Cooperative strategies of emission reduction in the 3PL-led supply chain

Abstract

Accepted by: M. Zied Babai

The third-party logistics (3PL) industry has grown rapidly over the past few years, and its emission reduction behaviour is gaining attention. This paper considers a supply chain system composed of a manufacturer, a retailer and a 3PL provider, in which both the manufacturer and the 3PL make the low-carbon investment. 3PL is a leader in the low-carbon supply chain. To promote emission reduction in logistics, the manufacturer and the retailer separately share the logistics emission reduction costs of the 3PL. Through comparing the no-sharing, manufacturer-sharing and retailer-sharing models, we discuss the cost-sharing strategy preference of each participant and analyze the impact on environmental benefit and social welfare. The results show that cost-sharing can effectively improve product demand, which also supports society in obtaining higher benefits. Moreover, the 3PL tends to be shared by the retailer when the low-carbon investment cost of logistics is high and the investment cost of production is low. Both the manufacturer and the retailer prefer the other party to share the cost, but sharing it together can effectively alleviate free-rider behaviour.

1. Introduction

In the face of the global warming crisis caused by massive carbon emissions, governments have introduced a series of regulatory methods (Oukil, 2023). The carbon cap-and-trade mechanisms have been widely implemented. By setting a reasonable quota, this mechanism prompts companies to find effective abatement measures¹. Specifically, a company is penalized if the actual emission level exceeds the quota, otherwise, it can sell the extra quota in the carbon market. The European Commission proposed that Europe would become the first carbon-neutral continent in human history by 2050². To achieve the target, the European Union (EU) reduced the free quota of enterprises to promote their emission reduction efforts. Moreover, the EU encourages enterprises to actively into low-carbon production through the ‘Invest in EU’ programme³. China has established seven carbon trading pilot cities, covering many manufacturing companies (Xu  et al., 2022a,b; Ji  et al., 2023). In addition, Chinese government has announced the goal of achieving the carbon peaking by 2030 and carbon neutrality by 2060⁴. The USA has also committed to reducing emissions by 50% in 2030 compared with 2005 and to achieve net zero emissions by 2050⁵. The tougher carbon regulation has driven enterprises to pay more attention to their impacts on the environment (Ghosh  &  Shah, 2015; Hong  &  Guo, 2019). For example, Nike used organic cotton for its production (Chan  et al., 2020). P&G expanded its renewable energy power procurement scale and reduced 15 million tons of carbon emissions⁶. Meanwhile, many environmentally conscious consumers are concerned about the corporate actions on sustainable development (Liu  et al., 2021a,b; Thuy  et al., 2020), as well as the carbon footprint throughout the production cycles (Gao  &  Souza, 2022), which gives enterprises more incentive to investment in sustainability.

Furthermore, after the development of globalization, the supply chain participants such as manufacturers, retailers and consumers are merged to form a complex supply chain network. To better develop their core business, enterprises have to consider outsourcing logistics-related activities to third-party logistics providers (3PL). Based on 3PL’s experience, enterprises can obtain a wide range of logistics solutions and value-added services (Jiang  et al., 2014; Jazairy  et al., 2017; Yadav  et al., 2020). For instance, in the automotive manufacturing industry, a large number of companies apply 3PL to save on operational costs. The global 3PL market is also expanding rapidly and is occupying an important position in the supply chain. In 2022, the global 3PL market was valued at $1034 million. From 2023 to 2030, its compound annual growth rate is predicted to be 10.7%⁷. However, it is worth noting that the environmental problems in the field of logistics have also become increasingly severe. According to the International Energy Agency, the transport sector contributes 24.6% of global carbon dioxide emissions. The increase in global warming and economic disasters has enforced a larger need for more sustainable logistics services (Demir  et al., 2022).

Nowadays, governments have made some restrictions on carbon emissions in the transportation industry (Centobelli  et al., 2017; Randrianarisoa  &  Gillen, 2021; Baglio  et al., 2022). As shown in Table 1, the EU proposes standards of carbon dioxide emission limitation for light trucks. Other countries also impose strict limits on the carbon emissions for trucking transportation. Besides, The International Maritime Organization formulated a greenhouse gas strategy, which aims to reduce 40% carbon intensity by 2030⁸. Therefore, 3PL has to adopt sustainable practices to reduce carbon emissions. Some companies use low-carbon or carbon-neutralization energy in shipping (Aakko-Saksa  et al., 2023). For example, DHL, a logistics firm, uses sustainable biofuels instead of heavy oil on board container ships⁹. The Maersk also designs a marine battery energy storage system, aiming at improving marine performance¹⁰. But these measures are undoubtedly accompanied by high costs.

Faced with this situation, 3PL actively achieves the balance between economic and environmental performance through cost-sharing contracts (Jiang  et al., 2014; Chu  et al., 2021). For instance, Maersk negotiates with suppliers, such as Levi Strauss & Co., BMW and H&M to invest in sustainable fuels. In addition, Maersk also bargains with large retailers like Amazon and Walmart to determine the optimal delivery time¹¹. DHL cooperated with other participants to reduce 40% of transportation space by using the newly developed packaging algorithm⁵. In fact, it is common for the manufacturer and the retailer to work with 3PL to reduce emissions. For example, Kuehne + Nagel and Lenovo have developed a new logistics service to reduce greenhouse gas emissions¹². With the help of Ekornes, DB SCHenker started operating zero-emission coastal container branch vessels¹³. Hellmann Worldwide Logistics acquired the European storage business from Ledvance¹⁴. By establishing distribution centres in Poland and Spain, Hellmann Logistics service speeds up deliveries and reduces carbon dioxide emissions. However, existing studies, such as Xu  et al.  (2017) and Hong  et al.  (2019), only analyzed the manufacturer’s low-carbon efforts in the production process. They ignored the emission reduction behaviour of 3PL. Therefore, it is significant to consider 3PL in the supply chain and analyze the impact of the cost-sharing contract. 

