Emission-Reduction Decision-Making in a Shipping Logistics Service Supply Chain Under Carbon Cap-And-Trade Mechanisms: Based on Two-Way Cost Sharing of AI Technology

Abstract

Under the background of the carbon cap and trading mechanism, the shipping logistics service supply chain faces pressure to reduce carbon emissions, and artificial intelligence technology provides a new technological path for emission reduction. In the context of a carbon cap-and-trade system, this study examines a shipping logistics service supply chain comprising a service provider and a service integrator, where the provider adopts AI technologies for direct emission reduction and the integrator contributes indirectly. It investigates optimal decision-making under two models: a single emission-reduction model (only provider uses AI) and a joint-emission-reduction model (both adopt AI), while also exploring one-way and two-way cost-sharing contracts between them. The study establishes these models to analyze the impact of cost-sharing contracts on emission reduction levels, total service volume, and profits, and further examines how government regulation of carbon trading prices can promote reduction. Findings reveal that cost-sharing contracts effectively enhance emission reduction, output, and member benefits; one-way contracts are conducive to operations, while two-way contracts are effective only within a small cost-sharing ratio range. The joint model outperforms the single model under specific parameter thresholds, and cost-sharing ratios influence decentralized versus centralized decision-making. Government carbon price regulation can encourage reduction but must consider its effects on low-carbon logistics volume and profits.

1. Introduction

To cope with increasingly severe environmental challenges, various countries have introduced policies and regulatory measures to reduce greenhouse gas emissions and promote green shipping. For instance, carbon cap-and-trade has been widely used in shipping logistics service supply chains (SLSSCs) to incentivize firms to reduce emissions and promote the green transformation of industry [1,2]. Under such schemes, shipping firms receive a predetermined quota of carbon-emission allowances, defining their permissible emissions within a specific timeframe. Operational discrepancies—where actual emissions exceed or fall short of allocated allowances—necessitate managerial responses. Firms facing excess emissions must either procure additional allowances from the carbon market or invest in technological improvements to enhance production efficiency and reduce emissions. These operational trade-offs underscore the strategic importance of integrating carbon considerations into daily decision-making [3,4]. Accordingly, this study investigates emission-reduction decision-making within an SLSSC under the carbon cap-and-trade framework.

In an SLSSC, the shipping logistics service provider (SLSP) and the shipping logistics service integrator (SLSI) both play important roles. The SLSP participates in carbon-emission reduction by improving service technologies and using environmentally friendly energy while the SLSI becomes indirectly involved in carbon-emission reduction by building low-carbon solutions. This mode of cooperation and joint emission reduction affects the operational decisions of the SLSSC [5,6,7]. In recent years, SLSSC members, such as logistics service providers and port operators, have increasingly adopted artificial intelligence (AI) technologies to reduce carbon emissions in logistics. Among these efforts, optimizing ship routes and speeds through machine learning algorithms helps reduce fuel consumption. Predictive maintenance based on the Internet of Things (IoT) and AI can detect equipment failures in advance, preventing abnormal operations that consume excessive energy. Additionally, digital twin technology simulates the entire logistics process, enabling dynamic adjustments to energy allocation and transportation strategies for systematic carbon-emission reduction.

For example, Maersk, the world’s largest shipping company, cooperated with Google Cloud in 2021 to develop a smart route-optimization system based on AI and machine learning to optimize transportation routes and scheduling systems; this not only improved transportation efficiency but also helped reduce carbon emissions. Meanwhile, the Port of Rotterdam in the Netherlands used AI for the intelligent planning of port layouts and the efficient management of loading and unloading operations. Using AI to predict and analyze data such as cargo throughput and ship arrival times, the port has been able to more reasonably allocate resources to reduce waiting time and energy consumption. During the Suez Canal blockage incident in 2022, the system warned of delays in cargo arrivals 48 h in advance, thus helping to adjust the berthing order of 17 ships and avoid large economic losses. AI has also helped the port automate loading and unloading operations, significantly reducing emissions during port operations through the precise control and optimization of operational processes. These applications of AI not only demonstrate the innovative efforts of SLSSC members in carbon-emission reduction but also provide support for the low-carbon, high-efficiency development of the entire industry.

However, SLSSCs face significant cost dilemmas in adopting AI to achieve emission-reduction goals. AI has great potential for optimizing transportation routes, improving loading and unloading efficiency, and reducing energy consumption, but its high R&D and implementation costs constrain its widespread application [8,9,10]. As a result, SLSSC members frequently grapple with the trade-off between cost containment and the realization of emission-reduction benefits. In this study, set within the context of a carbon cap-and-trade framework, the SLSP applies AI to directly reduce emissions, while the SLSI supports emission-reduction efforts indirectly. To account for the sequential nature of these investments, we propose two analytical models: a single emission-reduction model involving only the SLSP and a joint-emission-reduction model featuring simultaneous participation by both the SLSP and SLSI. This framework allows us to explore optimal decision strategies and cost-sharing contracts. The study is guided by the following research questions:

(1) How does the implementation of a cost-sharing contract influence equilibrium decision-making in decentralized and centralized SLSSC structures when the SLSP adopts AI for carbon-emission reduction under a cap-and-trade system?

(2) How does a cost-sharing contract affect equilibrium strategies within the SLSSC when both the SLSP and the SLSI simultaneously adopt AI-based emission-reduction measures under carbon cap-and-trade?

(3) When comparing different emission-reduction models, how can the SLSSC determine its optimal operational strategy, and how do carbon trading prices and cost-sharing ratios impact emission-reduction decisions?

Accordingly, this study explores joint-emission-reduction strategies within an SLSSC under a carbon cap-and-trade system, emphasizing the role of a two-way cost-sharing contract between the SLSP and SLSI in facilitating AI-driven emission reduction. We formally integrate cost-sharing contracts into the SLSSC structure by developing both one-way and two-way contractual models and conduct a detailed analysis of their effects on the chain’s operational decision-making processes. This study makes the following key contributions: (1) We propose two emission-reduction models under carbon cap-and-trade: a single emission-reduction model, where only the SLSP adopts AI, and a joint-emission-reduction model, where both the SLSP and SLSI use AI. Corresponding one-way and two-way cost-sharing contracts are developed to analyze collaborative strategies. (2) We investigate the optimal contract design and strategic choices for the SLSSC, assessing the cost-sharing contract’s influence on emission-reduction levels, service capacity, and the profitability of supply chain participants. (3) The study offers practical managerial insights and policy recommendations, highlighting how governments can incentivize carbon reduction in SLSSCs through carbon trading price regulation.

Section 2 presents a review of the relevant literature. Section 3 outlines the foundational framework of carbon cap-and-trade. Section 4 develops and solves decision models for SLSSC carbon-emission reduction under two-way AI cost-sharing contracts in both decentralized and centralized settings. Section 5 provides a comparative analysis of emission-reduction strategies based on AI cost-sharing mechanisms. Section 6 conducts a case-based simulation to evaluate the impact of AI cost-sharing proportions and carbon trading prices on emission levels, output, and the profitability of SLSSC members. Finally, Section 7 concludes with managerial implications and policy recommendations.

2. Literature Review

This section reviews the literature relevant to constructing the game model in this study. It is divided into three parts: decision-making in SLSSC under carbon cap-and-trade, game-theoretic decisions on technology investment for emission reduction in supply chains, and cost-sharing contracts for emission reduction in supply chains.

2.1. SLSSC Decision-Making Under Carbon Cap-And-Trade

As vital components of the global economy, SLSSCs are directly influenced by carbon cap-and-trade policies in their operational decision-making. A growing body of literature has explored the implications of such regulatory frameworks on SLSSC firms. These studies often rely on supply chain network modeling to examine optimal ordering decisions, expected profit maximization, and other strategic variables under varying carbon-reduction policies [11,12]. In addition, scholars have analyzed the coordination issues that arise under cap-and-trade systems, assessing the applicability and limitations of conventional supply chain coordination mechanisms [13]. By adjusting interests between members, these contractual mechanisms incentivize firms to adopt more environmentally friendly production methods, thus reducing carbon emissions. As investments in emission reduction increase and unit carbon emissions decrease, market demand for low-carbon logistics services rises. Typically conducted within the framework of linear demand functions, such studies treat price and emission-reduction levels as key exogenous variables, demonstrating that emission-reduction behaviors can effectively stimulate market demand growth by enhancing environmental reputation or complying with policies [14,15].

Beyond firm-level analysis, scholars have explored the broader impact of cap-and-trade on the overall operational and environmental performance of SLSSCs. Some have found that a medium level of mandatory carbon caps can balance corporate profits and emission-reduction objectives. Moreover, the Pareto optimization of SLSSC performance can be achieved by considering factors such as firms’ carbon-emission efficiency, decision-making mode, and carbon cap size [16,17,18]. This implies that under cap-and-trade, SLSSCs can achieve both economic and environmental benefits by optimizing resource allocation and production decisions.

In recent years, with the broadening of artificial intelligence (AI) research, applying AI to emission reduction in SLSSCs has attracted attention in interdisciplinary research on logistics management and environmental science [19,20]. Such studies have shown how AI can save energy and reduce emissions by optimizing shipping routes, improving operational efficiency, and facilitating intelligent decision-making, demonstrating AI’s potential for achieving green transformation in the shipping industry [21,22]. While research in this area is rapidly developing, using AI to reduce emissions in SLSSCs still faces challenges, with the complexity and cost of AI implementation being major barriers to its widespread application. However, these studies generally assume that only the SLSP undertakes direct emission-reduction efforts, with limited attention to the potential role of the SLSI in contributing indirectly to emission reduction through AI adoption.

2.2. Game-Theoretic Decisions on Technology Investment for Emission Reduction in Supply Chains

The decision for supply chain members to invest in green technologies, such as AI for emission reduction, inherently involves strategic interactions. Game theory provides a natural framework for analyzing these technology investment decisions, particularly under regulatory constraints like carbon cap-and-trade. Early studies in this domain focused on the conditions under which firms unilaterally invest in emission-reduction technologies, often modeling the problem as a single-stage optimization where the investor bears the full cost and reaps the environmental benefits [23,24]. However, these models frequently overlook the strategic interdependence between supply chain partners, where the investment decision of a manufacturer or a logistics provider affects the operational choices and profits of others.

