The Impact of Carbon Allowance Allocation Rules on Remanufacturing Decisions in a Closed-Loop Supply Chain

Abstract

Remanufacturing has been widely adopted in the industrial sector due to carbon emission constraints and economic benefits. This paper discusses a closed-loop supply chain composed of an original equipment manufacturer (OEM), an authorized remanufacturer (AR), that is licensed by the OEM to carry out remanufacturing activities in the presence of strategic consumers under carbon cap-and-trade regulations. We establish a Stackelberg game model to identify the optimal manufacturing/remanufacturing decisions made by chain members, and compare the impacts of two different carbon allowance allocation rules on the optimal production decisions and profits, and on the environment. The results showed that optimal decisions in a closed-loop supply chain are affected by the carbon price, carbon allowance allocation, and consumer preferences for remanufactured products. In addition, for high-emission enterprises, the grandfathering rule performs better than the benchmarking rule, yielding higher profits and less environmental impact. The government should take into account the actual economic and production technological developments, implement the benchmarking rule for low-emission enterprises, and apply the grandfathering rule to high-emission enterprises.

1. Introduction

Climate change is a global problem facing human beings. The growth in carbon emissions has resulted in a surge in greenhouse gases, which pose a threat to life on earth. In order to address climate change, countries worldwide signed the Paris Agreement in 2016 and implemented a series of carbon reduction measures. Carbon emissions and economic growth are to be balanced through industrial, fiscal, and financial policies, as well as the use of policy measures offering incentives and disincentives, such as carbon emission quotas, carbon emission trading systems, carbon tax, and carbon reduction subsidies [1,2,3,4]. Subsequently, enterprises have optimized production strategies to reduce carbon emissions in order to comply with these laws and regulations. Increasingly, remanufacturing is being adopted in industries (such as automobile manufacturing, printer consumables, fast-moving consumer goods, and electronic product components), promoting low-carbon green circular economies and achieving economic and environmental benefits [5,6].

Grandfathering and benchmarking are two typical initial free carbon allowance allocation rules under the cap-and-trade mechanism. Under the grandfathering rule, the allocated carbon emission quotas are based on the firm’s historical carbon emissions record. The advantage of the grandfathering rule is that the calculation of a company’s emission quota is simple. However, the disadvantage is that it is unfair, and companies with high historical emissions receive more quotas. Companies temporarily suspend energy-saving and emission reduction measures before entering the carbon trading market to obtain more initial quotas. The benchmarking rule relies on the average carbon emissions in the industry [7]. However, the difficulty of this rule lies in setting benchmark values for all products in all industries, requiring a precise definition and classification of homogeneous products. Regulators must have detailed information on the production process efficiency of various products in various industries, making it less feasible. Currently, except for the electricity and heat industries, it is not widely used.

The government’s carbon cap-and-trade mechanism plays an important role in promoting the sustainable development of the remanufacturing industry and low-carbon economic development. Many manufacturers engaged in remanufacturing have improved their companies’ economic and environmental performances, such as Xerox, Canon, Caterpillar, Bosch and HP. Since the remanufacturing process is complex and requires high investment, original equipment manufacturers (OEMs) prefer to focus on producing new products rather than remanufacturing. In contrast, third-party remanufacturers, such as an authorized remanufacturer (AR), are entering the market for recycling and remanufacturing of used products to reap the benefits of remanufacturing. This results in a high level of market competition between the manufacturer and remanufacturer. Due to consumers’ low-carbon preference, remanufactured products are eating into new products’ market shares. In addition, remanufacturers not only have the advantages of low production costs and low carbon emissions, but are also not subject to the restrictions of carbon allowance, due to the government’s support policy. Generally, OEMs increase technological investment in emission reduction and optimize production plans with a view to improving their core competitiveness. A number of academic studies have focused on how the government develops effective policies and how supply chain members make their production decisions in response to carbon emission quotas allocated by the government.

Under the carbon cap-and-trade regulations, production decisions in a closed-loop supply chain (CLSC) are challenging due to product competition. Moreover, consumer preference for low-carbon products has also intensified the complexity of the operational decisions for supply chain members. In such a context, this paper investigates the following questions:

(1) What are the optimal production decisions under each carbon allowance rule in a CLSC?

(2) How does consumer preference for low-carbon products affect production decisions of chain members?

(3) How do carbon price, initial carbon quotas and low-carbon technological investment affect the production decisions of the supply chain members?

(4) Which carbon emission permit allocation rules would maximize total profits and minimize carbon emissions emitted by a closed-loop supply chain?

The remainder of the paper is organized as follows. Section 2 presents the related literature review and explains our contributions.The model assumptions and notations are described in Section 3. Section 4 examines both models and analyzes the optimal decisions. Section 5 provides numerical examples and analyzes the impact of two different carbon allowance rules, and consumers’ preference for remanufactured products on the production decisions of chain members. Section 6 provides conclusions and further research directions. All proofs are given in the Appendix A.

2. Literature Review

Our work focuses on the operational decisions for manufacturing–remanufacturing under the carbon cap-and-trade mechanisms in closed-loop supply chain systems. Therefore, the relevant literature can be divided into the following two aspects: remanufacturing in a closed-loop supply chain, and the operational strategies under the cap-and-trade mechanism.

2.1. Remanufacturing in CLSCs

This stream of research focuses on the comparison of different reserve channels (i.e., collection, disassembly, remanufacturing and remarketing) in a closed-loop supply chain system [8,9,10,11,12].

The literature has shown significant interest in researching the collection of used products for remanufacturing. Savaskan et al. analyzed the optimal collection channel of used products for manufacturers, and concluded that the most effective collection was that done by the retailer [13]. Yi investigated a dual-recycling channel in the construction machinery industry and suggested that the remanufacturer can obtain more used products and revenues under the dual-recycling channel [14]. Kushwaha et al. studied the optimal combination of channels for collecting used products from several scattered regions for a manufacturer [15]. Liu and Xiao investigated the reverse channel structure strategy (the collection of used products by a manufacturer or retailer), and found that manufacturer collection led to a lower retail price and higher collection rate [16]. Huang et al. explored whether doing its own remanufacturing or licensing a third party to undertake remanufacturing was the optimal reverse channel choice for the manufacturer [17]. Shekarian et al. reviewed the stream of research on cooperation and competition among game participants, and delved into the factors influencing CLSCs [9].

