Carbon Emission Reduction Decision-Making in an Online Freight Platform Service Supply Chain Under Carbon Trading Mechanism

Abstract

Promoting carbon emission reduction in road freight transportation is important to achieve low-carbon development. The carbon trading mechanism is an effective market mechanism to promote carbon emission reduction. The digital and networked features of the online freight platform (OFP) service supply chain (SSC) not only help the platform reduce carbon emissions but also facilitate the government’s achievement of efficient and economic supervision of carbon emissions. Therefore, this paper proposes two types of carbon trading mechanism based on the OFP SSC to investigate the carbon emission reduction decision of the OFP, namely an absolute emission cap-based allocation (AC) model and an intensity-based allocation (IC) model. By using game theory, we then analyze the optimal solutions of the OFP SSC under the non-participation in carbon trading market (NC model), the AC model, and the IC model. By comparing these decisions, we explore the impact of the carbon trading mechanism on the OFP SSC. Results show the following: (1) Carbon trading mechanisms reduce OFP emissions, particularly under IC models with high free allowances. (2) High initial allowances and low service costs under the carbon trading mechanism enhance the OFP’s profit. (3) The carbon trading mechanism can reduce the carbon emissions of the road freight sector when initial allowances are sufficient or the off-platform trucker’s carbon emission coefficient is low. The study concludes that the IC model optimizes emission cuts while maintaining platform profitability. From a managerial perspective, the government should adopt dynamic allowance policies and incentivize the OFP’s participation through data integration. OFPs must balance network growth with low-carbon technology adoption to align commercial and environmental objectives.

1. Introduction

The Global Carbon Budget 2024 reported that global CO₂ emissions reached 41.6 billion tons in 2024, marking a 0.8% increase compared to 2023. With the continuous increase in CO₂ emissions, the risk of natural disasters such as rising sea levels, forest fires, and water scarcity are escalating in certain regions. To achieve the long-term temperature goal of the Paris Agreement, numerous countries, including China, the United States (U.S.), and the European Union (EU), have proposed carbon emission reduction targets and implemented a series of policies and measures. In September 2020, the Chinese government announced a powerful and visible “dual carbon” goal: striving to reach “carbon peaking by 2030 and carbon neutrality by 2060.” The ”dual carbon” goal highlights China’s resolve and strength in cutting emissions [1]. Cap-and-trade regulation is recognized as one of the most effective market-based mechanisms for curbing carbon emissions [2,3,4,5,6]. According to the EU carbon markets in 2024, emissions from power generation and heat supply decreased by 24% in 2023 compared to 2022. China’s Ministry of Ecology and Environment has stated that the development of the carbon trading market has led to an 8.78% cumulative reduction in the power sector’s carbon emission intensity. Under cap-and-trade regulation, firms are set mandatory limits, implemented either as aggregate carbon emission caps or carbon intensity limits (CO₂ per unit production) [7,8]. Free emission credits are allocated to the firms, and the firms can trade these emission credits with each other in the carbon trading market [9].

According to Statista data, global transportation CO₂ emissions increased by nearly 4% year-on-year in 2023, reaching 8.24 billion metric tons. What is more, road vehicles are the biggest contributors to transportation CO₂ emissions by far, accounting for 75% of the sector’s total carbon pollution in 2023. Thus, curbing the CO₂ emissions of the road freight sector (RFS) is essential for achieving the long-term temperature goal. Some scholars consider that China’s carbon trading mechanism can influence emission reductions in the transport industry [1,10]. While cap-and-trade regulation has been widely adopted in various sectors to mitigate carbon emissions, the RFS has yet to integrate this market-based mechanism into its decarbonization strategies. The road freight market comprises a large number of entities, predominantly small-scale individual truckers. This results in significant challenges for the RFS to directly participate in the carbon trading market. Key barriers include difficulties in data collection, emissions measurement, standardization, and high regulatory costs.

With the development of the Internet of Things and big data technologies, platform-based business concepts disrupt the road freight market, and the Online Freight Platforms (OFPs) gradually emerge in the RFS [11]. OFPs break traditional “shipper–individual trucker” direct connections and effectively integrate upstream shippers with downstream truckers. This integration forms an OFP service supply chain (SSC). Within the OFP SSC, the OFP does not directly provide transportation service to shippers but mainly exchanges information between shippers and truckers to make a feasible resource allocation. In order to improve the matching rate, the OFP intends to attract as many shippers as possible, as well as truckers, via the network effects. OFPs provide professional matching services by aggregating the scattered transportation capabilities of individual truck drivers and have integrated more than 20% of the truck drivers in China [12]. Moreover, the vehicle–cargo matching service provided by OFPs can reduce the carbon emissions of truck drivers [13,14]. As a hub of the service supply chain, OFPs optimize resource allocation via global data analytics and systematically lower carbon emissions in the RFS by minimizing ineffective transportation. Data from Full Truck Alliance (China’s largest OFP) indicates that each ton-kilometer of transport turnover by platform truckers reduces carbon emissions by 0.01 kg. What’s more, the vast number of truckers in the OFP provides economies of scale for adopting low-carbon technologies. For example, autonomous driving technology can significantly mitigate RFS carbon emissions. On 24 May 2023, Convoy (a leading digital freight platform) announced a partnership with Volvo Autonomous Solutions (V.A.S.). Similarly, Full Truck Alliance and Plus.ai showcased SAE Level 4 autonomous heavy trucks at the 2024 China International Big Data Industry Expo, demonstrating their collaboration in autonomous driving innovation.

In the road transport sector, vehicles are the main source of carbon emissions. However, the mobility of large-scale vehicle fleets makes it challenging for governments to monitor their emissions effectively. With the support of the OFP SSC, the government can achieve more efficient and cost-effective indirect monitoring of vehicle-related carbon emissions. For example, data from Full Truck Alliance indicates that carbon emission monitoring coverage in China’s Jiangsu Province increased from 31% in 2019 to 78% in 2023. Additionally, Convoy’s participation in the SmartWay program demonstrates a commitment to standardized data collection and reporting aligned with the Environmental Protection Agency’s (EPA) methodology. Hence, this paper proposes a carbon trading mechanism based on an OFP SSC to reduce the carbon emissions of the RFS. Under the carbon trading mechanism, the OFP serves as the authorized carbon trading entity by collecting, verifying, and aggregating carbon emission data from truckers. The Government allocates carbon allowances to the OFP, and the OFP participates directly in carbon trading. The carbon trading mechanism is specifically shown in Figure 1.

Under cap-and-trade regulation, the number of carbon allowances allocated by the government affects a firm’s carbon trading revenue. To enhance firms’ motivation for carbon emission reduction, it is necessary for the government to adopt an appropriate carbon allowance allocation (CAA) method. During the 15th Five-Year Plan period, China will implement a dual carbon control system that primarily adopts intensity-based regulation with absolute emission caps as a supplementary measure. Different from the absolute emission cap-based CAA method, Li et al. (2020) propose an intensity-based CAA method from a vehicle perspective and demonstrate the feasibility in the road transportation sector [15]. For the RFS, selecting between absolute cap-based and intensity-based CAA methods requires meticulous evaluation.

Existing research has not paid much attention to the carbon trading mechanisms integrating OFP SSCs and optimal CAA methods. In this paper, we aim to fill this research gap. Specifically, our research aims to answer the following questions. First, does the implementation of a carbon trading mechanism based on an OFP SSC significantly improve the carbon emission mitigation performance of the RFS? Second, does participation in the carbon trading mechanism generate significant profit enhancement for the OFP? Last, what CAA method can simultaneously mitigate carbon emissions in the RFS while enhancing platform profitability?

To address the above questions, we develop a carbon trading model based on an OFP SSC that includes a carbon trading market, an OFP SSC, and government. As a benchmark, we first analyze the decisions of the platform under the scenario of non-participation in the carbon trading market (NC model). Subsequently, under the carbon trading mechanism, we examine the decisions of the platform under the absolute emission cap-based CAA method (AC model) and the intensity-based CAA method (IC model) respectively. After that, we compare the carbon emission reduction decisions and profit of the platform under these models and further analyze the interaction between the AC model and IC model. Finally, we explore how to choose the appropriate CAA method to achieve the carbon emission reduction of the RFS.

