As the key link between ports and hinterlands, port consolidation and distribution system are not only the foundation for the survival and development of modern ports, but also the core driving force for regional economic integration and global trade prosperity. Since Shen and Khoong (1995) pioneered the application of system network optimization technology to the construction of decision support system (DSS) for container empty container deployment, the research in this field has been moving along a path of continuous evolution and innovation, gradually building up a more and more perfect theoretical system and practical framework. In the early exploratory stage, the research mainly focuses on the basic theory and model construction, and the decision support system of Shen, through integrating advanced system network optimization technology, provides an effective solution to the complex decision-making problem of container empty container deployment, which not only improves the utilization rate of empty containers, but also reduces the logistics cost significantly, and lays a solid foundation for the follow-up research. Janic (2007) expanded the research vision to the European freight system, constructed a comprehensive costing model, through the quantitative analysis of the cost-effectiveness of various modes of transport, to provide policymakers with a scientific basis for decision-making, and promote the optimization and upgrading of the European freight system.

In recent years, academic research on port consolidation and distribution systems mainly focuses on the operational efficiency of port consolidation and distribution networks, port consolidation and distribution network planning, port consolidation and distribution system optimization. He et al. (2023) in response to the problem of container collection and distribution efficiency in automated terminals, an external truck task scheduling optimization model is innovatively proposed to effectively improve the operational efficiency of automated terminals by jointly optimizing the scheduling of external trucks and yard booking automated rail gantry crane scheduling, which effectively improves the operational efficiency of the automated terminal. Xu et al. (2024) addressed the issue of generation method of tractor and trailer transport schemes under the influence of disrupted events, considering three transportation states, a scheduling model is constructed to minimize the total deviation cost including transportation time, transportation path, and number of used vehicles under the three states of tractors. Li et al. (2023) established a multi-objective fuzzy nonlinear planning model considering hybrid time window constraints for the intermodal transportation path planning problem under uncertain environment with cost, time and carbon emission as the optimization objectives. The model was defuzzified using the fuzzy expected value method and fuzzy opportunity constraint planning method, and a cooperative game theory-based multi-objective optimization method was proposed by combining the game theory method with the weighted sum method. Bütün et al. (2021) made an important breakthrough in the design of liner shipping hub-and-spoke network, and proposed the theory of directed circulation transportation hub siting and cargo path planning based on capacity constraints, which provided a new way of thinking for the optimal design of liner shipping network. In addition, system optimization and multi-objective decision-making have become a research hotspot. Halim et al. (2016) constructed a port-hinterland consolidation and distribution network model for multi-objective optimization, accurately estimated the distribution center location and network layout by combining multi-objective optimization and distributed service preference identification, deeply analyzed the port’s transportation cost and timeliness, and provided specific measure suggestions to enhance the connectivity between the port and the hinterland. Dai et al. (2018), on the other hand, constructed a dual-objective intermodal logistics model covering emission limits, tax and trade schemes from the shipper’s perspective and applied it to the policy analysis of the Yangtze River Economic Belt, which verified the model’s validity and practicability, and provided a strong support for the regional economic integration and the development of green logistics. Xin et al. (2023) proposed a bilevel programming model for liner alliance shipping network design. The model, which optimizes network and fleet design (upper level) and slot/empty container allocation (lower level), notably incorporates shippers’ choice inertia. Furthermore, an inverse optimization model was developed to ensure sustainable profit allocation among alliance members. This research provides crucial modeling support and algorithmic insights for optimizing shipping networks under multi-stakeholder strategic interactions. Wang et al. (2024) conducted an in-depth study of the impact of pricing strategies on the mixed hub port’s ability to simultaneously satisfy hinterland and transshipment demand, providing port operators with a scientific basis for pricing decisions. Fontes and Goncalves (2019) proposed a hub-and-spoke network structure for global liner shipping sub-hubs, which effectively reduces costs through economies of scale and path optimization and opens up a new path for the optimal design of global liner shipping networks. Alkaabneh et al. (2019) provide a new methodological support for the design of hub-and-spoke networks with inter-center economies of scale and center congestion effects through nonlinear mixed integer modeling combined with Lagrangian heuristic algorithms, which provides a new methodological support for dealing with this kind of complex problems. Chen et al. (2023a) addressed the dilemma of port development shifting from expansion to overcapacity by proposing an optimization model for port integration through capacity adjustment and market share trading. The model, solved using a genetic algorithm embedded in an inverse optimization model, aims to minimize total social cost by jointly optimizing berth construction schemes, market share trading, and government subsidies, offering a new optimization path for governments and port authorities to manage regional overcapacity and develop sustainable policies. Xu et al. (2025a) utilized a hierarchical regression model to evaluate the impact of natural factors and economic factors on the navigability of the Northeast Arctic Route (NER). The study confirmed that economic factors are the primary driver of cargo volume, and external events like major infrastructure projects and external shocks significantly alter shipping capacity and route selection. This analysis highlights the complexity and uncertainty of the external environment impacting global shipping networks, offering crucial references for the long-term planning and strategic decision-making of port consolidation and distribution systems. Liu et al. (2025) applied population ecology theory to revisit the concept and practices of smart ports. Using the Tianjin Port case study, they analyzed stakeholder relationships, system evolution, and information flow within the smart port ecosystem. Crucially, the study introduced the concept of “ecological health” for evaluating smart ports, operationalizing it through an evaluation framework which comprising four primary indicators to assess the system’s overall stability amid external uncertainties and readiness for operations.

