Retailer-Led Low-Carbon Supply Chain Coordination Considering Sales Effort

: This paper develops a Stackelberg game model for a retailer-led secondary low-carbon supply chain (L-CSC) comprising a manufacturer and a retailer. Then, a two-part pricing contract is designed to investigate the product pricing, carbon reduction, and sales effort decision problems, and relevant management insights are obtained through numerical analysis. The study shows an efﬁciency loss in decentralized decision making compared to centralized decision making. Considering the sales effort improves the efﬁciency of the supply chain, retail price, carbon emission reduction (CER), sales effort level, and supply chain proﬁt positively relate to product low carbon preference and sales sensitivity coefﬁcients. The designed two-part pricing contract can increase the proﬁt of the entire L-CSC and optimize the decision level under centralized decision making.


Introduction
In the face of severe climate change, green development and low-carbon transformation have become global hotspots of concern.The high level of carbon emissions not only leads to frequent natural disasters and extreme climate events, directly threatening the living environment of humanity, but also causes substantial economic losses to countries.Therefore, governments began to encourage and guide enterprises to pay attention to environmental issues, emphasizing the importance of low-CER technology investment to expect enterprises to improve resource utilization and reduce carbon dioxide emissions in the production and operation processes.From the joint signing of the Kyoto Protocol in 1997 to the Paris Agreement in 2015, international organizations and governments have partnered to launch a series of international treaties and policies for reducing low-carbon emissions.Among them, the Kyoto Protocol entered into force in 2005 and the number of countries signed by 2009 reached 183.It is the first international treaty to protect humanity from the threat of dramatic climate change by controlling greenhouse gas content.The Paris Agreement continues the efforts of the Protocol to address carbon emissions, calling on countries to commit to emission reduction targets and provide financial and methodological support for developing countries to address climate change.Countries have established CER and carbon neutrality targets in this context [1].For example, in 2000, the total carbon dioxide emissions of the European Union (EU) were 4545.97mt, 12.16% year-on-year compared with 1990.In 2019, the total carbon dioxide emissions of the EU were 3816.76 mt, down 26.25% from 1990.On 4 March 2020, the EU indicated in the European climate law that it would achieve "net zero emissions" by 2050.The EU's continuously improved CER policy system has played a leading role in emission reduction [2].Sweden is one of the first countries to implement a carbon tax globally.It has gradually increased from US $30 per ton of carbon dioxide in 1991 to US $137 today.After imposing carbon and value-added taxes on transportation fuel, the carbon dioxide emissions from transportation have decreased by nearly 11% annually on average [3].The German Bundestag passed The rest of the sections of the paper are arranged as follows: Section 2 provides a summary of the pertinent literature.Section 3 gives the model hypothesis and relevant symbolic meanings.Section 4 establishes basic mathematical models considering sales effort and analyzes the optimal decision level under decentralized and centralized decision making.Two pricing contracts are designed, and relevant conclusions are obtained.Section 5 includes the data analysis.Section 6 summarizes the relevant conclusions and gives the shortcomings of the research and the future research directions.