Subsequent research has adopted Stackelberg game frameworks to capture this leader-follower dynamic in green technology investment. For instance, studies have modeled a manufacturer as the Stackelberg leader investing in green product technologies, with a retailer follower responding through pricing or order quantity decisions [25]. These models reveal that the distribution of power and the nature of the strategic interaction critically shape the equilibrium level of green investment [26]. In the context of logistics, however, the game-theoretic analysis of technology investment is less-developed. Most existing studies treat the SLSSC structure as given and focus on the SLSP’s unilateral decision to adopt emission-reduction technologies, often neglecting the strategic role of the SLSI, whose operational decisions can amplify or diminish the effectiveness of the SLSP’s green investments. A key theoretical gap, therefore, lies in modeling a bilateral strategic interaction where both the SLSP and the SLSI can invest in AI for emission reduction, potentially with different cost structures and effectiveness, under a cap-and-trade regime.

2.3. Research on Cost-Sharing Contracts for Emission Reduction in Supply Chains

Early studies on cost-sharing contracts primarily focused on achieving synergies among supply chain members by sharing the burden of return uncertainty and risk instability [27]. Unlike other coordination contracts, cost-sharing mechanisms emphasize shared responsibility for investment risks and operational uncertainties. Subsequent research has specifically explored the application of cost-sharing contracts in emission-reduction decision-making [28,29]. Findings suggest that when a manufacturer’s initial carbon emissions are relatively low, both parties favor green production cost-sharing contracts, as these directly enhance product-level emission reduction. Conversely, when the manufacturer’s emissions are significantly high, green logistics cost-sharing contracts may be more suitable, as they can indirectly foster greener production practices. A notable feature of this literature is its predominant focus on one-way cost-sharing arrangements, where a downstream firm shares the cost of a specific green activity undertaken by an upstream firm [30]. In the SLSSC context, this would typically translate to the SLSI sharing the SLSP’s AI investment cost. However, the possibility and implications of two-way cost-sharing contracts-where both parties agree to share a portion of each other’s distinct but complementary AI-driven emission-reduction costs remain unexplored. This is a significant gap, especially considering that in practice, both logistics providers and integrators may undertake separate but synergistic green initiatives.

2.4. Literature Summary

The existing literature on SLSSCs and supply chain emission-reduction decision-making has made significant progress in analyzing operational decisions under cap-and-trade, exploring AI-based emission-reduction optimization, and examining cost-sharing contracts. However, our review reveals several critical theoretical gaps that this study aims to address.

First, while many studies have analyzed operational decision-making in SLSSCs, few specifically consider the strategic coordination and optimization of joint AI adoption by multiple interested parties. Existing models typically assume a unilateral emission-reduction effort by the SLSP, overlooking the potential for the SLSI to contribute indirectly through its own AI investments. The theoretical novelty of this study lies in its dual-AI-effort structure, where both the SLSP (direct reduction) and the SLSI (indirect reduction) invest in AI technologies. This moves beyond the single-investor paradigm and captures the complementary nature of green efforts in a service supply chain.

Second, the contractual cooperation modeled in existing studies is almost exclusively one-way and favors operational decisions. This study introduces and analyzes a two-way cost-sharing contract for AI investments, a feature absent from prior research. By comparing one-way and two-way contracts, we can delineate the conditions under which more complex, reciprocal cost-sharing arrangements are beneficial. This directly addresses the gap concerning the effect of bidirectional contractual cooperation on carbon-emission reduction.

Finally, the literature has not adequately examined how the carbon trading price, dynamically impacts AI-driven emission-reduction strategies under different contractual arrangements. By explicitly incorporating the carbon price as a variable and analyzing its effect on equilibrium outcomes under both single and joint-emission-reduction models, our study provides novel insights into the interaction between government regulation and private contractual mechanisms.

3. Model Description and Hypotheses

3.1. Model Description

In the context of carbon cap-and-trade, this study considers a two-level SLSSC emission-reduction model composed of one SLSP and one SLSI. First, in the initial stage, under the government-led carbon allowance allocation framework, the SLSP obtains initial carbon allowances based on industry carbon-emission benchmarks. Then, during the operation of the SLSSC, the SLSP carbon-emission difference will be traded in allowances through the carbon trading market. Finally, the SLSI builds an intelligent low-carbon logistics system by investing in AI to effectively allocate resources and reduce unnecessary resource consumption and emissions.

Based on the SLSSC emission-reduction model shown in Figure 1, we divide the emission-reduction decision-making process into three stages: In stage 1, the SLSSC-participating firms begin to commit to using AI to reduce carbon emissions in the context of market competition and environmental constraints. During this stage, the SLSP invests in AI to implement carbon-emission reduction alone while the SLSI maintains the traditional operation strategy. In the second stage, the SLSP faces the financial pressure of carbon-emission reduction, and low-carbon logistics prices are often higher than conventional logistics prices. To sustain SLSSC development, the SLSI will appropriately bear the SLSP’s AI costs and is committed to using AI to build a low-carbon logistics system for emission reduction in the whole chain. In the third stage, to promote AI application, the SLSP considers bearing part of the SLSI’s AI costs, forming in-depth AI-related cooperation between the two, and further promoting upstream and downstream SLSSC cooperation to reduce carbon emissions.

Table 1. Parameter symbols and descriptions.

Parameter Symbol	Description
$w$	SLSP’s unit logistics wholesale prices
$p$	SLSI’s sales price per unit of logistics
$c$	SLSP’s unit logistics service cost
$d$	Total volume of low-carbon logistics services in SLSP
$q$	Total potential demand for low-carbon logistics services
${\delta }_0$	SLSP’s initial carbon-emission level per unit of logistics
$\delta$	SLSP’s emission-reduction level per unit of logistics
$\epsilon$	SLSI’s level of emission-reduction effort
$Z$	Initial government carbon-emission cap
$\phi$	Carbon trading price per unit in the carbon trading market
${\lambda }_1$	Cost coefficient of carbon-emission reduction in SLSP
${\lambda }_2$	Cost coefficient of SLSI’s emission-reduction efforts
${\rho }_1$	Sensitivity coefficient of emission-reduction level to the total demand for low-carbon logistics
${\rho }_2$	Sensitivity coefficient of the level of emission-reduction effort to the total demand for low-carbon logistics
$\alpha$	Proportion of SLSI bearing SLSP’s AI cost
$\beta$	Proportion of SLSP bearing SLSI’s AI cost

shows the model-related parameters and variable symbols used in this study.

3.2. Model Hypotheses

For model analysis, we propose the following hypotheses:

Hypothesis 1.

The sales price set by the SLSI and the emission-reduction cost incurred by the SLSP are linearly related to the market demand for low-carbon logistics. This linear relationship between demand and price is commonly assumed in the existing literature. Specifically, as the SLSP increases its emission-reduction level, carbon emissions per unit of logistics decrease, which in turn stimulates greater market demand.

Hypothesis 2.

Carbon emissions per unit of logistics in an SLSSC are assumed to be constant, resulting in total emissions increasing linearly with the volume of logistics services. As this study focuses on emission reduction within the SLSSC, we consider only the emissions generated during the SLSP’s operations. In the absence of emission-reduction measures, the SLSP’s per-unit emissions remain unchanged, leading to a direct, linear relationship between total emissions and logistics activity [31,32].

Hypothesis 3.

The SLSP engages in carbon trading when actual emissions deviate from the allocated carbon cap, either exceeding or falling below it. In this context, the carbon trading price is treated as an exogenous variable shaped by market dynamics. For the cap-and-trade mechanism to remain viable, the carbon trading price must exceed the allowance selling price; otherwise, the system would fail to incentivize emission reduction effectively.

Hypothesis 4.

The emission-reduction cost of AI for the SLSP depends on its emission-reduction level while the carbon-emission reduction in the SLSI is determined by the level of low-carbon effort. Specifically, the emission-reduction function of the provider can be characterized as a monotonically increasing function of the emission-reduction level; the integrator implements carbon-emission reduction by adjusting the intensity of AI application, and its low-carbon effort will directly affect the intensity of AI application. This hypothesis does not affect the findings and is consistent with the cost settings of previous studies [33,34].

This study assumes that the emission-reduction cost for both the SLSP and SLSI follows a quadratic function of their AI investment, a formulation commonly adopted in prior research [35,36]. The main reason is that the quadratic function indicates that the revenue function has a concave form to the emission-reduction level of logistics firms. If the revenue function is monotonically increasing or decreasing to the emission-reduction level, the optimal emission-reduction level is always the bigger, the better or the smaller, the better. For this reason, it cannot be a decision variable. Also, in actual AI investment, a higher SLSSC emission-reduction level is bound to lead to an increase in the emission-reduction cost of participating firms. Later, as the emission-reduction level further increases, carbon-emission reduction becomes more difficult, leading to more costs for emission reduction. Therefore, the quadratic function can better reflect the actual situation of the SLSSC’s AI-based carbon-emission reduction. Accordingly, the SLSP’s cost of using AI to reduce carbon emissions is modeled by the function $c_P(\delta )={\displaystyle \frac{1}{2}}{\lambda }_1{\delta }^2$, where $\delta$ represents the SLSP’s emission-reduction level. For the SLSI, more intensive emission-reduction efforts in supporting low-carbon logistics incur higher associated costs. Thus, the SLSI’s emission-reduction cost is expressed as $c_I(\epsilon )={\displaystyle \frac{1}{2}}{\lambda }_2{\epsilon }^2$, where $\epsilon$ denotes the level of SLSI’s emission-reduction effort.

4. SLSSC Emission-Reduction Model Based on AI Cost Sharing

This section, based on the carbon cap-and-trade mechanism and taking the emission-reduction system of an SLSSC composed of a single SLSP and a single SLSI as the foundation, explores the total volume of low-carbon logistics and decision-making related to AI technology-based emission reduction. In this context, the SLSP directly applies AI technologies to implement carbon emission reduction, while the SLSI participates indirectly in carbon reduction efforts. Meanwhile, it analyzes the one-way AI technology cost-sharing model and the two-way AI technology cost-sharing model, and discusses the one-way cost-sharing model and the two-way cost-sharing model among the participating members of the SLSSC. Furthermore, it compares the decisions made by the SLSSC under decentralized and centralized decision-making scenarios, and analyzes the impacts of the AI technology cost-sharing ratio and carbon trading price on the SLSSC’s decisions.