Motivated by the above observations, we construct a three-tier low-carbon supply chain consisting of a manufacturer, a retailer and a 3PL. Under the carbon regulation, we consider that the manufacturer and the 3PL separately invest in production and logistics. Three supply chain structures are designed, that is, the first is that 3PL makes green investments by himself without cost-sharing (NS), the second is that 3PL cooperates with the manufacturer in green investment, denoted as manufacturer sharing (MS) and the third is that 3PL cooperates with the retailer, denoted as retailer sharing (RS). Furthermore, we discuss how the manufacturer or the retailer bargains with the 3PL to set the optimal cost-sharing proportion. By comparing the optimal decisions and profits under the three models, we aim to answer the following questions:

• (1) How does cost-sharing with 3PL affect carbon emissions reduction decisions?

• (2) What cost-sharing strategies do the supply chain participants prefer to choose? How do the sharing strategies impact environmental performance and social performance?

• (3) How do supply chain participants negotiate the sharing proportion?

The results show that first, sharing 3PL’s low-carbon investment cost can promote logistics emission reduction and product green design. In addition, the two cost-sharing models can make each participant obtain Pareto improvement, and have a positive impact on the environmental benefit, consumer surplus and social welfare. Moreover, the cost-sharing strategy of the 3PL depends not only on his own logistics low-carbon investment cost, but also on the manufacturer’s low-carbon investment cost. Specifically, the manufacturer and the retailer prefer the other side to share, which means that they have free-rider behaviour. Finally, we find that collectively sharing can alleviate free-rider behaviour and improve the overall performance of the supply chain. Therefore, 3PL can actively seek cooperation with other partners to improve low-carbon level. Besides, setting reasonable cost-sharing contract terms can also realize the revenue growth of each member.

The remainder of the paper is organized as follows. The literature review is presented in Section 2. In Section 3, the problem definition and assumptions are described. In Section 4, the equilibrium results are provided. In Section 5, several numerical analyses are presented. Section 6 presents the main conclusions. All mathematical proofs are shown in the Appendix.

2. Literature review

This paper focuses on the abatement decision and cost-sharing strategy with 3PL in the low-carbon supply chain. We also analyze the optimal solutions under different cooperation strategies with Nash bargaining. Therefore, we summarized the literature in three streams: carbon emission reduction decisions in the supply chain, carbon abatement cost-sharing contracts and Nash bargaining in the low-carbon cooperation.

2.1. Carbon emission reduction decisions in the supply chain

In recent years, environmental problems have gradually attracted attention during production and transportation. Previous studies have focused on the optimal emission reduction decisions of the supply chain partners, such as manufacturers and retailers. For example, based on the cap-and-trade regulation and consumers’ low-carbon preferences, Ji  et al.  (2017) studied the carbon abatement decisions of the manufacturer and the retailer. Xu  et al.  (2018) constructed centralized and decentralized supply chain systems and showed the importance of cap-and-trade measures. Li  et al.  (2021a,b) examined the impact of two types of government subsidies on optimal decisions of supply chain partners. They proved that when subsidies were available, both the manufacturer and the retailer tended to collaborate on green marketing. Mishra  et al.  (2021) proposed that sustainable inventory management could lead to higher profits in enterprises’ green investment processes. Rashi  et al.  (2023) investigated the effect of different carbon regulations on reducing carbon emissions in a three-tier supply chain. Fan  et al.  (2023) discussed how price volatility in the carbon trading market influenced the manufacturer’s emissions reduction level.

In addition, some scholars discussed the carbon abatement decisions of 3PL. For example, Chen  &  Wang  (2016) studied the 3PL’s optimal transportation mode under different emission reduction strategies. Considering the carbon emission in logistics and storage, Daryanto  et al.  (2019) established a three-level supply chain and found that the emission in a centralized supply chain was relatively lower. Jamali  &  Rasti-Barzoki  (2019) considered the 3PL’s optimal low-carbon inputs in logistics. Daryanto  &  Wee  (2020) proposed a supply chain inventory model integrated with carbon emissions. Ma  et al.  (2020) studied the impact of 3PL’s preservation effort on reducing the carbon emissions of a tertiary cold chain. Mahmoudi  et al.  (2021) studied the green investment problem of a multichannel supply chain with 3PL participation. Drent  et al.  (2023) compared supply chain carbon emissions under different transportation models of 3PL.

However, the above literature only paid attention to the equilibrium outcomes in the low-carbon supply chain. In contrast, our work also explores the impact of different cooperation models on the emission reduction decisions of the manufacturer and the 3PL.