Literature Review
Scholars have explored L-CSC decision making issues from the perspectives of government systems, consumer behavior, and decision-maker preferences and have achieved a wealth of valuable research results.At present, many scholars have rich research on supply chain coordination contracts.Effective coordination contract methods include wholesale price contracts, revenue-sharing contracts, component-sharing contracts, and two-part tariff contracts.Zou et al. analyzed the risk aversion issue under the carbon emission policy and coordinated the L-CSC utilizing the cost-sharing contract [13].Lin et al. investigated the pricing strategy and coordination of a L-CSC based on the self-executing side payment contract considering retailers' social preferences [14].Zhang et al. studied the effect of power structures and double government subsidy on decision variables such as retail product prices, supply chain profits, and recovery rates in low-carbon closed-loop supply chains [15].Yuan et al. verified the influence of retailers' risk avoidance on equalization strategy and channel coordination under the consumer preferences on LCP [16].Xu et al. studied the dual-channel supply chain coordination problem under mandatory carbon emission capacity regulation and designed a price discount contract for coordination [17].Li et al. employed the background of dual-source supply and low-carbon manufacturing to analyze the optimal strategy of a closed-loop supply chain system under competition, cooperation, and cost-sharing contract coordination structure.They verified the impact of emission reduction efforts and collection efficiency on supply chain performance [18].Wu et al. established decision making models of the supply chain under different contracts for L-CSCs whose demand is affected by manufacturers' CER, new retailers' services, and traditional retailers' promotions.The results indicate that opening up new retail is conducive to improving supply chain profits [19].Wang et al. took crop straw directfired power generation supply chain as the study object under the green development background, comprehensively considered CER and economic cost of the power generation cycle, introduced revenue sharing contract for coordination, and finally realized Pareto improvement [20].Wu et al. analyzed the achievement of L-CSC composed of capital-constrained manufacturers and retailers under three financing strategies.They established a cost-sharing contract to achieve the supply chain coordination and enhance cooperation among firms [21].Yang et al. investigated the effect of benefit-sharing and cost-sharing contracts on manufacturers' carbon emission reduction efforts.They found that revenue-sharing contracts are more conducive to manufacturers' carbon reduction efforts and the improvement of system profits [22].Yu et al. found that revenue-sharing and cost-sharing contracts help manufacturers reduce carbon emissions and increase profits by verifying the effects of the consumer carbon reduction reference and the manufacturer's cost learning.In addition, they found that manufacturers and supply chain systems prefer revenue-sharing contracts, while retailers prefer wholesale price contracts [23].Ran et al. designed a revenue-sharing contract to coordinate L-CSC in response to carbon tax policies and government subsidies.They analyzed both supply chain decision making and emission reduction strategies [24].Chen et al. coordinated the recycling and remanufacturing closed-loop supply chain by designing a cost-benefit sharing contract and formulated the optimal strategy considering consumer low-carbon awareness and manufacturers' efforts to reduce carbon emissions [25].
With the instant development of the low-carbon economy and the continuous improvement of people's awareness of green consumption, consumers have an increasingly strong demand for LCP.Therefore, scholars have gradually begun considering their role and influence on the supply chain by studying consumers' preferences for LCP.Huo et al. considered environmental regulation and consumers' low-carbon preferences from a dynamic perspective.Using the evolutionary game method, they studied the game strategy and influencing factors of enterprises' CER behavior in the two-level supply chain [26].Ding et al. considered the government's carbon cap-and-trade rules and consumers' lowcarbon preferences, studied the problem of manufacturer encroachment and CER, and compared the equilibrium decisions under four scenarios using the Stackelberg game [27].Zhang et al. verified the impact of consumer perception differences in corporate decision making.They found that a win-win situation could be achieved between corporate profits and social welfare under a small or large consumer perception gap [28].Xu et al. designed two cost-sharing contracts between manufacturers and retailers and analyzed the supply chain's dynamic changes under consumers' low-carbon preferences [29].Ghosh et al. found that the dual-channel model can be more useful when consumers have high low-carbon preferences and low initial product emissions by considering the random demand of government carbon quota, carbon trading regulation, and consumers' low-carbon preferences [30].Yang et al. compared and analyzed the equilibrium decision making level in the supply chain network considering the low-carbon consciousness of consumers under three standard carbon policies [31].Wu et al. studied the supply chain coordination problem between manufacturers and retailers on consumers' low-carbon preferences.The comparison between the four cases indicated that the retailer's cost-sharing contract could achieve the supply chain coordination and Pareto betterment between manufacturers and retailers [32].