As an emerging research field, intermodal transportation has gained the attention of many scholars in the past 20 years (Caris et al., 2013). With a series of environmental problems caused by the rapid development of the transportation industry, such as the increase in environmental pollution and the sharp rise in carbon emissions, the significant advantages and potential effects of intermodal transportation in energy saving and emission reduction have become the focus of competitive research in the academic community, which triggered a wide range of scholars and in-depth discussions. As a mode of transportation organization in the comprehensive transportation system, intermodal transportation has the characteristics of low cost, low pollution and high efficiency, which can effectively optimize the transportation structure and break through the bottleneck of economic development. In addition, intermodal transportation can also promote the formation of a unified market with interconnection between coastal and inland areas, and realize the pattern of “double circulation” at home and abroad (Yin et al., 2021). By synthesizing the existing literature, relevant studies can be roughly condensed into the following three broad categories: carbon emission reduction optimization strategies and model construction, analysis of carbon emissions and exploration of driving factors, carbon emission reduction response strategies for intermodal transportation considering uncertainty.

Carbon emission reduction optimization strategy and model construction, this kind of research focuses on the construction of optimization models and strategies to achieve the balance between carbon emission, cost, efficiency and other multi-objectives in the process of intermodal transportation, and provide specific optimization paths and decision-making basis for intermodal transportation carbon emission reduction. Some scholars are committed to constructing a comprehensive multi-objective optimization model, Yin et al. (2024) constructed a multi-objective planning model considering transportation cost, carbon trading cost, and transportation time, and obtained the Pareto optimal solution set with the help of NSGA-II algorithm, and verified the algorithm’s performance and model’s practicality through the arithmetic examples, meanwhile, carried out a sensitivity analysis on the subsidy of railroad freight transport, carbon quota, and carbon trading price, and provided the best solution for intermodal transportation operators. Lam and Gu (2016) developed a dual-objective optimization model to calculate the carbon emissions of intermodal container flows and constraints with the objectives of minimizing cost and transit time, and analyzed the impact of different carbon emission constraints on the design of intermodal transport networks through examples, which helps to build a cost-effective and cost-effective intermodal transport network that meets carbon emission reduction requirements. Sun and Lang (2015) established a mixed integer nonlinear planning model based on node arcs by considering multiple routes, road service capacity constraints, carbon emissions and customer demand factors, and verified the feasibility of the model solution and the effectiveness of the linearization method through the example of China’s inland container export business, which effectively solved large-scale practical multi-commodity intermodal transportation path problems and achieved carbon emission reduction while guaranteeing transportation efficiency. It effectively solves the large-scale practical multi-commodity intermodal transportation path problem, and realizes the goal of carbon emission reduction while guaranteeing the transportation efficiency.

