Reverse Logistics Network Model of Dual-Channel Recycling Boxes Based on Genetic Algorithm Optimization: A Multi-Objective and Uncertain Environment Perspective

Abstract

In the context of carbon neutrality, plastic ban, and green development, this paper aims to maximize the comprehensive interest of manufacturers in building a sustainable logistic network. It proposes a reverse logistics network model of a dual-channel model with multiple objectives and a random environment for the construction of recycling boxes projects and uses a Stackelberg game to develop pricing strategies for dual-channel recyclers and a genetic algorithm to optimize reverse logistics networks. This paper found the following: multi-objective evaluation is more conducive to sustainable development; when consumers are price-sensitive, a stronger rebate can significantly increase revenue; online platform recyclers should invest more in marketing than traditional recyclers; retailers’ willingness to cooperate in recycling has a significant impact on the overall benefits; the impact of government subsidies is marginal and needs to be controlled to a certain extent; the impact of green credit is insignificant, and the strength of commercial banks’ scrutiny of companies has little effect; an increase in environmental uncertainty within a certain range can lead to an overall loss of benefits, and an excessive impact can be out of line with extreme values. It provides a basis for decision-making on strategies for enterprises to build a logistics network of recycling boxes, government subsidies, green credit from banks, and dual-channel recyclers.

1. Introduction

1.1. Research Introduction

Due to the rapid development of e-commerce platforms, the vast number of orders has given rise to many logistics needs. In China, thousands of tons of logistics packaging are discarded every day. According to the “2021–2030 China Express Industry Green Packaging Carbon Emission Reduction Potential Research Report”, the total carbon emissions of China’s express packaging was 23,958,400 tons in 2020. This has increased China’s total carbon emissions on the one hand and created a massive amount of unmanageable plastic waste on the other, making it a long way to go to reach the carbon neutrality target.

The government has to take measures to alleviate these problems. On 19 January 2020, the Chinese government issued “Opinions on Further Strengthening the Control of Plastic Pollution” to ban plastic packaging bags in postal and express delivery outlets in Beijing, Shanghai, Jiangsu, Zhejiang, and Guangdong provinces by the end of 2022. In February 2021, China’s State Council put forward a guiding document for a green, low-carbon, and circular economic system with the goal of “carbon peaking and carbon neutrality,” with green planning, design, investment, production reforms, and transport. In addition, in response to the expansion of highly polluting enterprises, on 30 July 2007, the Chinese Environmental Protection Administration, the People’s Bank of China, and the China Banking Regulatory Commission introduced a credit policy that stipulates that compliance with environmental regulations by enterprises is a necessary condition for loan approval.

Faced with the pressure of plastic restrictions, carbon emission limits, and capital-raising assessments, building a sustainable logistics network is essential for production companies. In this context, recycling boxes, as long-lasting, multi-functional, and easy-to-recycle logistics tools, can help the courier industry significantly reduce carbon emissions between the production and retail ends.

In order to establish a sustainable recycling boxes logistics network, this paper aims to maximize a comprehensive interest that encompasses the economy, society, and the environment. Issues to be addressed in the process include how the logistics network is structured, strategies for dual-channel recyclers, and strategies for subsidies and green credits. The operation of recycling boxes relies not only on forward logistics, but reverse logistics is also essential to reduce energy consumption and transportation costs. Therefore, the design of logistics networks is critical and has been studied by many scholars.

1.2. Logistic Network Model

Minner [1] analyzed the safety stock cost effect of reverse logistics activities and found that the quantity of external material supplied was a determinant of other costs and that a synergistic material, even if there was no substantial cost advantage to product recovery, could lead to a reduction in safety stock and increase the profitability of this option. Chouinard et al. [2] analyzed the relationship between information flow and logistics supply chains, where materials and information are complementary, requiring not only macro information, but also information on the composition, components, and condition of products, orders, inventory levels to aid the efficient operation of the logistics network. Krikke et al. [3] designed a logistics network structure that is modular, repairable and recyclable. And using actual R&D data from a Japanese consumer electronics company, the model was applied to the problem of designing a closed-loop supply chain for refrigerators. Schultmann et al. [4] have taken end-of-life cars in Germany as the object of study and propose a closed-loop supply chain and gived more flexible algorithms. Ramezani et al. [5] proposed a reverse logistics model in an uncertain environment, with profit, customer responsiveness, and quality maximization as the objectives of the logistics network, and obtained a set of Pareto-optimal solutions. Wang et al. [6] investigated the cost of reverse logistics and customer satisfaction, established a reverse logistics network for faulty shared bikes, and used an improved genetic simulated annealing algorithm (MGSA) to solve the model. Wang et al. [7] studied the allocation strategy of government subsidies in e-waste recycling consisting of one collector, one remanufacturer, and two retailers, and the analysis showed that when the remanufacturer efficiency is low, the marginal utility of government subsidies is higher for the collector and the retailer. In addition, when remanufacturing efficiency is high, the marginal utility of government subsidies is higher for remanufacturers. Nikzamir and Baradaran [8] proposed a dual objective mixed integer mathematical formula to solve the new medical waste location-routing problem. In this regard, there are health care, treatment, and disposal centers, and medical waste is divided into infectious and non-infectious waste. The goal of the model is to minimize both total costs and pollution emissions. Rossit and Nesmachnow [9] reviewed research on municipal solid waste systems and found that while research has applied several optimization criteria and methods, few have considered uncertainty in model parameters and integrated approaches. Klenk et al. [10] suggested that the multi-level exchange of information at the core of reverse logistics has the potential to contribute to reducing uncertainty in the remanufacturing process and that increased information exchange in remanufacturing would bring some convenience. Manoj kumar [11] proposed a robust reverse logistics network to collect polishing powder samples of different routes. He found that the reverse logistics network ensures quality and reliable and stable polishing powder as input, which can increase the productivity of the used tire recycling plant. Hennequin et al. [12] built a multi-objective inventory management model that will allow the long-term average expected total function of economic, social, and environmental factors to minimize the basic storage of the basic storage and calculate the completion of the fruit. This is one of the few articles that consider multiple goals. Lai et al. [13] proposed a layered facility siting model to solve real-world military logistics network design problems and used an improved, simplified group optimization algorithm (iSSO) to optimize the model.