2.2. Carbon abatement cost-sharing contracts

Cost-sharing is often used as a means to improve overall performance in the supply chain (Yan  &  Zaric, 2016). For example, Ghosh  &  Shah  (2015) proved that sharing the manufacturer’s investment cost of green products could improve the environmental performance of the supply chain. Wang  et al.  (2016) and Xu  et al.  (2017) investigated how abatement cost-sharing contracts benefited supply chain participants. Yang  &  Chen  (2018) and Ma  et al.  (2021) studied the role of cost-sharing contracts in promoting the manufacturer’s emission reduction decisions. Li  et al.  (2019) compared the cost-sharing contract and revenue-sharing contract in the low-carbon supply chain. They found that the cost-sharing contract was more applicable. Li  et al.  (2021a,b) found that when low-carbon efforts were higher, both the manufacturer and the retailer preferred the cost-sharing contract. Heydari  et al.  (2021) analyzed how the green cost-sharing contract and the revenue-sharing contract could reduce product selling prices. Xu  et al.  (2023) examined the performance of the cost-sharing contract when taking into account the consumer ecological consciousness and low-carbon product reputation. The above literature focused on the cost-sharing strategy between the manufacturer and the retailer. Unlike them, our study also considers the cost-sharing contracts in which the 3PL participates.

Besides, many researchers have observed that 3PL has evolved from a service provider to a resource integrator (Jayaram  &  Tan, 2010). For instance, Jiang  et al.  (2016) found that cost-sharing became an effective strategy only when other members had sufficient profit space to compensate for 3PL’s logistics cost. Song  &  He  (2019) studied how 3PL’s preservation cost-sharing contract improved the supply chain performance. Ma  et al.  (2020) gave the conditions to achieve a win–win situation amongst the supplier, the 3PL and the retailer under the cost-sharing contract and revenue-sharing contract. Lou  et al.  (2020) constructed a model where the retailer shared the fixed costs and variable costs of the 3PL service. They found that the sharing model helped to improve the manufacturer’s profit. Rathnasiri  et al.  (2022) proposed a dynamic contract that enabled the integration of the supplier, the retailer and 3PL.

The abovementioned literature concluded that the cost-sharing contract was beneficial to supply chain partners under certain conditions. However, they ignored how to set the cost-sharing term that could be accepted by all participants.

2.3. Nash bargaining in the low-carbon cooperation

Nash bargaining was introduced by Nash  (1950, 1953). He showed that the negotiation model had the following characteristics: first, the distribution of gains resulting from the outcomes of the negotiation; second, the consequences might occur when the negotiation broke down. That theory also satisfied the properties of individual rationality, Pareto optimality and symmetry, and was widely used in contract signing amongst supply chain systems. Many scholars have applied the bargaining model in the cooperation of low-carbon supply chains. For example, Ghosh  &  Shah  (2015), Nie  &  Zhang  (2015), Song  &  Gao  (2018) and Li  et al.  (2019) considered the bargaining between the manufacturer and the retailer. They analyzed the optimal sharing rates under different cooperation strategies. Yang  &  Chen  (2020) studied the impact of negotiation terms on the RFID investment in the supply chain. Adhikari  &  Bisi  (2020) proved that the bargaining between the manufacturer and the retailer led to a higher green quality of product. Qian  et al.  (2020) verified that the Nash bargaining model could benefit both the retailer and the manufacturer. Feng  et al.  (2022) also analyzed the impact of multiunit bilateral negotiation. From the perspective of bargaining, our work is similar to Ghosh  &  Shah  (2015) and Song  &  Gao  (2018).

2.4. Research gap and contribution

The works by Ghosh  &  Shah  (2015) and Jamali  &  Rasti-Barzoki  (2019) are related to our paper and deserve special mention. Specifically, Ghosh  &  Shah  (2015) built a supply chain system consisting of a manufacturer who invested in green production and a retailer. They compared the retailer cost-sharing model and bargaining model. Jamali  &  Rasti-Barzoki  (2019) captured the interaction between a 3PL, two competing manufacturers and a retailer. They explored the optimal pricing and emission reduction decisions under different power structures. Theoretically, we also construct a game model including a 3PL, a manufacturer and a retailer. However, our model differs from them in multiple aspects.

First, regarding the model setting, Ghosh  &  Shah  (2015) assumed that market demand was positively related to the manufacturer's emission reduction effort. On this basis, Jamali  &  Rasti-Barzoki  (2019) described how 3PL's delivery time reduced the consumers' purchase intention. Differently, we assume that the manufacturer’s green level and the 3PL’s logistic abatement effort jointly increase market demand. This is also in line with the processes of low-carbon production and transportation.

Second, regarding the research question, Ghosh  &  Shah  (2015) studied the role of the cost-sharing model and the bargaining model in improving product sustainability. They also explored how the abatement investment influenced the supply chain profits. Jamali  &  Rasti-Barzoki  (2019) investigated the 3PL-led model and manufacturer-led model to achieve green development in the supply chain. In contrast, we focus on how the cost-sharing contracts between the manufacturer, the retailer and the 3PL impact environmental performance and social welfare. We also give the optimal sharing proportion under Nash negotiation.

Third, regarding the conclusion, Ghosh  &  Shah  (2015) showed that the bargaining model could lead to higher product greenness and supply chain profits. Jamali  &  Rasti-Barzoki  (2019) found that when the manufacturer acted as the leader, the supply chain carbon emissions were reduced. Different from their finding, our analysis presents that cost-sharing contracts can achieve Pareto improvement for each partner and increase social benefit.