As the retail industry gradually grows, the power structure in the supply chain also tends to diversify.Therefore, the power structure of the supply chain has also attracted widespread attention from scholars.Under the subsidy policy, Ma et al. studied multichannel supply chains' game characteristics and equilibrium strategies under three different power structures [33].Sane Zerang et al. conducted a study to examine the impact of sales effort and recovery rate on decision variables within a closed-loop supply chain led by the manufacturer.Their findings demonstrated the superiority of this particular supply chain model [34].Based on the existing research on the competition relationship between manufacturers and retailers in the closed-loop supply chain, Yang discussed whether, and how, the retailer's sales effort level affects the economic performance and sustainability of remanufacturing [35].Zand et al. studied the environmental goal decision making of manufacturers and retailers from different power perspectives under the background of the cooperation between the government and the manufacturer [36].Gu et al. studied whether online channels should be added to sell complementary green products in the supply chain dominated by retailers.They found that adding online channels depends on the degree of complementarity between online and offline channels [37].Ma et al. analyzed the dynamic decision of a bi-channel closed-loop supply chain consisting of manufacturers and retailers under different channel power structures.The results indicated that the manufacturer who opened the direct channel could earn huge game profits [38].Lee and Park analyzed the advantages and disadvantages of the two-channel powers by comparing the CER efforts and total carbon emissions under the two power structures dominated by upstream and downstream enterprises [39].Chen et al. analyzed and compared the remanufacturing flow innovation, pricing strategy, and cost-sharing mechanism of a closed-loop supply chain in three kinds of power structures [40].Pakdel Mehrabani et al. discussed the pricing decisions of the bi-channel supply chain dominated by retailers, given the demand affected by customer channel preferences [41].Yang et al. studied the impact of consumerexpected regret on the remanufacturing strategy of original manufacturers under threechannel power structures [42].Liu et al. studied the impact of different decision making methods on the profits of each member in the supply chain of community e-commerce platforms using game theory.They highlighted that improving value co-creation efforts can benefit the supply chain [43].Zhang et al. studied the impact of different supply chain power structures on production decisions, emission reduction decisions, and emission caps, considering government carbon caps and trading controls [44].Zhou et al. analyzed and compared the optimal decision making, carbon emissions reduction, and supply chain profits under three decision models when dominant retailers in the supply chain adopt altruistic preference policies towards manufacturers [45].
Currently, the research on the sales effort mainly focuses on contract design and channel structure.Based on penetration and predatory pricing strategies, Feng et al. studied the advance selling strategy and decision making problem of dual-channel retailers considering sales efforts [46].Taleizadeh et al. considered a closed-loop supply chain's pricing strategy, quality level, and sales effort decision under different recycling channels and sales channel structures [47].Cao et al. verified the effect of product quality, promotion efforts, and mixed channels on supply chain efficiency in four kinds of dualchannel structures [48].Wu studied four game scenarios in which government subsidies, green consumer preferences, and retailers' sales efforts affect demand simultaneously [49].Liu et al. studied the retailers' equilibrium investment and pricing decisions when their sales effort commitment is earlier and later than the manufacturer's quality effort decision [50].Ranjan and Jha studied the supply chain's pricing and contract coordination strategies in the context of manufacturers' green quality efforts and retailers' sales efforts [51].Cai et al. studied the difference in the decision of sales efforts of suppliers and retailers in the supply chain competition model of strategic customers.They realized Pareto improvement using a cost-sharing contract [52].Tian et al. considered that market demand is influenced by consumer channel preferences and sales efforts and verified the multichannel supply chains' coordination and control mechanism based on delayed decision making [53].Cai et al. studied the price tactics in a two-stage supply chain with sales effort and channel conflict [54].Saha et al. investigated the impact of product market demand on price and sales effort level.They studied the channel coordination of the three-tier supply chain comprising manufacturers, distributors, and retailers [55].Wang et al. extracted optimal pricing strategies for dual-channel supply chains with third-party product recycling and sales efforts [56].Li et al. verified the influence of the exhibition hall on the optimal pricing decision and service effort of the dual-channel supply chain, considering the cases of no-service, pre-service, and post-service.The research results indicate that the exhibition hall effect maximizes the enterprises' gain in the case of post-service [57].Tu et al. studied the supply chain coordination problem of agricultural products e-commerce platforms and third-party logistics enterprises.Among them, e-commerce platforms have promotion behavior, and third-party logistics have service promotion behavior.They analyzed the effect of fixed-price, benefit-sharing, and cost-sharing mechanisms on the equilibrium results of the supply chain [58].Alamdar et al. developed a risk-averse closed-loop supply chain with random demand, analyzed the decision making of supply chain members on price, recovery rate, and sales effort under distinct decision making mechanisms, and formulated a supply chain coordination plan based on the analysis of equilibrium results [59].Mondal and Giri established a two-stage green closed-loop supply chain model in which the market demand depends on the product's sales price, green level, and sales effort.They verified the influence of eco-innovation, sales effort, and recycling rate of waste products on closed-loop supply chain [60].Wang et al. analyzed the carbon reduction problem in agricultural products guided by government subsidies and sales efforts, focusing on how sales efforts and different government subsidies promote manufacturers' carbon emission reduction [61].In the context of carbon cap-and-trade policy, Xu et al. investigated the optimal production decision and sales effort level under cost-sharing and quantity discount contracts.They explored the impact of supervision and sales work on supply chain coordination [62].
Existing studies mainly focus on the manufacturer-led supply chain from the direction of channel structure and contract selection.However, there are few studies on the retailerled L-CSC, especially those combining sales efforts.At the same time, it is found that most of the existing literature combines the retailer's sales effort with the revenue-sharing contract and the cost-sharing contract.In addition, few studies combine the retailer's sales effort with the two-part pricing contract to analyze the effect of sales effort on the L-CSC.Accordingly, this paper researches the supply chain coordination in the case of the manufacturer's CER investment and retailer's sales effort to provide a decision making reference for a retailer-led L-CSC considering sales effort.