1.3. Dual-Channel Recycling Model

However, the shortcomings of traditional recycling methods are low efficiency, high breakage rate, uneven operational quality of personnel, and limited recycling capacity. It has led to traditional recycling channels not being popular with businesses. With the rise of network and logistics capabilities, network platform recyclers have taken to the stage, and a dual-channel recycling reverse logistics network pattern has been established. Cai et al. [14] evaluated the impact of price discount contracts and pricing schemes on competition in a dual-channel supply chain, analyzing them from the perspective of the Stackelberg and Nash games, and reported that scenarios with price discount contracts were superior and that consistent pricing schemes could reduce the intensity of conflict by giving retailers more profit. Chen et al. [15] studied manufacturers’ pricing strategies in a dual-channel supply chain. They found that contracts with supplementary agreements, such as two-part tariffs or profit-sharing agreements, can moderate supply chain conflicts and result in a win–win situation for both the manufacturer and the retailer. Zhou and Ye [16] proposed a dual-channel supply chain model in a low-carbon environment and obtained the most equilibrial strategy. The study found that wholesale price significantly impacts customer loyalty and that manufacturers’ efforts to reduce emissions are more outstanding in dual channels than in single channels. He et al. [17] investigated a Buy-online-and-deliver-from-store (BODS) strategy by comparing the BODS strategy with that of manufacturers operating separate online channels and retailers managing offline channels in the benchmark scenario and found that dual-channel supply chains are more likely to implement a BODS strategy in a competitive environment, and vice versa, under competitive conditions. Mu et al. [18] added credit transactions to dual-channel supply chain operational decisions and coordination. They found that credit sales are disadvantageous in a competitive dual channel, for which a two-part credit contract based on asymmetric Nash bargaining is proposed, which has a facilitating effect. Liu et al. [19] studied the optimal pricing strategies of manufacturers and retailers in a dual-channel supply chain. They added to the model the assumption that consumers tend to be overconfident. He et al. [20] discussed the optimal pricing and channel strategy of dual-channel enterprises in two periods. The results showed that dual-channel companies should adopt pre-announced pricing strategies rather than dynamic ones to counter strategic consumers. Lin et al. [21] developed a mixed integer linear programming (MILP) model to calculate the optimal strategy and found that compared with selfish pricing, the altruistic pricing strategy significantly increased the profit proportion of retailers, thus alleviating the channel conflict between manufacturers and retailers.

1.4. Multi-Objective Optimization Methods of Reverse Logistics Problems

The above studies are based on network optimization from a fully economic interest perspective. However, multi-objective optimization of supply chain and logistics network will be the trend in future. In real life, commercial banks will review the ESG (environmental, social, and governance) of companies, and within the green economy related lines, the environmental and social attributes of a company’s production and operations will be used as factors that influence whether a company can obtain green credit, so it is necessary to establish a multi-objective logistics network design.

In terms of solving logistics network models, traditional solution methods are unable to obtain optimal solutions in a large number of uncertain environments, i.e., large arithmetic, and complex systems. Therefore, heuristic algorithms such as the genetic algorithm, ant colony algorithm, and annealing algorithm have been reused, among which the genetic algorithm has been improved and applied by many scholars as a method serving service scheduling and path optimization. In the design process of sustainable reverse logistics network and general logistics network, it is usually necessary to consider such factors as economic, environmental, social objectives, welfare security, cost, and profit. At the same time, different cycles, different products, and uncertain influence factors also make the problem more complex, which makes the model have higher requirements for the solution method in the process in order to be closer to the actual situation.

For the solution of the single objective function, heuristic algorithms such as genetic or two-stage algorithms are often used to design the network. The heuristic algorithm is also often used to verify the mathematical model in simulation. For the solution of a multi-objective function, there is generally a unified objective function method, which converts each sub-objective function in the original objective function into a unified objective function through a certain method, and then solves by using the optimization method of a single objective function. The conversion methods include the weighted sum method proposed by Galanteet et al. [22], Nurjanni et al. [23], Hao et al. [24], and Nguyen et al. [25] and the global criterion method proposed by Temur et al. [26]. The normalized normal constraint method (HNCM) was published by Bortollini et al. [27]. In the literature of Nurjanni et al. [23], the weighted sum method and weighted Chebyshev method are used to convert double objectives based on cost and carbon emissions into single objectives for a solution. In the literature of Bortollini et al. [27], the normalized normal constraint method was used to convert multiple objectives, including cost and environmental impacts, into single objectives.

Intelligent optimization algorithms or heuristic algorithms are often used to solve optimization decision problems on a large scale. For example, a hybrid simulated annealing algorithm was used by Mohamadpour [28], a variable neighborhood search algorithm was used by Devika et al. [29], and ant colony optimization was used by Zohal et al. [30] and Govindan et al. [31]. Pourmohammadi et al. [32] developed a novel GA to effectively solve the large size problem instance problem and modeled aluminum scrap/byproducts from Los Angeles County, taking into account several costs. In the paper of Robles et al. [33], the GA was used to cope with the multi-objective formulation in the hydrogen supply chain (HSC). The GA obtained some compromise solutions in the multi-objective formulation. Compared with the MILP in the mono-criterion problem, the results generated by the GA exhibit the same order of magnitude. Gao and Chen [34] built a logistics distribution model with several suppliers serving several demands. Using the GA to obtain the optimal solution or approximate optimal solution in the problem and the calculation results demonstrates the effectiveness of the GA. Yan et al. [35] introduced open-loop and closed-loop remanufacturing reverse logistics (RL) network models. A mixed-integer linear program (MILP) is built due to the open-loop RL, using an adaptive genetic algorithm, and an effective solution can be obtained. Sadeghi et al. [36] proposed a mathematical model that can be used to optimize renewable energy supply chain logistics costs and carbon footprint. A designed genetic algorithm can obtain a near-optimal solution for this problem. The model results show that the proposed model’s input and output variables have good relationships.

The genetic algorithm is a general algorithm for solving search problems. It has the characteristics of easy implementation, parallel processing, and high efficiency. Unlike other heuristic algorithms, the genetic algorithm can iterate from a set of problem solutions, and the results iteration only relies on the fitness function to evaluate individuals in the search process. The fitness function is not only not subject to continuous differentiability constraints; it can also customize its definition domain. At the same time, the genetic algorithm does not use deterministic rules but guides its search direction according to probability. These characteristics give genetic algorithms strong adaptability to different problems and high robustness to the solution results. Genetic algorithms are often used to solve reverse logistics problems, so this paper will use genetic algorithms to solve the model.

1.5. Research Contribution

The above studies have the problems of reverse logistics network without considering the multi-objective, uncertain environment, very few empirical studies on recycling boxes, a lack of a mechanism for graded recycling, difficulty in combining mature, intelligent algorithms to solve them, and not considering green credit for enterprises. Therefore, this paper makes the following contributions:

• A mechanism for the quality of the recycler’s service to affect the recycling rate was included and found to impact the overall benefit significantly;
• Adding hierarchical logistics mechanisms into the model;
• Considering green credit and subsidy from commercial banks and government in the model and found that the impact of green credit was insignificant;
• Considering the environmental uncertainty when building a reserve logistic network, an increase in environmental uncertainty within a specific range was found to affect the overall benefits adversely;
• Enriching the empirical research on building recycling boxes reserve logistic network.
• Enriching the multi-objective research in the logistic network and genetic algorithm arena demonstrates that a multi-objective orientation is more appropriate to sustainable development than a single objective;
• Enriching the study of price sensitivity; the more price sensitive, the lower the overall return.