3. Model setup

3.1. Problem description

This paper considers a make-to-order supply chain composed of a manufacturer, a 3PL and a retailer. The retailer purchases products from the manufacturer at wholesale price |$w$| and sell to the market at the price |$p$|⁠. The manufacturer relies on 3PL for transportation and pays the transportation charges |$t$|⁠. Here both the 3PL and the manufacturer make low-carbon investments, that is logistics emission reduction level |$s$| and the product greenness |$g$|⁠.

To promote the development of low-carbon logistics, this paper considers two low-carbon investment cost-sharing models, i.e. manufacturer sharing and retailer sharing, which are represented by subscripts MS and RS, respectively. The parameter |$\phi$| represents the proportion of 3PL low-carbon investment cost shared by the manufacturer or the retailer under the two cost-sharing models, whereas |$\phi =\mu$| in MS model and |$\phi =\nu$| in RS model. The base model without cost-sharing is represented by subscript NS. The superscripts L, M and R represent the 3PL, the manufacturer and the retailer, respectively.

3.2. Model assumption

To better describe the problem, we consider some assumptions as follows:

(1) We assume that consumers have negative sensitivity to the retail price and positive sensitivity to the green product and low-carbon logistics (Dong  et al., 2016; Jamali  &  Rasti-Barzoki, 2019; Kuiti  et al., 2020). Thus, the demand function can be obtained by the following equation.

where |$\alpha >0$|⁠, |$\beta >0$|⁠, |${\lambda}_1>0$| and |${\lambda}_2>0$|⁠. Besides, consistent with the existing literature (Madani  &  Rasti-Barzoki, 2017; Jamali  &  Rasti-Barzoki, 2019), we assume |$\beta >{\lambda}_1+{\lambda}_2$| that the retail price sensitivity coefficient has a greater effect than the product greenness and logistics carbon reduction level on demand.

(2) Referring to Jamali  &  Rasti-Barzoki  (2019), Kuiti  et al.  (2020) and Yang  et al.  (2017), we assume that the low-carbon investment costs for the manufacturer and the 3PL are quadratic functions, i.e. |$C(g)=\frac{1}{2}{c}_g{g}^2,C(s)=\frac{1}{2}{c}_s{s}^2$|⁠, where |${c}_g$| and |${c}_s$| are the investment cost coefficient of product greenness and low-carbon logistics, respectively.

(3) The total carbon emissions in production are |$\left({e}_0- bg\right)D$|⁠, where |${e}_0$| is the base emission when the product greenness is zero, and |$b$| is the coefficient of product greenness on emission reduction. Regulated by the cap-and-trade regulation, the manufacturer initially receives a free quota of carbon emission |${e}_{cap}$|⁠. Thus, the initial emission cost can be expressed as |$\big({e}_0-{e}_{cap}\big)D{c}_e$|⁠. A similar setting can be found in Dong  et al.  (2016) and Xu  et al.  (2017).

(4) In order to ensure the manufacturer, the 3PL and the retailer are all profitable, we assume that the wholesale price is greater than the total cost of producing a unit of product, i.e. |$w>{C}_M$|⁠, where |${C}_M={c}_M+\big({e}_0-{e}_{cap}\big){c}_e$| represents the sum of production cost and emission cost. Moreover, the transportation charge is greater than its logistics service cost, i.e. |$t>{c}_L$|⁠. The retail price is also greater than its total cost of purchasing the unit of product, i.e. |$p>w+t>{C}_T$|⁠, where |${C}_T={c}_M+{c}_L+\big({e}_0-{e}_{cap}\big){c}_e$| represents the total cost of the supply chain. The notations used in this paper are summarized in Table 2.

4. Model solutions

In this section, we first construct a base model without cost-sharing, and analyze the impact of low-carbon parameters on optimal decisions. Then, we consider two cooperative models of manufacturer sharing and retailer sharing, and obtain the equilibrium solutions under these two models through Nash bargaining. Finally, we further compare the results of the above three models.

Specifically, we consider a game model consisting of a 3PL, a manufacturer and a retailer. The 3PL is the leader, the manufacturer is the sub-leader and the retailer is the follower. The sequence of events is shown in Fig 1. First, if supply chain members cooperate by cost-sharing (i.e., MS model or RS model), they will decide the cost-sharing proportion through Nash bargaining. Second, the 3PL determines the logistics emission reduction level |$s$| and the transportation charge |$t$|⁠. Observing the optimal decisions of the 3PL, the manufacturer decides the product greenness |$g$| and the wholesale price |$w$|⁠. Finally, the retailer declares the retail price |$p$| and sells the product to the market. Like Sabzevar  et al.  (2017), Zhang  et al.  (2021) and Xu  et al.  (2022a,b), the backward induction method is used to obtain the equilibrium solutions.

4.1. Base model

Consider a three-level Stackelberg competition, in which the three parties pursue their own profit maximization. Based on the above problem description, the expected profit functions of the 3PL, the manufacturer, the retailer and the whole supply chain are:

Specifically, the 3PL’s profit includes the profit from providing logistics services and the cost of low-carbon logistics investment. The manufacturer’s profit includes the profit from providing products and the cost of carbon emission reduction and green product investment. The retailer’s profit includes the revenue from selling products and the cost of purchasing products. Using backward induction, we can get the equilibrium solutions in Table 3.