There have been numerous studies on technology licensing in remanufacturing activities. Zou et al. indicated that the OEM gained more returns when remanufacturing and remarketing were outsourced to third party companies [18]. Wang et al. analyzed the remanufacturing strategy in the reverse channel for an OEM that sold both new and remanufactured products through their retailer, as well as the impacts on both parties’ profits and on the environment [19]. Zhou, Xiong and Jin proposed that it is beneficial for an incumbent OEM to license a third party to undertake remanufacturing when dealing with a competing OEM [11]. By means of the Cournot duopoly model, Liu, Pang and Hong investigated and compared three common licensing strategies to elucidate the optimal patent licensing strategy options for an OEM [6]. Huang et al. considered the impacts of technology licensing, collection and remanufacturing cost disruption in a CLSC [20]. Zheng and Jin compared equilibrium quantities and prices, profits, consumer surplus, environmental performance, and social welfare under two relicensing schemes by developing game-theoretical CLSC models consisting of an OEM, a retailer, and a third-party [21].

2.2. Operations Management under the Carbon Cap-and-Trade Regulations

The related research on operations management under cap-and-trade mechanisms has mainly focused on pricing, inventory, and low carbon technology investments. With regard to pricing and production decisions, Ma explored an optimal pricing strategy for low-carbon products within the mandated carbon emission allowance and taking into account consumer preference for low-carbon products [22]. Yenipazarli et al. adopted a Stackelberg game model to study the effect of carbon taxes on the optimal production and pricing decisions of a manufacturer, and to ascertain the optimal carbon tax policy to maximize economic and environmental benefits [23]. Xu et al. studied optimal joint pricing and production decisions under the cap-and-trade regulations in a make-to-order supply chain [24]. Hussain et al. investigated the impact of the emission reduction subsidy policy on the pricing decisions and green technology implementation of firms in a monopolistic market [25]. Yang, Hao and Hu established different collecting modes in a carbon cap-and-trade policy and explored optimal quantity and price decisions. They found that carbon emissions could be reduced effectively by the application of the carbon cap-and-trade policy [26]. Using a three-level supply chain, involving original equipment manufacturers (OEMs), independent remanufacturers (IRs), and retailers, Mao et al. built a game model with, and without, carbon emission quota policies, and examined the consequences of the carbon emission quota policy on product quality, sales, and price [27].

Another relevant stream of literature focuses on investments in low-carbon technology for carbon emission reduction. Toptal et al. investigated the optimal emission reduction investment and inventory replenishment under the Carbon constraint policies of carbon allowance, carbon tax, and cap-and-trade regulations [28]. Li et al. explored the impact of supply chain coordination strategy (revenue and cost sharing contracts) on carbon emission reduction efforts and firms’ profitabilities [29]. Yang et al. studied the reverse channel selection and carbon emission reduction decisions made by OEMs under carbon cap-and-trade regulations [30]. Yang et al. formulated mathematical models to quantify the optimal green technology investment and product pricing, and compared the effects of the two allocation rules on these operational decisions and total emissions [2]. Chen et al. discussed the impact of cap-and-trade mechanisms, including grandfathering and benchmarking mechanisms, on renewable energy investments and marketing efforts in the electricity market [3].

Although production decisions and low-carbon technology are subjects of recent research, much research focuses on how the carbon cap-and-trade mechanisms (such as grandfathering and benchmarking) affect optimal production and carbon emission reduction decisions. Ji et al. argued that over-allocated carbon allowance might damage a manufacturer’s profit. They also found that using low-carbon technology might increase total carbon emissions [31]. Xia et al. examined the influence of carbon trading on the sale volume of low-carbon products. They noted that carbon trading could increase the sale volume when a manufacturer only produced low-carbon products [32]. Xia, Li, and Wang investigated how emission reduction decisions made by manufacturers influence authorized remanufacturing under carbon trading [33]. Considering the impact of online channel structure on the manufacturer’s production and low-carbon investment strategy, Zhang et al. explored the economic and environmental performances of two rules: the traditional cap allocation rule and the linear cap allocation rule [34].

Researchers in the above studies examined the impact of carbon cap-and-trade regulations and investments in low-carbon technology on remanufacturing decisions, while ignoring the impacts of consumer low-carbon preferences. This study extends and integrates current research on remanufacturing in a CLSC under two carbon allowance allocation rules. However, in order to deeply understand the impact of carbon cap-and-trade regulations on remanufacturing decisions, multiple independent factors are investigated in this study, such as the following: the carbon permit allowance, investments in low-carbon technology, technology licensing fees, and consumer preferences for remanufactured products. The government and enterprises in a CLSC can gain more insight into production and emission reduction decisions by exploring these factors.

3. Problem Description and Assumptions

3.1. Model Assumptions and Notations

This paper considers a CLSC consisting of an original equipment manufacturer (OEM) and an authorized remanufacturer (AR), producing competitive new and remanufactured products, as illustrated in Figure 1. The OEM is regulated by cap-and-trade regulations, and, therefore, seeks to invest in emission reduction technology to maximize its profits. The AR is exempt from carbon quotas, due to the environmental benefits it offers. The OEM acts as the channel leader and authorizes the independent remanufacturer to undertake remanufacturing activities while charging patent licensing fees. Following the practice of many countries in allocating carbon permits, the CLSC is investigated for its economic and environmental performances under two typical allowance allocation rules: (i) the grandfathering rule; (ii) the benchmarking rule. Taking into consideration carbon emission constraints, a game model is developed between the OEM and AR to identify their optimal production decisions. Based on this model, we examine the impact of consumer preferences for remanufactured products and cap-and-trade regulations on equilibrium decisions regarding remanufacturing, both economically and environmentally.

We construct a Stackelberg game model consisting of an OEM, an AR and strategic consumers over a single period. At the beginning of this period, the OEM has a carbon emission quota. This carbon emission quota is subject to constraints imposed by either grandfathering or benchmarking and denoted by E and $e_0$, respectively. The OEM sells new products at price $p_n$. Additionally, the OEM authorizes the access of the AR to remanufacturing technology by charging a licensing fee f per unit. The AR collects used products, produces remanufactured products, and sells them at price $p_r$.

The sequence of events in this game is as follows. First, the OEM, as the leader in this game, decides the prices of new products $p_n$ and the level of investment in carbon emission reduction technology $\theta$. After that, the follower, the AR, makes decisions regarding remanufactured products in response to the OEM’s decisions. Finally, each consumer decides which type of products to purchase to maximize utilities. The list of notations used in this work is provided in

Table 1. Notations and definitions.