A logistics network that considers economic, social, and environmental multi-objective coordination is established by simulating the operational structure of an actual project and considering the hierarchical utilization characteristics of recycled boxes. A genetic algorithm is used to solve the logistics model. Finally, the data are brought in, and the validity of the model and algorithm is calculated, along with multi-objective value versus single-objective value, the pricing, rebating, marketing, response time and other strategies for dual-channel recyclers, recycling boxes service quality, subsidy strategy analysis of government, sensitivity of commercial bank green credit, and environmental uncertainty level on the overall recycling boxes network design.

2. Logistic Network Modeling

2.1. Definition of the Decision Problem

The project studied in this paper is a reverse logistics network for the recycling of recycling boxes. The participating parties are retailers, traditional recyclers, online platform recyclers, recycling boxes centers, recycling boxes lessors, remanufacturers, scrape recyclers, third party logistics, and scrap markets. The business processes of these nine participants are shown in Figure 1. Q stands for the number of recycling boxes. Waste material is still recorded according to individual boxes.

The reverse logistics of recycling boxes starts with the retailers. Traditional recyclers and online platform recyclers will pick up the boxes. The two recyclers constitute a competitive relationship; factors such as offer and quality of service will affect the percentage of business of the recyclers. After recovery, the boxes are delivered to a recycling centre, which is responsible for rating the condition of the recycled boxes. Generally speaking, recycling centers are rated on three levels: T1, T2, and T3.

T1: The recycled boxes have little damage;

T2: Average level of damage to the recycling bin;

T3: The recycled boxes have a high level of damage.

The recycling box has 11 parts, and the number of damaged parts determines the degree of damage. The judgment is based on the loss of the protective effect of the insulation and waterproofing on the goods; that is, it needs to be repaired or rebuilt. In general, more than one damaged part needs to be repaired, and more than three need to be remanufactured. T1 recycling boxes can be reused after cleaning and disposal, so they are transported directly from the recycling center to the recycling boxes lessor. Category T2 recycling boxes are damaged but can be reused by repairing them, so they are transported to remanufacturers. Category T3 recycling boxes are so damaged that only the boxes can be destroyed to recover the material, of which the plastic scrap recyclers can sell the raw material to the remanufacturer.

Finally, recycling box lessors re-deliver the boxes to third-party logistics and plastics recyclers hand over the raw materials that cannot be recycled to waste markets or disposal sites.

2.2. General Assumptions

In order to facilitate model building and arithmetic, for the above recycling boxes logistics network model, several assumptions are made.

(1)

Retailers’ willingness to cooperate with recycling will affect the recycling rate of recycling boxes: the lower the willingness to cooperate, the lower the recycling rate;

(2)

Retailers’ willingness to cooperate and demand are related to the recyclers’ service quality: The higher the quality of service, the higher the willingness to cooperate;

(3)

Alternative addresses for traditional recyclers, online platform recyclers, recycling centers, scrape recyclers, remanufacturers, recycled boxes lessors, third party logistics, and waste markets are known;

(4)

The distances between logistics nodes are equal;

(5)

Commercial banks will issue green credit based on the ESG rating of the participating entities and will be issued to traditional recyclers and online platform recyclers;

(6)

ESG rating is associated with reduced carbon emissions, reduced plastic pollution, green development of employees, average salary, etc.;

(7)

There is a game between dual-channel recyclers and recycling boxes centers, which is analyzed using the Stackelberg model, with recycling boxes centers being the dominant player in the game and traditional and online recyclers being the followers;

(8)

In order to promote the level of green development, the government will grant green subsidies to the participating subjects. The participating subjects of the subsidy are recycling boxes recyclers, recycling boxes centers, and recycling boxes lessors;

2.3. Multi-Objective Modeling

The multi-objectives are based on sustainable supply chain theory and are in terms of economic, social, and environmental aspects. The economic dimension of these objectives considers parameters such as the establishment costs of logistics points, production unit costs, recovery costs, transport costs, and recovery offers. The social dimension considers parameters such as the number of accidents in the production operation, the number of jobs offered, the salary level of the employees, and the training efforts for green development. The environmental dimension considers parameters such as carbon emissions from production, waste pollution, carbon emissions reduced by recycling, etc. The symbols and equations for the objective function are shown in

Table 1. Symbols and value ranges of parameters.

Symbols	Definition	Range of Values
AC	Number of accidents during the construction and operation of the recycling boxes center	[0, 10]
AO	The number of accidents when the network platform recyclers was built and operated	[0, 10]
AT	Number of accidents when traditional recyclers are built and operated	[0, 10]
BCO	Network platform offline point of construction costs	[1.5, 2.0] million
BCT	Traditional recyclers construction costs	[1.5, 2.0] million
CS	Commercial banks’ sensitivity to green rating	[0.8, 0.9].
DO	Number of online platform recyclers built	None
DT	Number of traditional recyclers built	None
EBC	Carbon emissions from setting up a recycling boxes center	[7000, 9000] tons
EBO	Establishing carbon emissions from online platform recyclers	[6000, 8000] tons
EBT	Establishing carbon emissions from traditional recyclers	[6000, 8000] tons
EC	Jobs created at the recycling boxes center	[30, 35] pcs.
EO	Jobs created by online platform recyclers	[15, 20] pcs.
EPM	Carbon emissions from remanufacturer production	[20, 30] million tons
EPP	Carbon emissions from transport unit recycling boxes	[3, 5] tons
EPS	Carbon emissions from scrap recyclers generation	[20, 30] million tons
ERC	Carbon emission reduction from recycling boxes center	[3, 5] million tons
ERO	Carbon emissions reduced by online platform recyclers	[3, 5] million tons
ERT	Carbon emissions reduced by traditional recyclers	[3, 5] million tons
ESGO	Green rating of network platform recyclers	None
ESGT	Green rating for traditional recyclers	None
ET	Jobs created by traditional recyclers	[20, 25] pcs.
FCC	Fixed costs of operating a recycling boxes center	[1, 1.5] million yuan/year
FCO	Fixed costs of operating network platform recyclers	[50, 100] million yuan/year
FCT	Fixed costs of operating traditional recyclers	[50, 150] million yuan/year
GIC	Green development input from the recycling boxes center	[30, 50] million
GIO	Green development input from online platform recyclers	[30, 50] million
GIT	Green development input from traditional recyclers	[30, 50] million
GSC	Government subsidies for recycling boxes centers	[30, 50] million
GSL	Government subsidies for recycling boxes renters	[30, 50] million
GSO	Government subsidies for online platform recyclers	[30, 50] million
GST	Government subsidies for traditional recyclers	[30, 50] million
MKTO	Marketing cost of online platform recyclers	[10–20] million
MKTT	Marketing cost of traditional recyclers	[10–20] million
PEM	Plastic pollution from remanufacturers	[500, 800] tons
PERC	Plastic pollution reduced by recycling boxes center	[100, 150] tons
PERO	Plastic pollution reduced by online platform recyclers	[80, 120] tons
PERT	Reduced plastic pollution from traditional recyclers	[80, 120] tons
PES	Plastic pollution caused by scrap recyclers	[500, 800] tons
PP	Unit offer from recycling boxes renters	[10, 15] Yuan *
PS	Unit price paid by scrap recyclers to recycling bin centers	[10, 15] Yuan *
Pt	Price per unit transport of recycling boxes	[5, 10] Yuan *
Q1	Number of recycling boxes transported from retailers to traditional recyclers	None
Q2	Number of recycling boxes transported from retailers to online platform recyclers	None
Q3	Number of recycling boxes transported from traditional recyclers to recycling boxes centers	None
Q4	Number of recycling boxes transported from online platform recyclers to recycling boxes centers	None
Q5	Number of recycling boxes transported from recycling boxes centers to recycling boxes lessors	None
Q6	Number of recycling boxes transported from recycling boxes centers to remanufacturers	None
Q7	Number of recycling boxes transported from recycling boxes centers to scrape recyclers	None
Q8	Number of recycling boxes transported from remanufacturers to recycling boxes lessors	None
Q9	Number of recycling boxes transported from scrape recyclers to remanufacturers	None
RBO	Rebates of online platform recyclers	[10–30] million
RBT	Rebates of traditional recyclers	[10–30] million
SCC	Recycling boxes center labor cost	[2, 3.5] million Yuan/year
SCO	Network platform recyclers labor costs	[100, 200] million yuan/year
SCT	Labor costs for traditional recyclers	[1.5, 2.0] million yuan/year
Β δ χ ε ф γ φ γ η	Weighting symbols of standardization	0.25, 0.25, 0.25, 0.25 0.5, 0.5 0.34, 0.33, 0.33