Based on the equilibrium solutions, we further explore the impact of the sensitivity coefficient |${c}_g$| and |${c}_s$| on the optimal decisions.  

(i) If |${\lambda}_1<{\lambda_1}^{\prime }$|⁠, then |$\frac{\partial{w}_{NS}^{\ast }}{\partial{c}_g}>0$|⁠; otherwise, |$\frac{\partial{w}_{NS}^{\ast }}{\partial{c}_g}<0$|⁠.

(ii) If |${\lambda}_1<{\lambda}_1^{{\prime\prime} }$|⁠, then |$\frac{\partial{p}_{NS}^{\ast }}{\partial{c}_g}>0$|⁠; otherwise, |$\frac{\partial{p}_{NS}^{\ast }}{\partial{c}_g}<0$| and |${\lambda_1}^{\prime \prime }<{\lambda_1}^{\prime }$|⁠.

where |${\lambda}_1^{\prime }=\frac{c_eb\left(4\beta{c}_s-{\lambda}_2^2\right)}{4{c}_s}$|⁠, |${\lambda}_1^{{\prime\prime} }=\frac{2\beta{c}_eb\left(\beta{c}_s-{\lambda}_2^2\right)}{6\beta{c}_s+{\lambda}_2^2}$|⁠.

Proposition 1 indicates that when consumers are less sensitive to the product greenness, the optimal wholesale price and the retail price will increase with the cost of green investment. That is, the manufacturer and the retailer prefer to raise the price to offset the relatively high investment cost. However, when consumers are highly sensitive to the greenness of the product, they will lower the product price to increase consumers' willingness to pay, even though the marginal profits may be reduced.

Proposition 1 further shows that when |${\lambda_1}^{\prime \prime }<{\lambda}_1<{\lambda_1}^{\prime }$|⁠, the rise in wholesale price does not inevitably raise the retail price. This is because when the wholesale price increases, the retailer has to pay the cost transferred by the manufacturer and reduce the retail price to mitigate the negative impact of the demand shrinking.

4.2. Cost-sharing model

In order to promote 3PL to further investment in low-carbon logistics, we consider two cost-sharing models: manufacturer sharing (MS model) and retailer sharing (RS model). Under cost-sharing, the manufacturer or the retailer shares the cost of the 3PL’s low-carbon investment in proportion |$\phi$|⁠. Specifically, under the MS model, the manufacturer shares the cost of 3PL’s low-carbon investment in proportion |$\phi$|⁠, where |$\phi =\mu$| and |$\nu =0$|⁠. Therefore, the profit functions of the 3PL and the manufacturer are:

Under the RS model, the retailer shares the cost of 3PL’s low-carbon investment in proportion |$\phi$|⁠, where |$\phi =\nu$| and |$\mu =0$|⁠. Therefore, the profit functions of the 3PL and the retailer are:

Through backward induction, the optimal decisions and expected profits under two cost-sharing models are obtained, which are shown in Table 3.  

The result of Corollary 1 is obvious. In the cost-sharing model, the optimal low-carbon investment decisions of the 3PL and the manufacturer will increase with the sharing proportion. This indicates that sharing 3PL’s low-carbon investment cost will not only improve the environmental performance of the 3PL, but also benefit the manufacturer. The reason is that the increase in the 3PL’s low-carbon investment can effectively increase the demand, which helps the manufacturer obtain more profits to support its investment behaviour and benefit by selling the remaining carbon emission quota.  

(i) When |$\phi =\mu$| and |$\nu =0$|⁠,

① |${\varPi}_{MS}^L\left(\mu \right)>{\varPi}_{MS}^{L\ast }$|⁠, |${\varPi}_{MS}^R\left(\mu \right)>{\varPi}_{MS}^{R\ast }$|⁠.

② If |$0<\mu <\min \left\{{\mu}^{\prime },{\mu}^{{\prime\prime}}\right\}$|⁠, then |${\varPi}_{MS}^M\left(\mu \right)>{\varPi}_{NS}^{M\ast }$|⁠; otherwise, |${\varPi}_{MS}^M\left(\mu \right)<{\varPi}_{NS}^{M\ast }$|⁠.

③ If |$0<\mu <\min \left\{{\mu}^{\prime },{\mu}^{{\prime\prime\prime}}\right\}$|⁠, then |${\varPi}_{MS}^T\left(\mu \right)>{\varPi}_{NS}^{T\ast }$|⁠; otherwise, |${\varPi}_{MS}^T\left(\mu \right)<{\varPi}_{NS}^{T\ast }$|⁠.

(ii) When |$\phi =\nu$| and |$\mu =0$|⁠,

① |${\varPi}_{RS}^L\left(\nu \right)>{\varPi}_{NS}^{L\ast }$|⁠, |${\varPi}_{RS}^M\left(\nu \right)>{\varPi}_{NS}^{M\ast }$|⁠.

② If |$0<\nu <\min \left\{{\nu}^{\prime },{\nu}^{{\prime\prime}}\right\}$|⁠, then |${\varPi}_{RS}^R\left(\nu \right)>{\varPi}_{NS}^{R\ast }$|⁠; otherwise, |${\varPi}_{RS}^R\left(\nu \right)<{\varPi}_{NS}^{R\ast }$|⁠.