Problem Description and Related Hypotheses
The paper considers a retailer-led secondary L-CSC, including a single manufacturer M and a single retailer R, in which consumers have low-carbon preferences.The manufacturer will increase the carbon reduction effort level by increasing its investment in carbon reduction technologies and the retailer will be responsible for the promotional effort in the sales chain of LCP so that consumers are willing to purchase them.Table 1 shows the meaning of this paper's relevant parameters, symbols, and variables.In order to facilitate the solution, the fundamental hypotheses are set as follows: Hypothesis 1.The supply chain members are risk neutral and entirely rational, with symmetrical information between them, and their decision making goal is to maximize their interests.The manufacturer has sufficient production capacity, and the production quantity equals the retailer's order quantity.Retailers can fully meet consumer demand, regardless of shortage and inventory costs.

Hypothesis 3.
Considering the profit-driven nature of suppliers and retailers, we have p>w>c; for ease of calculation, suppose p = w + x, where x>0.
Hypothesis 4. This paper employs the convex function attribute in the L-CSC.The quadratic cost function describes the input cost of CER technology.The cost function is C M = 1 2 λθ 2 ; similarly, the cost of retailers' efforts to sell LCP is C R = 1 2 ke 2 .

Decision Analysis without Considering Retailer Sales Efforts
In a supply chain without considering the sales efforts e, the decision making sequence of a retailer-led supply chain can be described as follows: in the first stage, the retailer acts as the leader and decides to retail mark-up x; in the second stage, manufacturers determine wholesale prices w and unit product carbon emissions reduction θ based on retailer decisions.The demand is only related to price and CER input without considering the sales effort.At this point, the market demand function becomes D = a − b × p + r × θ.The profit function of the L-CSC are as follows: (1) In order to avoid conflicts of interest among individual supply chain participants, manufacturers, retailers, and other supply chain members are considered as a whole to determine the retail price of LCP p, and product carbon emissions reduction θ to maximize the profits of the supply chain system.

Decentralized Decision Model-Model B
Proposition 2. Without considering the retailer's sales effort, under the decentralized decision making, when 2bλ − r 2 >0, the profit function is the joint concave function of the wholesale price and the unit CER, and both have optimal values.The best wholesale price, the best retail price, and the maximum unit CER are w , and , respectively, and the maximum profits of the manufacturer and the retailer are <0 means that the manufacturer's profit is lower than that of the retailer, indicating that the leading position in the L-CSC has brought more profits to the retailer.
The profit of the supply chain system is:

Decision Analysis Considering Retailer Sales Efforts
After considering the sales efforts of retailers, the decision making stages of the L-CSC can be described as follows: in the initial stage, the retailer, as the leader, determines the retail mark-up x and sales effort level e; subsequently, the manufacturer decides the wholesale price of LCP w and unit product carbon emissions reduction θ based on the retailer's decision.
The profit function of the manufacturer is: The profit function of the retailer is: The profit function of the L-CSC is: When considering the retailers' sales efforts under centralized decision making, when kr 2 − 2bkλ + z 2 λ<0, the profit function is the joint concave function of the retail price, unit CER, sales effort level, and all have optimal values.The optimal retail price, maximum unit CER, and optimal sales effort are p t = − −ckr 2 +akλ+bckλ−cz 2 λ

Decentralized Decision Model-Model D
When the supply chain is under decentralized decision making, manufacturers and retailers will make their own decisions to maximize their profits.Proposition 4. When considering retailers' sales efforts under decentralized decision making, when 2bλ − r 2 >0 and −2kr 2 + 4bkλ − z 2 λ>0, the manufacturer's profit function is the joint concave function of the wholesale price and unit CER, and the retailer's profit function is the joint concave function of retail mark-up and sales effort level, all of which have optimal values.The best wholesale price, the best retail price, maximum unit CER, and optimal sales effort are The maximum profits of retailers, manufacturers, and supply chains are More details are shown in Appendix A.

Equilibrium Comparative Analysis
Proposition 5.The low-carbon preference coefficient and the sales sensitivity coefficient positively impact the retail price, the manufacturer's unit CER, the retailer's sales effort level, and the profits of the manufacturer and the retailer.More details are shown in Appendix A.
Increasing the low-carbon preference and sales effort coefficients makes manufacturers and retailers more profitable.This is because the higher the consumer's preference for LCP, the more willing they are to buy green LCP at a higher price, leading to the expansion of market demand for them.The L-CSC will develop a high-price strategy to increase profits by increasing market prices.With the increase in consumers' low-carbon preference coefficient, manufacturers and retailers will increase CER input and sales effort level to meet consumers' purchase demand, and the CER and sales volume of products will also increase accordingly.As the cost increases due to increased inputs, retailers will increase the retail price so that both parties can profit more.When the sensitivity coefficient of sales effort increases, retailers will make more sales efforts to improve their market share.Meanwhile, manufacturers will also employ this effect to increase the CER of products to establish a low-carbon image of energy conservation and emission reduction.Proposition 6.The optimal sales price, unit CER, and the L-CSC system profit with the retailer's sales effort are greater than those without the retailer's sales effort.More details are shown in Appendix A.
Retailers should adopt more marketing methods and channels than ordinary products to make consumers know and understand LCP.When retailers invest in sales efforts, the cost of sales will increase due to the increase in investment.Therefore, retailers will increase the retail market price to ensure profits.Meanwhile, as consumers' recognition of LCP increases, manufacturers will take more measures to increase the investment in CER technology to meet the expansion of market demand, and the unit CER of products will also rise.With the increase in market demand and retail price, the overall profit of the L-CSC system will improve accordingly.

