Service is becoming increasingly important in global economies, making the concept of the service supply chain (SSC) conspicuous in current operations management (Cheng et al., 2011). According to Peng et al. (2009), research on the SSC could be divided into two directions: 1) SSC as related service activities in traditional supply chains; 2) SSC as an innovation that applies traditional supply chain theories to the service sector. Similarly, Wang et al. (2015) discussed the definitions of the SSC and classified it into service-only supply chains (SOSC) and product service supply chains (PSSC). In SOSC, no physical products are offered. For instance, Ren et al. (2022) studied the quality and pricing issues in IT service supply chains. And Farsi et al. (2020) explored supply chains that offer customized services such as customer maintenance and facility management. By contrast, in PSSC, service coexists with physical products. For instance, Jia et al. (2019) and Niu et al. (2022) analyzed logistics service supply chains that provide logistics and distribution services for products. And Liao et al. (2022) explored low-carbon service supply chains that reduce product carbon emissions.

Scholars have also studied the issue of contract design for low-carbon service supply chains. In examining the cost-sharing decision in low-carbon service supply chains, He et al. (2020) integrated the variable of corporate social responsibility into the research. They not only examined an ESCO but also a service integrator of low-carbon advertising. Shang et al. (2015) argued that issues in the benefits distribution of energy efficiency in embedded low-carbon service programs were a barrier to the rapid development of contracting. Qian and Guo (2014) also studied the design of revenue-sharing contracts between ESCOs and manufacturers and analyzed what revenue-sharing contracts were optimal. In addition, Ouyang and Ju (2017) examined how manufacturers differed in their choice of ESCO partnership models. Ding et al. (2017; 2018) analyzed the behavior of outsourced emission reduction services for coal-fired power plants. Ouyang and Fu (2020) explored how consumers’ low-carbon preference impacted the manufacturer’s choice of ESCOs. Zhang et al. (2020) examined the effect of the revenue-sharing rate on the quality of ESCO’s service. Mao et al. (2022) examined the effect of financing risk in the embedded low-carbon service supply chain. Liao et al. (2022) analyzed an embedded low-carbon service supply chain containing a manufacturer and an ESCO in a certain market context. They explored the issue of contract design with varying ESCO emission reduction efficiency under the information asymmetry between manufacturers and ESCOs.

Risk aversion is a strategy used by an enterprise to voluntarily discontinue from or alter the risk of loss of an action to avert potential risks associated with the action. Thus, in the low-carbon service supply chain, the risk aversion level may cause ESCOs and manufacturers to renounce or terminate the implementation of the supply chain. Das et al. (2022) established a two-stage risk-averse closed-loop supply chain. They noted that a risk-averse approach that incorporated the effects of stochastic outcome variability would provide a more robust performance compared to a risk-neutral approach. Qu and Yang (2015) explored the relationship between risk aversion level and social trust in supply chains. Liu et al. (2018) stated that the risk aversion level could impact channel optimization in supply chains. They also explored the effect of supply chain disruption risks on the channels. Luo et al. (2018) studied repurchase agreements in the supply chain considering the risk aversion level. Gupta and Ivanov (2020) examined the role of the risk aversion level on supply chain decisions in the sharing economy. Zhu et al. (2022) studied green investment solutions in a rice supply chain containing risk-averse growers and risk-neutral suppliers.

Many studies have adopted the MV approach regarding the measurement of risk aversion levels. For instance, Choi (2011) used the MV approach for a two-channel risk-averse supply chain and showed that radio frequency identification could add to the profitability of the supply chain. Using the MV approach, Gan et al. (2011) analyzed multiple risk aversion scenarios and proposed corresponding optimal solutions. Shen et al. (2013) explored suppliers’ risk-averse pricing strategies for price reduction in textile and apparel supply chains. Li et al. (2013) examined the supply chain containing a supplier and multiple retailers and analyzed how returns were made within the supply chain when they were all risk-averse. Wang and He (2018) examined the contractual design issue in a low-carbon service supply chain comprised of a supplier, a manufacturer and a low-carbon service provider. Furthermore, they analyzed the effect of risk aversion levels of the manufacturer and supplier on the contract. Goli et al. (2019) used the MV approach to determine the risk level of the product portfolio. Adopting an MV research framework, Wen and Siqin (2020) explored how risk aversion levels and the uncertainty of product quality might influence optimal decisions on sharing economy platforms. Zang et al. (2022) examined the sharing of external costs between risk-averse suppliers and manufacturers in two-stage supply chains with different power structures. They found that under the MV framework, the supplier and manufacturer who were more risk-averse earned less.