Symbol	Definition
Parameters
V	Consumer valuation for a new product.
$\alpha$	Consumer preference to remanufactured products compared to new ones.
$c_i,i=\{n,r\}$	Unit cost of new products and remanufactured products, respectively. (i.e., $c_n>c_r>0$)
$e_n$	Initial carbon emission produced per unit new product.
E	Total Free carbon cap allocated to the manufacturer under the grandfathering rule.
$e_0$	The unit carbon emission allowance allocated to each new product under the benchmarking rule.
$E^j,j=\{G,B\}$	The total carbon emissions from a CLSC.
$\beta$	Carbon reduction cost coefficient
$\omega$	The emission reduction coefficient per unit new product brought by carbon emission reduction investment.
$p_e$	Carbon price. We suppose the carbon sale price is equal to the purchase price.
${\Pi }_m^j,{\Pi }_r^j,j=\{G,B\}$	Profits of the OEM and AR, respectively.
Decision variables
$p_i,i=\{n,r\}$	Sale price per unit new and remanufactured products, respectively.
$q_n^j,q_r^j,j=\{G,B\}$	Quantity demanded of new products and remanufactured products, respectively.
$\theta$	The level of carbon emission reduction technology investment determined by the manufacturer.
f	Licensing fee per unit remanufactured product

.

In the face of carbon emission constraints, the OEM seeks to invest in emission reduction technology in order to avoid penalties related to excess emissions or to profit from the sale of unused portions under grandfathering or benchmarking regulations. Since remanufactured products generate much less carbon than new products, and the government often adopts incentive policies for remanufacturers, it is assumed that the carbon emissions generated by remanufacturers are not restricted by the carbon cap-and-trade regulations [35].

Under the grandfathering rule, the manufacturer’s carbon free emission allowance allocation is E. Under the benchmarking rule, the carbon emission allowance allocation is based on the benchmark emission of the industry $e_0$ times the quantity of new products. If the realized carbon emissions generated by production exceeds the free emission allowance, the OEM must buy the lacking carbon emission permits in a carbon trading market. If the realized carbon emissions generated by production falls below the free emission allowance, the OEM can obtain extra profit by selling any surplus quota on the carbon trading market. The initial carbon emission per new product and per remanufactured product without emission reduction investment are denoted as $e_n$ and $e_r$, respectively. The carbon trading price is denoted by $p_e$. We assume that the carbon purchasing price is equal to the selling price. The OEM invests in low-carbon technology to increase demand. Similar to the cases in much related research [36,37,38], the carbon emission reduction investment in sustainable technology is $\frac{1}{2}\beta {\theta }^2$, which can be measured as the level of investment in emission reduction technology $\theta$. The value $\beta$ is the cost coefficient of emission reduction, which is determined by industrial characteristics and investments in technological research and development. Without loss of generality, we assume that $\beta$ is greater than $\frac{{\left(e_n\omega p_e\right)}^2(2-\alpha )}{4(1-\alpha )}$ in combination with the industrial reality. Due to the implementation of emission reduction technology, the carbon emission per unit new product decreases to $(1-\omega \theta )e_n$. As the cost of reduction in carbon emissions is positively correlated with the level of investment in emission reduction technology, a greater level of emission reduction is not for the better of the OEM. The OEM makes decisions on the optimal pricing and emission reduction investment to maximize total profit.

3.2. Consumer Behavior

We assume that customers have varying valuations (denoted by V) of the new product, which are uniformly distributed in the interval of $[0,1]$. Following the literature [17,32,39], we further assume customers have different (typically lower) valuations for remanufactured products, which is $\alpha V$, where $\alpha$ is a discount or markup factor when customers evaluate remanufactured products. The total market size is normalized to 1. All consumers enter the market at the beginning of the period and each consumer buys, at most, one unit of the product in this period. A consumer’s utility obtained from purchasing a new or remanufactured product can be calculated as $U_n=V-p_n$ and $U_r=\alpha V-p_r$. Customers make purchasing decisions to maximize their utilities. Specifically, if the $U_n$ is non-negative and greater than the $U_r$, the consumer chooses to purchase a new product. If the $U_r$ is non-negative and greater than the $U_n$, the consumer chooses to buy a remanufactured product. Otherwise, the consumer leaves the market. Customers’ purchasing decisions are summarized in Proposition 1.

Proposition 1.

Given the price of the new and remanufactured products (i.e., $p_n$ and $p_r$), for any consumer, it is optimal for the consumer to base his or her purchasing decision on his or her base valuation V, as follows:

(i) if $1>V>max\left\{\frac{p_n-p_r}{1-\alpha },p_n\right\}$, he will buy a new product;

(ii) if $\frac{p_n-p_r}{1-\alpha }>V>min\left\{\frac{p_r}{\alpha },\frac{p_n-p_r}{1-\alpha }\right\}$, he or she purchases a remanufactured product.

As can be seen from Proposition 1, the value of $\alpha$ determines whether there is a demand for the remanufacturing product and whether the AR enters the remanufacturing market. Corollary 1 provides more detail.

Corollary 1.

A consumer’s willingness to pay for a remanufactured product results in three different remanufacturing scenarios, as follow:

(i) Low willingness of consumers to pay for a remanufactured product (i.e., $0<\alpha <\frac{p_r}{p_n}$) results in a no-remanufacturing scenario, in which consumers with a $V\in \left[p_n,1\right]$ purchase new products; and consumers with $V\in \left(0,p_n\right)$ do not buy any product.

(ii) Relatively high willingness of consumers to pay for a remanufactured product (i.e., $\frac{p_r}{p_n}\le \alpha \le 1-(p_n-p_r)$ results in a partial-remanufacturing scenario, in which consumers with a $V\in \left[\frac{p_n-p_r}{1-\alpha },1\right]$ will buy new products, and those with a $V\in \left[\left.\frac{p_r}{\alpha },\frac{p_n-p_r}{1-\alpha }\right)\right.$ buy remanufactured products. Consumers with a $V\in \left(0,\frac{p_r}{\alpha }\right)$ do not buy any product.

(iii) High willingness of consumers to pay for a remanufactured product (i.e., $\alpha >1-(p_n-p_r)$) results in a full-remanufacturing scenario, in which consumers with a $V\in \left[\frac{p_r}{\alpha },1\right]$ buy remanufactured products and no one wants to buy new products.