*: 1 Yuan = 0.15 Dollar.

.

$$\begin{array}{c}ObjE={\displaystyle \sum _{p}PP}\times Q10+{\displaystyle \sum _{s}PS}\times Q11-{\displaystyle \sum _{t}BCT\times DT}-{\displaystyle \sum _{t}FCT\times DT}\hfill \\ \hspace{1em}\hspace{1em} -{\displaystyle \sum _{t}SCT\times DT}-{\displaystyle \sum _{o}BCO\times DO}-{\displaystyle \sum _{o}FCO\times DO}-{\displaystyle \sum _{o}SCO\times DO}\hfill \\ \hspace{1em}\hspace{1em} -FCC-SCC+(ESGT+ESGO)\times CS+GST+GSO+GSL\hfill \\ \hspace{1em}\hspace{1em} -RBT-RBO-MKTT-MKTO-Pt\times (Q1+Q2+Q3+Q4\hfill \\ \hspace{1em}\hspace{1em} +Q5+Q6+Q7+Q8+Q9+Q10+Q11)\hfill \end{array}$$

(1)

$$\begin{array}{c}ObjS={\displaystyle \sum _{t}ET\times DT}+{\displaystyle \sum _{t}AT\times DT}+{\displaystyle \sum _{t}GIT\times DT}+{\displaystyle \sum _{o}EO\times DO}+{\displaystyle \sum _{o}AO\times DO}\hfill \\ \hspace{1em}\hspace{1em} +{\displaystyle \sum _{o}GIO\times DO}+EC+AC+GIC+\frac{SCT}{ET}+\frac{SCO}{EO}+\frac{SCC}{EC}\hfill \end{array}$$

(2)

$$\begin{array}{c}Obje=EPP\times (Q1+Q2+Q3+Q4+Q5+Q6+Q7+Q8+Q9\hfill \\ \hspace{1em}\hspace{1em} +Q10+Q11)-ERT\times Q3-ERO\times Q4-ERC\times (Q5+Q6+Q7)\hfill \\ \hspace{1em}\hspace{1em} +EPS\times Q7+EPM\times Q8+{\displaystyle \sum _{t}EBT\times DT}+{\displaystyle \sum _{o}EBO\times DO}\hfill \\ \hspace{1em}\hspace{1em} +EBC-PERT\times Q3-RERO\times Q4-PERC\times (Q5+Q6+Q7)\hfill \\ \hspace{1em}\hspace{1em} -PEM-PES\hfill \end{array}$$

(3)

The above formula gives a three-way objective function for the economy, society, and environment, and the model aims to maximize the objective function’s outcome. Furthermore, as can be seen from the above formula, the range and units of the many parameters in society and the environment vary. Data that differ by many orders of magnitude combined into a formula can result in specific parameters having no effect and specific parameters having a more significant effect. In order to allow for a reasonable calculation of the objective function, the parameters need to be processed. This paper uses a data standardization process to quantify the indicator ratios. For example, carbon emissions and unit recovery costs differ by orders of magnitude, so the range of values for each indicator is standardized to the [0, 1] interval, and the specific treatment is as follows. The company’s decision-makers determine the following weights.

$$ObjE=\min \left(\frac{ObjE}{Ma{x}_{profit}}\right)$$

(4)

$$ObjS=\min \left(\beta \times \frac{ObjA}{Ma{x}_{accident}}+\delta \times \frac{Objs}{Ma{x}_{salary}}+\chi \times \frac{ObjG}{Ma{x}_{Green}}+\epsilon \times \frac{ObjEm}{Ma{x}_{empolyment}}\right)$$

(5)

$$Obje=\min \left(\phi \times \frac{ObjC}{Ma{x}_{Carbon}}+\gamma \times \frac{ObjP}{Ma{x}_{Plastic}}\right)$$

(6)

$$Obj=\min \left(\varphi \times ObjE+\gamma \times ObjS+\eta \times Obje\right)$$

(7)

2.4. Constraints

The model assumes that each participating subject will keep inventory, so the number of recycling boxes outputs will not be greater than the number of inputs. The constraints are shown below.

$${\displaystyle \sum _{r}Q1}\ge {\displaystyle \sum _{t}Q3}$$

(8)

$${\displaystyle \sum _{r}Q2}\ge {\displaystyle \sum _{o}Q4}$$

(9)

$${\displaystyle \sum _{t}Q3}+{\displaystyle \sum _{o}Q4}\ge {\displaystyle \sum _{c}Q5}+{\displaystyle \sum _{c}Q6}+{\displaystyle \sum _{c}Q7}$$

(10)

$${\displaystyle \sum _{c}Q5}+{\displaystyle \sum _{m}Q8}\ge {\displaystyle \sum _{l}Q10}$$

(11)

$${\displaystyle \sum _{c}Q6}+{\displaystyle \sum _{s}Q9}\ge {\displaystyle \sum _{m}Q8}$$

(12)

$${\displaystyle \sum _{c}Q7}\ge {\displaystyle \sum _{s}Q9}+{\displaystyle \sum _{s}Q11}$$

(13)

$$Q1\le ST$$

(14)

$$Q2\le SO$$

(15)

$$Q3+Q4\le SC$$

(16)

$$Qn\ge 0,n=\{1,2,3,4,5,6,7,8,9,10,11\}$$

(17)

$$DT,DO\in \{0,1\}$$

(18)

The above constraints are mainly based on the number of recycling boxes in circulation. The total number of recycling boxes input to the participating entities should be greater than or equal to the amount output by the participating entities, as the participating entities themselves have a certain amount of storage capacity. In addition, the number of traditional recyclers, online platform recyclers, and recycling boxes centers per input is less than the maximum storage capacity. DT and DO are decision variables, where 0 is no construction and 1 is construction.