Many scholars have researched carbon policies concerning low-carbon emissions in supply chains. Jin et al. (2014) examined the three most common carbon policies: carbon taxes, strict carbon caps and the CCTM. And their research implications for companies include redesigning the supply chains and selecting different transport modes (truck, rail or water). Toptal et al. (2014) evaluated the role of multiple carbon policies on the optimal supply chain decision. Wang et al. (2017) analyzed the relationship between supply chain decisions and carbon tax policies. Tirkolaee et al. (2020) explored the optimization of supply chain operations by considering factors, such as carbon emissions and customer satisfaction. Xia et al. (2020) explored the effect of consumers’ low-carbon preference on the carbon emissions of supply chains. Golpîra and Javanmardan (2022) focused on optimizing CLSCs in the context of carbon emissions in their research. Another theme in the current literature is carbon trading. Considering the uncertainty of recycling quality, Zhao et al. (2021) investigated the optimal production decision for CLSC in a carbon market. Wei et al. (2021) evaluated the role of carbon trading in renewable energy investment and marketing activities based on an electricity supply chain. Entezaminia et al. (2021) discussed the joint production and carbon trading policies in supply chain systems under trading supervision. Yang et al. (2021) investigated the non-compliant behaviors of CLSC companies in carbon trading. They found that violation penalties, remanufacturing rates, and carbon emissions can affect all members’ decisions in the CLSC network. Kalantari et al. (2022) explored the effect of policies such as carbon trading and carbon tax on closed-loop supply chains in the scenario of inflation. Using the remanufacturing of spring pallets as an example, Haolan et al. (2022) analyzed the effect of carbon price fluctuations on CLSC under demand uncertainty.

Some scholars have examined the effect of the CCTM on supply chains using the Stackelberg game. The Stackelberg game is a simple game where both leaders and followers make decisions to maximize their respective profits (Meng et al., 2021). Adopting the Stackelberg approach, Du et al. (2015) examined the influence of the CCTM on CLSC. Du et al. (2016) addressed the issue of the manufacturer’s joint multi-product pricing when consumers have low-carbon preference. More specifically, they found conditions under which enterprises can maximize their profit in low-carbon production. With consumers’ low-carbon preference and social preference considered, Xia et al. (2018) examined the influence of carbon reduction and CCTM policies on the supply chain led by the manufacturer. Liu M. et al. (2021) developed a Stackelberg model to explore the best scenario for joint manufacturer and retailer emission reduction under the CCTM. And Qu et al. (2021) adopted the Stackelberg approach to analyze how to optimize the supply chain for emission reduction under the CCTM. In addition, Gong and Zhou (2013) analyzed a model to provide enterprises with optimal emissions trading, technology choices and production strategies under the CCTM. Xu et al. (2017) studied supply chains built upon the CCTM, pointing out that carbon price can significantly affect the optimal decision of supply chains. Drawing on the optimized consensus model and the basic allocation scheme from the closed-loop supply chain trading system that considered income and equity, Xu et al. (2021) proposed a theoretical innovation in their research and designed a flexible cap and trade scheme.