In a no-remanufacturing scenario, consumer willingness to pay for a remanufactured product ($\alpha$) is low. Therefore, the remanufacturer does not enter the market to participate in remanufacturing activities due to the low demand. In a partial-remanufacturing scenario, consumer willingness to pay for a remanufactured product ($\alpha$) is relatively higher. The demand for the remanufactured products in the market attracts the AR to engage in remanufacturing activities. In a full-remanufacturing scenario, environmentally conscious consumers exhibit a higher preference for remanufactured products over new ones. As a result, the OEM withdraws from the market and ceases to produce new products. Corollary 1 also summarizes the purchase behavior of consumers in the three scenarios.

In summary, the demand for new and remanufactured products can be solved as $q_n={\int }_{V\in {\Theta }_n}^{}f\left(V\right)dV$ and $q_r={\int }_{V\in {\Theta }_r}^{}f\left(V\right)dV$, in which ${\Theta }_n$ and ${\Theta }_r$ denote the range of valuations for the two groups of consumers, respectively. A similar technique was adopted in previous studies [18,40,41]. To focus on the competition between new and remanufactured products, we only consider the partial-remanufacturing scenario where new and remanufactured products co-exist in the market. Corollary 2 presents the product demand under this scenario.

Corollary 2.

Under the partial-remanufacturing scenario, the demands for new and remanufactured products are $q_n=1-\frac{p_n-p_r}{1-\alpha }$ and $q_r=\frac{p_n-p_r}{1-\alpha }-\frac{p_r}{\alpha }$, respectively.

4. Model Analysis

This section investigates the optimal pricing and the level of investment in carbon emission reduction technology under the two different allocation rules of grandfathering and benchmarking. In the following model, superscripts G, B denote the two different rules (grandfathering and benchmarking, respectively). The OEM decides the price of new products $p_n$ and the level of investment in carbon emission reduction technology $\theta$. Based on the expectations of the leader’s decisions, the AR decides the price of remanufactured products $p_r$.

4.1. Grandfathering Rule

In this subsection, we calculate the solutions to the mathematical model for maximizing the total profits over the sale horizon under the grandfathering rule. Thus, the profit functions of the OEM and AR can be, respectively, expressed as follow:

$$\begin{array}{cc}\hfill \underset{p_n,f,\theta }{Max}{\Pi }_m^G=& (p_n-c_n)q_n+f{q}_r-\left[e_n(1-\omega \theta )q_n-E\right]p_e-\frac{1}{2}\beta {\theta }^2\hfill \\ \hfill s.t.& q_n\ge 0,q_r\ge 0,\theta \ge 0,p_n>p_r,p_n>c_n\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill \underset{p_r}{Max}{\Pi }_r^G=& (p_r-c_r-f)q_r\hfill \\ \hfill s.t.& q_r\ge 0,p_r>c_r\hfill \end{array}$$

(2)

The total carbon emissions released by new and remanufactured products is as follows:

$$\begin{array}{cc}\hfill E^G=& e_n(1-\omega \theta )q_n+e_r{q}_r\hfill \end{array}$$

(3)

In the Equation (1), $e_n(1-\omega \theta )$ represents the carbon emission released per unit of a new product after the OEM invests in the carbon emission reduction technology, and $-\left[e_n(1-\omega \theta )q_n-E\right]p_e$ represents the carbon trading of the OEM. When $e_n(1-\omega \theta )q_n$ is larger than E, $-\left[e_n(1-\omega \theta )q_n-E\right]p_e$ represents the expenditure of the OEM on purchasing the carbon emission allowance allocation required for production in the carbon trading market; conversely, when $e_n(1-\omega \theta )q_n$ is less than E, $-\left[e_n(1-\omega \theta )q_n-E\right]p_e$ represents the income of the OEM from selling the remaining carbon emission allocation in the carbon trading market.

The OEM and AR make decisions on the pricing of new and remanufactured products to maximize total profits. According to the decisions of chain members, the total carbon emissions of the closed-loop supply chain are calculated.

4.2. Benchmarking Rule

In this subsection, the OEM must bear the cost of excess carbon emissions, which is the excess of the free allowance under the benchmarking rule. The objective function of the OEM and AR are, respectively, as follow:

$$\begin{array}{cc}\hfill \underset{p_n,\lambda }{Max}{\Pi }_m^B=& (p_n-c_n)q_n+f{q}_r-\left[e_n(1-\omega \theta )-e_0\right]q_n{p}_e-\frac{1}{2}\beta {\theta }^2\hfill \\ \hfill s.t.& q_n\ge 0,q_r\ge 0,\theta \ge 0,p_n>p_r,p_n>c_n\hfill \end{array}$$

(4)

$$\begin{array}{cc}\hfill \underset{p_r}{Max}{\Pi }_r^B=& (p_r-c_r-f)q_r\hfill \\ \hfill s.t.& q_r\ge 0,p_r>c_r\hfill \end{array}$$

(5)

Under the benchmarking rule, the total carbon emission released by the closed-loop supply chain is as follows:

$$\begin{array}{cc}\hfill E^B=& \left[e_n(1-\omega \theta )-e_0\right]q_n+e_r{q}_r\hfill \end{array}$$

(6)

4.3. Model Solving and Analysis

Based on the nonlinear constraints, the optimal price for products and the level of investment in low-carbon technology under the two different allowance allocation rules can be solved by Karush–Kuhn–Tucker (KKT) necessary conditions and backward induction. The superscript ‘*’ denotes the optimal solution.

Proposition 2.

Under the grandfathering rule, the optimal equilibrium strategy can be derived as follows:

$$\begin{array}{cc}\hfill p_n^{G*}=& -\frac{M}{8\beta -8\alpha \beta -4e_n^2{\omega }^2{p}_e^2+2\alpha e_n^2{\omega }^2{p}_e^2}\hfill \\ \hfill & \hfill \\ \hfill p_r^{G*}=& -\frac{N}{8\beta -8\alpha \beta -4e_n^2{\omega }^2{p}_e^2+2\alpha e_n^2{\omega }^2{p}_e^2}\hfill \\ \hfill & \hfill \\ \hfill {\theta }^{G*}=& \frac{e_n\omega p_e(c_r-2c_n-2\alpha +\alpha c_n-2e_n{p}_e+\alpha e_n{p}_e+2)}{4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2}\hfill \end{array}$$

$$\begin{array}{cc}\hfill f^{G*}=& \frac{\alpha -c_r}{2}\hfill \\ \hfill & \hfill \\ \hfill {\Pi }_m^{G*}=& -\frac{A-4E{\alpha }^2{e}_n^2{\omega }^2{p}_e^3+16E\beta {\alpha }^2{p}_e+8E\alpha e_n^2{\omega }^2{p}_e^3-16E\beta \alpha p_e}{4\alpha \left(4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2\right)}\hfill \\ \hfill {\Pi }_r^{G*}=& -\frac{D^2(\alpha -1)}{4\alpha \left(4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2\right)}\hfill \end{array}$$