3. Model Refinement and Solution

3.1. Dual-Channel Recovery

Based on the dual-channel recycling model, both parties need to source more recycling boxes from retailers in order to make more profit. The total number of potential recycling boxes that can be recovered by retailers is Q. Traditional recyclers have a stable channel, while online platform recyclers have a broader scope of publicity. In order to enhance competitiveness, online platform recyclers can engage in marketing practices such as advertising to increase the visibility of recycling boxes and capture the market of traditional recyclers. The demand of dual-channel recyclers is influenced by the response time t, service quality q, recycling price, and marketing efforts MKT. Therefore, the number of recycling boxes collected for the two recycling channels are placed in

Table 2. Symbols and value ranges of parameters in dual-channel recovery.

Symbols	Definition	Range of Values
b1	Sensitivity to own price	[5,000,000, 8,000,000]
b2	Opponent price sensitivity	[4,000,000, 7,000,000]
b3	Sensitivity to service time	[10,000,000, 30,000,000]
b4	Sensitivity to service quality	[10,000,000, 30,000,000]
b5	Sensitivity to marketing	[200, 400]
b6	Sensitivity to rebates	[500, 700]
MPT	The proportion of Q1 to Q	[0.4, 0.6]
PT3	T3 category of recycling boxes as a percentage of the number of damaged boxes	[0.2, 0.4]
qO	Service Quality	[6–10]
qT	Service Quality	[6–10]
RBPT	Breakage rate of recycling boxes from traditional recyclers	None
RBTO	Breakage rates of recycling boxes from network recyclers	None
tO	Reaction time	[1–9] days
tT	Reaction time	[1–9] days
SRB	Recycling boxes breakage rate is sensitive to service quality	−0.36

.

$$\begin{array}{c}Q1=MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT\hfill \\ \hspace{1em} +b4\times qT+b5\times MKTT+b6\times RBT\hfill \end{array}$$

(19)

$$\begin{array}{c}Q2=(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO\hfill \\ \hspace{1em} +b4\times qO+b5\times MKTO+b6\times RBO\hfill \end{array}$$

(20)

The breakage rate of the recycling boxes is separately linked to the quality of service and the sensitivity of the breakage rate of the recycling boxes is SRB, the breakage rate RBP is shown below.

$$RBPT=1-\phi (SRB\times qT)$$

(21)

$$RBPO=1-\phi (SRB\times qO)$$

(22)

For ease of calculation, the proportion of class T3 within the broken boxes will be T3P. In this case, the equation for Q5-Q7 is as follows.

$$Q5=Q3+Q4-(RBPT\times Q3+RBPO\times Q4)$$

(23)

$$Q6=(RBPT\times Q3+RBPO\times Q4)\times (1-T3P)$$

(24)

$$Q7=(RBPT\times Q3+RBPO\times Q4)\times T3P$$

(25)

3.2. Environmental Settings

Recycling boxes are influenced by many emerging industries and policies, such as carbon neutrality, fresh cold chain transport, and carbon trading. Therefore, the model sets up an environment full of uncertainty for recycling and the operation of recycling boxes. Based on the supply quantity formula obtained in the previous section, the Stackelberg game model is used to establish the interest function of each participating subject. Some scholars have conducted research on the Stackelberg game applying to dual channels. He and Zhou [37] studied a two-channel green supply chain consisting of a manufacturer leader and a retailer follower to analyze the impact of a promotion policy by using Stackelberg game. Pathak et al. [38] used the Stackelberg game to model the effects of channel preferences, price coefficients, sales, and collection effort coefficients on price and effort optimization decision parameters and to maximize profits in a closed-loop dual-channel supply chain.

Green rating of dual-channel recyclers:

$$ESGT=ERT+PERT-{\displaystyle \sum _{t}EBT\times DT}-EPP\times Q1+ET+GIT+\frac{SCT}{ET}$$

(26)

$$ESGO=ERO+PERO-{\displaystyle \sum _{o}EBO\times DO}-EPP\times Q1+EO+GIO+\frac{SCO}{EO}.$$

(27)

Benefit function for traditional recyclers:

$$\begin{array}{c}I(T)=PT\times Q3-RCT\times (MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT+b4\times qT\hfill \\ \hspace{1em}\hspace{1em}+b5\times MKTT)-BCT-FCT-SCT-MKTT+ESGT\times CS+GST\hfill \\ \hspace{1em}\hspace{1em}-Pt\times MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT+b4\times qT+b5\times MKTT\hfill \end{array}.$$

(28)

Benefit function for recyclers on network platform:

$$\begin{array}{c}I(O)=PO\times Q4-RCO\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO+b4\times qO\hfill \\ \hspace{1em}\hspace{1em} +b5\times MKTO]-BCO-FCO-SCO-RBO-MKTO+ESGO\times CS+GSO\hfill \\ \hspace{1em}\hspace{1em} -Pt\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO+b4\times qO+b5\times MKTO]\hfill \end{array}.$$

(29)

Benefit function for recycling centers:

$$\begin{array}{c}I(C)=PL\times Q5+PM\times Q6+PS\times Q7-PT\times Q3-PO\times Q4\\ -BCC-FCC-SCC+GSC-Pt\times Q3-Pt\times Q4\end{array}.$$

(30)

In the Stackelberg game model, the three actors involved need to distinguish between the dominant and the follower. In this logistics model, the recycling centers are the dominant players, and the traditional recyclers and online platform recyclers are the followers. Recycling centers receive recycling boxes from dual-channel recyclers, so the price per boxes in Q3 and Q4 affects the choice of recycling centers. The mechanism is for the recycling center to make a decision on PT and PO prices to maximize its own interest, followed by the traditional recycler and the web platform recycler, on the basis of this, deciding the cost of obtaining recycled boxes from the retailer RCT and RCO. Deriving the interest function for the recycling center, it is found that the recycling center will drop the PT and PO infinitely to zero, making it impossible for the dual channel to continue operating. So, the pricing is restricted to be less than the cost of the dual channel, and the dual channel is able to obtain a profit margin of R1 and R2 where costs exclude government subsidies and green credits.

$$PT=\frac{\begin{array}{c}RCT\times (MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT\hfill \\ +b4\times qT+b5\times MKTT)+BCT+FCT+SCT+RBT\hfill \\ +MKTT+Pt\times MPT\times Q+b1\times RCT-b2\times RCO\hfill \\ -b3\times tT+b4\times qT+b5\times MKTT\hfill \end{array}}{Q3}\times (1+R1)$$

(31)

$$PO=\frac{\begin{array}{c}RCO\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO\hfill \\ +b4\times qO+b5\times MKTO]+BCO+FCO+SCO+RBO\hfill \\ +MKTO+Pt\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT\hfill \\ -b3\times tO+b4\times qO+b5\times MKTO]\hfill \end{array}}{Q4}\times (1+R2)$$