This paper makes three major contributions. First, some previous literature mainly focuses on platform service supply chains (SSCs) of e-commerce, digital, and on-demand platforms. This paper further explores the platform SSC of online freight platforms (OFPs) within the road freight sector (RFS). It highlights how the operational management of an OFP SSC can contribute to carbon emission reduction in the RFS, filling a gap in the research on the environmental impact of OFP SSCs. Second, previous studies predominantly examine carbon trading in the manufacturing sector. This paper investigates the impact of the carbon trading mechanism on the RFS. What’s more, the study theoretically advances a carbon emissions reduction strategy in platform-mediated logistics by conceptualizing the OFP as a dual intermediary. OFPs connect fragmented transportation resources with the carbon market and enable data-driven coordination, representing a key innovation for promoting the low-carbon transition of the RFS. Last, this paper considers both the pricing decisions and low-carbon technology adoption of OFPs under a carbon trading framework. Furthermore, it introduces an intensity-based carbon allowance allocation (CAA) method in line with China’s dual carbon control system. By comparing two CAA methods, it provides insights for the government to choose an appropriate CAA method.

The remainder of this study is organized as follows. Section 2 reviews the related literature. We present the model setup in Section 3. In Section 4, we analyze the equilibrium decisions of the platform under three different scenarios. We then examine the effect of the carbon trading market in Section 5. In Section 6, we conduct numerical experiments to verify the propositions of Section 5. In Section 7, the main conclusions of this study and future research are proposed. All of the proofs are relegated to Appendix A.

2. Literature Review

This paper focuses on the adoption of the carbon trading model based on an OFP for the carbon emission reduction problem in road freight. The literature that is closely related to this paper focuses on four aspects: platform service supply chain, carbon emission reduction decisions under cap-and-trade regulation, green operation management of OFPs, and the carbon allowance allocation method.

2.1. Platform Service Supply Chain

Within a platform service supply chain, the platform does not have the products or services that it directly provides to its customers but mainly exchanges information [16]. Many studies on platform service supply chains mainly focus on the e-commerce retailing platform, especially online retailing platforms [17].

From the economic perspective, operational and strategic decisions of e-commerce retailing platforms, including channel encroachment [16,18,19], pricing [20,21,22], and logistics [23,24] are the main types of research questions. For the digital platform, Peng et al. (2023) constructed a PSSC network equilibrium model and found that enhanced service innovation capabilities significantly facilitate value creation processes among participants in PSSCs [25]. Bai et al. (2021) explored blockchain platform selection and adoption decision making in PSSCs [26]. Avinadav et al. (2022) focused on the value of information-sharing and found that the platform benefits from information-sharing [27]. With the development of diversification and customization of customer demands, on-demand service platforms have become the focus of scholars’ research. He et al. (2021) conducted a theoretical analysis of on-demand ride-hailing platforms (e.g., Didi, Uber), investigating how customers’ private information regarding horizontal preferences (such as service flexibility) and temporal preferences (such as delay sensitivity) influences platform operations [28].

From the social responsibility perspective, Kong et al. (2021) proposed an online double auction for on-demand pickup and delivery in order to maximize the social welfare and minimize transaction failures [29]. Li et al. (2021) confirmed that a time-based penalty fee is likely to maximize social welfare for car-hailing platforms [30]. Liu et al. (2021) explored how the government can regulate the big data discriminatory pricing behavior in PSSCs [31].

The above-mentioned literatures about PSSCs rarely consider the impact of OFP SSCs on the carbon emission reduction of the RFS. However, as we stated in the introduction, the digital and networked nature of the OFP SSC provides it with the ability to optimize globally and regulate accurately. Based on this, the OFP SSC integrates decentralized drivers into a unified management system and achieves bottom-up emission reduction behavior guidance through technical tools and rule design. Therefore, this paper makes a contribution by considering the impact of OFP SSCs on the carbon emission reduction of the RFS.

2.2. Carbon Emission Reduction Decision Under Cap-and-Trade Regulation

According to the carbon emission reduction decision literature, the carbon emission reduction decision is mainly affected by cap-and-trade regulation. Many early studies on carbon emission reduction decisions under cap-and-trade regulation mainly focus on carbon emission reduction strategies of manufacturers [32,33,34,35,36,37]. Because the manufacturing sector typically faces more carbon emission constraints, some studies further discuss the carbon emission reduction decisions of supply chains [38,39,40,41,42]. Moreover, consumers’ low-carbon preferences also affect the carbon emission reduction decisions of members in the supply chain [43,44,45,46].

In addition to the manufacturing sector, the transport sector is also one of the major contributors to carbon emissions. However, several scholars attempted to incorporate cap-and-trade regulations into the freight operations decisions. Routing optimization is one of the effective approaches for carbon emission reduction, and some scholars pay attention to the routing problem under cap-and-trade regulation. Li et al. (2015) focused on the truck routing problem, considering the load and speed of the vehicle among other factors [47]. Liao et al. (2019) studied the electric vehicles routing problem, considering carbon trading and exploring the impact of adopting electric vehicles on the cost and environment of logistics enterprises [48]. Liu et al. (2020) further considered the vehicle routing problem in cold chain logistics and examined a joint distribution model [49]. Islam et al. (2021) studied the mixed fleet-based green clustered logistics problem [50]. Xiao and Gao (2024) examined a multi-visit vehicle routing problem with a truck–drone collaborative delivery model [51]. The application of new energy trucks is seen as another effective approach to reduce carbon emissions. Yang et al. (2024) found that cap-and-trade mechanisms with purchase subsidies benefit the adoption and emission reduction of electric commercial vehicles [52].

The above-mentioned literature about the freight sector rarely considers the impact of the digital platform on the carbon trading market and carbon emission reduction efficiencies in the freight sector. However, as we stated in the introduction, there certainly exists a potential for carbon emission reduction in the OFPs. The OFP is not only an important participating entity of the RFS but also the intermediary platform that can effectively connect numerous truck drivers and the carbon trading market. Therefore, this paper makes a contribution by considering a carbon trading mechanism with an OFP to implement carbon trading.

2.3. Green Operations Management of OFPs

Many studies on OFPs mainly focus on price decisions [53,54,55], routing problems [56,57], and platform matching efficiency [58,59,60,61,62,63]. In addition to the above-mentioned themes, Atasoy et al. (2020) proposed dynamic pricing and incentive creation approaches to OFPs [64]. Deng et al. (2023) discussed the behavioral strategies among freight transportation participants from a sustainability perspective [65]. Yang et al. (2024) explored the implications of transportation services provided by OFPs for the logistics outsourcing strategy of manufacturers [66].

However, studies on the operations decisions of OFPs that consider green development are limited. Kwak et al. (2020) explored the factors affecting participants’ intentions to use green logistics platforms through empirical study, which is beneficial for the green development of OFPs [67]. Mei et al. (2021) investigated the optimal dispatching time and pricing level of an OFP, considering uncertain demand and carbon emission constraints [68]. Jiang et al. (2022) examined a dynamic benefit distribution optimization model to discuss the profit allocation problem of shippers under a carbon trading background [69].

The above-mentioned literature about the operations management of OFPs rarely considers the impact of the carbon trading market on the incentives for OFPs to implement low-carbon technology. However, as we stated in the introduction, the scale advantage of OFPs makes them more willing to implement low-carbon technology. Therefore, this paper makes a contribution by considering pricing decisions and the decision of low-carbon technology adoption simultaneously during the progress of operations management of OFPs under the carbon trading mechanism proposed in the introduction.

2.4. Carbon Allowance Allocation Methods

In the early carbon allowance allocation methods literature, fairness principle-based methods and efficiency principle-based methods are the main relevant research directions. With the rapid development of the ETS, more literature focuses on exploring comprehensive allocation methods, considering fairness and efficiency simultaneously [69,70,71,72,73,74].

Li and Tang (2017) provided several suggestions for initial allowance allocation models in the transport sector [75]. Han et al. (2017) sought to design a scientific and effective carbon allowance allocation method under the ETS in the Chinese road transport sector [76]. Li et al. (2020) proposed a novel approach from the perspective of the carbon emission intensity of vehicles [15]. Bai et al. (2023) constructed allocation models of transport carbon allowance from three perspectives in China’s top 10 economic regions and compared the allocative efficiency and the differences in regional abatement costs of three different transport allocation methods [77].

The above-mentioned literature about the carbon allowance allocation methods rarely considers the specificity of the RFS. However, as we stated in the introduction, decentralization of participating entities in the RFS makes it more difficult for the government to directly monitor the carbon emissions from vehicles. As a typically DP, an OFP can efficiently and economically monitor the carbon emissions and is seen as an effective tool for government to indirectly monitor the carbon emissions from vehicles. Referring to the concept of carbon emission intensity of vehicles [15], this paper makes a contribution by proposing the concept of carbon emission intensity of OFPs to make calculating the carbon emissions in the RFS easier.