Carbon emission reduction strategies and models are carried out for specific segments or subjects. Zhu et al. (2023) focus on shipping companies, explore the strategy of carbon emission cap-and-trade mechanism, and use a multi-objective particle swarm optimization algorithm based on the Pareto solution set to solve a two-layer model, which accurately depicts the interactions between governmental decision-making and that of shipping companies, and provides an effective reference to the market mechanism of carbon emission reduction in the shipping segment. Jiang et al. (2025) developed a marine fuel supply chain model involving the government, port, and dual fuel suppliers to address coordination challenges in green fuel adoption. By comparing four cooperation scenarios, the study demonstrated that a carbon tax effectively boosts green marine fuel sales, and collaboration among fuel suppliers significantly reduces government expenditure. Furthermore, findings revealed that increased substitutability between green and conventional fuels leads to higher profits for both the port and suppliers, offering a supply chain optimization perspective for green fuel promotion policies. Hu et al. (2025) proposed a multi-objective path optimization model, aiming to minimize carbon emissions and operating costs, while evaluating the impact of subsidy policy, carbon tax mechanism and energy structure on these objectives, which effectively solves the problem of the gap between the government’s and the enterprise’s objectives, and provides a decision-making basis for the choice of intermodal transport paths that takes into account the economy and environmental protection.

In addition, some studies explore carbon emission reduction optimization strategies from the perspective of supply chain and port dispatching. Wang et al. (2020b) propose an integrated scheduling model for supply chain management in port centers based on improved multi-heterogeneous coded genetic algorithm, and by analyzing the total cost and carbon emission under different operation strategies, they explore the impacts and countermeasures of the integrated scheduling on the optimization of supply chain system in the port centers and the carbon emission reduction policy, and achieve the dual goals of carbon emission reduction and efficiency improvement of port supply chain are achieved. Chen et al. (2014) proposed a new coastal liner route design model based on the user equilibrium allocation model, which can simultaneously determine the port of call, order of call, ship type, and service frequency, and minimize the state subsidy to coastal shipping operators under the given intermodal network carbon emission reduction target, providing a This provides a practical method for the design of coastal liner shipping routes to reduce carbon emissions.

Accurate accounting of carbon emissions and identification of key driving factors are the basis for formulating targeted carbon reduction measures. The second type of research centers on the accounting, estimation and analysis of drivers of intermodal transportation carbon emissions, providing data support and theoretical basis for the precise implementation of intermodal transportation carbon emission reduction measures. In terms of carbon emission analysis and driver research, studies are committed to constructing scientific accounting models and methods. Wang et al. (2020a) proposed a dynamic calculation method of intermodal transportation route parameters based on the simulation of Witness software, and established green evaluation indexes of intermodal transportation routes to evaluate the performance of routes under different intermodal transportation schemes, in which the green evaluation indexes cover the carbon emission-related content, which provides a good basis for intermodal transportation carbon emissions. Guo et al. (2022) focused on the inland container intermodal transport network, studied the estimation of carbon emissions and the identification of carbon emission reduction drivers, established a carbon emission estimation model, and estimated the carbon emissions of the hinterland-based container intermodal transport network in the last 10 years in the above seaport and the hinterland of Yangtze River Delta as an example, which provided a typical case of regional intermodal transport carbon emission accounting. Guo et al. (2023) on the other hand, proposed a simulation method for the peak time and peak value of carbon emissions from containerized intermodal transport networks, capturing the basic network elements through intermodal transport network modeling, combining the carbon emission model with scenario analysis, and simulating and predicting the probability of the peak time and value of carbon emissions by using the Monte Carlo algorithm, which not only achieves the estimation of the carbon emissions, but also makes a prediction of the peak value of the carbon emissions, and offers prospective suggestions for the long-term planning of intermodal transportation carbon emission reduction. emission reduction, which provides prospective guidance for the long-term planning of intermodal transportation. Xu et al. (2025d) compared various models and found that machine learning methods, due to their ability to capture nonlinear relationships, achieve significantly higher accuracy than traditional econometric models in predicting global shipping carbon dioxide emissions, thus offering more reliable policy support. Xu et al. (2025c) utilized the LMDI decomposition method to analyze the driving factors of carbon dioxide emissions, highlighting the upward pressure from global trade growth and advocating for the net-zero decarbonization pathway as the only effective route to achieving substantial reduction.