(32)

The results of PT and PO above are brought to I(T) and I(O), and the dual-channel benefit function is derived to find the optimal pricing for RCT and RCO.

$$\begin{array}{c}I(T)=[RCT\times (MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT\hfill \\ \hspace{1em}\hspace{1em}+b4\times qT+b5\times MKTT)+BCT+FCT+SCT+RBT+MKTT\hfill \\ \hspace{1em}\hspace{1em}+Pt\times MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT+b4\times qT\hfill \\ \hspace{1em}\hspace{1em}+b5\times MKTT]\times R1+ESGT\times CS+GST\hfill \end{array}$$

(33)

$$\begin{array}{c}I(T)/d(RCT)=R1\times (MPT\times Q+b1\times RCT-b2\times RCO-b3\times tT\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +b4\times qT+b5\times MKTT)+R1\times Pt\times b1\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =0\hfill \end{array}$$

(34)

$$RCT=\frac{-(MPT\times Q-b2\times RCO-b3\times tT+b4\times qT+b5\times MKTT+Pt\times b1)}{b1}$$

(35)

$$\begin{array}{c}I(O)=RCO\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO\hfill \\ \hspace{1em}\hspace{1em} +b4\times qO+b5\times MKTO]+BCO+FCO+SCO+RBO\hfill \\ \hspace{1em}\hspace{1em} +MKTO+Pt\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT\hfill \\ \hspace{1em}\hspace{1em} -b3\times tO+b4\times qO+b5\times MKTO]\times R2\hfill \\ \hspace{1em}\hspace{1em} +ESGO\times CS+GSO\hfill \end{array}$$

(36)

$$\begin{array}{c}I(O)/d(RCO)=R2\times [(1-MPT)\times Q+b1\times RCO-b2\times RCT-b3\times tO\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +b4\times qO+b5\times MKTO]+R2\times Pt\times b1\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} =0\hfill \end{array}$$

(37)

$$RCO=\frac{-(MPO\times Q-b2\times RCT-b3\times tT+b4\times qT+b5\times MKTO+Pt\times b1)}{b1}$$

(38)

3.3. Genetic Algorithm

3.3.1. Algorithm Process

The model in this paper belongs to a multivariable mixed integer nonlinear programming problem, which has certain complexity and is difficult to be solved by traditional methods. Therefore, a genetic algorithm is selected to solve the model.

The genetic algorithm mainly includes four steps: encoding, crossover, mutation, and optimization. The main process of the algorithm is shown in the Figure 2, and each step is explained in the following sections.

3.3.2. Encoding

The algorithm in this paper uses a four-digit floating-point number with a value range of 0 to 1 coding to express individual genes. This model has eight variables to solve, so each individual’s character is expressed by eight floating-point numbers. The more digits of floating point numbers, the higher the algorithm’s accuracy and the final solution will be. However, the corresponding amount of calculation will be enormous. Considering the parameter units in the model, there is no need for too-accurate solution results; four-digit floating point numbers are sufficient to solve a relatively accurate result in the problem in this paper. The individual gene encoding is shown in Figure 3.

3.3.3. Crossover

This step mimics the phenomenon of gene crossover in nature. In binary coding, a segment of two chromosomes is generally selected for random exchange. However, the algorithm in this paper is based on floating-point coding. In the crossover process, if the chromosome of the exact individual is going to crossover, another chromosome will be selected randomly from another random individual. After exchanging the value of these two chromosomes, the crossover process is completed. The example of crossover process is shown in Figure 4.

3.3.4. Mutation

This step mimics the phenomenon of gene mutation in nature. After each chromosome crossover step is completed, each individual’s chromosome will determine whether they are mutated. The probability of mutation is set at 20%. At the same time, the changing value of each mutation on chromosomes will decrease with the number of iterations; that is, the value change of each floating-point number will be smaller and smaller as the iteration processing. This method will be conducive to the convergence of problem solving.

3.3.5. Optimization

At the end of each iteration, each individual’s fitness is calculated, and the chromosome combination of the individuals with the highest fitness is obtained after comparison. In this paper, the last 20% of the individuals’ chromosomes with the lowest fitness in the population is replaced with the chromosome of the individuals with the highest fitness. In order to prevent the gene from massive changing with the increase of the number of iterations in the later stage, the elimination step is not carried out in the last 20% iteration.

4. Empirical Analysis

In order to verify the effectiveness of the improved genetic algorithm, this part takes the real project data as a reference, uses this model for optimization, and discusses the best strategy of dual-channel recovery.

4.1. Example Basic Information

According to the above supply chain relationship, setting 10 retailers, 10 recycling boxes recycling centers, 10 recycling boxes lessors, 10 remanufacturers, 10 scrap recycles, 10 third parity logistics, and 10 scrap markets, the number of traditional recyclers and network recyclers will change with the scale of the example.

The model assumes that population size N = 1000, chromosome node number (N_chrom_ = 8, iteration number (iter) = 1000, mutation probability (mut_ = 0.2, crossover probability (acr) = 0.2. The symbols and value ranges of other parameters are shown in the table below. A proportion of data are collected from Ployrocks chemistry company which is located in Guangdong Province, China. Generally, the probability of selected chromosome crossing and mutation are between 0% and 20%, and the selection of this probability is generally artificial. In order to reduce the number of iterations, the probability of chromosome crossing and mutation are both selected as 20%, and it is proved in subsequent experiments that this probability can generate robust and satisfying solution results in the setting iteration of N.

4.2. Multi-Objective Analysis

The model judges the decision effect from the three goals of economy, environment, and society, and compares it with the result of the single goal.

As can be seen from the

Table 3. The multi-objective and single-objective value of each example scale.

Number	Scale	Objective Value
1	5 × 5	Multi-objective	Obj	0.9615
		Single-objective	ObjE	0.9292
			ObjS	0.9498
			Obje	0.9684
2	10 × 10	Multi-objective	Obj	0.9830
		Single-objective	ObjE	0.9576
			ObjS	0.9559
			Obje	0.9720
3	20 × 20	Multi-objective	Obj	0.9376
		Single-objective	ObjE	0.9264
			ObjS	0.9239
			Obje	0.9464
4	40 × 40	Multi-objective	Obj	0.9341
		Single-objective	ObjE	0.9109
			ObjS	0.9289
			Obje	0.9268
5	60 × 60	Multi-objective	Obj	0.9333
		Single-objective	ObjE	0.9057
			ObjS	0.9191
			Obje	0.9315
6	80 × 80	Multi-objective	Obj	0.9328
		Single-objective	ObjE	0.9028
			ObjS	0.9289
			Obje	0.9274
7	100 × 100	Multi-objective	Obj	0.9325
		Single-objective	ObjE	0.9017
			ObjS	0.9282
			Obje	0.9265

and Figure 5, the overall Obj reaches the maximum at the case size of 10 × 10, then shows a downward trend, and then gradually becomes stable. The trend is similar for other objective values, which all reach their highest values in the 10 × 10 scale. It should be noted that ObjE is most affected by the increase of example size, and its size drops to around 0.9 in the 100 × 100 scale.