③ If |$0<\nu <\min \left\{{\nu}^{\prime },{\nu}^{{\prime\prime\prime}}\right\}$|⁠, then |${\varPi}_{RS}^T\left(\nu \right)>{\varPi}_{NS}^{T\ast }$|⁠; otherwise, |${\varPi}_{RS}^T\left(\nu \right)<{\varPi}_{NS}^{T\ast }$|⁠.

where |${\mu}^{{\prime\prime} }<{\mu}^{{\prime\prime\prime} }$|⁠, |${\nu}^{{\prime\prime} }<{\nu}^{{\prime\prime\prime} }$| and |${\mu}^{{\prime\prime\prime} }={\nu}^{{\prime\prime\prime} }$|⁠. The detailed proof and the value of |${\mu}^{{\prime\prime} }$|⁠, |${\nu}^{{\prime\prime} }$|⁠,|${\mu}^{{\prime\prime\prime} }$| and |${\nu}^{{\prime\prime\prime} }$| are given in Appendix A.4.

Corollary 2 shows that, under the cost-sharing model, no matter what the cost-sharing proportion is, the profits of 3PL and the members will increase. When the sharing proportion is small, the cost-sharing member can also obtain more benefits from the demand expansion effect. Therefore, the cost-sharing strategy can achieve Pareto improvement (as the blue-shaded part shown in Fig. 2). Moreover, the valid cost-sharing region and Pareto region are different under the two sharing models. This is because of the manufacturer’s profit is also affected by its own carbon emission reduction cost. For example, when the investment cost of green products is high, the manufacturer will be more willing to share the investment cost of 3PL, rather than bear the huge cost to improve the greenness of product.

4.3. Cost-sharing through bargaining model

The increase in the sharing proportion can improve the performance of the supply chain when the sharing proportion is exogenous. However, the member who shares the cost may suffer from the loss of their interests and be reluctant to cooperate. Therefore, we further consider the case where the sharing proportion is endogenous. We also discuss how the optimal sharing proportion impacts the cost-sharing strategy preferences of each member. Referring to Ghosh  &  Shah  (2015) and Chen  et al.  (2019), we model the bargaining process and take the members’ profits without cost-sharing as the starting point of negotiation. To simplify the model, we assume that the 3PL and the cost-sharing member have equal bargaining positions. Therefore, the Nash bargaining models are constructed as follows:

By solving the Nash bargaining solutions, we get the following proposition.  

(ii) ① When |${c}_g>{c}_g^{{\prime\prime} }$|⁠, if |${c}_s>{c}_s^{{\prime\prime} }$|⁠, then |${\nu}^{\ast }=0$|⁠;

if |${c}_s<{c}_s^{{\prime\prime} }$|⁠, then |${\nu}^{\ast }=\frac{4{c}_g{c}_s{A}_1^2\left(6\beta{c}_s-{\lambda}_2^2\right)-4{c}_s^2{A}_1^4-{c}_g^2\left(4\beta{c}_s-{\lambda}_2^2\right)\left(8\beta{c}_s-{\lambda}_2^2\right)}{c_s\left[2{c}_s{A}_1^4+\beta{c}_g^2\left(64\beta{c}_s-7{\lambda}_2^2\right)-{c}_g{A}_1^2\left(24\beta{c}_s-{\lambda}_2^2\right)\right]}<{\nu}^{{\prime\prime} }$|⁠.

② When |${c}_g<{c}_g^{{\prime\prime} }$|⁠, if |${c}_s<{c}_s^{{\prime\prime} }$|⁠, then |${\nu}^{\ast }=0$|⁠;

if |${c}_s>{c}_s^{{\prime\prime} }$|⁠, then |${\nu}^{\ast }=\frac{4{c}_g{c}_s{A}_1^2\left(6\beta{c}_s-{\lambda}_2^2\right)-4{c}_s^2{A}_1^4-{c}_g^2\left(4\beta{c}_s-{\lambda}_2^2\right)\left(8\beta{c}_s-{\lambda}_2^2\right)}{c_s\left[2{c}_s{A}_1^4+\beta{c}_g^2\left(64\beta{c}_s-7{\lambda}_2^2\right)-{c}_g{A}_1^2\left(24\beta{c}_s-{\lambda}_2^2\right)\right]}<{\nu}^{{\prime\prime} }$|⁠.

Where |${c}_g^{{\prime\prime} }=\frac{A_1^2}{2\beta }$| and |${c}_s^{{\prime\prime} }=\frac{c_g{\lambda}_2^2}{2\left(2\beta{c}_g-{A}_1^2\right)}$|⁠.

Proposition 2 shows when the sharing proportion is endogenous, all members can realize Pareto improvement through cost-sharing. Interestingly, Proposition 2(ii) shows that the cost shared by the retailer is feasible only when the total low-carbon investment costs of the supply chain are at a medium level. This is because when the total investment cost is low, the willingness of the manufacturer and the 3PL to invest in emission reduction is strong. The retailer can earn profits from the increased demand without sharing the investment cost. On the contrary, when the total investment cost of the supply chain is high, it is difficult to improve the low-carbon level, so the retailer is also unwilling to share the cost.  