This paper differs from the previous literature in three ways. First, the previous literature on platform service supply chains mainly focused on the e-commerce retailing platform, digital platform, and on-demand platform. Many scholars study the operation and strategic decisions from an economic perspective and a social responsibility perspective. As a living force in the RFS, the operation management of OFP SSCs is conducive to reducing the carbon emissions of the platform, thus realizing carbon emission reduction in the RFS. Therefore, this paper makes a contribution by considering the impact of OFP SSCs on the carbon emission reduction of the RFS. Second, although there is extensive research in the field of carbon emission reduction decisions under the carbon trading background, it mainly focuses on the manufacturing sector. As explained earlier, the OFP is not only an important participating entity of the RFS but also the intermediary platform that can effectively connect numerous truck drivers and the carbon trading market. Hence, this paper differs from the literature by further considering the impact of the OFP on carbon emission reduction under cap-and-trade regulation. Third, the previous literature on green operations management of OFPs rarely considers the adoption of low-carbon technology. Some empirical studies verify that the carbon trading mechanism can incentivize the innovation and adoption of low-carbon technologies [78,79,80,81]. Hence, this paper differs from the literature by considering the pricing decision and the decision of low-carbon technology adoption of an OFP simultaneously under the carbon trading mechanism. Last, the previous literature on carbon allowance allocation methods mainly focused on the equitable scheme, efficient scheme, and comprehensive scheme from the perspective of total carbon emissions. During the 15th Five-Year Plan period, China will implement a dual carbon control system that primarily adopts intensity-based regulation with absolute emission caps as a supplementary measure. Based on this, this paper further proposes an intensity-based carbon allowance allocation method and compares the roles played by the two methods in carbon emission reduction.

3. The Model and Benchmark

3.1. Model Description

In this paper, we build a carbon trading model that includes a carbon trading market, an OFP SSC, and government. There is only an OFP (labeled P) which provides a freight matching service for shippers (labeled S) and truckers (labeled T) in the road freight market. The OFP employs a subscription-based membership model and only imposes membership fees on shippers at a price of $p_S$. In practice, Full Truck Alliance provides a freight listing service for shippers by charging membership fees for posting orders on the platform. Flexport provides different levels of Flexport+ membership service for shippers and charges corresponding membership fees. We assume that the unit service cost of platform is $c_P$ and the probability of successful two-sided user transactions is $\lambda$, $0<\lambda <1$. The default number of transactions is 1. The average freight fee of freight order is $p_0$. Due to the bilateral market characteristics of the OFP, we assume that each shipper (trucker) receives a benefit, $B_i$, $i=S,T$, from making an interaction with the truckers (shippers) on the “opposite” side [82]. Such a benefit is, in fact, an indirect network externality. Parameters $B_S$ and $B_T$ represent the strengths of network externality in different directions across the platform and are assumed to be exogenous. $n_S$ and $n_T$ represent the number of shippers and truckers on the platform, respectively. Compared with the traditional offline matching mode, a new mode based on the OFP improves the efficiency of vehicle–cargo matching and decreases the communication cost. Hence, shippers and truckers can obtain the basic utility, $V_S$ and $V_T$, respectively, when joining the platform. After buying the road freight service, shippers obtain utility, $V_0$. In addition, $t_S$ represents the unit conversion cost of the shipper that is solely attributable to the platform, and $t_T$ represents the unit conversion cost of the trucker that is solely attributable to the platform [54]. $U_S$ and $U_T$ indicate the utility obtained by the shipper and trucker, respectively.

We can obtain the utility of the shipper and the utility of trucker as

$$U_S=V_S+V_0+B_S{n}_T-p_0\lambda n_T-p_S-t_S{n}_S.$$

(1)

$$U_T=V_T+B_T{n}_S+p_0\lambda n_S-t_T{n}_T.$$

(2)

On the right-hand side of (1), the third term denotes the network externality utility from truckers. The fourth term denotes the road freight fee. The last term denotes the conversion cost of the shipper to join the platform.

On the right-hand side of (2), the third term denotes the network externality utility from shippers. The fourth term denotes the road freight fee. The last term denotes the conversion cost of the trucker to join the platform.

We assume that both shippers and truckers act as rational economic agents and will only participate in the platform if their expected utility is non-negative. At equilibrium, we consider the marginal shipper and marginal trucker to be indifferent between participating and not participating, i.e., their utility is zero. This is consistent with standard practice in two-sided market entry models. The number of shippers and truckers available for the platform is given by

$$n_S={\displaystyle \frac{\left(B_S-p_0\lambda \right)V_T+t_T(V_S+V_0-p_S)}{t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right)}}.$$

(3)

$$n_T={\displaystyle \frac{t_S{V}_T+\left(B_T+p_0\lambda \right)(V_S+V_0-p_S)}{t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right)}}.$$

(4)

The average carbon emissions of per trucker are $e_0$, $e_0>0$. The amount of carbon emissions from the platform is represented by $E_P$. By providing vehicle–cargo matching services, the platform reduces the driver empty-running rates, thereby reducing the carbon emissions generated in the transport process. As a result, the actual average carbon emissions per trucker before joining the platform are $\delta e_0$, $\delta >1$. The number of truckers in the RFS is denoted as $N_T$, and $E_F$ denotes the total carbon emissions in the RFS, and $E_F=\delta e_0{(N}_T-n_T)+E_P$, $N_T\ge n_T$. At the same time, under the carbon trading mechanism, as the platform undertakes the collection of carbon emission data, the unit service cost is recorded as $\gamma c_P$; $\gamma$ represents unit service cost coefficient under the carbon trading mechanism, $\gamma >1$. The implementation of low-carbon technology can reduce the carbon emissions of truckers, and we assume that the carbon emission reduction rate per unit trucker is $w$, $0\le w<1$. Referring to Chen et al. (2021) [83], the cost of carbon emission reduction is a one-time input, in line with the law of the diminishing marginal effect: with the gradual increase in carbon emission reduction investment, carbon emission reduction per unit investment decreases. The investment cost of low-carbon technology is $C\left(w\right)=k{w}^2/2$; $k$ represents carbon emission reduction cost coefficient [84]. The total amount of carbon emissions is determined based on the carbon emission reduction target, and then the carbon allowance is allocated to OFPs for free [84]. We assume that the price of per unit carbon emission allowance is $P_C$, $P_C>0$. Under the absolute emission cap-based CAA method, the free initial carbon allowance allocated by government is $E$. Under the intensity-based CAA method, the intensity of free initial carbon allowance allocated by government is $e$. ${\mathsf{\Pi }}_P$ represents the profit of the platform.

In order to better explain, the pricing and carbon emission reduction strategy of the OFP SSC under three models (NC model, AC model, and IC model) is shown in Figure 2. The key notations in this paper are listed in

Table 1. Main variables and parameters.

Decision Variables
$p_S$	The membership fee of shipper
$w$	The carbon emission reduction rate per trucker
Other Parameters
$P_C$	The price of per unit carbon emission allowance
$p_0$	The average freight fee of freight order
$B_s$	The indirect network externality of shipper
$B_T$	The indirect network externality of trucker
$\lambda$	The probability of successful two-sided user transactions
$c_p$	The unit service cost of OFP without carbon trading mechanism
$\gamma$	The unit service cost coefficient of OFP under carbon trading mechanism
$n_S$	The number of shippers in OFP
$n_T$	The number of truckers in OFP
$N_T$	The number of truckers in RFS
$V_S$	The basic utility obtained by shipper from joining OFP
$V_T$	The basic utility obtained by trucker from joining OFP
$V_0$	The utility obtained by shipper after buying services
$t_S$	The unit conversion cost of shipper
$t_T$	The unit conversion cost of trucker
$e_0$	The average carbon emissions per trucker in OFP
$\delta$	The unit carbon emissions coefficient per trucker off OFP
$E_P$	The amount of carbon emissions of OFP
$E_F$	The amount of carbon emissions of RFS
$C\left(w\right)$	The investment cost of low-carbon technology
E	The free initial carbon allowance under AC model
e	The free initial carbon allowance under IC model
${\mathsf{\Pi }}_P$	The OFP’s profit

, respectively.

3.2. Non-Participation in Carbon Trading Market (NC Model)

To establish a benchmark, we first study the scenario in which the platform has no access to participate in the carbon trading market. Because only enterprises in the electricity sector are eligible by the government to buy or sell carbon allowance in China, this scenario is practical. The platform sets the membership fee $p_S$ for shippers and determines the level of carbon emission reduction $w$. Shippers and truckers in the RFS decide whether to join the platform. After that, the amount of carbon emissions and the membership fee revenue of the platform are collected. Finally, the amount of carbon emissions in the RFS and the profit of the platform are available. See Figure 3 for an illustration.

The OFP decides membership fee $p_S$ and level of carbon emission reduction $w$ to maximize its profit:

$${\mathsf{\Pi }}_P=p_S{n}_S-c_P(n_S+n_T)-C\left(w\right).$$

(5)

In (5), the first term denotes membership fee revenue. The second term denotes operation management cost. The last term denotes low-carbon technology investment cost.