4.1. One-Way Cost-Sharing Model for AI

Based on the three stages of SLSSCs using AI to reduce carbon emissions (Figure 1), we classify them into two types for discussion. The first type is a one-way cost-sharing contract in which only the SLSP invests in AI and the SLSI bears part of the upstream SLSP’s AI costs; this is why it is called a one-way AI cost-sharing model. The second type is a two-way AI sharing contract, in which the SLSI starts to invest in AI while the SLSP and the SLSI share part of each other’s AI-based emission-reduction costs; this is why it is called a two-way AI cost-sharing model. We will discuss decentralized and centralized decision-making scenarios under different cost-sharing models, aiming to achieve equilibrium in low-carbon logistics volume, emission-reduction level, level of effort, and total revenue.

We first analyze the one-way AI cost-sharing model, in which the SLSP implements AI investment and the SLSI bears part of the SLSP’s AI-based emission-reduction cost. According to Hypothesis 1, market demand is influenced by both the sales price and the emission-reduction level. Referring to previous studies [37,38], we set the function form as

$$d=a-p+{\rho }_1\delta .$$

(1)

For the sake of model simplicity and to highlight the key content of this study, we will temporarily disregard the elastic impact of price on market demand, which will be the focus of future analysis. Next, we analyze SLSSC emission-reduction equilibrium decision-making in the decentralized and centralized scenarios.

4.1.1. One-Way AI Cost-Sharing Model in the Decentralized Scenario

In the decentralized scenario, SLSP first invests in low-carbon logistics technology and determines the wholesale price $w$ and emission-reduction level $\delta$ of shipping logistics based on costs and benefits. SLSI responds by making decisions on low-carbon logistics pricing or order quantity, and sets the sales price $p$ with the goal of maximizing its own profits. Therefore, in the Stackelberg game between SLSP and SLSI, SLSP is the leader and SLSI is the follower. In this paper, the cost-sharing ratios $\alpha$ and $\beta$ can be interpreted as an equilibrium result stemming from a comprehensive game involving factors such as bargaining power among members, reservation utilities, and investment efficiencies. For example, a relatively high cost-sharing ratio may indicate that the corresponding member has stronger bargaining power or makes a greater contribution to the success of the cooperation. In the inference section of this paper, the focus will be on discussing that, to achieve coordination and optimization of the SLSSC, these ratios must meet the incentive-compatibility constraint. That is, they should ensure that the benefits each party receives after participating in the cooperation are superior to their respective reservation utilities.

Based on the previously stated assumptions, the revenue functions of the SLSP and SLSI, denoted as (${\pi }_P^{sd}$) and (${\pi }_I^{sd}$) respectively, are given by

$${\pi }_P^{sd}=(w-c)d-[({\delta }_0-\delta )d-Z]\phi -(1-\alpha )c_P(\delta ),$$

(2)

$${\pi }_I^{sd}=(p-w)d-\alpha c_P(\delta ).$$

(3)

For concision, the decentralized and centralized decision-making scenarios in the one-way AI cost-sharing model are denoted by superscripts $sd$ and $sc$, respectively. $\ast$ represents the optimal solution of the corresponding scenarios. By applying the method of backward induction, we derive the optimal solution to the model, as formally stated in Proposition 1.

Proposition 1.

In the one-way AI cost-sharing model in the decentralized scenario, the optimal wholesale price $w^{sd\ast }$, sales price $p^{sd\ast }$, and emission-reduction level ${\delta }^{sd\ast }$ of the SLSSC are as follows:

$$\begin{gathered} w^{sd\ast }={\displaystyle \frac{(q+c+\phi {\delta }_0)[2(1-\alpha ){\lambda }_1-{\rho }_1\phi ]-{\phi }^{2}q-{\rho }_1^2(c+\phi {\delta }_0)}{4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2}}, \\ {p}^{sd\ast }={\displaystyle \frac{q[3(1-\alpha ){\lambda }_1-{\rho }_1\phi -{\phi }^2]+(c+\phi {\delta }_0)[(1-\alpha ){\lambda }_1-{\rho }_1\phi -{\phi }^2]}{4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2}}, \\ {\delta }^{sd\ast }={\displaystyle \frac{(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2}}. \end{gathered}$$

Substituting the above optimal solutions $w^{sd\ast }$, $p^{sd\ast }$, and ${\delta }^{sd\ast }$ into Equations (1)–(3), the optimal low-carbon logistics volume $d^{sd\ast }$ and the optimal revenues ${\pi }_P^{sd\ast }$ and ${\pi }_I^{sd\ast }$ of the SLSP can be obtained:

$$\begin{gathered} d^{sd\ast }={\displaystyle \frac{{\lambda }_1(1-\alpha )(q-c-\phi {\delta }_0)}{4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2}}, \\ {\pi }_P^{sd\ast }=\phi Z+{\displaystyle \frac{{(q-c-\phi {\delta }_0)}^2[4{(1-\alpha )}^2{\lambda }_1^2-{\lambda }_1(1-\alpha ){(\phi +{\rho }_1)}^2]}{2{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2]}^2}}, \\ {\pi }_I^{sd\ast }={\displaystyle \frac{{(q-c-\phi {\delta }_0)}^2[2{(1-\alpha )}^2{\lambda }_1^2-{\lambda }_1\alpha {(\phi +{\rho }_1)}^2]}{2{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2]}^2}}. \end{gathered}$$

Proof. 

In the one-way AI cost-sharing model, the interaction between the SLSP and the SLSI is formulated as a Stackelberg game. Using backward induction, we first derive the SLSI’s optimal selling price as the follower and then determine the SLSP’s optimal wholesale price and emission-reduction level as the leader. Accordingly, taking the first- and second-order derivatives of the SLSI’s profit function with respect to the selling price p yields the following:

$${\displaystyle \frac{\partial {\pi }_I^{sd}}{\partial p}}=q+\delta {\rho }_1+w-2p, {\displaystyle \frac{{\partial }^2{\pi }_I^{sd}}{\partial p^2}}=-2.$$

□

From the second-order derivative condition ${\partial }^2{\pi }_I^{sd}/\partial p^2<0$, it can be established that the SLSI’s revenue function ${\pi }_I$ is strictly concave with respect to its selling price $p$. The optimal price is determined by setting $\partial {\pi }_I^{sd}/\partial p=0$. Under the assumption of symmetric information within the SLSSC, this optimal selling price $p=(q+\delta {\rho }_1+w)/2$ is then substituted into Equation (2) to facilitate the SLSP’s optimization. Subsequently, the first-order derivatives of the SLSP’s profit function with respect to both the wholesale price $w$ and the emission-reduction level $\delta$ are derived as follows:

$$\begin{gathered} {\displaystyle \frac{\partial {\pi }_P^{sd}}{\partial w}}={\displaystyle \frac{q}{2}}+{\displaystyle \frac{c+\phi {\delta }_0}{2}}+{\displaystyle \frac{{\rho }_1-\phi }{2}}\delta -w, \\ {\displaystyle \frac{\partial {\pi }_P^{sd}}{\partial \delta }}={\displaystyle \frac{\phi q}{2}}+{\displaystyle \frac{{\rho }_1-\phi }{2}}w-{\displaystyle \frac{c+\phi {\delta }_0}{2}}{\rho }_1+\delta [\phi {\rho }_1-{\lambda }_1(1-\alpha )]. \end{gathered}$$

At this point, the Hessian matrix of the SLSP’s revenue function ${\pi }_P^{sd}$ is

$$H({\pi }_P^{sd})=\left[\begin{array}{cc}-1& {\displaystyle \frac{{\rho }_1-\phi }{2}}\\ {\displaystyle \frac{{\rho }_1-\phi }{2}}& \phi {\rho }_1-{\lambda }_1(1-\alpha )\end{array}\right].$$

According to the matrix $H({\pi }_P^{sd})$, the parameter ${\lambda }_1$ assumed in this study is large enough so that when $H{({\pi }_P^{sd})}_{11}<0$, $H({\pi }_P^{sd})$ is a negative definite matrix. To ensure the maximum value of the concavity of wholesale price $w$ and emission-reduction level $\delta$ in the model, let $Det[H({\pi }_P^{sd})]={\lambda }_1(1-\alpha )-{\displaystyle \frac{1}{4}}{({\rho }_1+\phi )}^2>0$, and we can obtain ${\lambda }_1>{\displaystyle \frac{{({\rho }_1+\phi )}^2}{4(1-\alpha )}}$. Let ${\displaystyle \frac{\partial {\pi }_P^{sd}}{\partial w}}=0$ and ${\displaystyle \frac{\partial {\pi }_P^{sd}}{\partial \delta }}=0$; then, we can solve for the optimal wholesale price $w^{sd\ast }$, selling price $p^{sd\ast }$, and emission-reduction level ${\delta }^{sd\ast }$ of the SLSSC. Furthermore, we can obtain the optimal low-carbon logistics volume $d^{sd\ast }$ as well as the optimal revenues ${\pi }_P^{sd\ast }$ and ${\pi }_I^{sd\ast }$. Thus, Proposition 1 is proved.

Based on the optimal solution of Proposition 1, Corollary 1 is further derived.

Corollary 1.

The optimal equilibrium solutions for emission-reduction level ${\delta }^{sd\ast }$ and low-carbon logistics volume $d^{sd\ast }$ are $\partial {\delta }^{sd\ast }/\partial \alpha >0$ and $\partial d^{sd\ast }/\partial \alpha >0$, respectively, which in turn lead to ${\delta }^{sd\ast }\ge {\delta }_{\alpha =0}^{sd\ast }$ and $d^{sd\ast }\ge d_{\alpha =0}^{sd\ast }$.

Proof. 