In conclusion, the following research gaps can be identified: 1) Studies related to traditional low-carbon service supply chains focus more on the bargaining power of manufacturers and ESCOs. There lack studies on closed-loop supply chains for embedded low-carbon service in an uncertain market, considering factors like supply chain risks, carbon price, carbon allowances, and product recycling. 2) Studies on closed-loop supply chains for recycling and remanufacturing that use the MV approach to measure supply chain risks and incorporate ESCOs are scarce. 3) Few studies consider the role of the CCTM in the decision-making of the closed-loop supply chain for embedded low-carbon service. Therefore, considering demand uncertainty and the risk aversion level of ESCOs and manufacturers, this paper will build a Stackelberg model of a risk-averse closed-loop supply chain for embedded low-carbon service to explore how embedded low-carbon service in supply chains lowers manufacturer’s carbon emission and maintains economic growth. A comparison of the relevant literature reviewed is shown in Table 1.

To explore the role of embedded low-carbon service in supply chains in lowering manufacturer’s carbon emissions and maintaining economic growth, this paper examines a closed-loop supply chain for embedded low-carbon service that includes a manufacturer who is responsible for recycling, production and remanufacturing and an ESCO who provides low-carbon service (shown in Figure 1). And both of them have different risk aversion levels facing market demand uncertainty, consumers’ low-carbon preference and the CCTM. Aligned with Liao et al. (2022), the ESCO ( t ) is not only responsible for emission reduction investments but also offers low-carbon service to the manufacturer ( m ), who is responsible for recycling, production and remanufacturing. And the two parties share the earnings obtained from low-carbon products.

This paper will build a Stackelberg model and construct the expected utility function using the MV approach. The reason for adopting the MV approach is that it can portray the risk aversion level of supply chain participants, which is a risk analysis method widely used in supply chain studies (Zhu et al., 2022). Meanwhile, the market demand in this paper is uncertain and follows a normal distribution. The manufacturer and ESCO will make equilibrium decisions between high returns and low risks.

The Stackelberg approach model is a game between leaders and followers. Since it considers the status and information asymmetries that exist between the participants, which is close to reality, it is widely used in pricing and decision-making in the supply chain (Yang et al., 2021). In the Stackelberg game, the leader has a significant advantage in predicting followers’ reactions and making decisions to maximize profits (Meng et al., 2021). In this paper, the game’s leader is the manufacturer, and the ESCO is the follower. Therefore, the sequence of decision-making is as below: firstly, the manufacturer proposes the revenue-sharing and recycling rates to the ESCO. Then the ESCO decides on the sum of carbon reduction in light of revenue maximization. The methodological framework is shown in Figure 2.

To construct the profit functions for the manufacturer and ESCO, this paper assumes that the model of the closed-loop supply chain for embedded low-carbon service satisfies the following conditions.

1) Both participants in the closed-loop supply chain for embedded low-carbon service are risk-averse. Their risk characteristics are measured by the MV function (Wei and Choi, 2010). The expected utility function is written as E ( U i ( π i ) ) = E ( π i ) − k i V a r ( π i .

Other relevant variables and parameters are described in Table 2.

The sequence of the game in the closed-loop supply chain for embedded low-carbon service is as follows: First, the manufacturer proposes to the ESCO ϕ as well as θ , and then the ESCO makes a decision based on the principle of revenue e maximization. At this point, according to the model variables and parameters given in Section 3.2, the ESCO’s profit is expressed as follows: π t e = 1 − ϕ p X − m e q − 1 2 μ λ 2 (1)

In Equation 1, the first term indicates the earnings allocated to the ESCO from the manufacturer’s sales of low-carbon products; the second term indicates the ESCO’s emission reduction cost; the third term is the fixed cost of the ESCO’s investment in emission reduction technology.

The manufacturer’s profit is expressed below: π m ϕ , θ = ϕ p X − c g e 0 − e q − G − c m q + ∆ − b θ q − 1 2 h θ 2 (2)

In Equation 2, the first term indicates the earnings allocated to the manufacturer from its sales of low-carbon products; the second term is the benefit or cost of the manufacturer’s carbon allowance; the third term refers to the production cost; the fourth term means the cost savings from remanufacturing; the fifth term indicates the total fixed investment cost of recycling.

