case 1), washing machines only (case 2), and refrigerators and washing machines (case 3) over four periods. The results reveal that the largest revenues are gained in period four for the three cases. Moreover, the expected revenues from the RSC of two products (case 3) increase by about 1.70 and 0.59 times that from RSCs of the washing machines (case 2) and refrigerators only (case 1), respectively. Regarding the environmental impact objective function that is presented by the total CO2 emissions from the network processing and transportation activities, a comparison of CO2 emissions between the best and worst cases was conducted over four periods as illustrated in Figure 11. At each of periods one to three, the expected amounts of CO2 emissions are close and slightly change over the first three periods for both cases. But the amount of CO2 emissions significantly decreases (increases) during the fourth period for the best (worst) case by about 18.0% (22%) of that in the first period.

5.2. Sensitivity Analyses

The sensitivity analyses were conducted to investigate the effects of decreasing the values of the quantity of returns (return rate), quality of returns, availability for repair, and market price volatility on RSC performance. The results are presented in the following subsections.

(a)

Changes in the quantity of returns

The effects of increasing and decreasing the quantity of returns by 10% and 20%, respectively, on the performance of RSC are examined. The results are then presented in

Table 19. Sensitivity analysis on the quantity of returns.

Scenario 10		−20%	−10%	Initial	+10%	+20%	Δ
Quantity of returns	$t_1$	2397	2697	2997	3297	3597
	$t_2$	2430	2730	3030	3330	3630
	$t_3$	2371	2671	2971	3271	3571
	$t_4$	2406	2706	3006	3306	3606
	Total	9604	10,804	12,004	13,204	14,404
Profit		109,735	328,743	547,750	766,757	985,764
Revenues		1,936,387	2,178,700	2,421,012	2,663,325	2,905,637
Processing cost		161,327	181,465	201,603	221,741	241,880
Transportation cost		25,325	28,492	31,659	34,826	37,994
Construction cost		1,640,000	1,640,000	1,640,000	1,640,000	1,640,000
Total cost		1,826,652	1,849,957	1,873,263	1,896,568	1,919,873
Environmental impact		113,983	128,231	142,479	156,725	170,976
Carbon emissions from processing		28,445	31,997	35,549	39,100	42,652
Carbon emissions from transportation		85,537	96,234	106,931	117,627	128,324
Social impact		317	283	249	214	179

, where it is noticed that when the quantity of returns increases, the network revenues and profit increase. An increase in the quantity of returns by 10% increases profit by about 40%. In addition, the increase in the number of returns leads to an increase in the processing and transportation activities as well as the processing and transportation costs. It is noticed that when the quantity of returns is increased by 20%, the total network cost slightly increases by about 2.5%.

For the CO2 emissions, it is noted that when the processing and transportation activities increase, the CO2 emissions resulting from processing and transportation increase. Finally, from a social perspective, as the quantity of returns increases, so will the processing activities of these quantities, resulting in an increase in the expected number of lost days due to work-related injuries. Hence, increasing the number of returns by 10% results in decreasing the social impact by about 14.1%.

(b)

Changing in quality of returns

The effects of increasing and decreasing the quality of returns by 10% and 20%, respectively, on the performance of RSC as presented in

Table 20. Sensitivity analysis on quality of returns.

Scenario 10	−20%	−10%	Initial	+10%	+20%	Δ
Profit	187,506	367,628	547,750	727,872	907,994
Revenues	2,114,091	2,267,552	2,421,012	2,574,473	2,727,934
Processing cost	247,304	224,454	201,603	178,753	155,902
Transportation cost	39,281	35,470	31,659	27,849	24,038
Construction cost	1,640,000	1,640,000	1,640,000	1,640,000	1,640,000
Total cost	1,926,585	1,899,924	1,873,263	1,846,601	1,819,940
Environmental impact	176,859	159,669	142,479	125,290	108,100
CO2 emissions from processing	44,092	39,820	35,549	31,277	27,006
CO2 emissions from transportation	132,767	119,849	106,931	94,012	81,094
Social impact	170	209	249	288	328

, which reveals that by increasing the quality of returns the total network revenues and profit will increase and that because processing and transportation activities will decrease resulting in decreasing in processing and transportation cost accordingly. Thus, by increasing the quality of returns by 20%, the total network cost, processing cost, and transportation cost decreased by 2.9%, 29.3%, and 31.7%, respectively. Furthermore, regarding CO2 emissions, as processing and transportation activities decrease, CO2 emissions resulting from processing and transportation will decrease accordingly. The total CO2 emissions will decrease by 31.8% by increasing the quality of returns by 20%. In addition, regarding the social impact objective, as the quality of returns increases, the processing activities of these quantities will decrease accordingly, resulting in a decrease in the expected number of lost days due to work-related injuries. Thus, by increasing the quality of returns by 10%, the social impact will increase by about 24.1%.

(c)

Changing the availability of repairing

The effects of increasing and decreasing the availability of repairing by 10% and 20%, respectively, on the performance of RSC are examined.

Table 21. Sensitivity analysis on availability for repairing.