Proposition 7.
Centralized decision making provides a lower retail price, a higher CER per unit product of the manufacturer and the sales effort level of the retailer, and a higher total profit of the L-CSC than decentralized decision making.More details are shown in Appendix A.
It can be concluded that the decision making level of the L-CSC under a centralized decision making mode is higher than that under a decentralized decision making mode.When making decentralized decisions manufacturers and retailers pay too much attention to their interests and ignore the overall development, eventually forming a double marginal effect, degrading the supply chain efficiency.In addition, price factors can also decrease the market demand to a certain extent, thus decreasing the market share and ultimately causing a profit loss.Therefore, each member of the L-CSC should take the initiative to develop a reasonable contract mechanism to improve the overall decision making level of the L-CSC.

Two-Part Tariff Contract Coordination
The decision making level of the supply chain under the decentralized decision making mode is lower than in the centralized decision making mode.Therefore, to achieve supply chain coordination, it is necessary to formulate an effective contract to encourage cooperation between manufacturers and retailers, improve the sales profit of their products, and improve the overall performance of the supply chain.This paper adopts a two-part tariff contract, where its basic ideas are as follows: First, since the retailer is in a dominant position, the retailer sets retail mark-up x = p − w and sales effort level e based on its profit level, and the manufacturer sets the unit wholesale price w and fixed operating expenses F TS for LCP.Second, retailers provide manufacturers with a wholesale price w TS based on unit production costs and fixed operating expenses F TS , which manufacturers can accept or refuse based on their profit situation.Finally, retailers and manufacturers reach a contract through continuous negotiations.
Under the two-part tariff contract, the profit functions of the manufacturer and retailer are: The sequential game is adopted to solve the problem in reverse.The first-order partial derivative of Equation ( 9) concerning p and e are obtained as follows: Continuing to find the second-order partial derivative, the Hessian matrix can be obtained as −2b z z −k .Since −2b<0, the matrix is negative definite when 2bk − z 2 >0.
π RTS is a joint concave function of p and e, and there exists an optimal solution.Let the first-order partial derivative be equal to 0. We can obtain: By substituting ( 12) and ( 13) into (8), we can obtain: The first-order partial derivative of ( 14) concerning θ is obtained as follows: Continuing with the second-order partial derivative, we have ∂ 2 π MTS ∂θ 2 = −λ<0, where π MTS is a concave function of θ, and there exists an optimal solution.If the first-order partial derivative equals 0, we can obtain: Substituting ( 12), (13), and ( 16) into ( 8) and ( 9), the profit functions of the supplier and retailer under a two-part pricing contract can be obtained as follows: As indicated in the previous section, 2 .After adding the two-part pricing tariff contract coordination, the manufacturer's profit will exceed the profit under decentralized decision making.At this time, the manufacturer's profit satisfies π MTS π * Md and makes it 0, and can obtain: Substituting (19)  : The first-order and second-order partial derivatives of Equation ( 20) concerning w TS are obtained as follows: π rTS is a concave function of w TS , and there is an optimal solution.Let the first-order partial derivative be equal to 0, then: By substituting ( 23) into the two-part pricing tariff contracts, the optimal fixed operating expenses, optimal CER, optimal sales effort level, and optimal retail price can be obtained as follows: where

Numerical Analysis
In order to dig deeper into the potential conclusions of the model and validate the model analysis results, this paper employs MATLAB R2021a software to perform an arithmetic analysis to further illustrate the above conclusions.Based on the parameter assignments studied in [30,31], and combined with the prerequisites proposed by the established model, the parameters are assigned as follows: a = 100, b = 4, r = 8, z = 10, c = 5.

Comparative Analysis of Optimal Decision and Profit Results
Let k = 60 and λ = 30.Table 2 compares the L-CSC's optimal decision and profit results under distinct models.Table 2 shows that after considering the sales efforts of sales retailers, whether in the centralized or decentralized decision making modes, the manufacturer's product unit CER, unit product price, and profits of various entities in the supply chain have been increased.The decision variables in the centralized decision making mode are better than those in the decentralized mode, with or without considering the level of the sales effort, further demonstrating the conclusions of Propositions 6 and 7.

Influence of CER Investment Cost Coefficient
Let k = 60 and λ ∈ [30, 100].Figures 1-4 show the effect of changes on various decision variables in the supply chain.