Substituting (3) and (4) into (5), we then can obtain the optimal membership price ${p_S}^{\mathrm{*}}$ and the optimal carbon emission reduction rate $w^{\mathrm{*}}$ under the NC model. Subsequently, substituting ${p_S}^{\mathrm{*}}$ and $w^{\mathrm{*}}$ into (3) and (4), we can obtain the optimal carbon emissions of the OFP ${E_P}^{\mathrm{*}}$ and the optimal carbon emissions of the RFS ${E_F}^{\mathrm{*}}$. Then, we can obtain the following proposition:

Proposition 1.

Under the NC model, there exists a unique optimal solution ${p_S}^{*}, w^{*}$, and the detailed optimal solutions are shown in

Table 2. The detailed optimal solutions under the NC model.

Symbol	Detailed Optimal Solution
${p_S}^{*}$	${\displaystyle \frac{\left(B_S-p_0\lambda \right)V_T+\left(B_T+p_0\lambda +t_T\right)c_P+t_T(V_S+V_0)}{2t_T}}$
$w^{*}$	$0$
${E_P}^{*}$	${\displaystyle \frac{(t_T{t}_S+A)V_T{e}_0+\left(B_T+p_0\lambda \right)\left[t_T\right(V_S+V_0)+\left(B_T+p_0\lambda +t_T\right)c_P]e_0}{2t_T[t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right)]}}$
${E_F}^{*}$	$$\begin{gathered} \delta e_0{N}_T-{\displaystyle \frac{(\delta -1)t_S{V}_T{e}_0}{t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right)}} \\ -{\displaystyle \frac{(\delta -1)\left(B_T+p_0\lambda \right)\left[t_T\right(V_S+V_0)-\left(B_S-p_0\lambda \right)V_T+\left(B_T+p_0\lambda +t_T\right)c_P]e_0}{2t_T[t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right)]}} \end{gathered}$$

.

4. Adoption of Absolute Emission Cap-Based CAA Method (AC Model)

Referring to the carbon allowance allocation method widely used in several kinds of emission trading systems, the government sets an annual target value for total carbon emissions for the entities in the carbon trading market. The platform sets the membership fee $p_S$ for shippers and determines the level of carbon emission reduction $w$. Shippers and truckers in the RFS decide whether to join the platform. After that, the amount of carbon emissions, the membership fee revenue, and the carbon trading revenue of the platform are collected. Finally, the amount of carbon emissions in the RFS and the profit of the platform are available. See Figure 4 for an illustration.

The OFP decides membership fee $p_S$ and level of carbon emission reduction $w$ to maximize its profit:

$${\mathsf{\Pi }}_P=p_S{n}_S-c_P\left(n_S+n_T\right)-C\left(w\right)+P_C\left[E-\left(1-w\right)e_0{n}_T\right].$$

(6)

In (6), the first term denotes membership fee revenue. The second term denotes operation management cost. The third term denotes low-carbon technology investment cost. The last term denotes carbon trading revenue.

Substituting (3) and (4) into (6), we then can obtain the optimal membership price ${p_S}^{\mathrm{*}}$ and the optimal carbon emission reduction rate $w^{\mathrm{*}}$ under the AC model. Subsequently, substituting ${p_S}^{\mathrm{*}}$ and $w^{\mathrm{*}}$ into (3) and (4), we can obtain the optimal carbon emissions of the OFP ${E_P}^{\mathrm{*}}$ and the optimal carbon emissions of the RFS ${E_F}^{\mathrm{*}}$. Then, we can obtain the following proposition:

Proposition 2.

Under the AC model, there exists a unique optimal solution ${p_S}^{*}, w^{*}$, and the detailed optimal solutions are shown in Table 3.

Table 3. The detailed optimal solutions under the AC model.

Symbol	Detailed Optimal Solution
${p_S}^{*}$	${\displaystyle \frac{AkG-\left(B_T+p_0\lambda \right){e_0}^2{P_C}^2{V}_T{t}_S-D(V_S+V_0)}{2t_{T}Ak-D}}$
$w^{*}$	${\displaystyle \frac{e_0{P}_{C}H-D}{2t_{T}Ak-D}}$
${E_P}^{*}$	$$\begin{gathered} {\displaystyle \frac{2A{k}^2{t}_T{e}_0[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)]}{{(2t_{T}Ak-D)}^2}} \\ -{\displaystyle \frac{k{e_0}^2{P}_{C}H[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)]}{{(2t_{T}Ak-D)}^2}} \end{gathered}$$
${E_F}^{*}$	$$\begin{gathered} \delta e_0{N}_T-{\displaystyle \frac{k\delta e_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{2t_{T}Ak-D}} \\ +{\displaystyle \frac{2A{k}^2{t}_T{e}_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}Ak-D\right)}^2}} \\ -{\displaystyle \frac{k{e_0}^2{P}_{C}H\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}Ak-D\right)}^2}} \end{gathered}$$

Table 3. The detailed optimal solutions under the AC model.

Symbol	Detailed Optimal Solution
${p_S}^{*}$	${\displaystyle \frac{AkG-\left(B_T+p_0\lambda \right){e_0}^2{P_C}^2{V}_T{t}_S-D(V_S+V_0)}{2t_{T}Ak-D}}$
$w^{*}$	${\displaystyle \frac{e_0{P}_{C}H-D}{2t_{T}Ak-D}}$
${E_P}^{*}$	$$\begin{gathered} {\displaystyle \frac{2A{k}^2{t}_T{e}_0[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)]}{{(2t_{T}Ak-D)}^2}} \\ -{\displaystyle \frac{k{e_0}^2{P}_{C}H[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)]}{{(2t_{T}Ak-D)}^2}} \end{gathered}$$
${E_F}^{*}$	$$\begin{gathered} \delta e_0{N}_T-{\displaystyle \frac{k\delta e_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{2t_{T}Ak-D}} \\ +{\displaystyle \frac{2A{k}^2{t}_T{e}_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}Ak-D\right)}^2}} \\ -{\displaystyle \frac{k{e_0}^2{P}_{C}H\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}Ak-D\right)}^2}} \end{gathered}$$

where

$$A=t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right),$$

$$D={e_0}^2{\left(B_T+p_0\lambda \right)}^2{P_C}^2,$$

$$G=\left(B_S-p_0\lambda \right)V_T+\left(V_S+V_0\right)t_T+\left(B_T+p_0\lambda +t_T\right)\gamma c_P+e_0\left(B_T+p_0\lambda \right)P_C,$$

$$H=\left(t_T{t}_S+A\right)V_T+\left(B_T+p_0\lambda \right)\left(V_S+V_0\right)t_T-\left(B_T+p_0\lambda \right)\left(B_T+p_0\lambda +t_T\right)\gamma c_P.$$

Proposition 3.

Under the AC model, carbon emissions of the OFP${E_P}^{*}$ decrease in the unit service cost coefficient under carbon trading mechanism $\gamma$. Carbon emissions of the RFS${E_F}^{*}$ increase in the unit service cost coefficient under carbon trading mechanism $\gamma$.

The membership fee ${p_S}^{\mathrm{*}}$ increases in $\gamma$. Shippers are price-sensitive, and the increase in membership fee leads to a reduction in the number of shippers on the platform. Due to the existence of indirect network externality, this subsequently results in a decrease in the number of truckers on the platform as well. The carbon emission reduction rate $w^{\mathrm{*}}$ decreases in $\gamma$. It means that the actual carbon emissions per trucker on the platform increase. The carbon emissions of the OFP are influenced by both the number of shippers on the platform and the actual carbon emissions per trucker. Although the carbon emissions per trucker increase, the reduction in the number of carriers has a more pronounced effect on the platform’s carbon emissions. Consequently, as the unit service cost coefficient $\gamma$ rises, the carbon emissions of the OFP decrease.

The carbon emissions of the RFS comprise emissions from digital freight platforms and emissions from truckers outside the platform. Given the carbon-reducing role of the OFP, carbon emissions per trucker on the platform are lower than those off the platform. The number of truckers on the platform decreases in $\gamma$. Given a fixed total number of truckers in the RFS, a decrease in the number of truckers on the platform necessarily increases the number of truckers off the platform. Carbon emissions per trucker off the platform are high, and the number of truckers off the platform increases. Consequently, carbon emissions of the RFS increase as the unit service cost coefficient $\gamma$ rises.

5. Adoption of Intensity-Based CAA Method (IC Model)

In this section, we consider the CAA method from carbon emission intensity perspective, in which the government sets an annual target value for carbon emission intensity. The sequence of events is as follows. First, the platform determines the membership fee $p_S$ for shippers and the level of carbon emission reduction $w$. Next, shippers and truckers in the RFS decide whether to join the platform. The amount of carbon emissions, the membership fee revenue, and the carbon trading revenue of the platform are collected. Finally, the amount of carbon emissions in the RFS and the profit of platform are available. See Figure 5 for an illustration.