According to the MV approach, the expected utility functions of the ESCO and the manufacturer are written as below: E U t π t e = E π t e − k t D π t e = 1 − ϕ p − m e a + δ e − k t 1 − ϕ p σ − μ e 2 2 e 0 2 (3) E U m π m ϕ , θ = ϕ p a + δ e − k m ϕ p σ − c g e 0 − e + c m − ∆ − b θ a + δ e + c g G − 1 2 h θ 2 (4)

The equations are solved using inverse operations. Lemma 1 is the result of the equilibrium decision (details in Appendix A).

Lemma 1

The recycling rate, revenue-sharing rate and unit carbon emission reduction for the equilibrium decision are as follows: θ * = b − ∆ μ a + σ k m + δ e 0 2 a m + p δ − δ c m − c g a + δ e 0 + 2 m σ k m A (5) ϕ * = ( δ 2 e 0 4 ( 2 h p δ c g − ( a m + p δ ) ( 2 h m − δ b − ∆ 2 ) + 2 h m ( 2 m σ k m − δ c m ) ) + δ μ e 0 2 ( a ( δ b − ∆ 2 − 3 h m ) + h ( a c g − δ c m + 4 m σ k m ) − h p δ ) − h δ 2 μ c g e 0 3 − 2 h m δ 3 c g e 0 5 + h μ 2 ( σ k m − a ) ) / A p δ 2 e 0 2 (6) e * = a h μ + δ e 0 2 a ( 3 h m − δ ( b − ∆ 2 ) + h δ c m + h c g ( δ e 0 − a ) − h p δ ) − h σ ( μ + 2 m δ e 0 2 ) k m δ A (7) where A = − 2 h μ + δ e 0 2 − 4 h m + δ ( b − ∆ 2 + 2 h c g . Substitute θ * , ϕ * and e * into E U t π t e and E U m π m ϕ , θ , then the expected utility of the ESCO and the manufacturer can be obtained.

Firstly, the impact of k t and k m on the recycling rate of used products, revenue-sharing rate and unit carbon reduction is analyzed. The equilibrium solution shows that the ESCO’s risk aversion level k t has no effect on the three equilibrium decisions, and the impact of the manufacturer’s risk aversion level k m is shown in Figure 3.

Based on Figure 3, as manufacturers become increasingly risk-averse, the recycling rate of used products and unit carbon reduction rise, but the revenue-sharing rate declines. Furthermore, when k m > 0.9 , the recycling rate of used products exceeds 1; when k m < 0.35 , the unit carbon reduction is below 0; when k m < 0.05 , the revenue-sharing rate exceeds 1 that it does not satisfy the equilibrium constraint. When 0.35 < k m < 0.9 , the revenue-sharing rate and the recycling rate of used products are between 0 and 1, and the carbon emission reduction is less than the initial carbon emission but greater than 0, satisfying the equilibrium constraint. Therefore, only when the manufacturers’ risk aversion level is between 0.35 and 0.9 can they choose to form supply chains for embedded low-carbon services by entering into revenue-sharing contracts with ESCOs.

Secondly, the impact of k t and k m on the expected utility of the manufacturer and the ESCO is studied and the results are shown in Figure 4.

According to Figure 4, the manufacturer’s expected utility drops as its risk aversion level rises; when ESCO’s risk aversion level changes, it remains unchanged. When k m > 0.16 , the ESCO’s expected utility diminishes as its risk aversion level ascends. When k m < 0.16 , the ESCO’s expected utility rises as its risk aversion level increases. This advises that the manufacturer’s risk aversion level affects the expected utility of the manufacturer and the ESCO, as well as the ESCO’s risk aversion level. A higher expected utility can be achieved for both parties when the manufacturer has a high risk aversion level and the ESCO has a low risk aversion level.

In addition, the impact of δ on the recycling rate of used products, revenue-sharing rate and unit carbon reduction is studied, and the results are shown in Figure 5.