$$\begin{array}{cc}\hfill Here,M& =4\alpha \beta -4\beta -4\beta c_n+4\alpha \beta c_n-4\beta e_n{p}_e+4e_n^2{h}^2{p}_e^2-3\alpha e_n^2{\omega }^2{p}_e^2+c_r^2{e}_n^2{\omega }^2{p}_e^2\hfill \\ \hfill & +4\alpha \beta e_n{p}_e,\hfill \\ \hfill N& =4{\alpha }^2\beta -2\beta c_r-4\alpha \beta -2\alpha \beta c_n+2\alpha \beta c_r+2{\alpha }^2\beta c_n+3\alpha e_n^2{\omega }^2{p}_e^2+c_r^2{e}_n^2{\omega }^2{p}_e^2\hfill \\ \hfill & +2{\alpha }^2\beta e_n{p}_e-2{\alpha }^2{e}_n^2{\omega }^2{p}_e^2-2\alpha \beta e_n{p}_e,\hfill \\ \hfill A& =2\beta {\alpha }^2{c}_n^2+4\beta {\alpha }^2{c}_n{e}_n{p}_e-8\beta {\alpha }^2{c}_n+{\alpha }^2{e}_n^2{\omega }^2{p}_e^2+2\beta {\alpha }^2{e}_n^2{p}_e^2-8\beta {\alpha }^2{e}_n{p}_e\hfill \\ \hfill & +4\beta {\alpha }^2-4\beta \alpha c_n^2+4\beta \alpha c_n{c}_r-8\beta \alpha c_n{e}_n{p}_e+8\beta \alpha c_n-2\alpha c_r{e}_n^2{\omega }^2{p}_e^2+4\beta \alpha c_r{e}_n{p}_e\hfill \\ \hfill & -4\beta \alpha e_n^2{p}_e^2+8\beta \alpha e_n{p}_e-4\beta \alpha +c_r^2{e}_n^2{\omega }^2{p}_e^2-2\beta c_r^2,\hfill \\ \hfill D& =2\alpha \beta c_n-2\beta c_r-\alpha e_n^2{\omega }^2{p}_e^2+c_r{e}_n^2{\omega }^2{p}_e^2+2\alpha \beta e_n{p}_e.\hfill \end{array}$$

Proposition 3.

Under the benchmarking rule, the optimal decision for production in a CLSC can be derived as follows:

$$\begin{array}{cc}\hfill p_n^{B*}=& -\frac{M+4\beta e_0{p}_e-4\alpha \beta e_0{p}_e}{8\beta -8\alpha \beta -4e_n^2{\omega }^2{p}_e^2+2\alpha e_n^2{\omega }^2{p}_e^2}\hfill \\ \hfill p_r^{B*}=& -\frac{N-2{\alpha }^2\beta e_0{p}_e+2\alpha \beta e_0{p}_e}{8\beta -8\alpha \beta -4e_n^2{\omega }^{2}p{e}^2+2\alpha e_n^2{\omega }^2{p}_e^2}\hfill \\ \hfill {\theta }^{B*}=& \frac{e_n\omega p_e\left(c_r-2c_n-2\alpha +\alpha c_n+2e_0{p}_e-2e_n{p}_e-\alpha e_0{p}_e+\alpha e_n{p}_e+2\right)}{4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2}\hfill \\ \hfill f^{B*}=& \frac{\alpha -c_r}{2}\hfill \\ \hfill & \hfill \\ \hfill {\Pi }_m^{B*}=& -\frac{A-4\beta {\alpha }^2{c}_n{e}_0{p}_e+2\beta {\alpha }^2{e}_0^2{p}_e^2-4\beta {\alpha }^2{e}_0{e}_n{p}_e^2+8\beta {\alpha }^2{e}_0{p}_e+8\beta \alpha c_n{e}_0{p}_e-4\beta \alpha c_r{e}_0{p}_e-4\beta \alpha e_0^2{p}_e^2+8\beta \alpha e_0{e}_n{p}_e^2-8\beta \alpha e_0{p}_e}{4\alpha \left(4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2\right)}\hfill \\ \hfill {\Pi }_r^{B*}=& -\frac{(\alpha -1){\left(D-2\alpha \beta e_0{p}_e\right)}^2}{4\alpha {\left(4\beta -4\alpha \beta -2e_n^2{\omega }^2{p}_e^2+\alpha e_n^2{\omega }^2{p}_e^2\right)}^2}\hfill \end{array}$$

Corollary 3.

The effects of the carbon emission reduction level on optimal solutions are as follow:

(i) $\frac{\partial p_n^{i*}}{\partial \theta }$ <0, $\frac{\partial p_r^{i*}}{\partial \theta }$ <0; (ii) $\frac{\partial q_n^{i*}}{\partial \theta }$ >0, $\frac{\partial q_r^{i*}}{\partial \theta }$ <0, $\frac{\partial (q_n^{i*}+q_r^{i*})}{\partial \theta }$ >0; (iii) $\frac{\partial E^{i*}}{\partial \theta }$ >0;

(iv)$\frac{\partial {\Pi }_r^{i*}}{\partial \theta }$<0; when ${\theta }^i<{\theta }^{i*}$, $\frac{\partial {\Pi }_m^{i*}}{\partial \theta }$ >0; where $i=\left\{G,B\right\}$

Corollary 3 shows that, due to the implementation of the carbon cap-and-trade regulations, the OME increases investments in carbon emission reduction to reduce carbon emissions released by new products. Furthermore, the lower-carbon advantage of remanufactured products declines. Therefore, the demand for new products increases, whereas the demand for remanufactured products decreases. The reduction in carbon emissions per unit new product motivates the OEM and AR to further reduce the price of both products, thus increasing the total demand for new and remanufactured products. Consequently, an increase in the level of investment in the carbon emission reduction technologies leads to an increase in the total demands for new and remanufactured products, resulting in an increase of the total carbon emissions in a CLSC.

However, further investment in emission reduction technology by the OEM is not for the better. When the emission reduction level of the new product is greater than a certain threshold, the OEM’s profit decreases as the emission reduction level increases. Hence, the OEM should make a reasonable decision on its carbon emission reduction level. The OEM’s investment in emission reduction technology benefits total social production and the environment, while the AR’s profit is damaged. Therefore, the government should give full consideration to market competition factors and design carbon trading system elements in combination so as to couple the manufacture–remanufacturing markets in order to form policy synergy to produce positive effects which not only restrict the behavior of the original manufacturer, but also encourage remanufacturing activities.