In general, the objective value considering multiple objectives is higher than that considering only a single objective. In addition, for the actual project in this paper, 10 × 10 scale is the best choice; that is, the number of traditional recyclers and network recyclers is 10. Therefore, considering multi-objective management decisions is helpful to build a more healthy and sustainable supply chain.

4.3. Strategy Analysis of Dual-Channel

The above part has determined that the overall objective value is optimal under the condition of example 10 × 10 and considering multiple objectives in management decision-making. Therefore, the system is stabilized in a 10×10 multi-objective environment to analyze the strategy of dual-channel recyclers and adjust the specific coefficient.

The optimal values of each decision factor are shown in

Table 4. The optimal values of each decision factor.

Decision Making Factor	RBT	RBO	MKTT	MKTO	qT	qO	tT	tO
Value	10.4830	10.4830	10.5087	10.5087	6.9841	6.9841	1.0096	1.0096
Range	[10–30]	[10–30]	[10–20]	[10–20]	[6–10]	[6–10]	[1–9]	[1–9]

.

Because the above models and values do not distinguish between network recyclers and traditional recyclers, in reality, the rebate sensitivity of online recyclers is higher than that of traditional recyclers, and the characteristics of online recyclers, such as higher marketing sensitivity, are not taken into account in the model. Therefore, this part puts forward certain assumptions based on reality:

The rebate sensitivity of online recyclers is higher;

Online recyclers have higher marketing sensitivity;

Traditional recyclers respond faster than online recyclers.

Based on the above assumptions, the value of the coefficient is adjusted. The b6 for traditional recyclers belong to 500–700, while online’s b6 belong to 600–800. The b5 for traditional recyclers belong to 200–400, while online’s b5 belong to 300–500. The b3 for traditional recyclers belong to 10,000,000–30,000,000, while online’s b3 belong to 15,000,000–45,000,000.

The optimal values of each decision factor are shown in

Table 5. The optimal values of each decision factor after adjusting.

Decision Making Factor	RBT	RBO	MKTT	MKTO	qT	qO	tT	tO
Value	13.1914	16.1639	13.8408	15.007	6.3135	6.3932	1.0009	1.0154
Range	[10–30]	[10–30]	[10–20]	[10–20]	[6–10]	[6–10]	[1–9]	[1–9]

.

As can be seen from the above table, the rebate intensity of dual-channel recyclers increases—especially the rebate input of network recyclers—by improving the sensitivity of rebates. The results of marketing were similar. The investment of recyclers on online platforms increased more, indicating that higher sensitivity would effectively enhance recyclers’ emphasis on advertising. The change of sensitivity of reaction time has no obvious influence on the strategy of reaction time, and the two-channel recyclers all adopt the shortest reaction time.

The special one is the quality of service, whose value will affect the breakage rate of the recycling boxes. By adjusting the sensitivity of the breakage rate to the quality of service and the breakage rate itself, the influence of the service quality and the breakage rate of the recycling boxes on the multi-objective results can be analyzed.

With the increase of service quality sensitivity, the damage rate is gradually increasing, and the complete recovery rate is gradually decreasing in

Table 6. The relationship between service quality sensitivity and objective value.

SRB	1−RBPT	1−RBPO	Obj	ObjE	ObjS	Obje
−0.36	0.9441	0.9382	0.9721	0.9577	0.9559	0.9658
−0.34	0.9192	0.9131	0.9542	0.9494	0.9609	0.9523
−0.32	0.881	0.879	0.9407	0.9320	0.9404	0.9277
−0.30	0.8508	0.8554	0.9267	0.9168	0.9201	0.9220
−0.28	0.8106	0.8153	0.9037	0.8931	0.9013	0.8947
			F = 307.417, p = 0.000	F = 120.976, p = 0.002	F = 27.905, p = 0.013	F = 102.271, p = 0.002
			Significant negative correlation (95%)	Significant negative correlation (95%)	Significant negative correlation (95%)	Significant negative correlation (95%)

and Figure 6. At the same time, the multi-objective value shows a declining trend, indicating that the retailer’s sensitivity to service quality will significantly affect the benefits of the logistics network.

In addition, the price and price sensitivity of the recyclers is also very important. Based on the above parameter settings, the price sensitivity of dual-channel recyclers is adjusted to study the change of multi-objective value.

In the environment where dual-channel recyclers compete with each other, as price competition becomes more and more fierce, consumers are more and more sensitive to price; in particular, the change of the sensitivity of the other party’s product price will lead to the change of the multi-objective and single-objective values. As shown in

Table 7. The relationship between price sensitivity and objective value.

b1	b2	Obj	ObjE	ObjS	Obje
6,500,000	5,500,000	0.9721	0.9577	0.9559	0.9658
6,500,000	6,500,000	0.9677	0.9553	0.9522	0.9640
6,500,000	7,500,000	0.9579	0.9459	0.9426	0.9607
6,500,000	8,500,000	0.9509	0.9322	0.9264	0.9498
6,500,000	9,500,000	0.9277	0.9245	0.9168	0.9389
		F = 30.601, p = 0.012	F = 70.838, p = 0.004	F = 76.471, p = 0.003	F = 27.581, p = 0.013
		Significant negative correlation (95%)	Significant negative correlation (95%)	Significant negative correlation (95%)	Significant negative correlation (95%)

and Figure 7, the overall goal and the value of the three levels of goals all show a downward trend with the improvement of the sensitivity of price competition. This is because changes in competitors’ prices affect recyclers’ demand for their products more significantly than their own. In addition, the decline in demand will lead to an increase in the proportion of fixed costs and a decline in profitability; Obj fell by 4.6321%, Obje by 3.46%, ObjS by 4.0876%, and Obje by 2.783%. The data show that multi-objective price sensitivity has the greatest impact, followed by social objectives, economic objectives, and finally environmental objectives. This result was roughly in line with expectations, except that the social goals varied more than the economic ones.

4.4. Influence of Subsidy and Green Credit Sensitivity

As policy makers and facilitators, governments need to subsidize recyclers, recycling centers, and others to improve the sustainability of the entire supply chain. Chang et al. [39] used the global Malmquist–Luenberger (GML) index method to explore the significant symbolic effects of subsidy and tax rebate policies on the R&D efficiency of green firms. The results show that under the significant level of 10%, subsidies have a great effect on enterprises’ scientific research investment, personnel training, and other aspects. Similarly, in the aspect of commercial banks, ESG grade will change the green credit intensity of banks to enterprises. This section will discuss the impact of changes in government subsidies and green credit on the multi-objective value of the system.

With the increase of government subsidies, the overall target value of the system will increase, but the increase range will decrease with the increase of subsidy amount. It shows in

Table 8. The relationship between subsidy and objective value.