Based on Figure 5, as consumers’ low-carbon preference goes up, the recycling rate of used products and unit carbon reduction increase, but the revenue-sharing rate goes down. However, when δ > 0.9 , the recycling rate of used products exceeds 1; when δ < 0.35 , the unit carbon reduction is below 0, and the revenue-sharing rate exceeds 1 meaning the equilibrium constraint is not satisfied. Hence, consumers’ low-carbon preference is a vital influencing factor in the manufacturer’s emission reduction. When consumers’ low-carbon preference is high, manufacturers will be more likely to consider emission reduction and seek cooperation with ESCOs for low-carbon service.

Then, the impact of δ and c g on the expected utility of the manufacturer and the ESCO is analyzed. Based on Figure 5, the range of δ is from 0.35 to 1, and the results are shown in Figure 6.

According to Figure 6, the expected utility of both the manufacturer and the ESCO grows when consumers’ low-carbon preference and the carbon price rise, suggesting that higher consumers’ low-carbon preference and a higher carbon price prompt manufacturers to reduce their carbon emissions. Meanwhile, when c g > 10 and δ < 0.9 , the manufacturer’s expected utility is greater than that of the ESCO, with both parties’ expected utility at a relatively high level.

The ESCO’s risk aversion level k t does not affect the manufacturer’s expected utility before and after introducing an embedded ESCO. Thus, it does not cause a change in the value of the manufacturer’s expected utility growth E 0 * . Further reasoning of the relationship between the manufacturer’s risk aversion level k m and E 0 * is shown in Figure 7.

According to Figure 7, when the manufacturer’s risk aversion level rises, its expected utility growth decreases and then increases, and it becomes negative when k m < 0.65 , E 0 * < 0 . In other words, only when the manufacturer has a greater risk aversion level that the introduction of an embedded ESCO can improve the manufacturer’s expected utility and reduce carbon emissions.

After that, the impact of δ and c g on the manufacturer’s expected utility growth is analyzed, with δ ranging from 0.35 to 1. The results are presented in Figure 8.

Based on Figure 8, the manufacturer’s expected utility growth is positively associated with consumers’ low-carbon preference. To be more specific, when δ < 0.48 , the expected utility growth falls and then rises as the carbon price declines. When δ > 0.48 , the expected utility growth rises as the carbon price rises. The reason is that market demand rises with consumers’ low-carbon preference and carbon emission reduction. And consumers’ low-carbon preference certainly affects the amount of carbon emission reduction. When consumers’ low-carbon preference is lower, the rise in market demand is moderate. However, given that the product price remains the same after the introduction of ESCOs, and manufacturers need to share part of the profit with ESCOs, so when δ < 0.55 or δ < 0.7 , c g < 4 , the manufacturer’s expected utility growth may be less than 0 and sees negative growth. This indicates that consumers’ low-carbon preference plays a decisive role in the manufacturer’s expected utility growth. Manufacturers can cooperate with ESCOs for low-carbon emission reduction only when consumers’ low-carbon preference and the carbon price are high so that they can retain their profits.

The results obtained from the analysis of the impact of k t and k m on the total amount of emission reduction of the closed-loop supply chain for embedded low-carbon service are shown in Figure 9.

Based on Figure 9, the ESCO’s risk aversion level doesn’t affect the total amount of emission reduction. However, when the manufacturer’s risk aversion level rises, the total emission reduction increases. When k m < 0.35 , the total emission reduction is less than 0, indicating that introducing an embedded ESCO does not serve the purpose of low-carbon emission reduction. Therefore, the embedded ESCO should not be introduced for low-carbon emission reduction when the manufacturer has a lower risk aversion level.

The results of the impact of δ and c g on the total amount of emission reduction of the closed-loop supply chain for embedded low-carbon service are shown in Figure 10.

According to Figure 10, the total emission reduction rises with the carbon price and consumers’ low-carbon preference. When δ < 0.5 , c g < 6 , the total emission reduction is below 0. When δ > 0.8 , c g > 8 , the total emission reduction will increase rapidly, indicating that total emission reduction is greatly influenced by the carbon price and consumers’ low-carbon preference. However, when consumers’ low-carbon preference is small, embedded low-carbon service may result in negative growth in total emissions reduction.