Numerical Analysis
In order to dig deeper into the potential conclusions of the model and validate the model analysis results, this paper employs MATLAB R2021a software to perform an arithmetic analysis to further illustrate the above conclusions.Based on the parameter assignments studied in [30,31], and combined with the prerequisites proposed by the established model, the parameters are assigned as follows:  = 100,  = 4,  = 8,  = 10,  = 5.

Comparative Analysis of Optimal Decision and Profit Results
Let  = 60 and  = 30.Table 2 compares the L-CSC's optimal decision and profit results under distinct models.Table 2 shows that after considering the sales efforts of sales retailers, whether in the centralized or decentralized decision making modes, the manufacturer's product unit CER, unit product price, and profits of various entities in the supply chain have been increased.The decision variables in the centralized decision making mode are better than those in the decentralized mode, with or without considering the level of the sales effort, further demonstrating the conclusions of Propositions 6 and 7.

Influence of CER Investment Cost Coefficient
Let k = 60 and  ∈ 30,100 .Figures 1-4 show the effect of changes on various decision variables in the supply chain.Figures 1-4 show that, whether the supply chain is in centralized or decentralized decision making, when retailers invest in sales efforts, the carbon emissions reduction in products in the supply chain, wholesale price of products, retail price of products, and total system profit are always greater than the corresponding decision making levels without considering the retailer's sales effort in the corresponding state, confirming the conclusion of Proposition 6.At the same time, whether the retailer invests in sales effort or not, the product carbon emissions, sales effort level, and supply chain system profit in centralized decision making are always higher than those in decentralized decision making.The retail and wholesale prices of products in centralized decision making are lower than those in decentralized decision making.Decentralized decision making provides a higher retail price of products and a lower profit compared with centralized decision making.Figures 1-4 show that, whether the supply chain is in centralized or decentralized decision making, when retailers invest in sales efforts, the carbon emissions reduction in   Figures 1-4 show that, whether the supply chain is in centralized or decentralized decision making, when retailers invest in sales efforts, the carbon emissions reduction in   Figures 1-4 show that, whether the supply chain is in centralized or decentralized decision making, when retailers invest in sales efforts, the carbon emissions reduction in It shows that supply chain efficiency loss occurs under decentralized decision making, demonstrating the conclusion of Proposition 7.With the increase in CER investment cost coefficient, all decision variables in the supply chain show a downward trend, and the product CER decreases faster under centralized decision making.This shows that: (1) Increasing the investment cost coefficient of CER means that manufacturers must invest more in CER to achieve the same effect.Thus, they will reduce their investment in CER for their interests, thus reducing the unit carbon emission.The CER per unit of LCP will reduce consumers' demand for low-carbon preferences.Hence, manufacturers and retailers attract consumers by reducing wholesale and retail prices.At this point, retailers will also reduce their sales efforts to ensure their profits due to a decrease in product retail prices.Therefore, the cost coefficient of CER investment weakens the L-CSC's overall profit and gradually declines the L-CSC's overall profit.(2) Compared with the L-CSC under centralized decision making, there is always a loss of decision making efficiency in the L-CSC under decentralized decision making, which decreases while increasing the cost coefficient of CER investment.(3) When retailers invest in sales efforts, the decision making levels in the supply chain are improved, and the sales efforts of retailers develop the entire decision making efficiency of the supply chain.
From the entire supply chain perspective, L-CSC members should further strengthen information sharing and cooperation while encouraging retailers to make sales efforts.

Influence of Consumers' Low Carbon Preference Coefficient
Let k = 60, λ = 30, r ∈ [8, 12].Figures 5 and 6 show the effect of observed changes on various decision variables in the L-CSC.centralized decision making are always higher than those in decentralized decision making.The retail and wholesale prices of products in centralized decision making are lower than those in decentralized decision making.Decentralized decision making provides a higher retail price of products and a lower profit compared with centralized decision making.
It shows that supply chain efficiency loss occurs under decentralized decision making, demonstrating the conclusion of Proposition 7.With the increase in CER investment cost coefficient, all decision variables in the supply chain show a downward trend, and the product CER decreases faster under centralized decision making.
This shows that: (1) Increasing the investment cost coefficient of CER means that manufacturers must invest more in CER to achieve the same effect.Thus, they will reduce their investment in CER for their interests, thus reducing the unit carbon emission.The CER per unit of LCP will reduce consumers' demand for low-carbon preferences.Hence, manufacturers and retailers attract consumers by reducing wholesale and retail prices.At this point, retailers will also reduce their sales efforts to ensure their profits due to a decrease in product retail prices.Therefore, the cost coefficient of CER investment weakens the L-CSC's overall profit and gradually declines the L-CSC's overall profit.(2) Compared with the L-CSC under centralized decision making, there is always a loss of decision making efficiency in the L-CSC under decentralized decision making, which decreases while increasing the cost coefficient of CER investment.(3) When retailers invest in sales efforts, the decision making levels in the supply chain are improved, and the sales efforts of retailers develop the entire decision making efficiency of the supply chain.
From the entire supply chain perspective, L-CSC members should further strengthen information sharing and cooperation while encouraging retailers to make sales efforts.