Scenario 10	−20%	−10%	Initial	+10%	+20%	Δ
Profit	514,408	531,079	547,750	564,421	581,092
Revenues	2,393,569	2,407,291	2,421,012	2,434,734	2,448,455
Processing cost	205,363	203,483	201,603	199,723	197,843
Transportation cost	33,789	32,729	31,659	30,590	29,521
Construction cost	1,640,000	1,640,000	1,640,000	1,640,000	1,640,000
Total cost	1,879,161	1,876,212	1,873,263	1,870,313	1,867,364
Environmental impact	150,473	146,476	142,479	138,483	134,486
CO2 emissions from processing	36,576	36,062	35,549	35,035	34,521
CO2 emissions from transportation	113,897	110,414	106,931	103,447	99,964
Social impact	238	243	249	254	259

shows that the total network revenues and profit increase by increasing the availability of repair because processing and transportation activities regarding material extraction and material recycling decrease resulting in a decrease in processing and transportation costs accordingly. Consequently, by increasing the availability of repair by 20%, the total network costs, processing costs, and transportation costs slightly decreased by 0.3%, 1.9%, and 6.8%, respectively. Furthermore, when processing and transportation activities decrease, the CO2 emissions resulting from processing and transportation decrease accordingly. The total CO2 emissions slightly decrease by 5.6% by increasing the availability of repair by 20%. Finally, as the availability of repair increases, the processing activities of these quantities decrease resulting in a decrease in the expected number of lost days due to work-related injuries. It is noted that when the quality of returns increases by 10%, the social impact slightly increases by about 4.0%.

(d)

Market price volatility

The effects of increasing and decreasing the prices of products and parts by 10% and 20%, respectively, on the performance of RSC are examined.

Table 22. Sensitivity analysis on products’ selling prices.

Scenario 10	−20%	−10%	Initial	+10%	+20%	Δ
Profit	209,345	345,536	547,750	749,962	952,175
Revenues	2,082,608	2,218,799	2,421,012	2,623,225	2,825,438
Processing cost	201,603	201,603	201,603	201,603	201,603
Transportation cost	31,659	31,659	31,659	31,659	31,659
Construction cost	1,640,000	1,640,000	1,640,000	1,640,000	1,640,000
Total cost	1,873,263	1,873,263	1,873,263	1,873,263	1,873,263
Environmental impact	142,479	142,479	142,479	142,479	142,479
CO2 emissions from processing	35,549	35,549	35,549	35,549	35,549
CO2 emissions from transportation	106,931	106,931	106,931	106,931	106,931
Social impact	249	249	249	249	249

and

Table 23. Sensitivity analysis on parts selling price.

Scenario 10	−20%	−10%	Initial	+10%	+20%	Δ
Profit	512,014	529,882	547,750	565,617	583,485
Revenues	2,385,277	2,403,145	2,421,012	2,438,880	2,456,748
Processing cost	201,603	201,603	201,603	201,603	201,603
Transportation cost	31,659	31,659	31,659	31,659	31,659
Construction cost	1,640,000	1,640,000	1,640,000	1,640,000	1,640,000
Total cost	1,873,263	1,873,263	1,873,263	1,873,263	1,873,263
Environmental impact	142,479	142,479	142,479	142,479	142,479
CO2 emissions from processing	35,549	35,549	35,549	35,549	35,549
CO2 emissions from transportation	106,931	106,931	106,931	106,931	106,931
Social impact	249	249	249	249	249

show that the total network revenues and profit increase by increasing the price of products and parts. Moreover, increasing products selling price by 10% results in increasing profit by 37%. While increasing parts selling price by 20% results in 7% increase in network profit.

6. Concluding Remarks

This research considered the optimal design of RSC for e-waste by formulating a multi-stage, multi-objective, multi-period, and multi-product stochastic programming model under the existence of uncertainty in the quantity and quality of returns and the availability of repair. The objective functions aimed to maximize the total profit of the network and social impact, as well as minimize the impact on the environment related to CO2 emissions. To test the applicability of the proposed RSC design, a case study of a household appliances company located in Jordan was examined. The results indicated that by implementing the proposed RSC design, the expected average profit is USD 547,750 from selling various refurbished products, repaired parts, and extracted raw materials at different markets while reducing the environmentally dangerous consequences of EOL products. Furthermore, regarding the reduction in natural resource consumption, the processing of various materials that exist in products and parts is expected to generate 123.025 tons of sold raw materials at the end of the fourth year which will generate revenues of USD 220,207. Finally, the profit gained by the proposed multi-product RSC is 2.3 times that of the single-product RSC. In practice, the proposed stochastic model can help the decision-makers deal with strategic decisions regarding facility opening and operational decisions regarding the physical reverse flow. Moreover, the proposed model is expected to minimize network total CO2 emissions by choosing the optimal transport path and mode. Finally, new job opportunities are expected to be created by opening different network facilities, increasing social impact. In conclusion, the proposed RSC helps manufacturing firms enhance their environmental and social image by dealing with recovering EOL products, reducing e-waste harmful environmental impacts, and improving the efficiency and effectiveness of product return operations. This study considered a single transportation mode and assumed a normal probability distribution for the quantity of returns. In addition, known and certain fixed costs were assumed. Future research, therefore, considers developing RSC of e-waste using multi-modal transport systems with well-modeled probability distributions for model parameters, uncertain facility costs, and with weighted social impact measures.