Subsidy	Obj	ObjE	ObjS	Obje
40	0.9725	0.9579	0.9554	0.9652
50	0.9746	0.9946	0.9614	0.9684
60	0.9925	0.9978	0.9888	0.9866
70	0.9947	0.9991	0.9978	0.9902
80	0.9974	0.9991	0.9955	0.9964
90	0.9999	0.9999	0.9980	0.9999
	F = 42.064, p = 0.003	F = 17.294, p = 0.014	F = 16.745, p = 0.015	F = 94.313, p = 0.001
	Significant positive correlation (95%)	Significant positive correlation (95%)	Significant positive correlation (95%)	Significant positive correlation (95%)

and Figure 8 that government subsidies have a certain diminishing marginal effect, and subsidies within a reasonable range can increase income. The most obvious effect of government subsidies is the logistics network with economy as the single goal.

The relationship between the sensitivity of green credit and the objective value is not clear in

Table 9. The relationship between sensitivity of green credit and objective value.

CS	Obj	ObjE	ObjS	Obje
0.8	0.9722	0.9579	0.9551	0.9658
0.9	0.9758	0.9618	0.9596	0.9795
1.0	0.9811	0.9705	0.9883	0.9883
1.1	0.9819	0.9707	0.9699	0.9883
1.2	0.9682	0.9702	0.9574	0.9764
1.3	0.9632	0.9704	0.9689	0.9883
	F = 1.206, p = 0.334	F = 10.001, p = 0.034	F = 0.114, p = 0.752	F = 2.333, p = 0.201
	Not significant (95%)	Significant positive correlation (95%)	Not significant (95%)	Not significant (95%)

and Figure 9. With the increase of CS, the objective value experienced a brief increase, followed by a different performance. The value of multiple goals decreased after 1.1, the economic goals remained stable, and the social and environmental goals decreased and then rebounded.

4.5. Influence of Uncertainty Environment

An uncertain environment is a hypothesis that is closer to reality than a certain environment, so researchers often add uncertain factors into the model environment in the study of model operation. Tsao et al. [40] proposed an interactive method based on two-phase stochastic programming and fuzzy probabilistic multi-objective programming to overcome problems related to uncertainty. The validity of the model is verified by numerical analysis. Gumte et al. [41] used an unsupervised learning approach based on machine learning, utilizing fuzzy transcription of discontinuous uncertain parameter spaces. A data-driven robust optimization method was developed to solve the uncertainty of demand, import product price and biomass feed supply.

There are a lot of ways to simulate an uncertain environment, this model uses Gaussian white noise as a tool to create the uncertainty. In the recycling boxes supply chain, uncertainty often occurs in the demand and recovery ratio. Therefore, the part of the multi-objective model containing demand and recovery rate is multiplied by Gaussian white noise. By setting wgn (m,n,p), a matrix of white Gaussian noise with m rows and n columns can be generated, and p specifies the intensity of output noise with dBW as the unit.

The above objective value is the average value of 10 operations. With the increase of noise output intensity, both the multi-objective value and the single-objective value show a downward trend in

Table 10. The relationship between intensity of output noise and objective value.

p	Obj	ObjE	ObjS	Obje
0	0.9721	0.9577	0.9559	0.9658
1	0.8835	0.8394	0.8082	0.8541
2	0.9151	0.8187	0.8747	0.7978
3	0.7926	0.7583	0.7525	0.7317
4	0.8165	0.8394	0.8082	0.9999
5	0.9854	0.9286	0.9795	0.9101
	F = 0.045, p = 0.842	F = 0.091, p = 0.778	F = 0.000, p = 0.996	F = 0.080, p = 0.791
	Not significant (95%)	Not significant (95%)	Not significant (95%)	Not significant (95%)

and Figure 10. However, when the intensity is 4, the objective value becomes unstable and tends to rise. It is speculated that there are more extreme values in the uncertain environment, leading to a large change in the mean value. However, in general, the uncertainty of demand and recovery will lead to the instability of recovery system and have a negative impact on objective value. However, in an environment of too much volatility, it is impossible to determine how the overall benefits of the recovery system will change.

5. Conclusions

This paper builds a recycling model of reverse logistics of recycling boxes, divides recyclers into dual-channel recyclers, traditional recyclers, and online recyclers, and divides recycling boxes into three levels, which can be used for hierarchical recycling. It provides a multi-objective function for reverse logistics, which takes into account economic, environmental, and social factors such as income, carbon emission, plastic pollution, and production accidents. Furthermore, we construct the game between the dual-channel recyclers, with the recycling boxes recycling center as the leader and the dual-channel recyclers as the followers and deduce the optimal price. Moreover, we use the MATLAB software to solve the genetic algorithm and obtain the objective value under the various scale examples. In addition, the effects of single and multi-objective comparison, the game strategy of dual-channel recyclers, the impact of government subsidies, and green credit and the influence of uncertain environmental intensity changes are also analyzed. The following results were found.

When constructing this reverse logistics network model, the objective value considering multiple goals is higher than that considering only single goals, indicating that decision-makers need to take multiple goals as the standard to evaluate the effect of the overall model. It can effectively enhance the capacity of sustainable development.

Among multiple example scales, the 10 × 10 example scale is the most consistent with this model because it has the highest objective value, while the value of the increased example scale is lower and remains stable.

In the competition of dual-channel recyclers, the change of rebate sensitivity will cause a significant change in rebate intensity, indicating that if consumers attach importance to the discount, recyclers should carry out a significant intensity of rebate.

In the competition of dual-channel recyclers, changes in marketing will cause significant changes in rebate intensity, indicating that if consumers are sensitive to advertising or the advertising effect is outstanding, recyclers should carry out intensive promotion, especially recyclers on online platforms.

In the competition of dual-channel recyclers, traditional recyclers and network platform recyclers will choose the fastest response time. Sensitivity to reaction time is of little use because the cost of reaction time is difficult to estimate, leading the recyclers to choose this strategy.

The higher the retailer pays attention to the service quality, the higher the degree of uncooperative will be, and the damage rate of recycling boxes will increase, which has a significant impact on the overall interests of the logistics network.

Government subsidies can improve the sustainability of the overall logistics network, but they need to be kept within an appropriate range. The impact of the sensitivity of green credit on sustainability is not obvious, indicating that the intensity of commercial banks’ examination of ESG grade does not significantly affect the sustainability of logistics network.

With the increase in the intensity of white noise interference, objective value presents a downward trend, indicating that the increase in environmental uncertainty will lead to damage to the overall interests. Nevertheless, sustainability becomes difficult to predict after the intensity reaches a certain point because of the extreme values.

This paper proposes mechanisms by which retailers’ willingness to cooperate can be influenced by recyclers’ service quality and analyzes multiple strategies for dual-channel recyclers, factoring green credit, hierarchy, and environmental uncertainty into the model. It enriches the application of multi-objectives in reverse logistics network construction and genetic algorithms and provides a decision basis for enterprises to create a sustainable reverse logistics network.