Influence of Consumers' Low Carbon Preference Coefficient
Let  = 60,  = 30,  ∈ 8,12 .Figures 5 and 6 show the effect of observed changes on various decision variables in the L-CSC.Figure 5 shows that with the develop in consumers' low carbon preference coefficient r, the retail prices of LCP continue to increase under centralized or decentralized decision making.The increase in the low-carbon preference coefficient means that consumers have increased environmental awareness.Now, manufacturers will increase their investment in carbon reduction technologies to expand their market share.Subsequently, they will compensate for the cost increase caused by the increase in investment by increasing the price of LCP.
Figure 6 shows that the total profits under centralized and decentralized decision making will increase as the consumers' low carbon preference coefficient increases with Figure 5 shows that with the develop in consumers' low carbon preference coefficient r, the retail prices of LCP continue to increase under centralized or decentralized decision making.The increase in the low-carbon preference coefficient means that consumers have increased environmental awareness.Now, manufacturers will increase their investment in carbon reduction technologies to expand their market share.Subsequently, they will compensate for the cost increase caused by the increase in investment by increasing the price of LCP.
Figure 6 shows that the total profits under centralized and decentralized decision making will increase as the consumers' low carbon preference coefficient increases with or without considering the retailer's sales efforts.Therefore, improving consumers' awareness of sustainable development can increase the entire efficiency of the L-CSC.Companies should increase investment in carbon-reducing technologies and raise consumer awareness of low-carbon and environmental protection.

Influence of Sales Effort Sensitivity Coefficient
Let k = 60, λ = 30, z ∈ [10, 20]. Figure 7 shows the trend of the L-CSC decision variables with the z value.

Coordination Analysis of the Two-Part Pricing Contract
Based on the above analysis, this section discusses the change in the supply chain decision making level after adding two-part pricing contract coordination.Let  = 30 and  ∈ 30,60 .Figure 8 shows the supply chain decision variables trend with the z value.The impact of adding a two-part pricing contract on various decision variables in the supply chain is described in Table 3 and Figure 8.As shown in Figure 7, within a specific range, the sales effort sensitivity coefficient z positively impacts the retail product price, wholesale price, sales effort level, and unit CER.The more sensitive consumers are to sales efforts, the more retailers will invest in sales efforts to increase profits.The increase in sales efforts increases the cost of retailers.Accordingly, retailers control the increase in costs by increasing the retail price of their products.Since retailers are dominant, manufacturers will increase wholesale prices and unit carbon emissions reductions correspondingly.

Coordination Analysis of the Two-Part Pricing Contract
Based on the above analysis, this section discusses the change in the supply chain decision making level after adding two-part pricing contract coordination.Let λ = 30 and k ∈ [30, 60]. Figure 8 shows the supply chain decision variables trend with the z value.The impact of adding a two-part pricing contract on various decision variables in the supply chain is described in Table 3 and Figure 8.
As shown in Table 2, the level of sales efforts has increased after the coordination of the two contracts.At the same time, the unit CER, retail, and wholesale prices of LCP have all decreased.The reason is that after implementing the two-part tariff contract, manufacturers and retailers adopt a cooperative pricing mechanism, decreasing the retail and wholesale prices of LCP.Although manufacturers' unit CER has declined, the decline is not significant, and the cost of CER technology investment has also declined without losing the interests of manufacturers.

Coordination Analysis of the Two-Part Pricing Contract
Based on the above analysis, this section discusses the change in the supply chain decision making level after adding two-part pricing contract coordination.Let  = 30 and  ∈ 30,60 .Figure 8 shows the supply chain decision variables trend with the z value.The impact of adding a two-part pricing contract on various decision variables in the supply chain is described in Table 3 and Figure 8.    Figure 8 shows that manufacturers' profits remain unchanged before and after coordination.After coordination, the total profits of retailers and supply chain systems are greater than before, and the profit level further increases.Therefore, the two-part tariff contract reduces the efficiency loss of the L-CSC.The decision making level of the L-CSC is further increased, reaching or approaching the centralized decision making mode; that is, the two-part tariff contract finally realizes the Pareto improvement of both parties.