The OFP decides membership fee $p_S$ and level of carbon emission reduction $w$ to maximize its profit:

$${\mathsf{\Pi }}_P=p_S{n}_S-c_P\left(n_S+n_T\right)-C\left(w\right)+P_C\left[e-\left(1-w\right)e_0\right]n_T.$$

(7)

In (7), the first term denotes membership fee revenue. The second term denotes operation management cost. The third term denotes low-carbon technology investment cost. The last term denotes carbon trading revenue.

Then, we substitute (3) and (4) into (7). (7) is a jointly concave function with respect to ($p_S$, $w$), satisfying the conditions for optimal decision-making. We then can obtain the optimal membership price ${p_S}^{\mathrm{*}}$ and the optimal carbon emission reduction rate $w^{\mathrm{*}}$ under the IC model. Subsequently, substituting ${p_S}^{\mathrm{*}}$ and $w^{\mathrm{*}}$ into (3) and (4), we can obtain the optimal carbon emissions of the OFP ${E_P}^{\mathrm{*}}$ and the optimal carbon emissions of the RFS ${E_F}^{\mathrm{*}}$. Then, we can obtain the following proposition:

Proposition 4.

Under the IC model, there exists a unique optimal solution ${p_S}^{*}, w^{*}$, and the detailed optimal solutions are shown in Table 4.

Table 4. The detailed optimal solutions under the IC model.

Symbol	Detailed Optimal Solution
${p_S}^{*}$	${\displaystyle \frac{Ak[G-\left(B_T+p_0\lambda \right)P_{C}e]-\left(B_T+p_0\lambda \right){e_0}^2{P_C}^2{t}_S{V}_T-D(V_S+V_0)}{2t_{T}kA-D}}$
$w^{*}$	${\displaystyle \frac{e_0{P}_{C}H-D+e_0{\left(B_T+p_0\lambda \right)}^2{P_C}^{2}e}{2t_{T}kA-D}}$
${E_P}^{*}$	$$\begin{gathered} {\displaystyle \frac{2A{k}^2{t}_T{e}_0{\left(B_T+p_0\lambda \right)}^2{P}_{C}e}{{\left(2t_{T}kA-D\right)}^2}}-{\displaystyle \frac{kD{\left(B_T+p_0\lambda \right)}^2{P}_C{e}^2}{{\left(2t_{T}kA-D\right)}^2}} \\ +{\displaystyle \frac{k{e}_0(2Ak{t}_T-P_{C}H{e}_0)\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}kA-D\right)}^2}} \\ -{\displaystyle \frac{kD\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+H\right]e}{{\left(2t_{T}kA-D\right)}^2}} \end{gathered}$$
${E_F}^{*}$	$$\begin{gathered} -{\displaystyle \frac{k\delta e_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+{\left(B_T+p_0\lambda \right)}^2{P}_{C}e\right]}{2t_{T}kA-D}} \\ +{\displaystyle \frac{k{e}_0\left(2Ak{t}_T-P_{C}H{e}_0\right)\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}kA-D\right)}^2}} \\ -{\displaystyle \frac{kD{\left(B_T+p_0\lambda \right)}^2{P}_C{e}^2}{{\left(2t_{T}kA-D\right)}^2}}+{\displaystyle \frac{2A{k}^2{t}_T{e}_0{\left(B_T+p_0\lambda \right)}^2{P}_{C}e}{{\left(2t_{T}kA-D\right)}^2}}+\delta e_0{N}_T \\ -{\displaystyle \frac{kD\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+H\right]e}{{\left(2t_{T}kA-D\right)}^2}} \end{gathered}$$

Table 4. The detailed optimal solutions under the IC model.

Symbol	Detailed Optimal Solution
${p_S}^{*}$	${\displaystyle \frac{Ak[G-\left(B_T+p_0\lambda \right)P_{C}e]-\left(B_T+p_0\lambda \right){e_0}^2{P_C}^2{t}_S{V}_T-D(V_S+V_0)}{2t_{T}kA-D}}$
$w^{*}$	${\displaystyle \frac{e_0{P}_{C}H-D+e_0{\left(B_T+p_0\lambda \right)}^2{P_C}^{2}e}{2t_{T}kA-D}}$
${E_P}^{*}$	$$\begin{gathered} {\displaystyle \frac{2A{k}^2{t}_T{e}_0{\left(B_T+p_0\lambda \right)}^2{P}_{C}e}{{\left(2t_{T}kA-D\right)}^2}}-{\displaystyle \frac{kD{\left(B_T+p_0\lambda \right)}^2{P}_C{e}^2}{{\left(2t_{T}kA-D\right)}^2}} \\ +{\displaystyle \frac{k{e}_0(2Ak{t}_T-P_{C}H{e}_0)\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}kA-D\right)}^2}} \\ -{\displaystyle \frac{kD\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+H\right]e}{{\left(2t_{T}kA-D\right)}^2}} \end{gathered}$$
${E_F}^{*}$	$$\begin{gathered} -{\displaystyle \frac{k\delta e_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+{\left(B_T+p_0\lambda \right)}^2{P}_{C}e\right]}{2t_{T}kA-D}} \\ +{\displaystyle \frac{k{e}_0\left(2Ak{t}_T-P_{C}H{e}_0\right)\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)\right]}{{\left(2t_{T}kA-D\right)}^2}} \\ -{\displaystyle \frac{kD{\left(B_T+p_0\lambda \right)}^2{P}_C{e}^2}{{\left(2t_{T}kA-D\right)}^2}}+{\displaystyle \frac{2A{k}^2{t}_T{e}_0{\left(B_T+p_0\lambda \right)}^2{P}_{C}e}{{\left(2t_{T}kA-D\right)}^2}}+\delta e_0{N}_T \\ -{\displaystyle \frac{kD\left[2t_T{t}_S{V}_T+2t_T(V_S+V_0)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+H\right]e}{{\left(2t_{T}kA-D\right)}^2}} \end{gathered}$$

where

$$A=t_S{t}_T-\left(B_S-p_0\lambda \right)\left(B_T+p_0\lambda \right),$$

$$D={e_0}^2{\left(B_T+p_0\lambda \right)}^2{P_C}^2,$$

$$G=\left(B_S-p_0\lambda \right)V_T+\left(V_S+V_0\right)t_T+\left(B_T+p_0\lambda +t_T\right)\gamma c_P+e_0\left(B_T+p_0\lambda \right)P_C,$$

$$H=\left(t_T{t}_S+A\right)V_T+\left(B_T+p_0\lambda \right)\left(V_S+V_0\right)t_T-\left(B_T+p_0\lambda \right)\left(B_T+p_0\lambda +t_T\right)\gamma c_P.$$

Proposition 5.

Under the IC model, carbon emissions of the OFP${E_P}^{*}$ decrease in the unit service cost coefficient under carbon trading mechanism $\gamma$ . Carbon emissions of the RFS${E_F}^{*}$ increase in the unit service cost coefficient under carbon trading mechanism $\gamma$.

The membership fee ${p_S}^{\mathrm{*}}$ increases with the increase of $\gamma$. With the increase of membership fee, the number of shippers and truckers on the platform decreases. The carbon emission reduction rate $w^{\mathrm{*}}$ decreases with the increase of $\gamma$. Because the carbon emission reduction effect of fewer truckers outweighs increased carbon emissions per trucker, the carbon emissions of the OFP decrease.

The number of truckers on the platform decreases in $\gamma$. The decrease in the number of truckers on the platform means an increase in the number of truckers off the platform. Because the carbon emissions per trucker off the platform are more than those on the platform, the increase in the number of truckers off the platform represents the increase of carbon emissions of the RFS. Consequently, carbon emissions of the RFS increase as the unit service cost coefficient $\gamma$ rises.

6. Comparison Analysis

In this section, we will answer the main questions of this paper by comparing the optimal decisions under the NC model, AC model, and IC model.

6.1. OFP Perspective

As shown in Proposition 1, the OFP will not invest in low-carbon technology to reduce carbon emissions when unable to participate in the carbon trading market. Under the carbon trading mechanism, the main goal for the OFP to reduce carbon emissions is to obtain the carbon trading revenue and increase their own profit. Therefore, this subsection focuses on answering these questions: Can the carbon trading mechanism reduce the carbon emissions of the OFP? What CAA method can reduce more OFP carbon emissions? Can the carbon trading mechanism improve the OFP’s profit? What CAA method can improve the OFP’s profit the most? Comparing Propositions 1, 2 and 4, we then have the following results.