(i) Only if |${c}_g<{c}_g^{{\prime\prime} }$| and |${c}_s>{c}_s^{{\prime\prime} }$|⁠, then |${\nu}^{\ast }>{\mu}^{\ast }$|⁠; otherwise |${\mu}^{\ast }>{\nu}^{\ast }$|⁠.

(ii) ① If |${\nu}^{\ast }>{\mu}^{\ast }$|⁠, then |${p}_{RS}^{\ast }>{p}_{MS}^{\ast }>{p}_{NS}^{\ast },{w}_{RS}^{\ast }>{w}_{MS}^{\ast }>{w}_{NS}^{\ast },{t}_{RS}^{\ast }>{t}_{MS}^{\ast }>{t}_{NS}^{\ast },{g}_{RS}^{\ast }>{g}_{MS}^{\ast }>{g}_{NS}^{\ast }$|⁠,|${s}_{RS}^{\ast }>{s}_{MS}^{\ast }>{s}_{NS}^{\ast },{\varPi}_{RS}^{L\ast }>{\varPi}_{MS}^{L\ast }>{\varPi}_{NS}^{L\ast }$|⁠.

② If |${\mu}^{\ast }>{\nu}^{\ast }$|⁠, then |${p}_{MS}^{\ast }>{p}_{RS}^{\ast}\ge{p}_{NS}^{\ast },{w}_{MS}^{\ast }>{w}_{RS}^{\ast}\ge{w}_{NS}^{\ast },{t}_{MS}^{\ast }>{t}_{RS}^{\ast}\ge{t}_{NS}^{\ast },{g}_{MS}^{\ast }>{g}_{RS}^{\ast}\ge{g}_{NS}^{\ast }$|⁠,|${s}_{MS}^{\ast }>{s}_{RS}^{\ast}\ge{s}_{NS}^{\ast },{\varPi}_{MS}^{L\ast }>{\varPi}_{RS}^{L\ast}\ge{\varPi}_{NS}^{L\ast }$|⁠.

Proposition 3 also reveals the relationships between the equilibrium solutions in the three models. The results are similar to those of Corollary 1 where the sharing proportion is exogenous. Specifically, from Corollary 1, we know that a greater sharing proportion can improve the low-carbon degree of the supply chain and the profit of the 3PL. Therefore, the 3PL will choose to cooperate with the members who can share a larger proportion of its costs. According to Proposition 3, when the manufacturer’s low-carbon investment cost is low and the 3PL’s low-carbon investment cost is high, the manufacturer is more inclined to make the low-carbon investment by himself than to share the 3PL’s low-carbon investment cost. Here the 3PL will choose to cooperate with the retailer. Otherwise, it will choose to cooperate with the manufacturer. The preference for the sharing strategy of the 3PL depends not only on its own investment cost but also on the investment cost of the manufacturer. Since the comparisons of the manufacturer’s profits and the retailer’s profits are more complicated, we further choose numerical experiments to discuss.

4.4. Environment, consumer surplus and social welfare

The previous subsection discusses the influence of cost-sharing on enterprises’ decisions and profits. This subsection will focus on the perspective of society to discuss the impact of cost-sharing on consumer surplus, environmental benefit and social welfare.

Referring to common settings in the literature (e.g. Esenduran  et al., 2016; Shen  et al., 2019), we define social welfare as the sum of total profits of the supply chain, consumer surplus and environmental benefit. Besides, consumer surplus is the difference between the actual price of products and consumers’ willingness to pay (see, Panda, 2014):

Here environmental benefit represents the degree of environmental improvement, that is, the total emission reduction in production and transportation:

Therefore, social welfare is:

Furthermore, combined with Table 3, we can get the expressions of consumer surplus, environmental benefit and social welfare under the different models, as shown in Table 4.

Comparing the |$CS$| and |$EB$| under three models, we can obtain the following Corollary.  

Because consumer surplus is related to the level of product demand, and the environmental benefit is related to the product greenness and the logistics emission reduction level of the supply chain, the comparison results are similar to Proposition 3. The results show that the cost-sharing strategy can effectively improve the consumer surplus and environmental benefit. Moreover, the environmental benefit increases with the proportion of cost-sharing. Therefore, the 3PL, as a supply chain coordinator, should actively explore cooperation with supply chain partners.

As the comparison result of social welfare is complicated, we use Fig. 3 for further explanation.

Figure 3 depicts the variation of social welfare in the three models with the low-carbon logistics investment cost |${c}_s$|⁠. Obviously, as the cost coefficient increases, social welfare gradually decreases. This shows that a high investment cost is not conducive to increasing social welfare. Besides, social welfare under the RS model is the largest, because the cost-sharing proportion under the RS model is the highest, which greatly promotes 3PL’s investment. Here the increase in consumer surplus and environmental benefits compensate for the loss of the enterprise interests. Therefore, under the cooperation of cost-sharing, the supply chain system has better social performance.

5. Numerical analysis

This section will show the sharing strategy preference of each member, and consider the impact of simultaneous cost-sharing between the manufacturer and the retailer on the results. Referring to Dong  et al.  (2016) and Jamali  &  Rasti-Barzoki  (2019), the values of relevant parameters are shown in Table 5.

First, we compare the profits of three members under two cost-sharing models to analyze the cost-sharing strategy preferences of each member.