There are many uncertainties in the intermodal transportation process, such as transportation time, demand changes, etc., which will have an impact on the realization of carbon emission reduction targets. Such studies aim to construct models and methods to cope with uncertainty and guarantee the stability and effectiveness of intermodal transportation carbon emission reduction strategies. Some studies incorporate uncertainty factors into the construction of optimization models. Sun et al. (2022) measure the service level based on a fuzzy soft time window, set the travel time and carbon emission factor as variable parameters, and incorporate travel time uncertainty and road network service capacity factors to enhance route feasibility, apply trapezoidal fuzzy number customized uncertainty, and propose a fuzzy multi-objective nonlinear integrated truck departure time planning optimization model, demonstrating the effectiveness of the methodology through empirical case studies and discussing the impact of optimization results with improved confidence levels and service levels, providing ideas for coping with transport time uncertainty in intermodal transport to achieve carbon emission reduction. Hrušovský et al. (2018) proposed a framework combining optimization modeling and simulation, where the simulation model includes stochastic elements in the form of uncertain travel times, while the optimization model represents the Deterministic and Linear Multi-commodity Service Network Design Formulation, Considering the multi-objectives of cost, time and carbon emission, the solution is proposed for a transportation network of up to 250 services and 20 orders, and identifies possible disruptions and alternatives to accommodate unreliable transportation schedules, which guarantees the stable operation of intermodal carbon-reducing transportation networks in uncertain environments.

From a more macroscopic perspective, Sheng et al. (2017) constructed a multidimensional comprehensive assessment model from the government’s perspective, integrated the dynamic effects of the game between regional port competition and shipping companies, and analyzed and compared the market equilibrium states under different regulatory scenarios through a two-stage game framework. Although the study does not directly focus on the uncertainty factors, there are many uncertainties in the game process of regional port competition and shipping companies, such as fluctuations in market demand, strategic adjustments of competitors, etc. The study provides a reference for the government to formulate intermodal transportation carbon emission reduction related regulatory policies under the complex and volatile market environment, which can help to maintain the stability of the intermodal transportation market and indirectly safeguard the realization of carbon emission reduction goals. Xu et al. (2025b) employed a Stackelberg game model to explore the impact of government subsidies on the strategic decisions of two competing port operators regarding Shore-to-Ship Electricity (SSE) infrastructure construction, aiming to maximize social welfare. The study revealed that a lack of subsidies can lead to a Prisoner’s Dilemma where both ports construct SSE despite its economic infeasibility under high conversion degree. Furthermore, they cautioned that subsidies, while promoting construction, may reduce the likelihood of simultaneously achieving both environmental and economic benefits, offering insights for designing effective subsidy schemes to accelerate maritime decarbonization.

In summary, existing literature has yielded fruitful results in path planning of port consolidation and distribution networks, carbon emission accounting, and emission reduction strategies from a single perspective. However, most studies rely on static optimization based on a global optimal perspective, often overlooking the bounded rationality and strategic interactions among independent stakeholders, and few have deeply analyzed how multi-party subjects resolve conflicts of interest under the constraints of “Dual Carbon” goals. Therefore, distinguishing itself from existing static optimization studies, this paper adopts a dynamic evolutionary game framework, incorporating the bounded rationality and strategic interactions of multiple agents into the analytical framework. We specifically investigate the dynamic decision-making mechanisms of different subjects in response to external policies, such as management effort and subsidies and internal additional incomes. Furthermore, rather than solely pursuing system cost minimization, this study focuses on resolving conflicts of interest to achieve a green collaborative equilibrium that satisfies the profit maximization objectives of all parties, thereby offering a more practical theoretical framework for the “Dual Carbon” transformation of port consolidation and distribution systems.