Proposition 6.

The optimal carbon emissions of the OFP under the NC model ($E_P^{NC}$), AC model ($E_P^{AC}$), and IC model ($E_P^{IC}$) have the following relationship:

(i) $E_P^{AC}$ is always less than $E_P^{NC}$, that is, $E_P^{AC}$ <$E_P^{NC}$.

(ii) $E_P^{IC}$ is always less than $E_P^{NC}$, that is, $E_P^{IC}$ <$E_P^{NC}$.

(iii) There exists a critical threshold$e$ such that $E_P^{IC}$ <$E_P^{AC}$ only when$e>\overline{e}$, where

$$\overline{e}={\displaystyle \frac{2Ak{t}_T-P_C{e}_0\left[2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right)+H\right]}{e_0{\left(B_T+p_0\lambda \right)}^2{P_C}^2}}.$$

Proposition 6 shows that the carbon trading mechanism can effectively reduce the carbon emissions of the OFP. The IC model can reduce more carbon emissions of the OFP when the free initial carbon allowance under the IC model is high. The underlying reasons are as follows. Carbon emissions of the OFP are relevant to the actual carbon emissions per trucker and the number of truckers on the platform. First, the optimal membership fee under the IC model $p_S^{IC}$ and the optimal membership fee under the AC model $p_S^{AC}$ are always higher than the optimal membership fee under the NC model $p_S^{NC}$. It means that the number of truckers on the platform under both the IC model and AC model is smaller than that under the NC model. The actual carbon emissions per trucker under both the IC model and AC model are smaller than those under the NC model. As a result, $E_P^{AC}<E_P^{NC}$, $E_P^{IC}<E_P^{NC}$. Second, $p_S^{IC}$ is always lower than $p_S^{AC}$. It means that the number of truckers on the platform under the AC model is smaller than that under the IC model. The actual carbon emissions per trucker under the AC model are larger than those under the IC model. When the free initial carbon allowance under the IC model is high, the increased actual carbon emissions of per trucker overweigh the actual carbon emissions of increased truckers. Hence, $E_P^{IC}<E_P^{AC}$.

From Proposition 6, we can obtain the following management insight. First, in order to reduce the carbon emissions of the OFP by implementing the carbon trading mechanism, the government should be concerned about the CAA method. When choosing the IC method, the government needs to set a high free initial carbon allowance. On the contrary, the government can merely choose the AC method. Second, under the guidance of sustainable development goals, OFPs have an inherent motivation for carbon emission reduction. In recent years, Full Truck Alliance has leveraged its platform advantages to pioneer innovative pathways for green freight transportation. In 2022, in collaboration with government agencies, Full Truck Alliance developed China’s first carbon emission reduction group standard for the RFS. The platform further introduced carbon accounts for truckers in 2023. These carbon accounts facilitate the provision of green incentives to low-carbon truckers while enabling systematic emission reductions across the platform.

We now compare the optimal OFP’s profit under the NC model (${\mathsf{\Pi }}_P^{NC}$), AC model (${\mathsf{\Pi }}_P^{AC}$), and IC model (${\mathsf{\Pi }}_P^{IC}$). However, the expression of the profit function is too complex to be compared directly, so we next conduct numerical studies, and our results are depicted in Figure 6. In the numerical studies of this paper, if not specified otherwise, the parameter values are set as $B_s=6$; $B_T=3$; $\lambda =1$; $c_p=0.1$; $B_s=6$; $t_S=5$; $t_T=10$; $V_0=5$; $V_S=5; V_T=10$; $e_0=2$; $k=10$; $P_C=2$; $p_0=1$.

Observation 1.

Under three models, the unit service cost coefficient$\gamma$ impacts the optimal OFP’s profit${\mathsf{\Pi }}_P$ as follows:

(i) The OFP’s profit under both the AC model and IC model decreases in the unit service cost coefficient  $\gamma$.

(ii) When the free initial carbon allowance under the IC model (AC model) is low, no matter how$\gamma$ changes, the OFP’s profit under the IC model (AC model) is smaller than that under the NC model. See Figure 6a,d,g–i.

(iii) When the free initial carbon allowance under the IC model (AC model) is high, no matter how$\gamma$ changes, the OFP’s profit under the IC model (AC model) is higher than that under the NC model. See Figure 6a–c,f,i.

(iv) When the free initial carbon allowance under the IC model (AC model) is in the middle, the unit service cost coefficient$\gamma$ is low, and the OFP’s profit under the IC model (AC model) is higher than that under the NC model. Otherwise, the OFP’s profit under the IC model (AC model) is lower than that under the NC model. See Figure 6b,d–f,h.

Observation 1 shows that the free initial carbon allowance allocated by the government and unit service cost coefficient effects the OFP’s profit. First, under the carbon trading mechanism, the OFP’s profit consists of the membership fee revenue, operation management cost, low-carbon technology investment cost, and carbon trading revenue. With the increase of the unit service cost coefficient, the operation management cost of the OFP increases. As a result, the OFP’s profit decreases. Second, high free initial carbon allowances can encourage OFPs to reduce more carbon emissions through low-carbon technology. More carbon emission reduction can generate more carbon trading revenues. Carbon trading revenues under the AC model (IC model) overweigh the increased operation management cost of the OFP, the increased investment cost of low-carbon technology, and decreased membership revenue. Hence, when the free initial carbon allowance is at a high level, the carbon trading mechanism can improve the OFP’s profit. Third, a low free initial carbon allowance means limited carbon trading revenue. The expensive investment cost of low-carbon technology and increased operation management cost overweigh limited carbon trading revenue, so the OFP’s profit decreases under the carbon trading mechanism. Last, when the free initial carbon allowance is in the middle, the OFP can achieve considerable carbon trading revenue by implementing low-carbon technology. When the unit service cost coefficient is low, carbon trading revenues under the AC model (IC model) overweigh the increased operation management cost of the OFP, the increased investment cost of low-carbon technology, and decreased membership revenue.

Observation 2.

Under the AC model and IC model, the unit service cost coefficient$\gamma$ impacts the optimal OFP’s profit${\mathsf{\Pi }}_P$ as follows:

(i) When the free initial carbon allowance under the IC model is high, no matter how$\gamma$ and the free initial carbon allowance under the AC model change, the OFP’s profit under the IC model is higher than that under the AC model. See Figure 6a–c.

(ii) When the free initial carbon allowance under the IC model is in the middle, the free initial carbon allowance under the AC model is high, no matter how$\gamma$ changes, and the OFP’s profit under the IC model is lower than that under the AC model. See Figure 6f. When the free initial carbon allowance under the IC model and AC model are in the middle, the unit service cost coefficient$\gamma$ is low, and the OFP’s profit under the IC model is higher than that under the AC model. See Figure 6e. When the free initial carbon allowance under the IC model is in the middle, the free initial carbon allowance under the AC model is low, no matter how$\gamma$ changes, and the OFP’s profit under the IC model is higher than that under the AC model. See Figure 6d.

(iii) Only when the free initial carbon allowance under the IC model and AC model are low, no matter how$\gamma$ changes, is the OFP’s profit under the IC model higher than that under the AC model. See Figure 6g. On the contrary, when the free initial carbon allowance under the IC model is low, and the free initial carbon allowance under the AC model is high or in the middle, no matter how$\gamma$ changes, the OFP’s profit under the IC model is lower than that under the AC model. See Figure 6h,i.

Observation 2 shows that the free initial carbon allowance has a more significant effect on the OFP’s profit. The unit service cost coefficient affects the OFP’s profit only when the free initial carbon allowance under the IC model and AC model are in the middle. The level of the free initial carbon allowance under the IC model and AC model influences the OFP’s profit. Which level is higher determines under which model the OFP’s profit is higher. When the level is high or low, the OFP’s profit under the IC model is always higher than that under the AC model. Because the intensity-based method can bring more carbon trading revenue for the OFP, and the increased carbon trading revenue overweighs the increased operation management cost of the OFP and the investment cost of low-carbon technology. When the free initial carbon allowance is in the middle, the unit service cost coefficient affects the OFP’s profit. When the unit service cost coefficient is low, the OFP’s profit under the IC model is higher because the increased membership revenue and carbon trading revenue are larger than the increased operation management cost of the OFP and the investment cost of low-carbon technology.

From Observations 1 and 2, we can obtain the following management insight. First, the government needs to set appropriate free initial carbon allowances. High free initial carbon allowances can incentivize OFPs to achieve greater emission reductions through internal optimization (e.g., low-carbon technology). Second, the intensity-based method is a better CAA method for the OFP. Compared with the AC method, the intensity-based method can improve the OFP’s profit more under most conditions. Third, the OFP should be concerned about the carbon emission data collection technology and make efforts to reduce the cost of the technology. For the OFP, the decrease in operation management costs means improvement in profits.

