As an important tool to improve product quality, control chart plays a vital role in quality monitoring. Traditional control charts typically assume that the process follows known distributions such as normal distribution, binomial distribution, Poisson distribution, etc., and such control charts require a sufficient number of samples to estimate parameters, also known as parameter control charts. But, with the rapid development of the current technological environment and the increasing demand for personalized products, small batch production has gradually become an important production mode to meet diverse market demands. In a small batch production mode, the sample size often cannot meet the requirements of the parameter control chart, resulting in the traditional control chart no longer to be applicable.
In order to adapt to the characteristics of small batch production, non-parametric control charts are proposed and widely used. This control charts have the advantage of not relying on accurate estimation of process distribution parameters, and can still play a role in limited sample sizes. However, non-parametric control charts are generally weak at monitoring abnormal process shifts. In order to improve the monitoring efficiency of non-parametric control chart, this paper combines dynamic control charts and memory-based control charts, and constructs a dynamic non-parametric Exponentially Weighted Moving Average Sign (EWMA-SN) control chart using Variable Sampling Interval (VSI).
In the design of control charts, being statistical and being economic play equally important and irreplaceable roles as the main indicators for evaluating the performance of control charts. Therefore, this paper uses the Markov chain method to calculate the Average Product Length (APL) and the average product quality cost of the control chart. As a statistical evaluation index, APL in out-of-control state represents the performance of the control chart in actual operation, while the average quality cost reflects the cost-effectiveness of the control chart from an economic point of view. Using both as common objective functions, a multi-objective optimization design model for non-parametric VSI EWMA-SN control charts is constructed and the effectiveness of the model in practical applications is verified through specific examples and sensitivity analysis. Finally, by comparing and analyzing several other existing non parametric control chart methods, the results show that the VSI EWMA-SN control chart has significant advantages in both statistical and economic aspects.
In this study, only the variable sampling interval design is carried out on the model, and the sample size remains fixed. The subsequent study will consider the variable sample size design of the model to achieve a more comprehensive dynamic optimization.

As supply chain management becomes leaner and more globalized, supply chain has extended in terms of time and space, increasing its complexity. Moreover, potential factors such as political instability, trade frictions, and natural disasters exacerbate the risks of random supply disruptions. Consequently, how manufacturers develop effective strategies to mitigate supply disruption risks has become an urgent issue.
A two-tier supply chain system is constructed, comprising two suppliers and two manufacturers. In this system, the product manufacturer procures critical components externally to produce product 1, while the integrated manufacturer can produce both critical components and product 2. Considering consumers’ heterogeneous preferences for products and the coopetition scenarios between manufacturers, the study formulates a procurement game model with three strategies: (1)the primary supplier does not experience supply disruption(N strategy), (2)the primary supplier experiences disruption and replenishment is sourced from a backup supplier (S strategy), and (3)the primary supplier experiences disruption and replenishment is sourced from the integrated manufacturer (M strategy).
The study results show that: (1)The effects of “market predation” and “order strategic allocation” during the competitive-cooperative process between manufacturers are identified and quantified at the risk of supply disruptions. The product manufacturer can limit the integrated manufacturer’s profit accumulation through “order strategic allocation”, while the integrated manufacturer can counteract this through “market predation” to accumulate profits. (2)Counterintuitively, the product manufacturer’s profit is higher when the primary supplier experiences supply disruption than that when there is no disruption. The presence of backup supplier facilitates replenishment cooperation between competing manufacturers, and the product manufacturer can leverage the backup supplier to increase bargaining power during replenishment negotiations with the integrated manufacturer. (3)Replenishment cooperation between competitive manufacturers has spillover effects both upstream and downstream, increasing the product manufacturer’s procurement volume from the primary supplier while also boosting the total product supply in the downstream market. This research achieves profit maximization and customer satisfaction maximization, providing theoretical and practical value for supply chain disruption mitigation strategies.
In practical operations, manufacturers often face challenges in accurately obtaining supply disruption information. This information asymmetry can lead to overstocking or understocking, thereby impacting production and sales. Future research could explore multi-sourcing replenishment strategies under conditions of asymmetric supplier reliability information. Additionally, this study focuses solely on consumers’ product preferences. However, in practice, consumers’ purchasing decisions may also be influenced by factors such as the quality, performance, and brand reputation of critical components. Future work could examine how consumer preferences for critical components from different sources affect the replenishment strategies of product manufacturers.