Taking the first-order derivatives of the optimal emission-reduction level ${\delta }^{sd\ast }$ of the SLSP and the optimal total low-carbon logistics volume $d^{sd\ast }$, we can obtain ${\displaystyle \frac{\partial {\delta }^{sd\ast }}{\partial \alpha }}={\displaystyle \frac{4{\lambda }_1(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2]}^2}}>0$ and ${\displaystyle \frac{\partial d^{sd\ast }}{\partial \alpha }}={\displaystyle \frac{{\lambda }_1(q-c-\phi {\delta }_0){(\phi +{\rho }_1)}^2}{{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2]}^2}}>0$. Since $\partial {\delta }^{sd\ast }/\partial \alpha >0$ and $\partial d^{sd\ast }/\partial \alpha >0$, we know that variables ${\delta }^{sd\ast }$ and $d^{sd\ast }$ are positively correlated with parameter $\alpha$; that is, when $\alpha =0$, ${\delta }_{\alpha =0}^{sd\ast }$ and $d_{\alpha =0}^{sd\ast }$ are minimized. Thus, Corollary 1 is proved. □

Corollary 1 indicates that both the SLSP’s emission-reduction level ${\delta }^{sd\ast }$ and the low-carbon logistics volume $d^{sd\ast }$ are positively correlated with the proportion $\alpha$ of AI costs shared by the SLSI. As $\alpha$ increases, the emission-reduction level and low-carbon logistics volume for the SLSP also increase. When the SLSI actively bears the emission-reduction cost of the SLSP, the SLSP is more inclined to implement AI in carbon-emission reduction, thus promoting green logistics practices in the whole SLSSC. This finding is consistent with existing shipping and logistics practices. As the SLSI increases its share of AI costs, the cost pressure faced by the SLSP is alleviated, thus contributing to the overall level of carbon-emission reduction. Maersk, one of the world’s leading shipping logistics firms, has not only adopted advanced AI in its operations to reduce its carbon footprint but has also incentivized and supported the SLSP to adopt AI through a collaborative model with the SLSP. This cooperative approach reduces the additional costs the SLSP incurs to implement AI to reduce emissions, thus promoting carbon-emission reduction in shipping logistics as a whole. Moreover, when the SLSI shares a portion of the upstream AI costs, both the emission-reduction level and the low-carbon logistics volume increase significantly. This finding underscores the effectiveness of the one-way AI cost-sharing contract in enhancing carbon-emission reduction within the SLSSC.

4.1.2. One-Way AI Cost-Sharing Model in the Centralized Scenario

In the centralized scenario, the SLSP and SLSI jointly make decisions to maximize the total benefit of the SLSSC. The corresponding revenue function of the SLSSC (${\pi }^{sc}$) is given by

$${\pi }^{sc}=(p-c)d-[({\delta }_0-\delta )d-Z]\phi -c_P(\delta ).$$

(4)

Proposition 2 can be obtained from Equation (4).

Proposition 2.

In the one-way AI cost-sharing model in the centralized scenario, the optimal selling price $p^{sc\ast }$ and emission-reduction level ${\delta }^{sc\ast }$ of the SLSSC, the low-carbon logistics volume $d^{sc\ast }$, and the overall revenue ${\pi }^{sc\ast }$ are as follows:

$$\begin{gathered} p^{sc\ast }={\displaystyle \frac{({\lambda }_1-{\rho }_1\phi )(q+c+\phi {\delta }_0)-{\rho }_1^2(c+\phi {\delta }_0)-q{\phi }^2}{2{\lambda }_1-{(\phi +{\rho }_1)}^2}}, \\ {\delta }^{sc\ast }={\displaystyle \frac{(\phi +{\rho }_1)(q-c-\phi {\delta }_0)}{2{\lambda }_1-{(\phi +{\rho }_1)}^2}}. \end{gathered}$$

By substituting the above optimal solutions $p^{sc\ast }$ and ${\delta }^{sc\ast }$ into Equations (1) and (4), the optimal low-carbon logistics volume $d^{sc\ast }$ and overall revenue ${\pi }^{sc\ast }$ of the SLSSC can be obtained:

$$\begin{gathered} d^{sc\ast }={\displaystyle \frac{{\lambda }_1(q-c-\phi {\delta }_0)}{2{\lambda }_1-{(\phi +{\rho }_1)}^2}}, \\ {\pi }^{sc\ast }={\displaystyle \frac{[2{\lambda }_1^2-{\lambda }_1{(\phi +{\rho }_1)}^2]{(q-c-\phi {\delta }_0)}^2}{2{[2{\lambda }_1-{(\phi +{\rho }_1)}^2]}^2}}+\phi Z. \end{gathered}$$

Proof. 

Similar to the way Proposition 1 is proved, solving for the first-order derivative of the SLSSC revenue function with respect to sales price $p$ and emission-reduction level $\delta$ and then solving for the second-order derivative leads to the following:

$${\displaystyle \frac{{\partial }^2{\pi }^{sc}}{\partial p^2}}=-2, {\displaystyle \frac{{\partial }^2{\pi }^{sc}}{\partial p\partial \delta }}={\displaystyle \frac{{\partial }^2{\pi }^{sc}}{\partial p\partial \delta }}={\rho }_1-\phi , {\displaystyle \frac{{\partial }^2{\pi }^{sc}}{\partial {\delta }^2}}=2{\rho }_1\phi -{\lambda }_1.$$

□

At this point, the Hessian matrix of the SLSSC revenue function ${\pi }^{sc}$ is

$$H({\pi }^{sc})=\left[\begin{array}{cc}-2& {\rho }_1-\phi \\ {\rho }_1-\phi & 2\phi {\rho }_1-{\lambda }_1\end{array}\right].$$

Based on matrix $H({\pi }^{sc})$, to ensure that the SLSSC achieves maximum profit under the centralized scenario, this paper assumes that parameter ${\lambda }_1$ is sufficiently large. Consequently, $H{({\pi }^{sc})}_{11}<0$ is set in such a way that $H({\pi }^{sc})$ becomes a negative definite matrix. The corresponding concave function can guarantee the existence of a maximum profit value. Meanwhile, to ensure the concavity and the existence of maximum values for the selling price $p$ and the carbon-emission reduction level $\delta$ in the model, by setting $Det[H({\pi }^{sc})]=2{\lambda }_1-{(\phi +{\rho }_1)}^2>0$, we can obtain ${\lambda }_1>{\displaystyle \frac{{({\rho }_1+\phi )}^2}{2}}$. Under this condition, the SLSSC in the centralized scenario can achieve profit maximization. The optimal selling price $p^{sc\ast }$ and emission-reduction level ${\delta }^{sc\ast }$ of the SLSSC can be obtained by letting ${\displaystyle \frac{\partial {\pi }^{sc}}{\partial p}}=0$ and ${\displaystyle \frac{\partial {\pi }^{sc}}{\partial \delta }}=0$. Subsequently, the optimal total low-carbon logistics volume $d^{sc\ast }$ and overall revenue ${\pi }^{sc\ast }$ can be solved. Thus, Proposition 2 is proved.

The optimal solution of Proposition 2 further leads to Corollary 2.

Corollary 2.

(1) 

When $0\le \alpha <1/2$, ${\delta }^{sc\ast }>{\delta }^{sd\ast }$; when $1/2<\alpha \le 1$, ${\delta }^{sc\ast }<{\delta }^{sd\ast }$.

(2) 

When $0\le \alpha <{\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}$, $d^{sc\ast }>d^{sd\ast }$; when ${\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}<\alpha \le 1$, $d^{sc\ast }<d^{sd\ast }$.

Proof. 

Since the parameter ${\lambda }_1$ is large enough, it satisfies $2{\lambda }_1-{(\phi +{\rho }_1)}^2>0$ and $4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2>0$. This section mainly analyzes the effect of the proportion $\alpha$ of emission-reduction costs borne by the SLSI for the SLSP on low-carbon logistics volume $q$ and emission-reduction level $\delta$. □

(1) From Propositions 1 and 2, it follows that

${\delta }^{sc\ast }-{\delta }^{sd\ast }={\displaystyle \frac{2{\lambda }_1(1-2\alpha )(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2][2{\lambda }_1-{(\phi +{\rho }_1)}^2]}}$. Therefore, when $0\le \alpha <1/2$, ${\delta }^{sc\ast }>{\delta }^{sd\ast }$; when $1/2<\alpha \le 1$, ${\delta }^{sc\ast }<{\delta }^{sd\ast }$.

(2) Similarly, it follows from Propositions 1 and 2 that

$d^{sc\ast }-d^{sd\ast }={\displaystyle \frac{{\lambda }_1(q-c-\phi {\delta }_0)[2{\lambda }_1(1-\alpha )-\alpha {(\phi +{\rho }_1)}^2]}{[4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2][2{\lambda }_1-{(\phi +{\rho }_1)}^2]}}$. Therefore, when $0\le \alpha <{\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}$, $d^{sc\ast }>d^{sd\ast }$; when ${\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}<\alpha \le 1$, $d^{sc\ast }<d^{sd\ast }$. Now, Corollary 2 has been proved.

The comparison in Corollary 2 reveals that centralized decision-making does not universally lead to superior outcomes in terms of emission-reduction level and low-carbon logistics volume under a cap-and-trade regime. According to part (1) of Corollary 2, when the SLSI’s AI cost-sharing proportion $0\le \alpha <1/2$ is relatively low, centralized coordination results in a higher emission-reduction level than decentralized decision-making. However, when $1/2<\alpha \le 1$ is sufficiently high, the decentralized model produces better emission-reduction outcomes. This suggests that when the SLSI bears a relatively small share of the SLSP’s AI cost, centralized decision-making enhances carbon-emission reduction. However, as the SLSI assumes a greater share of the cost—thereby alleviating the SLSP’s emission-reduction burden—decentralized decision-making becomes more effective for promoting emission reduction in the SLSSC.

According to part (2) of Corollary 2, the centralized scenario yields a higher low-carbon logistics volume than the decentralized scenario when the SLSI bears a smaller share of the SLSP’s AI costs ($0\le \alpha <{\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}$). Conversely, when the SLSP assumes a lower share of AI costs (${\displaystyle \frac{2{\lambda }_1}{2{\lambda }_1+{(\phi +{\rho }_1)}^2}}<\alpha \le 1$), the decentralized scenario results in greater logistics volume. These findings suggest that centralized decision-making enhances low-carbon logistics output when the SLSI’s cost participation is minimal. In contrast, when the SLSI bears a higher proportion of AI costs, decentralized decision-making aligns more closely with market preferences for low-carbon logistics.

4.2. Two-Way Cost-Sharing Model for AI

In the two-way AI cost-sharing model, the SLSI starts to invest in AI to enhance its green logistics abilities and reduce the emission-reduction pressure faced by the SLSP. At this time, the SLSP and the SLSI share part of each other’s AI costs, in which the SLSP directly implements carbon-emission reduction in its logistics while the SLSI indirectly implements carbon-emission reduction through low-carbon operations, as shown in Figure 1.

Based on Hypothesis 1 and with reference to the existing functional form [39,40], the correlation function of market demand with sales price and emission-reduction level is as follows:

$$d=a-p+{\rho }_1\delta +{\rho }_2\epsilon .$$

(5)

The equilibrium decision-making of the SLSSC two-way AI cost-sharing model are analyzed below in the decentralized and centralized scenarios.