6.2. Government Perspective

The carbon emissions of the RFS consist of the carbon emissions of an OPF and those of truckers off the platform. The free initial carbon allowance can influence the carbon emission reduction strategy of an OFP and lead to the transfer effect of carbon emissions. Therefore, this subsection focuses on answering these questions: Can the carbon trading mechanism reduce the carbon emissions of the RFS? What CAA method can reduce more RFS carbon emissions? Comparing Propositions 1, 2 and 4, we then have the following results.

Proposition 7.

The optimal carbon emissions of the RFS under the NC model ($E_F^{NC}$), AC model ($E_F^{AC}$), and IC model ($E_F^{IC}$) have the following relationship:

(i)$E_F^{IC}$ is always less than $E_F^{AC}$, that is, $E_F^{IC}$ <$E_F^{AC}$.

(ii) There exists a critical threshold $\delta$ such that $E_F^{AC}$ <$E_F^{NC}$ only when $\delta <\overline{\delta }$ where $\overline{\delta }={\displaystyle \frac{2t_{T}Ak{e}_0\left(2Ak{t}_T-P_{C}H{e}_0\right)I-J-K}{2t_{T}Ak{e}_{0}I-J-K}}$.

$$I=2t_T{t}_S{V}_T+2t_T\left(V_S+V_0\right)\left(B_T+p_0\lambda \right)-G\left(B_T+p_0\lambda \right),$$

$$J=2{\left(2t_{T}Ak-D\right)}^2{t}_T{t}_S{V}_T{e}_0,$$

$$K={\left(2t_{T}Ak-D\right)}^2\left(B_T+p_0\lambda \right)\left[t_T\left(V_S+V_0\right)-\left(B_S-p_0\lambda \right)V_T+\left(B_T+p_0\lambda +t_T\right)c_P\right]e_0.$$

(iii) There exists a critical threshold $e$ such that $E_F^{IC}$ < $E_F^{NC}$only when $e>\overline{e}$ where $\overline{e}={\displaystyle \frac{-L_2+\sqrt{{L_2}^2-4L_1{L}_3}}{2L_1}}.$

$$L_1=2t_{T}AkD{\left(B_T+p_0\lambda \right)}^2{P}_C,$$

$$L_2=2t_{T}Ak\left[D\left(I+H\right)-2t_{T}Ak{e}_0{\left(B_T+p_0\lambda \right)}^2{P}_C-\left(2t_{T}kA-D\right)e_0{\left(B_T+p_0\lambda \right)}^2{P}_C\delta \right],$$

$$L_3=-2t_{T}Ak{e}_{0}I\left[\left(2t_{T}kA-D\right)\delta +\left(2Ak{t}_T-P_{C}H{e}_0\right)\right]-J\left(\delta -1\right)-K\left(\delta -1\right).$$

Proposition 7 implies that the carbon trading mechanism can effectively reduce the carbon emissions of the RFS under certain conditions. Under the carbon trading mechanism, the IC model can reduce more RFS carbon emissions than the AC model. When the unit carbon emissions coefficient of truckers off the platform are low, the AC model can reduce the carbon emissions of the RFS. When the free initial carbon allowance under the IC model is high, the IC model can reduce the carbon emissions of the RFS. The underlying reasons are as follows. The carbon emissions of the RFS consist of the carbon emissions of the OPF and those of truckers off the platform. Since the number of truckers in the RFS is fixed, the fewer truckers on the platform, the more truckers off the platform. Carbon emissions of truckers off the platform increase, and the increased carbon emissions are far greater than the carbon emission reduction of the platform. First, under the AC model, the number of truckers on the platform is fewer than that under the IC model. Therefore, the carbon emissions of the RFS under the AC model are always greater than those under the IC model. Second, under the NC model, the number of truckers on the platform is more than that under the AC model. As a result, carbon emissions of truckers off the platform under the AC model are more than those under the NC model. As shown in Proposition 6, carbon emissions of the OPF under the AC model are less than those under the NC model. When the unit carbon emissions coefficient of truckers off the platform is low, the increased carbon emissions of truckers off the platform are less than the carbon emission reduction of the platform. Hence, the carbon emissions of the RFS under the AC model are less than those under the NC model. Third, similar to the AC model, carbon emissions of truckers off the platform under the IC model are more than those under the NC model. As shown in Proposition 6, carbon emissions of the OPF under the IC model are less than those under the NC model. When the free initial carbon allowance under the IC model is high, the increased carbon emissions of truckers off the platform are less than the carbon emission reduction of the platform. As a result, the carbon emissions of the RFS under the IC model are less than those under the NC model.

From Proposition 7, we can obtain the following management insight. First, in order to reduce the carbon emissions of the RFS, the government should be concerned about the carbon trading mechanism. The carbon trading mechanism may lead the OPF to force more truckers to switch to non-platform operations with higher emissions. The government needs to monitor the transfer effect of emissions both inside and outside the platform after the implementation of carbon trading mechanism and adjust policies in a timely manner. Second, in order to reduce the carbon emissions of the RFS, the government should choose the intensity-based method and set a high free initial carbon allowance. Under the IC model, with the incentive of high free initial carbon allowance, the OFP will implement low-carbon technology and increase the number of truckers on the platform.

6.3. Sensitivity Analysis

This section employs numerical simulation to examine the impact of the probability of successful two-sided user transactions on the pricing strategy, carbon emission reduction rate, profit, and carbon emissions of online freight platforms, as well as on the carbon emissions of the road freight sector, under different models (NC model, AC model, and IC model). Referring to Gu et al. (2023) [54] and Yuan et al. (2022) [84], the parameter values are set as $B_s=6$; $B_T=3$; $\gamma =2$; $c_p=0.1$; $B_s=6$; $t_S=5$; $t_T=10$; $V_0=5$; $V_S=5;V_T=10$; $e_0=2$; $k=10$; $P_C=2$; $p_0=1$; $E=7;e=3$. Numerical simulations are implemented through MATLAB R2018b.

This study examines the impact of changes in $\lambda$ on the pricing strategy, carbon reduction rate, profit, carbon emissions of online freight platforms, and carbon emissions of the road freight sector. Our results are depicted in

Table 5. The sensitivity analysis of $\lambda$.

$\mathit{\lambda }$	${\mathit{p}}_{\mathit{s}}^{\mathit{N}\mathit{C}}$	${\mathit{p}}_{\mathit{s}}^{\mathit{A}\mathit{C}}$	${\mathit{p}}_{\mathit{s}}^{\mathit{I}\mathit{C}}$	${\mathit{w}}^{\mathit{N}\mathit{C}}$	${\mathit{w}}^{\mathit{A}\mathit{C}}$	${\mathit{w}}^{\mathit{I}\mathit{C}}$
0.2	6.466	8.218	7.233	0	0.704	0.717
0.4	6.367	8.119	7.067	0	0.725	0.738
0.6	6.268	8.018	6.900	0	0.745	0.759
0.8	6.169	7.916	6.730	0	0.763	0.779
1	6.070	7.813	6.560	0	0.781	0.798
$\lambda$	${\mathsf{\Pi }}_P^{NC}$	${\mathsf{\Pi }}_P^{AC}$	${\mathsf{\Pi }}_P^{IC}$	$E_P^{NC}$	$E_P^{AC}$	$E_P^{IC}$
0.2	12.896	15.313	13.848	3.927	1.048	1.061
0.4	12.685	14.957	13.977	4.057	1.003	1.014
0.6	12.442	14.589	14.087	4.184	0.955	0.964
0.8	12.166	14.212	14.178	4.304	0.906	0.912
1	11.858	13.827	14.246	4.419	0.856	0.858
λ	$E_F^{NC}$		$E_F^{AC}$		$E_F^{IC}$
0.2	34.292		33.332		32.341
0.4	33.771		32.787		31.643
0.6	33.266		32.259		30.950
0.8	32.782		31.753		30.269
1	32.325		31.274		29.605

.

Observation 3.

Under three models, the probability of successful two-sided user transactions $\lambda$ impacts $p_s$, w, ${\mathsf{\Pi }}_P$, $E_P$, and $E_F$ as follows:

(i) Under three models, $p_s$ decreases in the probability of successful two-sided user transactions $\lambda$. $p_s^{NC}<p_s^{IC}<p_s^{AC}$.

(ii) Under the NC model, the OFP will not engage in the adoption of low-carbon technologies. Under the AC model and the IC model, w increases in the probability of successful two-sided user transactions$\lambda$. $w^{AC}<w^{IC}$.