Figure 4 shows that the higher low-carbon investment cost of product greenness |${c}_g$| can increase the willingness of the manufacturer to share the 3PL’s cost. When |${c}_g$| is low enough, the manufacturer is completely unwilling to share the 3PL’s cost, because it can directly obtain the profit by improving the product greenness rather than promoting the logistics emission reduction. Here all members prefer retailer-sharing (i.e. RS, RS, RS). Moreover, according to Proposition 3, when |${c}_g$| is relatively small, the whole supply chain can obtain higher environmental and economic benefits under retailer-sharing. When |${c}_g$| is at a medium level (the blue-shaded part in Fig. 4), the manufacturer and the retailer prefer the other side to share, and this free-riding behaviour will damage the interests of the whole supply chain.

Next, we consider the situation where the manufacturer and the retailer collectively share the 3PL’s low-carbon investment cost. The parameter |${c}_g$| is the cost coefficient of the manufacturer’s greenness investment, and |${c}_s$| is the cost coefficient of 3PL’s low-carbon logistics investment. We first consider the case of |${c}_g=2.5,{c}_s=4$| in Fig. 5(a). Then we investigate how the change of the values of these parameters impacts the Pareto region. First, we keep |${c}_s=4$| unchanged and adjust |${c}_g=3$| in Fig. 5(b). Second, we keep |${c}_g=2.5$| unchanged and adjust |${c}_s=3.5$| in Fig. 5(c). It can be found that |${c}_g$| has a greater impact than |${c}_s$| on the variation of regions. Although the Pareto zone may shrink, the main results are robust.

Combined with Proposition 2, under the single-member sharing model, the maximum sharing proportion of the manufacturer is 0.06 and that of the retailer is 0.25. When the two members share together, the total share proportion can reach 0.57 (⁠|${c}_g=2.5,{c}_s=4$|⁠). This is because jointly sharing can avoid the free-riding behaviour of the manufacturer and the retailer, so that the supply chain’s profit can be reasonably allocated. Moreover, the increase in total cost-sharing proportion can promote the 3PL to improve its low-carbon investment and enable the supply chain to obtain higher environmental benefit.

6. Conclusion

6.1. Theoretical contributions

This paper considers a low-carbon supply chain composed of a manufacturer, a 3PL and a retailer, and studies the cost-sharing strategy of 3PL’s low-carbon investment. By comparing the equilibrium outcomes under the non-sharing (model NS), manufacturer sharing (MS model) and retailer sharing (RS model), we have the following findings.

First, Jamali  &  Rasti-Barzoki  (2019) found that collaboration amongst supply chain players may reduce sustainability. However, our research shows cost-sharing strategy can improve the environmental performance.

Second, the cost-sharing strategy of the 3PL depends on its low-carbon investment cost and the manufacturer’s low-carbon investment cost. Specifically, the 3PL prefers to cooperate with the members who can share a larger proportion. Here the larger cost-sharing proportion can improve environmental benefit, consumer surplus and social welfare.

Third, like Liu  et al.  (2022), we find that the manufacturer and the retailer have free-rider behaviour, that is they prefer the other party to share the cost of the 3PL. Moreover, in line with Ghosh  &  Shah  (2015) and Wang  et al.  (2016), we discover that cost-sharing between the manufacturer and the retailer will be more conducive to enhancing economic benefit.

Our study provides solutions to the three questions, which are posed in the introduction. First, it can be observed that in the cost-sharing model, the optimal carbon abatement decisions of 3PL and manufacturer gradually increase with the sharing ratio. Therefore, the cost-sharing contract improves the low-carbon level of the supply chain. Second, the cost-sharing strategy is effective only when the costs of supply chain members are moderate. In addition, through numerical experiments, we find that the cost-sharing strategy can also improve the performance of society.

6.2. Managerial implications

Based on the above analysis, this section puts forward the following managerial insights.

First, under the cost-sharing model, the low-carbon investment decisions of the 3PL and the manufacturer will increase with the sharing proportion. Therefore, the manufacturer can consider bargaining with 3PL to improve the product greenness and reduce carbon emissions.

Second, the cost-sharing contract signed by 3PL with the retailer or the manufacturer may increase the efficiency of the supply chain, but reduce the profit of one member. In order to ensure the active participation of each partner, 3PL can seek more forms of cooperation, such as revenue sharing and other contract terms, to achieve a fair distribution of the supply chain profits.

Third, the joint participation of supply chain members in sharing the 3PL’s cost may be the best option. The government can intervene in 3PL to cooperate with the manufacturer and the retailer and improve economic and social benefits.

6.3. Future directions

Although this paper contributes to the literature on low-carbon logistics investment with cost-sharing, there are still some limitations. We assume that the market demand is deterministic. However, the supply chain will face the risk of uncertain demand for various reasons. Furthermore, price fluctuations in the carbon market will also impact the optimal abatement decisions and expected profits of supply chain members. Therefore, future research can discuss the impact of uncertain carbon trading prices on contract selection. Other cooperation strategies such as direct investment and revenue sharing can also be taken into account in the 3PL-led supply chain. In addition, the effects of information asymmetry and members’ behaviour preferences, such as risk aversion, fairness concerns and altruistic preferences, can be also considered to further verify and supplement the existing theoretical results.

Funding

This research is supported by Major Program of the National Social Science Foundation of China (Grant No. 21&ZD102).

Data availability

No new data were generated or analyzed in support of this research.

Footnotes

References