4.2.1. Two-Way AI Cost-Sharing Model in the Decentralized Scenario

As in the one-way contract scenario, the two-way AI cost-sharing model is structured as a two-stage Stackelberg game. The SLSP, acting as the leader, first determines the wholesale price $w$ and its emission-reduction level $\delta$. Subsequently, the SLSI, as the follower, sets the selling price $p$ and its own emission-reduction effort $\epsilon$ in response to the SLSP’s decisions. Based on the prior assumptions, the profit functions of the SLSP and SLSI, denoted by ${\pi }_P^{bd}$ and ${\pi }_I^{bd}$ respectively, are as follows:

$${\pi }_P^{bd}=(w-c)d-[({\delta }_0-\delta )d-Z]\phi -(1-\alpha )c_P(\delta )-\beta c_I(\epsilon ),$$

(6)

$${\pi }_I^{bd}=(p-w)d-\alpha c_P(\delta )-(1-\beta )c_I(\epsilon ).$$

(7)

We denote the decentralized and centralized decision-making scenarios in the two-way AI cost-sharing model with superscripts $bd$ and $bc$, respectively. The asterisk symbol $\ast$ indicates the optimal values under each scenario. Using the method of backward induction, we obtain Proposition 3.

Proposition 3.

In the decentralized two-way AI cost-sharing model, the optimal wholesale price $w^{bd\ast }$, sales price $p^{bd\ast }$, emission-reduction level ${\delta }^{bd\ast }$, and emission-reduction effort ${\delta }^{bd\ast }$ of the SLSSC are as follows:

$$\begin{gathered} w^{bd\ast }=q+{\rho }_1{\delta }^{bd\ast }-{\displaystyle \frac{{\lambda }_1(1-\alpha )[2{\lambda }_2(1-\beta )-{\rho }_2^2]{\delta }^{bd\ast }}{{\lambda }_2(1-\beta )(\phi +{\rho }_1)}}, \\ {p}^{bd\ast }={\displaystyle \frac{{\lambda }_2(1-\alpha )(q+{\rho }_1{\delta }^{bd\ast }+w^{bd\ast }]-{\rho }_2^2{w}^{bd\ast }}{2{\lambda }_2(1-\beta )-{\rho }_2^2}}, \\ {\delta }^{bd\ast }={\displaystyle \frac{{\lambda }_2^2{(1-\beta )}^2(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{{\lambda }_1{\lambda }_2(1-\alpha )[4{\lambda }_2{(1-\beta )}^2-(2-3\beta ){\rho }_2^2]-{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2}}, \\ {\epsilon }^{bd\ast }={\displaystyle \frac{{\lambda }_1{\lambda }_2{\rho }_2(1-\alpha )(1-\beta )(q-c-\phi {\delta }_0)}{{\lambda }_1{\lambda }_2(1-\alpha )[4{\lambda }_2{(1-\beta )}^2-(2-3\beta ){\rho }_2^2]-{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2}}. \end{gathered}$$

Substituting the above optimal solutions $w^{bd\ast }$, $p^{bd\ast }$, ${\delta }^{bd\ast }$, and ${\epsilon }^{bd\ast }$ into Equations (5)–(7) leads to the optimal low-carbon logistics volume $d^{bd\ast }$ as well as the optimal revenues ${\pi }_P^{bd\ast }$ and ${\pi }_I^{bd\ast }$ for the SLSP:

$$\begin{gathered} d^{bd\ast }={\displaystyle \frac{{\lambda }_1{\lambda }_2^2(1-\alpha ){(1-\beta )}^2(q-c-\phi {\delta }_0)}{{\lambda }_1{\lambda }_2(1-\alpha )[4{\lambda }_2{(1-\beta )}^2-(2-3\beta ){\rho }_2^2]-{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2}}, \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\pi }_P^{bd\ast }=\phi Z+{\displaystyle \frac{{\lambda }_1^2{\lambda }_2^2{(1-\alpha )}^2[4{\lambda }_2^2{(1-\beta )}^2-(2-3\beta ){\lambda }_2{\rho }_2^2]}{{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2}}{({\delta }^{bd\ast })}^2-{\displaystyle \frac{1}{2}}{\lambda }_1(1-\alpha ){({\delta }^{bd\ast })}^2, \\ \hspace{1em}\hspace{1em}\hspace{1em}{\pi }_I^{bd\ast }={\displaystyle \frac{{\lambda }_1^2{(1-\alpha )}^2[4{\lambda }_2^2{(1-\beta )}^2-(1-\beta ){\lambda }_2{\rho }_2^2]}{{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2}}{({\delta }^{bd\ast })}^2-{\displaystyle \frac{1}{2}}{\lambda }_1\alpha {({\delta }^{bd\ast })}^2. \end{gathered}$$

Proof. 

The proof of this proposition is similar to that of Proposition 1. The solution is first found for the optimal wholesale price $w^{bd\ast }$, sales price $p^{bd\ast }$, emission-reduction level ${\delta }^{bd\ast }$, and emission-reduction effort ${\epsilon }^{bd\ast }$ of the SLSSC. Then, the optimal low-carbon logistics volume $d^{bd\ast }$ and the optimal revenues ${\pi }_P^{bd\ast }$ and ${\pi }_I^{bd\ast }$ are derived. The specific process will not be repeated; thus, Proposition 3 is proved. □

According to the optimal solution of Proposition 3, Corollary 3 can be obtained.

Corollary 3.

(1) 

When $0\le \beta <1/3$, $\partial {\delta }^{bd\ast }/\partial \beta >0$ and $\partial d^{bd\ast }/\partial \beta >0$; when $1/3<\beta \le 1$, $\partial {\delta }^{bd\ast }/\partial \beta <0$ and $\partial d^{bd\ast }/\partial \beta <0$.

(2) 

When $0\le \beta <1/2$, ${\delta }^{bd\ast }>{\delta }_{\beta =0}^{bd\ast }$ and $d^{bd\ast }>d_{\beta =0}^{bd\ast }$, ${\delta }^{bd\ast }>{\delta }_{\alpha =0}^{bd\ast }$, and $d^{bd\ast }>d_{\alpha =0}^{bd\ast }$; when $1/2<\beta \le 1$, ${\delta }^{bd\ast }<{\delta }_{\beta =0}^{bd\ast }$ and $d^{bd\ast }<d_{\beta =0}^{bd\ast }$.

Proof. 

(1)

For the emission-reduction level ${\delta }^{bd\ast }$ and low-carbon logistics volume $d^{bd\ast }$ in Proposition 3, solving the first-order derivatives with respect to $\beta$ leads to the following:

$$\begin{gathered} {\displaystyle \frac{\partial {\delta }^{bd\ast }}{\partial \beta }}={\displaystyle \frac{{\lambda }_1{\lambda }_2^3{\rho }_2^2(1-\alpha )(1-\beta )(1-3\beta )(\phi +{\rho }_1)(q-c-\phi {\delta }_0)}{{\{{\lambda }_1{\lambda }_2(1-\alpha )[4{\lambda }_2{(1-\beta )}^2-(2-3\beta ){\rho }_2^2]-{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2\}}^2}}, \\ {\displaystyle \frac{\partial d^{bd\ast }}{\partial \beta }}={\displaystyle \frac{{\lambda }_1^2{\lambda }_2^3{\rho }_2^2(1-\alpha ){(1-\beta )}^2(1-3\beta )(q-c-\phi {\delta }_0)}{{\{{\lambda }_1{\lambda }_2(1-\alpha )[4{\lambda }_2{(1-\beta )}^2-(2-3\beta ){\rho }_2^2]-{[{\lambda }_2(1-\beta )(\phi +{\rho }_1)]}^2\}}^2}}. \end{gathered}$$

Thus, when the proportion of the SLSP bearing the emission-reduction costs of the SLSI is $0\le \beta <1/3$, $\partial {\delta }^{bd\ast }/\partial \beta >0$ and $\partial d^{bd\ast }/\partial \beta >0$. When $1/3<\beta \le 1$, $\partial {\delta }^{bd\ast }/\partial \beta <0$ and $\partial d^{bd\ast }/\partial \beta <0$.

(2)

Based on emission-reduction level ${\delta }^{bd\ast }$, the following can be obtained:

$${\delta }^{bd\ast }={\displaystyle \frac{{\lambda }_2^2(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{{\lambda }_1{\lambda }_2(1-\alpha )\{4{\lambda }_2-[(2-3\beta ){\rho }_2^2/{(1-\beta )}^2]\}-{[{\lambda }_2(\phi +{\rho }_1)]}^2}}.$$

□

From the above equation, it is easy to obtain ${\delta }_{\beta =1/2}^{bd\ast }={\delta }_{\beta =0}^{bd\ast }$. According to the derivative in (1), when $0\le \beta <1/2$, ${\delta }^{bd\ast }>{\delta }_{\beta =0}^{bd\ast }$, and when $1/2<\beta \le 1$, ${\delta }^{bd\ast }>{\delta }_{\beta =0}^{bd\ast }$. A similar method can be used to obtain the low-carbon logistics volume $d^{bd\ast }$. Now, Corollary 3 has been proved.

Corollary 3(1) analyzes the effect of the SLSP’s cost-sharing proportion $\beta$ for the SLSI’s AI investment on emission-reduction levels and low-carbon logistics volume. As $\beta$ increases, both variables exhibit consistent but nonmonotonic behavior. Specifically, when $0\le \beta <1/3$, the emission-reduction level and logistics volume are positively correlated with $\beta$; when $1/3<\beta \le 1$, the emission-reduction level and low-carbon logistics volume $\beta$ are negatively correlated with the cost proportion of AI. These findings suggest that, within a certain range, the SLSP bearing a portion of the SLSI’s AI cost supports greater emission reduction and increases low-carbon logistics volume. However, when the cost-sharing proportion $\beta$ exceeds a critical threshold, this effect reverses. The main reason is that, limited cost sharing alleviates the SLSI’s financial burden, thereby expanding market demand for low-carbon services and motivating the SLSP to invest further in emission reduction. Conversely, excessive cost-sharing imposes operational strain on the SLSP, ultimately hindering its ability to sustain emission-reduction initiatives and low-carbon logistics.

Corollary 3(2) investigates how different cost-sharing configurations—specifically one-way and two-way AI cost-sharing arrangements—affect the emission-reduction level and low-carbon logistics volume in the SLSSC. The results show that when $0\le \beta <1/2$, the emission-reduction level and low-carbon logistics volume are significantly better when the SLSP bears AI costs than when it does not. Similarly, when $1/2<\beta \le 1$, the emission-reduction level and low-carbon logistics volume are significantly better when SLSI bears AI costs than when it does not. Overall, both one-way and two-way AI cost-sharing contracts can enhance SLSSC performance, provided the SLSP’s cost-sharing proportion falls within an appropriate range ($0\le \beta <1/2$).