Corollary 4.

The optimal level of the OEM’s investment in carbon emission reduction technology under the benchmarking rule is higher than that under the grandfathering rule, that is ${\theta }^{B*}>{\theta }^{G*}$. Meanwhile, the gap between the OEM’s optimal level of investment in carbon emission reduction technology under carbon allocation rules becomes larger with increase in the carbon trading price $\left(\frac{\partial ({\theta }^{B*}-{\theta }^{G*})}{\partial p_e}>0\right)$.

Corollary 4 indicates that the benchmarking rule is more effective than the grandfathering rule in motivating the OEM to invest in carbon emission reduction technology. Under the grandfathering rule, the total amount of free carbon allowance allocated to the OEM is based on its historical emission record. There is no strong incentive for the OEM to implement low-carbon emission reduction technologies. In contrast, the carbon quota of each unit product is restricted under the benckmarking rule. Since all manufacturers are allocated the same benchmark, the OEM is guided to increase investment in carbon emission reduction technology. Consequently, the OEM decides on a higher carbon emission reduction level under the benchmarking rule.

The level of investment in carbon emission reduction decided by the OEM is affected by the government’s different carbon quota allocation rules. According to Corollary 4, the government can allocate the carbon quota and raise carbon trading prices based on the benchmarking rule to motivate OEMs to invest in emission reduction. The government can adopt differentiated carbon allocation rules for different manufacturers according to their emission reduction costs and industry characteristics to improve the effectiveness of the carbon allowance allocation.

Corollary 5.

Under the two different carbon allowance allocation rules, the optimal production decisions of new and remanufactured products satisfy relations as follow:

(i) $p_n^{G*}>p_n^{B*}$, $p_r^{G*}>p_r^{B*}$, $f^{G*}=f^{B*}$;

(ii) $q_n^{G*}<q_n^{B*}$, $q_r^{G*}>q_r^{B*}$;

Corollary 5 shows that the optimal pricing of new and remanufactured products under the grandfathering rule is higher than that under the benchmarking rule. Combined with Corollary 4, it is observed that, under the grandfathering rule, the OEM has less reduction in carbon emissions than that under the benchmarking rule and tends to increase the pricing of both products to reduce the output of products so that it can ensure total carbon emissions meet the government’s carbon emission permit requirements. Based on these reasons, the optimal quantities of new products under the grandfathering rule are smaller than under the benchmarking rule. Under the benchmarking rule, the carbon emission reduction cost of the OEM is relatively lower, so it can reduce the price of new products, which promotes increasing quantities of new products and reversely induces decreasing quantities of remanufactured products.

Under pressure from the cost of carbon trading, the quantities fall as the price of new products rises. The coupling effects pose a challenge to the original manufacturer’s operations. As the leader in the game, the OEM can transfer the remanufacturing and carbon trading income by choosing an appropriate remanufacturing mode. Furthermore, the government should make carbon quota allocation rules based on optimal joint decisions for pricing or quantities of new and remanufactured products to achieve the lowest cost in carbon emission reduction per unit product.

Corollary 6.

The optimal profits of the OEM and AR satisfy the following relations under two different carbon allowance allocation rules:

(i) If $E>\frac{\beta e_0\left(2\mathrm{cr}-4\mathrm{cn}-4\alpha +2\alpha \mathrm{cn}+2e_{0}pe-4enpe-\alpha e_{0}pe+2\alpha enpe+4\right)}{8\beta -8\alpha \beta -4{\mathrm{en}}^2{h}^2{\mathrm{pe}}^2+2\alpha {\mathrm{en}}^2{h}^2{\mathrm{pe}}^2}holds$, then ${\Pi }_m^{G*}>{\Pi }_m^{B*}$;

(ii) If $e_0<\frac{2\alpha \beta \mathrm{cn}-2\beta \mathrm{cr}-\alpha {\mathrm{en}}^2{h}^2\mathrm{pe}{\mathrm{e}}^2+\mathrm{cr}en{}^2{h}^2{\mathrm{pe}}^2+2\alpha \beta enpe}{\alpha \beta p_e}holds$, ${\Pi }_r^{G*}>{\Pi }_r^{B*}$;

Colloray 6 indicates that carbon quotas play a significant role in determining profitability for the manufacturers of the two types of products. When the total carbon quota and the carbon benchmark quota per unit product are greater than a certain threshold, the OEM’s profit increases under both carbon cap-and-trade regulations. Since a high cap on carbon emissions provides an opportunity for the OEM to sell more spare carbon allowances in the carbon trading market, the OEM has a larger choice regarding profit. As a result, When the total carbon quota and the carbon benchmark quota per unit new product satisfy, respectively, certain conditions, the optimal profits of the OEM and AR under the grandfathering rule are greater than under the benchmarking rule. For manufacturers with high carbon emissions, the government should first make relatively large carbon emission quotas. Loose carbon policies not only increase manufacturers’ profits, but also reduce their resistance to emission reduction and their impact on market supply, facilitating the promotion and implementation of emission reduction policies. Then, by gradually reducing the carbon quota, manufacturers are inspired to share environmental responsibility and gradually realize low-carbon transition.

Corollary 7.

The impact of different carbon emission allowance allocation rules on the environment is as follows: $E^{B*}>E^{G*}.$

Based on Corollary 7, the total carbon emissions under the grandfathering rule is lower than that under the benchmarking rule. This suggests that it is more friendly to the environment by limiting the overall carbon emissions released by the OEM. Since the environmental impact is mainly related to the quantities of the two types of products, the carbon price and the carbon quota, the implementation of the carbon cap-and-trade policies by the government does not necessarily reduce the impacts of the two products on the environment. By designing carbon trading policies, the government can reduce environmental impacts, as well as influence OEM investment in emission reduction and AR production decisions.

5. Numerical Study

In this section, numerical examples are provided to examine the impacts of consumer preference for remanufactured products ($\alpha$) and the carbon price ($p_e$) on the optimal operational decisions of the OEM and AR under the two different carbon allowance rules. To verify the above conclusions, and to further analyze the impact of carbon trading regulations on the closed-loop supply chain, the examples are based on data released by the China Association of Automobile Manufacturers on auto parts remanufacturing, and reference is made to relevant literature. We set the values of the related parameters in the following subsections.