(iii) Under the NC model and the AC model, ${\mathsf{\Pi }}_P$ decreases in the probability of successful two-sided user transactions $\lambda$. Under the IC model, ${\mathsf{\Pi }}_P$ increases in the probability of successful two-sided user transactions $\lambda$. When $\lambda$ is high, ${\mathsf{\Pi }}_P^{NC}<{\mathsf{\Pi }}_P^{AC}<{\mathsf{\Pi }}_P^{IC}$. Otherwise, ${\mathsf{\Pi }}_P^{NC}<{\mathsf{\Pi }}_P^{IC}<{\mathsf{\Pi }}_P^{AC}$.

(iv) Under the NC model, $E_P$ increases in the probability of successful two-sided user transactions $\lambda$. Under the AC model and the IC model, $E_P$ decreases in the probability of successful two-sided user transactions $\lambda$. $E_P^{AC}<E_P^{IC}<E_P^{NC}$.

(v) Under the three models, $E_F$ decreases in the probability of successful two-sided user transactions $\lambda$. $E_F^{IC}<E_F^{AC}<E_F^{NC}$.

Observation 3 shows that increasing the probability of successful two-sided user transactions under the IC model is an effective method for OFPs to simultaneously achieve profit increases and carbon emission reduction of RFS targets.

Under the NC model, the OFP is unwilling to make efforts to reduce carbon emissions. The underlying reason is that as far as the platform itself is concerned, there is insufficient incentive to realize the low carbon transition. In practice, it is difficult for platforms to find a balance between cost and green premium due to the inadequate supporting infrastructure and the lack of economical and low-carbon ways for road freight. The OFP’s profit and the carbon emissions of the RFS are negatively correlated with the probability of successful two-sided user transactions. Carbon emissions of the OFP are positively correlated with the probability of successful two-sided user transactions. As the probability of successful two-sided user transactions increases, the membership fee of the shipper decreases. As a result, the number of shippers and truckers on the platform increases. Due to the increased operation management cost overweighing the increased membership fee revenue, the OFP’s profit decreases. Carbon emissions of the OFP increase because the number of truckers on the platform increases. Since the number of truckers in the RFS is fixed, the more truckers on the platform, the fewer truckers off the platform. Carbon emissions of truckers off the platform decrease, and the increased carbon emissions of the OFP are far less than the decreased carbon emission of truckers off the platform. Hence, carbon emissions of the RFS decrease.

Under the AC model, the OFP’s profit and carbon emissions and carbon emissions of the RFS are negatively correlated with the probability of successful two-sided user transactions. With the increase of the probability of successful two-sided user transactions, the membership fee of the shipper decreases and the carbon emission reduction rate increases. Hence, the number of shippers and truckers on the platform increases and the investment cost of low-carbon technology increases. Due to the increased operation management cost and increased investment cost of low-carbon technology overweighing the increased membership fee revenue and carbon trading revenue, the OFP’s profit decreases. Carbon emissions of the OFP decrease because carbon emissions of the increased truckers are less than the carbon emission reduction of the platform. Because carbon emissions of truckers off the platform decrease, and carbon emissions of the OFP decrease, and carbon emissions of the RFS decrease.

Under the IC model, carbon emissions of the OFP and carbon emissions of the RFS are negatively correlated with the probability of successful two-sided user transactions. The OFP’s profit is positively correlated with the probability of successful two-sided user transactions. When the membership fee of the shipper decreases and the carbon emission reduction rate increases, the number of shippers and truckers on the platform increases and the investment cost of low-carbon technology increases. Because the increased membership fee revenue and carbon trading revenue overweighs the increased operation management cost and increased investment cost of low-carbon technology, the OFP’s profit increases. Carbon emissions of the OFP decrease because the carbon emissions of increased truckers are less than the carbon emission reduction of the platform. Because carbon emissions of truckers off the platform decrease, and carbon emissions of the OFP decrease, carbon emissions of the RFS decrease.

From Propositions 1, 2 and 4, $p_s^{NC}<p_s^{IC}<p_s^{AC}$, $w^{NC}=0$, $w^{AC}<w^{IC}$. The results are consistent with Observation 3. Similar to Observation 1 and Observation 2, when the free initial carbon allowance under the IC model and AC model are in the middle, and the unit service cost coefficient is low, the OFP’s profit under the IC model and the AC model are larger than that under the NC model. When the probability of successful two-sided user transactions is high, the OFP’s profit under the IC model is larger than that under the AC model. Because the free initial carbon allowance under the IC model is smaller than the critical threshold; $E_P^{AC}<E_P^{IC}<E_P^{NC}$ is consistent with Proposition 6. Because the free initial carbon allowance under the IC model is smaller than the critical threshold, the unit carbon emissions coefficient per trucker off the OFP is low; $E_F^{IC}<E_F^{AC}<E_F^{NC}$ is consistent with Proposition 7.

From Observation 3, we can obtain the following management insight. First, the carbon trading mechanism promotes the active participation of OFPs in carbon reduction by internalizing the cost of carbon emissions. It is often assumed that improving the efficiency of vehicle and cargo matching is an effective method of reducing carbon emissions of the RFS. Without the support of the carbon trading mechanism, the OFP’s pursuit of improved matching efficiency can neither increase the OFP’s profit nor reduce its carbon emissions. The government should establish a carbon trading mechanism based on OFPs as soon as possible. Second, in order to simultaneously achieve increased profitability of the OFP and carbon emission reduction of the RFS, the government should choose the intensity-based method and set appropriate free initial carbon allowances.

7. Practical Implications and Conclusions

7.1. Practical Implications

Our analysis and results lead to the following managerial insights: First, considering both the OFP’S profit and the carbon emissions of the RFS, the government should choose an intensity-based method and set a high level of free initial carbon allowance. Second, the OFP should make full use of digital and big data technologies to reduce the cost of collecting carbon emissions data. A low carbon emissions data collection cost will not only have a positive impact on the OFP’s profit but also reduce the carbon emissions of the RFS. Third, the OFP should strengthen cooperation with the government to formulate unified carbon emission standards. Unified carbon emission standards will facilitate the setting of a free initial carbon allowance and verification of carbon emissions by the government. This lays the foundation for the RFS to access the carbon trading market. Last, OFPs should actively participate in the carbon trading mechanism, as improving matching efficiency alone—without carbon trading—cannot enhance profitability and reduce carbon emissions of the RFS at the same time. Improving the vehicle–cargo matching efficiency is a key lever for OFPs to achieve high-quality development and low-carbon operations. It not only enhances the platform’s operational efficiency and profitability but also optimizes the service experience and benefits for both shippers and carriers. Ultimately, it drives the RFS toward a greener, more coordinated, and efficient development path. Intensity-based carbon trading mechanisms enable OFPs to simultaneously increase profit and reduce carbon emissions of the RFS, making them a preferable choice for platform-led green transitions. From a government perspective, to balance economic development and environmental goals, an intensity-based CAA method with a well-designed initial carbon allowance should be prioritized, as it provides stronger incentives for sustainable platform behavior.

7.2. Conclusions

This paper considers an OFP service supply chain with an OFP, shippers, and truckers. We start by deriving the optimal solutions of the supply chain under the NC model, the AC model, and the IC model. Firstly, we find that both the AC model and the IC model can reduce the carbon emissions of the OFP. If the free initial carbon allowance under the IC model is high, the IC model leads to a decrease in the carbon emissions of the OFP compared with the AC model. Secondly, the free initial carbon allowance and the unit service cost coefficient affect profit of the OFP under the AC model and the IC model. When the free initial carbon allowance is high, and the unit service cost coefficient is low, the OFP’s profits under the AC model and IC model are always larger than that under the NC model. Whichever level is higher, the OFP’s profit under that model is higher. When the level is high or low, the OFP’s profit under the IC model is always higher than that under the AC model. When the free initial carbon allowance is in the middle, and the unit service cost coefficient is low, the OFP’s profit under the IC model is higher. Thirdly, we find that from the perspective of the government, an appropriate carbon trading mechanism not only decreases carbon emissions of the RFS but also controls the transfer effect of emissions both inside and outside the platform. Simultaneously, the carbon emissions of the RFS under the IC model are always lower than those under the AC model. Lastly, under the IC model, improving the efficiency of vehicle and cargo matching can simultaneously increase the OFP’s profit and reduce the carbon emissions of the RFS. When the efficiency of vehicle and cargo matching is high, the OFP’s profit is the highest.

There are a few interesting topics for further research. First, this study only considered the aggregate OFP. In the future, we will consider a carrier-based OFP. Second, in practice, the carbon emission reduction method by the OFP includes not only the application of low-carbon technology but also the incentives for truckers. In the future, we will further consider the incentives for truckers. Last, in commercial practice, fierce competition exists between OFPs. Hence, we next will explore the carbon emission reduction decisions of two competitive OFPs.