4.2.2. Two-Way AI Cost-Sharing Model in the Centralized Scenario

In the centralized scenario, the SLSP and SLSI jointly determine emission-reduction strategies under the two-way AI cost-sharing model. The corresponding emission-reduction revenue function of the SLSSC is given by

$${\pi }^{bc}=(p-c)d-[({\delta }_0-\delta )d-Z]\phi -c_P(\delta )-c_I(\epsilon )$$

(8)

Similarly, solving for the optimal solution of the model leads to Proposition 4.

Proposition 4.

In the two-way AI cost-sharing model in the centralized scenario, the optimal selling price $p^{bc\ast }$, emission-reduction level ${\delta }^{bc\ast }$, and emission-reduction effort ${\epsilon }^{bc\ast }$ of the SLSSC are as follows:

$$\begin{gathered} {\delta }^{bc\ast }={\displaystyle \frac{{\lambda }_2(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{{\lambda }_1[2{\lambda }_2-{\rho }_2^2]-{\lambda }_2{(\phi +{\rho }_1)}^2}}, \\ {\epsilon }^{bc\ast }={\displaystyle \frac{{\lambda }_1{\rho }_2(q-c-\phi {\delta }_0)}{{\lambda }_1[2{\lambda }_2-{\rho }_2^2]-{\lambda }_2{(\phi +{\rho }_1)}^2}}, \\ {p}^{bc\ast }={\displaystyle \frac{{\lambda }_2(q-c-\phi {\delta }_0)[{\lambda }_1-\phi (\phi +{\rho }_1)]}{{\lambda }_1[2{\lambda }_2-{\rho }_2^2]-{\lambda }_2{(\phi +{\rho }_1)}^2}}+\phi {\delta }_0+c. \end{gathered}$$

Substituting the above optimal solution into Equations (5)–(8) leads to the SLSP’s optimal low-carbon logistics volume $d^{bc\ast }$ and the SLSSC’s optimal revenue ${\pi }^{bc\ast }$:

$$\begin{gathered} d^{bc\ast }={\displaystyle \frac{{\lambda }_1{\lambda }_2(q-c-\phi {\delta }_0)}{{\lambda }_1[2{\lambda }_2-{\rho }_2^2]-{\lambda }_2{(\phi +{\rho }_1)}^2}}, \\ {\pi }^{bc\ast }={\displaystyle \frac{{\lambda }_1{\lambda }_2{(q-c-\phi {\delta }_0)}^2[2{\lambda }_1{\lambda }_2-{\lambda }_1{\rho }_2^2-{\lambda }_2{(\phi +{\rho }_1)}^2]}{2{[{\lambda }_1(2{\lambda }_2-{\rho }_2^2)-{\lambda }_2{(\phi +{\rho }_1)}^2]}^2}}+\phi Z. \end{gathered}$$

Proof. 

The proof process is similar to that of Proposition 2 and will not be repeated here. □

The optimal equilibrium solution obtained from Proposition 4 leads to Corollary 4.

Corollary 4.

(1) 

When $2{\lambda }_2{(1-\beta )}^2(1-2\alpha )\ge (3\alpha \beta -2\alpha -{\beta }^2-\beta +1){\rho }_2^2$, ${\delta }^{bc\ast }\ge {\delta }^{bd\ast }$; when $2{\lambda }_2{(1-\beta )}^2(1-2\alpha )<(3\alpha \beta -2\alpha -{\beta }^2-\beta +1){\rho }_2^2$, ${\delta }^{bc\ast }<{\delta }^{bd\ast }$.

(2) 

When $(1-{\beta }^2-\beta ){\rho }_2^2/{\lambda }_2(1-{\beta }^2)+\alpha {({\rho }_1+\phi )}^2/{\lambda }_1(1-\alpha )\ge 2$, $d^{bc\ast }\le d^{bd\ast }$; when $(1-{\beta }^2-\beta ){\rho }_2^2/{\lambda }_2(1-{\beta }^2)+\alpha {({\rho }_1+\phi )}^2/{\lambda }_1(1-\alpha )<2$, $d^{bc\ast }>d^{bd\ast }$.

Proof. 

The proof process is similar to that of Corollary 2 and will not be repeated here. □

In Corollary 4, we compare the emission-reduction level and low-carbon logistics volume in the two-way AI cost-sharing model for both decentralized and centralized scenarios. The analysis reveals that, under certain conditions, centralized decision-making consistently outperforms decentralized decision-making. Specifically, according to (1) in Corollary 4, when $2{\lambda }_2{(1-\beta )}^2(1-2\alpha )\ge (3\alpha \beta -2\alpha -{\beta }^2-\beta +1){\rho }_2^2$, the emission-reduction level in the centralized scenario exceeds that of the decentralized scenario. Otherwise, the emission-reduction level in the decentralized scenario is higher. According to part (2) of Corollary 4, when $(1-{\beta }^2-\beta ){\rho }_2^2/{\lambda }_2(1-{\beta }^2)+\alpha {({\rho }_1+\phi )}^2/{\lambda }_1(1-\alpha )\ge 2$, the low-carbon logistics volume in the decentralized decision-making scenario exceeds that in the centralized scenario. Otherwise, the centralized scenario results in a higher low-carbon logistics volume. This demonstrates that in the two-way AI cost-sharing model between the SLSP and the SLSI, the cost-sharing proportion plays a significant role in influencing the SLSSC’s emission-reduction strategies. While centralized decision-making is typically optimal for carbon-emission reduction, under specific conditions, decentralized decision-making can lead to superior outcomes in both emission reduction and logistics volume.

5. Comparative Analysis of SLSSC Emission-Reduction Strategies Based on AI Cost Sharing

In this section, by comparing the optimal equilibrium solutions under both the one-way and two-way AI cost-sharing models, we analyze how different emission-reduction strategies influence the decision-making process in each model. This allows us to identify the SLSSC’s optimal AI-driven emission-reduction model under various conditions.

Here, by comparing optimal equilibrium solutions under the one-way and two-way AI cost-sharing models, we analyze the effect of different emission-reduction strategies on the decision-making of either model to determine the SLSSC’s optimal model based on AI-driven carbon-emission reduction under different conditions.

Corollary 5.

The comparison of the one-way and two-way AI cost-sharing models in the decentralized scenario shows that when $0<\beta <2/3$, ${\delta }^{bd\ast }>{\delta }^{sd\ast }$ and $d^{bd\ast }>d^{sd\ast }$; when $2/3<\beta <1$, ${\delta }^{bd\ast }<{\delta }^{sd\ast }$ and $d^{bd\ast }<d^{sd\ast }$.

Proof. 

According to Propositions 1 and 3, simplifying the optimal level of carbon-emission reduction and the low-carbon logistics volume of the SLSSC in the decentralized scenario leads to

$$\begin{gathered} {\delta }^{sd\ast }={\displaystyle \frac{(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{4{\lambda }_1(1-\alpha )-{(\phi +{\rho }_1)}^2}}, \\ {\delta }^{bd\ast }={\displaystyle \frac{(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{{\lambda }_1(1-\alpha )[4-(2-3\beta ){\rho }_2^2/{\lambda }_2{(1-\beta )}^2]-{(\phi +{\rho }_1)}^2}}. \end{gathered}$$

□

By comparing the two equations ${\delta }^{sd\ast }$ and ${\delta }^{bd\ast }$, it is easy to see that in terms of the proportion of the SLSP bearing AI costs, when $0<\beta <2/3$, ${\delta }^{bd\ast }>{\delta }^{sd\ast }$. By contrast, when $2/3<\beta <1$, ${\delta }^{bd\ast }<{\delta }^{sd\ast }$. Likewise, the relationship between the optimal low-carbon logistics volume under different models can be proved using the same method. Corollary 5 is thus proved.

Corollary 5 compares the optimal carbon-emission-reduction level and low-carbon logistics volume across different models in the decentralized scenario. The optimal equilibrium under the two-way cost-sharing model exceeds that of the one-way model when the SLSP’s share of the AI cost is below a certain threshold, i.e., $0<\beta <2/3$. Conversely, when the SLSP’s share surpasses this threshold, i.e., $2/3<\beta <1$, the one-way model yields a higher optimal equilibrium. This suggests that when the SLSP’s share of the SLSI’s AI costs is low, the two-way AI cost-sharing model is more effective in achieving higher emission-reduction levels and low-carbon logistics volumes. As the proportion of cost sharing increases, the advantage of the two-way AI cost-sharing model gradually decreases. When the SLSP’s cost-sharing proportion is too high, the SLSSC will choose the one-way AI cost-sharing model. We can see that the AI costs borne by the SLSP will compel the SLSI to improve its low-carbon efforts and further incentivize it to increase the emission-reduction level and low-carbon logistics volume. However, when the proportion of the AI cost borne by the SLSP surpasses a critical threshold, the two-way AI cost-sharing contract begins to have detrimental effects on the emission-reduction activities of the SLSI, ultimately hindering the overall emission-reduction efforts of the SLSSC.

Corollary 6.

A comparison of the one-way and two-way AI cost-sharing models in the centralized scenario leads to ${\delta }^{bc\ast }>{\delta }^{sc\ast }$ and $d^{bc\ast }>d^{sc\ast }$.

Proof. 

According to Propositions 2 and 4, simplifying the optimal level of the carbon-emission reduction and low-carbon logistics volume of the SLSSC in the centralized scenario leads to

$$\begin{gathered} {\delta }^{sc\ast }={\displaystyle \frac{(\phi +{\rho }_1)(q-c-\phi {\delta }_0)}{2{\lambda }_1-{(\phi +{\rho }_1)}^2}}, {\delta }^{bc\ast }={\displaystyle \frac{(q-c-\phi {\delta }_0)(\phi +{\rho }_1)}{[2{\lambda }_1-{\lambda }_1{\rho }_2^2/{\lambda }_2]-{(\phi +{\rho }_1)}^2}}; \\ {d}^{sc\ast }={\displaystyle \frac{{\lambda }_1(q-c-\phi {\delta }_0)}{2{\lambda }_1-{(\phi +{\rho }_1)}^2}}, d^{bc\ast }={\displaystyle \frac{{\lambda }_1(q-c-\phi {\delta }_0)}{[2{\lambda }_1-{\lambda }_1{\rho }_2^2/{\lambda }_2]-{(\phi +{\rho }_1)}^2}}, \end{gathered}$$

where ${\lambda }_1{\rho }_2^2/{\lambda }_2>0$. Thus, it follows that ${\delta }^{bc\ast }>{\delta }^{sc\ast }$ and $d^{bc\ast }>d^{sc\ast }$. Corollary 6 is proved. □

Corollary 6 presents a comparison of the optimal emission-reduction level and low-carbon logistics volume across different models in the centralized decision-making scenario. The findings indicate that the two-way AI cost-sharing model yields a higher optimal equilibrium than the one-way model. This outcome can be attributed to the fact that the two-way model alleviates cost pressures on both the SLSI and the SLSP, thereby fostering greater carbon-emission reductions and expanding the low-carbon logistics market. As a result, both emission-reduction levels and logistics volumes are improved. When the proportion of costs $\beta$ borne by the SLSP for the SLSI falls within a specific threshold, the two-way model proves more effective than the one-way model.