Conclusions
This paper studies a retailer-led two-stage L-CSC, including a manufacturer and a retailer.Considering the manufacturer's CER input and the retailer's sales effort, comparative equilibrium analysis was performed using the Stackelberg game model, and the decision making problems of product pricing, CER, and sales effort were studied.Accordingly, two-part tariff contracts were added to improve the decision making efficiency of the L-CSC.The numerical analysis provides a reference marketing strategy selection for retailers.
The following conclusions can be drawn: (1) Low-carbon preference coefficient and sales sensitivity coefficient positively impact retail product price, manufacturer's unit CER, retailer's sales effort level, and manufacturer and retailer's profit.(2) The optimal selling price, unit CER, and supply chain system profit with the retailer's selling effort are greater than those without the retailer's selling effort.(3) Centralized decision making provides a lower retail price, a higher manufacturer's carbon reduction per product unit and the retailer's sales effort level, and a higher total supply chain profit than decentralized decision making.
(4) The two pricing contracts can further increase the profits of the entire L-CSC, reduce the efficiency loss of the L-CSC, and achieve or approach the efficiency level under the centralized decision making mode.Consumers can also buy LCP at lower prices.
This paper enriches the theoretical research in L-CSC coordination and provides some management suggestions for the main bodies of the L-CSC.These are as follows.(1) Although manufacturers should strengthen green low-carbon technology innovation and increase CER investment, they should not invest blindly.They should choose low-cost and efficient CER technologies to control the cost coefficient of the investment within a reasonable range to maximize the effect.(2) As the leader of the L-CSC, retailers should employ different marketing channels and promotion methods to advocate the concept of green low-carbon, guide and cultivate consumers' low-carbon awareness, and encourage low-carbon consumption to enhance the performance of consumers' environmental awareness fully in promoting supply chain profits.Moreover, it has important practical significance for energy conservation, emission reduction, preservation of natural resources and long-term economic growth.(3) Member enterprises in the L-CSC should strengthen cooperation with upstream and downstream partners, actively implement the two-part pricing contract, achieve Pareto improvement of profits, and reach a win-win situation of economic development and environmental emission reduction.
Future research can also consider the situation of risk preference, information asymmetry, and the comparison of different power structures.These issues should be discussed and expanded in the follow-up research to obtain more realistic conclusions.

Proposition 1 .
Without considering retailers' sales efforts, under centralized decision making, when 2bλ − r 2 >0, the profit function is the joint concave function of the retail price and unit CER, and both have optimal values.The optimal retail price and maximum unit CER are p * tn = − −cr 2 +aλ+bcλ r 2 −2bλ , θ * tn = (−a+bc)r r 2 −2bλ , and the maximum profit of the L-CSC is π * Stn = (a−bc) 2 λ −2r 2 +4bλ .More details are shown in Appendix A.

Figure 1 .
Figure 1.The influence of  on the retail price of the LCP.Figure 1.The influence of λ on the retail price of the LCP.

Figure 1 .
Figure 1.The influence of  on the retail price of the LCP.Figure 1.The influence of λ on the retail price of the LCP.

Figure 2 .
Figure 2. The influence of  on the total profit of the L-CSC.

Figure 3 .
Figure 3.The influence of  on the wholesale price of the LCP.

Figure 4 .
Figure 4.The influence of  on the sales effort level.

Figure 2 . 24 Figure 2 .
Figure 2. The influence of λ on the total profit of the L-CSC.

Figure 3 .
Figure 3.The influence of  on the wholesale price of the LCP.

Figure 4 .
Figure 4.The influence of  on the sales effort level.

Figure 3 . 24 Figure 2 .
Figure 3.The influence of λ on the wholesale price of the LCP.

Figure 3 .
Figure 3.The influence of  on the wholesale price of the LCP.

Figure 4 .
Figure 4.The influence of  on the sales effort level.

Figure 4 .
Figure 4.The influence of λ on the sales effort level.

Figure 5 .
Figure 5.The influence of r on the retail prices of the LCP.

Figure 5 . 24 Figure 6 .
Figure 5.The influence of r on the retail prices of the LCP.

Figure 6 .
Figure 6.The influence of r on the profits of the L-CSC system.

Sustainability 2023 , 24 Figure 7 .
Figure 7.The influence of z on different decision variables.

Figure 8 .
Figure 8.The effect of k on the profit of the L-CSC system.

Figure 7 .
Figure 7.The influence of z on different decision variables.

Figure 8 .
Figure 8.The effect of k on the profit of the L-CSC system.

Figure 8 .
Figure 8.The effect of k on the profit of the L-CSC system.

Table 1 .
Description of parameters.

Table 2 .
Comparing the best decision and profit under distinct models.

Table 2 .
Comparing the best decision and profit under distinct models.

Table 3 .
Decision variables before and after supply chain coordination

Table 3 .
Decision variables before and after supply chain coordination

Table 3 .
Decision variables before and after supply chain coordination.