Generally speaking, evolutionary games assume that the participants are finitely rational, and then study the dynamic evolution process of their strategies. This paper analyzes the game relationship between multiple stakeholders and investigates the impact of different evolutionary states of each subject on the coordinated development of the consolidation and distribution system, including port operators, river-sea intermodal transport operators and road transport operators. The game relationship of each party is as follows:

In order to establish an evolutionary game model and to study the strategies of each participant, the stability of the equilibrium point, and the interactions between the parameters, the following hypotheses are proposed:

Based on the above description, the symbols in the model are defined as shown in Table 1.

Based on the above model assumptions, the game payoff matrix is obtained, as shown in Table 2. Among them, the incomes of port operators, river-sea transport operators, road transport operators are τ1, τ2, τ3.

For the equilibrium point (1, 0, 0), there exists a stable evolutionary strategy when it satisfies Et−Ms−Mr−G−L<0, Ms+ Ss−Es<0, Mr+Sr−Er<0. Under this condition, its simulation parameter assignments are shown in Table 5 Scene 1. As shown in Figure 2, as the evolution progresses, the probability of river-sea intermodal transport operators choosing “competition” and road transport operators choosing “traditional mode” strategy increases, which is due to the fact that under the condition of Corollary 1, the management effort loss of river-sea intermodal transport operators choosing “competition” is smaller than the difference between the additional cost and subsidy of choosing “cooperation”; Meanwhile, under the hypothetical condition, the management effort loss of road transport operators choosing “traditional mode” is smaller than the difference between the additional cost and subsidy of choosing “ low-carbon mode “, Therefore, river-sea intermodal transport operators and road transport operators will tend to choose the “competition” and “traditional mode” strategies respectively. Under the condition of Et−Ms−Mr−G−L<0, the difference between the additional cost and the management effort gain, indirect gain of the port operators choosing “active progression” is smaller than the indirect loss of the “negative progression” strategy, so the port operators will prefer “active progression” to enhance the reputation of the status and to promote the coordinated cooperation of the operators. In this case, the stabilization strategies of port operators, river-sea intermodal transport operators and road transport operators are “active progression”, “com- petition” and “traditional mode” respectively.

For the equilibrium point (0, 1, 1), there exists a stable evolutionary strategy when it satisfies G+L−Et−Ss−Sr<0, Es−As<0, Er−Ar<0. Under this condition, its simulation parameter assignments are shown in Table 5 Scene 2. As shown in Figure 3, as the evolution progresses, the probability of river-sea intermodal transport operators choosing “cooperation” and road transport operators choosing “low-carbon mode” strategy increases. This is because under the condition of Corollary 2, the additional income of the river-sea intermodal transport operators choosing “cooperation” are more than the additional cost; Meanwhile, under the hypothetical condition, the additional income of the road transport operators choosing “low-carbon mode” are more than the additional cost, so the river-sea intermodal transport operators and the road transport operators will tend to choose “cooperation” and “low-carbon mode”, respectively. Therefore, river-sea transport operators and road transport operators will tend to choose the “cooperation” and “low-carbon mode” strategies respectively. Under the condition of G+L−Et−Ss−Sr<0, the indirect loss of the port operators choosing “negative progression” is smaller than the difference between the additional cost, expenditure subsidy and indirect gain when choosing “active progression”, so in order to avoid excessive capital expenditure, the port operators will tend to choose the strategy of “negative progression” strategy. In this case, the stabilization strategies for port operators, river-sea intermodal transport operators, and road transport operators are “negative progression”, “cooperation”, and “low-carbon mode”, respectively.