Corollary 7.

A comparison of the optimal revenues from the SLSSC carbon-emission reduction under the one-way and two-way AI cost-sharing models in the centralized scenario shows that ${\pi }^{sc\ast }<{\pi }^{bc\ast }$.

Proof. 

According to Propositions 2 and 4, simplifying the optimal revenue of the SLSSC in the centralized scenario yields

$$\begin{array}{c}{\pi }^{sc\ast }={\displaystyle \frac{{\lambda }_1{(q-c-\phi {\delta }_0)}^2}{2[2{\lambda }_1-{(\phi +{\rho }_1)}^2]}}+\phi Z,\hfill \\ {\pi }^{bc\ast }={\displaystyle \frac{{\lambda }_1{(q-c-\phi {\delta }_0)}^2}{2[2{\lambda }_1-{\lambda }_1{\rho }_2^2/{\lambda }_2]-{(\phi +{\rho }_1)}^2}}+\phi Z.\hfill \end{array}$$

□

As is the case with Corollary 6, since ${\lambda }_1{\rho }_2^2/{\lambda }_2>0$, it follows that ${\pi }^{sc\ast }<{\pi }^{bc\ast }$. Thus, Corollary 7 is proved.

Corollary 7 compares the optimal revenues derived from carbon-emission reductions under a centralized scenario across alternative SLSSC configurations. The analysis reveals that the two-way AI cost-sharing scheme yields greater revenue than its one-way counterpart. This outcome underscores the beneficial effect of the SLSI’s emission-reduction initiatives and the reciprocal cost-sharing arrangement on the SLSSC’s aggregate revenue. Accordingly, Corollary 7 establishes that, in a centralized decision context, the two-way AI cost-sharing model is invariably optimal.

6. Case Simulation

Here, we use case simulation under cap-and-trade to analyze the SLSSC’s optimal decision-making based on the two-way AI cost-sharing model and the coordinated SLSSC model. China’s SCO Yongding (Xiamen) International Shipping Co., Ltd., Xiamen, China, provides bulk energy transportation services on a global scale. Its routes mainly cover important energy transportation routes around the world. With a large fleet and globalized shipping network, the company can efficiently perform transcontinental and transnational transportation tasks to meet the needs of the global energy market. In recent years, SCO Yongding has aimed to implement intelligent shipping to reduce emissions. Through cooperation with SCO Linteng (Xiamen) Digital Technology Co., Ltd., Xiamen, China, the company has established a digital platform for shipping that covers the whole process of intelligent management, such as shipping scheduling, logistics management, ship monitoring, cargo tracking, and emission reduction. It helps solve problems commonly found in the industry, such as high transportation costs, low emission-reduction efficiency, and a high rate of idle shipowners. Moreover, through AI, the company can monitor the navigation status of ships in real time, predict the voyage, optimize the shipping route, improve transportation efficiency, and reduce emissions and energy consumption in the shipping process. Below, we use an SLSSC consisting of SCO Yongding (a single SLSP) and SCO Linteng (a single SLSI) as a case study and perform simulation analysis by investigating the company’s operations as it uses AI to reduce emissions.

For a clearer comparison of the effect of the parameters related to two-way AI cost sharing on SLSSC emission-reduction decision-making under cap-and-trade, as well as the sensitivity changes in different models with key parameters, we use MATLAB 2024b for numerical simulation to verify the model’s feasibility and effectiveness. This paper combines the actual emission-reduction operation status and cost–benefit characteristics of AI technologies in the case enterprise, and on the basis of satisfying the parameter relationship constraints in Section 3.2 of the model assumptions, the specific parameters are set as follows: $q=60$, $c=6$, ${\rho }_1=3$, ${\rho }_2=2$, ${\delta }_0=3$, $\phi =3$, $Z=8$, ${\lambda }_1=120$, ${\lambda }_2=30$, $\alpha =0.3$, and $\beta =0.3$. Although different firms’ operating parameters are not consistent, if the parameter values are in line with the inequality conditions in our hypotheses, it will not affect the numerical analysis results.

Below, we first analyze the effect of the proportion of the SLSI’s and SLSP’s AI costs on the revenues of each member of the SLSSC. Then, we explore the effect of the carbon trading price on the emission-reduction level, output, and revenue of each shipping logistics member.

6.1. Effect of AI Cost-Sharing Proportion on SLSSC Revenues

To better analyze the effect of the SLSI’s AI cost-sharing proportion, we require that the AI cost-sharing proportion $\alpha$ vary in the interval [0, 0.68051], mainly because the SLSI revenue ${\pi }_I^{sd\ast }$ < 0 when $\alpha$ > 0.68051. It is not reasonable for the SLSI to have a negative revenue for itself after sharing the SLSP’s AI cost. Figure 2 depicts the effect of the SLSI’s AI cost-sharing proportion on the revenues of each member of the SLSSC in the decentralized scenario.

In Figure 2, we can see that under the one-way AI cost-sharing model in the decentralized scenario, the optimal revenues of the SLSI without sharing AI costs are ${\pi }_P^{sd\ast }(\alpha =0)$ = 297.6486 and ${\pi }_I^{sd\ast }(\alpha =0)$ = 147.9182. The SLSP’s revenue is significantly higher when the SLSI shares the AI cost than when it does not. However, the SLSI’s revenue is higher when it does not share AI costs within a certain threshold range. When AI cost-sharing proportion $\alpha$ = 0.03751, the maximum value of ${\pi }_I^{sd\ast }(\alpha =0)$ = 147.9533 is reached. The results indicate that when the SLSI contributes to sharing AI costs, both the SLSP and the SLSI experience increased revenues, within a defined threshold range, resulting in a mutually beneficial outcome. On the other hand, the SLSP’s one-way AI cost-sharing contract consistently favors the SLSP, leading to carbon-emission reductions within the SLSSC, but this effect is limited to a specific range.

As shown in Figure 3, in the two-way AI cost-sharing model in the decentralized scenario, as the SLSP’s AI cost-sharing proportion $\beta$ increases, the SLSP’s revenue first gradually increases and then decreases. When the SLSP’s cost-sharing proportion $\beta$ = 0.3333, the SLSP’s revenue reaches the maximum value. That is, when the SLSP’s AI cost-sharing proportion $\beta$ is within a certain threshold range of 0 < $\beta$ < 0.3333, the SLSP’s revenue in the decentralized scenario gradually increases as $\beta$ increases while the SLSI’s revenue gradually decreases as $\beta$ increases. Additionally, the higher $\beta$ is, the faster the SLSI’s revenue decreases. We can see that when 0 < $\beta$ < 0.3333 in the two-way AI cost-sharing model in the decentralized scenario, the cost-sharing strategy of the SLSP is conducive to its own revenue but not to the SLSI’s revenue.

Figure 3 contrasts the one-way and two-way AI cost-sharing schemes under a decentralized setting and shows that, when the SLSI’s cost-sharing proportion $\beta$ is below 0.6666, the SLSP achieves higher revenue under the two-way scheme than under the one-way alternative (i.e., ${\pi }_P^{sd\ast }>{\pi }_P^{bd\ast }$ ($\alpha$ = 0.3)). Conversely, when the SLSI’s cost-sharing proportion $\beta$ exceeds 0.6666, the one-way scheme generates greater revenue for the SLSP than the two-way scheme. Likewise, when the SLSI’s cost-sharing proportion $\beta$ is below 0.4894, the two-way scheme yields higher revenue for the SLSI than the one-way scheme. By contrast, once $\beta$ surpasses 0.4894, the SLSI’s revenue under the two-way scheme falls below that obtained under the one-way scheme. These results indicate that the two-way AI cost-sharing scheme is optimal for SLSSC members provided that the SLSI’s cost-sharing proportion $\beta$ lies in the interval [0, 0.4894]. Taken together with Corollary 5, the evidence supports the conclusion that the two-way AI cost-sharing scheme constitutes the optimal emission-reduction strategy for the SLSSC when the cost-sharing parameter remains within the specified threshold.

6.2. Carbon Trading Price on SLSSC Decision-Making for AI-Based Emission Reduction

The carbon trading price under cap-and-trade is an exogenous variable, determined jointly by the government and the carbon trading market. Based on the SLSSC’s emission-reduction operations and the practical dynamics of carbon emissions trading, we define the variation interval of the unit carbon trading price as ranging from 0 to 6. Figure 4 illustrates the impact of different carbon trading prices $\phi$ on the sensitivity of the AI-driven SLSSC’s emission-reduction level across four scenarios.

As depicted in Figure 4, the AI-driven carbon emission-reduction level exhibits a positive correlation with the carbon trading price across all cap-and-trade scenarios. Furthermore, within the centralized decision-making framework, under both one-way and two-way AI cost-sharing models, the acceleration in the rate of emission-reduction is observed with an increase in the carbon trading price. This finding indicates that higher carbon trading prices incentivize the SLSP to increase its adoption of AI for emission-reduction. Under a cap-and-trade system, should the SLSP’s carbon emissions exceed the government-allocated allowance following its emission-reduction initiatives, the SLSP is obligated to purchase additional allowances from the carbon market. Consequently, an increase in the carbon trading price escalates the cost associated with acquiring these requisite allowances. Conversely, if the SLSP’s carbon emission level falls below its initial allowance subsequent to emission-reduction efforts, it gains the opportunity to sell surplus carbon allowances in the carbon trading market, thereby generating additional revenue. Under these circumstances, an augmented carbon trading price enhances the SLSP’s revenue. This observation underscores that with rising carbon trading prices, the SLSP exhibits a greater propensity to implement AI-based carbon emission-reduction measures, irrespective of the specific scenario. Therefore, within the carbon cap-and-trade system, both the costs incurred and potential profits accrued from the SLSP’s carbon trading activities are significantly influenced by fluctuations in the carbon trading price. From a policy standpoint, during the initial phases of carbon emission-reduction, where emission reduction levels are typically modest, the carbon trading market can incentivize the SLSP to adopt AI-based emission reduction strategies by increasing the carbon trading price. In subsequent stages, as the SLSP attains a higher level of emission reduction, it is more likely to sell surplus carbon allowances in the market, thereby augmenting its revenue. To further stimulate emission reduction efforts, the carbon market can elevate the trading price, thereby encouraging the SLSP to persist in applying AI-based strategies. This underscores the pivotal role of the carbon market in fostering emission reductions via the strategic regulation of carbon trading prices.