5.1. The Impact of Consumer Preference for the Remanufactured Product on Production Decisions

Through numerical analysis, this section explores the variational trend of product pricing, the level of investment in emission reduction, demand and profit of the two types of products, with consumer preference for the remanufactured product ($\alpha$), as well as the impact of consumer preference for the remanufactured product ($\alpha$) on total carbon emissions. Specifically, the parameters are set to the following values: $c_n=0.3, c_r=0.1,$$\beta =0.5, \omega =3, e_n=0.5, e_r=0.2, E=2, e_0=0.2, p_e=0.2$.

Figure 2 reveals that the optimal prices of new and remanufactured products under the grandfathering rules are higher than under the benchmarking rule, which is consistent with Corollary 5. Meanwhile, they both increase as consumer preference for the remanufactured product ($\alpha$) increases. Combined with Figure 2, Figure 3 indicates that the OEM would raise the price appropriately to mitigate the loss caused by a decrease in sales, while the remanufacturer would raise the price to increase the profit due to the consumers favoring remanufactured products.

It can be observed in Figure 4, that the license fee is positively correlated with consumer preference for remanufactured products, which is equal under the two different carbon allocation rules. Furthermore, the relationship between the optimal levels of carbon emission reduction under the two rules in Corollary 4 is confirmed in Figure 4. The higher the consumer preference for remanufactured products, the lower the level of investment in carbon reduction technology. The increased demand for remanufactured products, which is described in Figure 3, and their low carbon and low cost advantages force the OEM to invest less in emission reduction technology.

Figure 5 suggests that the closed-loop supply chain operating under the benchmarking rule more serious impacts the environment than when operating under the grandfathering rule, which is consistent with Corollary 7. With the increase of $\alpha$, the demand for new products decreases sharply and the demand for remanufactured products increases significantly (as described in Figure 3), so there is little impact on the environment under the grandfathering rule.

As described in Figure 6 and Figure 7, the profits of the OEM and AR under the grandfathering and benchmarking rules are both positively related to consumer preference for remanufacutred products ($\alpha$), and increase with $\alpha$. When consumer preference for remanufacutred products is relatively large, the OEM raises the price to relieve the lower demand for new products, so its profit still increases, while the profit of the remanufacturer increases significantly, because of the dramatically increased demand and freedom from carbon emissions, and the fact that the remanufacturer is not subject to a carbon quota.

5.2. The Impact of the Carbon Price on Production Decisions

In this subsection, we provide a numerical example to investigate the impact of the carbon price ($p_e$) on production decisions, based on the following parameter values: $c_n=0.3$, $c_r=0.1$, $\alpha =0.6, \beta =0.4, \omega =1.5, e_n=0.4, e_r=0.2, E=2, e_0=0.2$. Subsequently, the trend in optimal production decisions with different carbon prices $p_e$ is described in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 below.

As shown in Figure 8, the prices of new and remanufactured products under the grandfathering rule are positively correlated with the carbon price ($p_e$). The prices increase first and then decrease as the carbon price increases under the benchmarking rule. Combined with Corollaries 4 and 5, the OEM has a low level of carbon reduction (as described in Figure 9) and tends to raise the price of new products to reduce output and control total carbon emissions under the grandfathering rule. On the contrary, the OEM has a high level of investment in emission reduction investment, since the government has less stringent carbon constraints on original manufacturers under the benchmarking rule. When the carbon price is less than a certain threshold, the OEM tends to recover the loss caused by the carbon reduction cost through increasing the price appropriately and reducing output. However, When the carbon price is larger than a certain threshold, the OEM lowers prices and, thus, increases production to compensate for the higher carbon reduction costs, while the AR follows suit by lowering price in order to improve market competitiveness.

Figure 9 reveals that the level of investment in carbon reduction technology increases with the carbon price under the benchmarking rule, whereas the level of investment in carbon reduction technology first increases and then decreases with $p_e$ under the grandfathering rule. Meanwhile, the difference in emission reduction levels under the benchmarking and grandfathering rules increases with the carbon price, which is consistent with Corollary 4. This is because the carbon emission quota per unit product is limited by the benchmarking rule. As the carbon price increases, the OEM must increase the level of investment in emission reduction in order to control the carbon trading costs under the benchmarking rule. The OEM has less constraints on the carbon emissions quota under the grandfathering rule, but the high level of investment in carbon emission reduction leads to a decrease in profits. Therefore, when the carbon price exceeds a certain threshold, the OEM would reduce the level of investment in emission reduction, reduce production and sell the remaining carbon emission allocation in order to obtain profits.

As depicted from Figure 10, under the grandfathering rule, the quantity of new products decreases with the carbon price, while the quantity of new products increases with the carbon price. With an increasing carbon price, the OEM passes on the emission reduction cost by increasing the price, which decreases the quantity of new products, while market competition increases the quantity of remanufactured products sold. Under the benchmarking rule, the quantity of new products first decreases and then increases with the carbon price, while the quantity of remanufactured products first increases and then decreases, which is caused by the price changes of the two types of products with the carbon price.

Figure 11 indicates that the environmental impact of the two products is negatively correlated with the carbon price under the grandfathering rule. Nevertheless, the environmental impacts of the two products first decrease and then increase under the benchmarking rule, which is more serious than that under the grandfathering rule. The environmental impact of two products is not only related to the emission reduction level of the OEM, but also to the quantities of the two products. Consequently, the quantity of new products is relatively smsall, and the quantity of remanufactured products is larger, so the impact on the environment is lower under the grandfathering rule. Specifically, under the benchmarking rule, the quantity of new products first decreases and then increases with the carbon price (as shown in Figure 10), which is far greater than that under the grandfathering rule, so the environmental impact of the two products first decreases and then increases. The same conclusion as in Corollary 7 suggests that it is more beneficial to the environment by restricting the total carbon emissions of the OEM under the grandfathering rule.

From Figure 12 and Figure 13, under the grandfathering rule, the profits of the OEM and AR increase with the carbon price. As the carbon price increases, the level of investment in emission reduction first increases and then decreases to control the output of new products. At this time, the OEM can sell the remaining carbon emission allocations to obtain more profits, which exceeds the investment cost of emission reduction, so the OEM’S profit increases. Moreover, the price and quantity of remanufactured products increases with $p_e$, and the AR’s profit increases accordingly. Meanwhile, under the benchmarking rule, the AR’s profit increases first and then decreases with the carbon price, since both the price and quantity of remanufactured products increase first and then decrease with the carbon price (as seen in Figure 8 and Figure 10). In this way, When determining the carbon price, the government should consider its impact on the profits of the two types of products. Profits drive the OEM and AR to transform to low-carbon production.