For the equilibrium point (1, 1, 1), there exists a stable evolution strategy for it when Et+Ss+Sr−G−L<0, Es−As−Ms−Ss<0, Er−Ar−Mr−Sr<0 are satisfied. Under this condition, its simulation parameter assignments are shown in Table 5 Scenario 3. As shown in Figure 4, as the evolution progresses, the probability of river-sea intermodal transport operators choosing “cooperation” and road transport operators choosing “low-carbon mode” increases, This is because under the condition of Corollary 3, the difference between the additional cost and the additional income, subsidy of choosing “cooperation” is smaller than the management effort loss when choosing “competition”; Meanwhile, under the hypothetical conditions, the additional cost and the additional income, subsidy of road transport operators choosing “low-carbon mode” are smaller than the management effort loss when choosing “competition”. Therefore, river-sea intermodal transport operators and road transport operators will tend to choose the “cooperation” and “low-carbon mode” strategies, respectively. Under the condition of Et+Ss+Sr−G−L<0, the difference between the additional cost and subsidy and indirect gain for port operators choosing “active promotion” is smaller than the indirect loss when choosing “negative progression”, and port operators will tend to choose the “active progression” strategy. The difference between the additional cost, subsidy and the indirect gain is smaller than the indirect loss when choosing “negative progression”. In this case, the three parties actively cooperate to promote the coordinated development of the consolidation and distribution network, and the stabilization strategies of port operators, river-sea intermodal transport operators and road transport operators are “active progression”, “ cooperation” and “low-carbon mode” respectively.

In summary, under the two stable evolution states of (1, 0, 0) and (0, 1, 1), the operators and port operators choose the strategies of “competition”, “traditional mode” and “negative progression”, respectively. “. In this case, the expected benefits of all three parties cannot be maximized. In the stable state of (1, 1, 1), the port operators actively promotes the cooperation of operators, the river-sea intermodal transport operators choose the “cooperation” strategy, the road transport operators choose the “low-carbon mode”, the rapid operation of the consolidation and distribution network, the port operators does not have to bear indirect loss, and because of the positive response of the operators, the port operators cannot implement the management effort, thus saving the cost of supervision, rational optimization of inputs and expenditures, to achieve the ideal maximization of income. Therefore, the optimal strategy combination is (1, 1, 1), that is, the port operators choose “active progression” strategy, the river-sea intermodal transport operators choose “cooperation” strategy, the road transport operators choose “low-carbon mode” strategy, to realize the high-speed operation of the consolidation and distribution network and achieve the ideal maximization of the tripartite benefits.

In this paper, from the perspective of “Dual Carbon” goal, based on the dynamic game theory, by constructing a dynamic evolution game model of port operators, river-sea intermodal transport operators and road transport operators in the consolidation and distribution system, and analysed the stability of the strategy choices of each party, the stability of the equilibrium strategy combinations of the gaming system, and the influence of the relationship between each parameter. Matlab numerical simulation is used to analyse the factors and interaction mechanisms affecting the decision-making choices of each party. The study analyses different equilibrium states and explores the influence and change mechanism of port operators, river-sea intermodal transport operators, and road transport operators in the cooperative dynamic game of consolidation and distribution network, and the following conclusions can be obtained:

When port operators promote operator collaboration, they should prioritize optimizing the design of management efforts rather than relying solely on subsidy measures, and guide the evolution of operator strategies by dynamically adjusting the intensity of regulation while focusing on the policy’s role in shaping the industry’s reputation, in order to achieve the dual goals of system stability and efficiency improvement. In view of the low sensitivity of the decision-making parameters of the port operators, it is necessary to introduce external regulatory measures such as governmental reward and punishment mechanisms. By constructing a reward and punishment function that is deeply bound to the interests of the port operators, the intrinsic decision-making threshold can be broken through, accelerating the coordinated process of the consolidation and distribution network under the premise of maintaining the stability of the system. The government should design a dynamic subsidy mechanism to compensate for incremental port operators’ costs, regulate port operators decision-making thresholds, and optimize the indirect gain distribution mechanism to prevent system instability caused by strategy reversal, while maintaining fiscal sustainability. Special attention needs to be paid to the negativity of port operators ‘ strategies under the autonomous stabilization state of the operators, and the positive feedback effect of system coordination should be strengthened through the institutional design of, so as to realize the efficiency enhancement of the low-carbon transition.