Figure 5 illustrates the relationship between carbon trading prices and the optimal low-carbon logistics volume of the SLSP applying AI across four different scenarios. In the decentralized decision-making scenario, an increase in the carbon trading price leads to a decrease in the SLSSC’s low-carbon logistics volume, suggesting that excessively high carbon trading prices directly reduce low-carbon logistics trade volume. However, in the centralized decision-making scenario, the relationship between carbon trading price and logistics volume is not straightforward. When the carbon trading price is below a certain threshold $\phi \le 4$, the low-carbon logistics volume decreases as the price rises; when the carbon trading prices exceeds this threshold $\phi >4$, the low-carbon logistics volume increases with higher carbon trading prices.

Under a carbon cap-and-trade framework, in the initial stages of carbon trading, the level of AI-driven carbon emission reduction tends to be relatively low, necessitating the SLSP to acquire additional carbon allowances from the market. During this period, an increase in the carbon trading price escalates costs, which consequently discourages further AI investment and leads to a reduction in the volume of low-carbon logistics. However, as the carbon trading price progressively increases over time, the level of AI-based emission reduction accelerates, resulting in an increased demand for low-carbon logistics. At this juncture, the SLSP can sell its surplus carbon allowances, generating additional revenue that can offset the costs of AI investment, thereby further enhancing low-carbon logistics volume.

Therefore, to meet market demand and expand its market share, the SLSP is compelled to leverage AI to increase the supply of low-carbon logistics. From a policy perspective, during the early stages of carbon emission-reduction, the carbon trading market can incentivize the adoption of AI-based emission reduction measures by elevating the carbon trading price, leading to a modest increase in the provision of environmentally friendly logistics. However, in the intermediate and later stages, when emission reductions have reached a relatively high level in the decentralized scenario, the carbon trading market may consider lowering the carbon trading price to ensure the sustained adoption of AI for low-carbon logistics. Therefore, fluctuations in the carbon trading price will directly influence the level of carbon emission reduction achieved by the SLSSC through AI-based solutions.

Corollary 7 provides an analysis of revenue differences across various SLSSC models in the centralized decision-making scenario. We then proceed to compare the impact of the carbon trading price on emission-reduction revenues for AI-based SLSSCs in the other two scenarios, as depicted in Figure 6. The figure illustrates that the effect of the carbon trading price on emission-reduction revenues remains consistent in the decentralized decision-making scenario. As the carbon trading price rises, the revenues of the SLSSC’s participants decline. This result arises from the fact that an increase in the carbon trading price leads to a reduction in low-carbon logistics volume, directly affecting the revenues of the SLSSC’s members. In addition, under this setup, the revenues of the SLSSC are greater under the two-way AI cost-sharing model than under the one-way model. This indicates that the effect of an increase in the carbon trading price on the revenues of AI-based SLSSC members is negative. From a policy perspective, setting the carbon trading price at a medium level is recommended. This approach would facilitate a balance between the level of AI-based carbon-emission reduction and the revenue generation of the SLSSC, enabling the provision of more low-carbon logistics services while ensuring that sufficient revenues are obtained.

In summary, under the carbon cap-and-trade system, carbon trading can result in either costs or revenues for the SLSSC. Therefore, the carbon trading price has a direct impact on the AI-based level of carbon-emission reduction, the volume of low-carbon logistics, and the revenues of the supply chain participants. While increasing the carbon trading price enhances the SLSSC’s carbon-emission reduction, it simultaneously leads to a significant reduction in both low-carbon logistics volume and member revenues.

In the early stages of AI-based carbon-emission reduction, the carbon trading market can increase the carbon trading price to achieve higher emission reductions, without needing to prioritize low-carbon logistics volume or emission-reduction revenues. However, in the middle and later stages of adopting AI for carbon-emission reduction, the carbon trading price should be appropriately reduced. This helps strike a balance between maintaining emission reductions and ensuring that the SLSSC generates sufficient revenue from these activities. Therefore, the carbon trading market can adjust the emission-reduction level of the AI-based SLSSC through changes in the carbon trading price. However, careful attention must also be given to the effects of such adjustments on the low-carbon logistics volume and the revenues generated by the SLSSC.

7. Conclusions and Management Insights

7.1. Research Conclusions

This study explores low-carbon logistics volume and decision-making within an SLSSC emission-reduction system comprising a single SLSP and a single SLSI, under the carbon cap-and-trade framework. The SLSP directly implements AI for carbon-emission reduction, while the SLSI’s involvement is indirect. Given the sequential nature of AI-based emission reductions, we analyze both one-way and two-way AI cost-sharing models and discuss the relationships between participating members of the SLSSC. The study considers both decentralized and centralized decision-making scenarios, comparing the optimal solutions for emission reduction, and investigating the effects of AI cost-sharing proportions and carbon trading prices on SLSSC decision-making.

First, in the one-way AI cost-sharing model, the SLSI only shares part of the SLSP’s AI cost. When the SLSI shares the AI cost, the SLSSC’s emission-reduction level and low-carbon logistics volume are improved, and the SLSP’s and SLSI’s revenues increase accordingly.

Therefore, the one-way AI cost-sharing model initiated by the SLSI facilitates carbon emission reduction within the SLSSC. In contrast, the two-way AI cost-sharing model takes into account the shared AI costs between the SLSP and the SLSI. The proportion of the SLSI’s AI costs shared by the SLSP influences the emission-reduction level, low-carbon logistics volume, and the emission-reduction revenues of SLSSC members. When the cost-sharing proportion is low, the emission-reduction level, low-carbon logistics volume, and SLSP revenues all rise, with these increases becoming more pronounced as the proportion of shared costs increases. When the sharing proportion exceeds a specific value, the relevant indicators all decrease, and the decrease becomes greater as the sharing proportion increases. When the SLSP shares the AI cost of the SLSI, the SLSI’s emission-reduction revenue decreases.

Second, under decentralized governance, a modest SLSP-borne share of AI expenditures within the unidirectional cost–allocation scheme yields superior emission abatement, decarbonized logistics throughput, and stakeholder returns under a bilateral allocation mechanism. In contrast, with an elevated SLSP cost-share, the unidirectional scheme becomes the preferred arrangement for the SLSSC. Under centralized governance, the bilateral cost–allocation arrangement consistently surpasses the unidirectional model across emission abatement, low-carbon logistics throughput, and member profitability.

Moreover, within the cap-and-trade regime, allowance costs-set by the permit price-modulate the SLSSC’s decarbonization initiatives and operational performance. Permit-price escalation enhances AI-driven abatement efficacy. In decentralized governance, aggregate low-carbon throughput contracts with rising permit prices, whereas under centralized governance, throughput initially contracts before rebounding. Nonetheless, member revenues contract as permit prices ascends.

7.2. Management Insights

Based on the research conclusions above, this paper offers the following management insights for SLSSC enterprises and policymakers.

Firstly, for enterprises within the SLSSC, it is always beneficial for the overall system’s emission-reduction performance when the Logistics Service Integrator (SLSI) proactively shares the AI costs of the Logistics Service Provider (SLSP). However, whether the SLSP is willing to reciprocally share the SLSI’s AI costs depends on the proportion of the share. Taking the example of the shipping giant Maersk (acting as the SLSI) introducing an AI platform: when it only shares part of the AI R&D costs of Nautilus Labs (acting as the SLSP)-representing a one-way sharing model-Maersk not only secures a more favorable service procurement price but also effectively advances its fleet’s goal of achieving “net-zero emissions by 2050,” thereby increasing its own revenues. In this scenario, both parties choosing centralized decision-making maximizes overall benefits. Conversely, if they enter a phase of two-way cost sharing, such as COSCO SHIPPING (as the SLSP) and Shanghai International Port Group (as the SLSI) jointly investing in the construction of an AI-powered smart port platform, the outcome differs. If the proportion borne by the SLSP (COSCO) is low, the two-way model yields higher emission-reductions and throughput. However, if the sharing proportion becomes too high, the one-way model becomes more advantageous for the SLSP. Therefore, enterprises should flexibly choose between centralized and decentralized decision-making based on the proportion of costs they bear, in order to maximize their own emission reduction revenues.

Secondly, for regulators, the carbon trading price serves as a crucial lever to modulate the emission-reduction behaviors of the SLSSC. Regulatory strategies should be adjusted according to the different developmental stages of AI-based emission-reduction technologies. In the initial phase of AI technology application, to overcome emission-reduction bottlenecks, regulators can appropriately increase the carbon trading price. Although this might suppress logistics volume in the short term, it effectively incentivizes SLSPs and SLSIs to increase investment in AI technology in exchange for deeper emission-reductions. This mirrors how the EU ETS, in its third and fourth phases, tightened allowances and raised carbon prices to force the shipping industry towards decarbonization. However, in the mid-to-late stages, as the emission reduction benefits brought by AI mature and are gradually realized, regulators can moderately lower the carbon price to balance enterprises’ logistics output and financial returns. For instance, drawing on the experience of China’s regional pilot carbon markets, which gradually relaxed allowance allocation after achieving stable operation, carbon prices could be dynamically adjusted based on the actual emission reduction performance of the industry. This approach would incentivize the SLSSC to adopt AI for deep decarbonization while also considering the sector’s low-carbon logistics throughput and economic benefits.

7.3. Limitations and Future Research

This paper assumes that the market demand of the SLSSC is a linear function under the context of symmetric information. However, in practice, there is generally asymmetric information during the cooperation between SLSI and SLSP. Therefore, in the future, consideration can be given to asymmetric information, nonlinearity, and market demand with price elasticity. Additionally, while this study focuses on the SLSP’s carbon-emission reduction, it does not account for the carbon emissions resulting from the application of AI. Future work should consider the total carbon emissions across the entire process. Finally, further analysis of the equilibrium conditions in carbon allowance trading would be valuable for a more comprehensive understanding.