5.3. The Impact of Carbon Emission Quotas on Optimal Decisions

This section discusses the impact of carbon emission initial quotas (E and $e_0$) on optimal equilibrium decisions under grandfathering and benchmarking, respectively. Figure 14 shows that the profit collected by the OEM increases as the total amount of initial carbon emission quotas E increases under the grandfathering rule. Based on the assumption that the AR is shielded from carbon allowance allocation regulations by government patronage, the profit of the AR is not affected by E.

Under the benchmarking rule, Figure 15 indicates that the OEM’s profit increases as the carbon emission quota $e_0$ per unit of a new product increases, while the AR’s profits decline. Moreover, Figure 16 shows that, with an increase of $e_0$, the optimal prices of new and remanufactured products decrease, while the level of investment in low-carbon technologies increases. Unlike other research conclusions, such as thpse of Xia X.Q. [33], the smaller the carbon emissions quota per unit of new product, the less positive the OEM’s initiative to invest in emission reduction technology. Meanwhile, Figure 17 indicates that the demand for new products increases as the carbon emission quota increases, while that for remanufactured products decreases.

5.4. Discussion of Findings

The numerical study was conducted to investigate the effects of relevant factors, such as customer preference for remanufactured products, carbon price, and carbon quotas on the optimal equilibrium decisions.

The results indicated that, under the carbon allowance allocation rules, optimal decisions, such as for pricing, the license fee, and the profits of the OEM and AR, are positively related to consumer preference for remanufactured products. However, total carbon emissions, and investment in reduction emission technology are negatively related to consumer preferences for remanufactured products. These findings are consistent with the research conclusions of many scholars, such as Wang S.Y., Chen W. and Xia X.Q. In particular, the demand for remanufactured products is positively correlated with consumer preference for remanufactured products. In contrast, the demand for new products is negatively correlated with consumer preference for remanufactured products.

As a result of the numerical study, it was found that the optimal pricing and maximum profits of the OEM and AR were significantly positively correlated with the carbon price under the grandfathering rule. However, the optimal pricing and maximum profit of the OEM was negatively correlated with the carbon price under the benchmarking rule. Moreover, the AR’s optimal production quantity and maximum profit had a nonlinear relationship with the carbon price. Furthermore, when the carbon price was greater than a certain threshold, the AR’s optimal production quantity and maximum profit decreased. Therefore, if the government sets a higher carbon price under the grandfathering rule, although it increases the total benefits of manufacturers and remanufacturers, it actually reduces the enthusiasm of the original manufacturer to invest in emission reduction technology, resulting in an increase in total carbon emissions. On the contrary, under the benchmarking rule in the emission trading system, if the government sets a higher carbon price, it reduces the total benefits of the supply chain. Then, it forces manufacturers to increase investment in emission reduction technology to meet the limit for unit product carbon emissions, thereby reducing total carbon emissions. This is because a higher carbon price increases the production costs of enterprises, thereby reducing their profitability.

Under the grandfathering rule, we found that the initial carbon emission quotas E only affected the OEM profits, while other operational decisions were unrelated to it. Subsequently, under the benchmarking rule, as the initial carbon allowance for manufacturers increased, the total profit of remanufacturers decreased due to the reduced competitiveness of the remanufactured products. When the initial carbon allowance for manufacturers increased, the total profit of the supply chain increased, but the total carbon emissions increased. Therefore, the government should set a reasonable initial carbon quota based on the total amount of carbon emissions control, as this could not only improve the AR’s competitiveness but also reduce pressure on the OEM to invest in technology innovation. Furthermore, it was found that the benchmarking rule affects the optimal decisions of the closed-loop supply chain, including pricing, demand, and profit.

6. Conclusions and Future Research

In this paper, we investigated a CLSC wherein the manufacturer licenses an AR to implement remanufacturing under the grandfathering and benchmarking rules. Modeling and analyzing the effects of two different carbon quota allocation rules on manufacturing/remanufacturing decisions were carried out using a game model for the OEM and AR under the cap-and-trade mechanisms. In addition, we also analyzed the impact of consumer preference for remanufactured products, the carbon price and initial carbon quotas on production decisions. The main conclusions and management insights in this paper are as follow.

The carbon permit allowance rules significantly affect the optimal decisions of the OEM and AR. The grandfathering rule helps to control the total carbon emissions of high-emission enterprises. The grandfathering rule helps to control carbon emissions in high-emissions enterprises. It works better than the benchmarking rule, yielding higher profits and lower environmental impact.

The numerical analysis indicated that consumer preference for remanufactured products and the carbon price exert a significant impact on production decisions in a closed-loop supply chain under carbon cap-and-trade mechanisms. By appropriately increasing the carbon price, the government can prompt OEMs to adopt emission reduction technologies, enhancing their profitability and that of the ARs, and mitigating environmental impacts. The government should take into account the actual economic and production technological developments, implement the benchmarking rule for low-emission enterprises, and apply the grandfathering rule to high-emission enterprises. The government should facilitate low-carbon remanufacturing in enterprises by implementing a reasonable carbon pricing mechanism and setting a cap on carbon emissions, thereby promoting the transition to a low-carbon economy.

This study examined the impact of exogenous variables, namely carbon initial emission quotas and carbon price, on optimal equilibrium decisions related to pricing, demand, and profit in a closed-loop supply chain. Additionally, two different carbon emission regulations were compared in terms of their economic and environmental effects on the entire supply chain. Subsequently, we conducted a comparative analysis of the economic and environmental impacts between the benchmarking and grandfathering rules across the entire supply chain. Finally, we explored the optimal carbon permit allocation strategy for various industries with different levels of carbon emissions.

To simplify the calculation, it was assumed, in this paper, that remanufacturers are exempt from carbon emission quotas. In the future, we will examine the optimal decision-making process for a closed-loop supply chain that adheres to carbon allowance allocation regulations, even when remanufactured products are subject to carbon emission quotas. In addition, this paper will be expanded in various directions in the future. The impact of carbon emission allocation on remanufacturing models, such as outsourcing remanufacturing, will be further explored. Future research could consider the role of emission reduction financing and government subsidies in promoting the production of remanufactured goods. Moreover, given the presence of rival products in the market, this study will investigate optimal strategies for a closed-loop supply chain operating under carbon permit allocation regulations within a competitive environment.