Many critical infrastructures and services, such as power, communications and transportation systems, depend on the proper functioning of the network. The interdependence of the system improves the performance and efficiency of the system to a certain extent. However, this interdependence also brings certain risks. When there is interaction between different networks, if a network or a node within it fails, it will cause the other network nodes that depend on it to also fail, causing cascading failures and eventually leading to the complete collapse of these interdependent networks. If these interdependent networks cascade down, it can lead to power outages, communication outages, traffic jams and other serious consequences, which can have a significant impact on social stability and people’s daily lives. Therefore, we should not only study the system composed of a single network, but should focus on multiple network systems that interact with each other to have a more comprehensive understanding of the operating mechanism of network systems in reality.
Based on the classical cascading failure model, this paper introduces a load-sharing coupling system for the dependence between coupled systems. Specifically, when a system experiences a failure, its component load will increase due to the existence of propagation pressure. This paper quantifies this pressure as the load amount, that is, the evolution of cascading failure of the coupling system is caused by the steadily increasing load, and through the quantitative analysis of load growth, the strength and speed of fault propagation within and between different subsystems are better measured. Based on the dynamic Markov model, a stochastic dynamic model of cascaded failure propagation in an interdependent system is established. In order to more accurately assess system reliability, the traditional two-state model is extended to classify component states into normal operation, overload operation and fault state. In this paper, the multi-stage characteristics of the dynamic failure rate are considered, and the influence of multiple factors such as component life, component overload and interdependence between systems on the failure rate is analyzed in the model, and the law of overload probability and failure rate with the number of failures of the two subsystems is given, the repair time and the number of repair equipment are included in the model, and the state transfer rate matrix of the coupling system and the analytical expression of the system reliability are given.
The effectiveness of the proposed method is verified by numerical analysis, and a coupled dependent system is constructed, and each subsystem has a repair equipment. Since the subsystem needs to assume its own load and responsibility when performing its own tasks, the coupled system plays more of a coordinating and regulating role in this case, and therefore, in the cascade process, each subsystem has its own pressure, which is higher than the pressure exerted on it by the coupled system. It is calculated that when the number of faults in systems A and B increases, the amount of additional load required by the remaining working parts of the entire coupled system increases, and the failure rate increases accordingly. The results show that system A is more likely to fail than system B when subject to the same overload. Finally, the state transition rate matrix and reliability of the coupling system are calculated.
The influence of the initial load, the life of the component itself, the number of faults in the subsystem where the component is located, the dependence between the systems and the repairability of the component on the cascading failure propagation process are considered, and the Markov load-sharing coupling system model is established by using the continuous Markov process, which makes the reliability model closer to reality. It can be extended to different network topologies, coupling strengths and different load sharing modes to further study the cascading failure mechanism of the system and its reliability analysis.

A queueing-inventory system is an integrating system that integrates a queueing process of customers into an inventory system. Upon arrival, customers require both the product and the service time for tasks such as inspection, preparation, packaging,and loading. Therefore, a queueing-inventory system is also called a service-inventory system. Compared to traditional inventory systems, queueing-inventory systems are universal and practical. This kind of systems has a wide application in many fields such as integrated supply chain management, airline and train ticketing systems, transportation, and healthcare services. The frequent occurrence of events such as pandemics, floods, and trade wars increases the uncertainty of customer demand, so as to lead to supply chain uncertainties and frequent stock-outs. This uncertainty challenges the efficiency of traditional queueing-inventory systems. Especially in the context of constructing new, high-quality, and efficient service systems, enhancing the system’s ability to adapt to demand uncertainty has become an urgent issue.
This study proposes a novel M/M/1/∞ queueing-inventory system model. It incorporates a mixed vacation policy with a r-random order size policy to enhance system adaptability and efficiency. The server takes vacation when the inventory is empty at the epoch of the completion of customer’s service. The mixed vacation policy means that if the inventory is still empty at the end of the server’s vacation, the server returns from the vacation with probability q, or takes another vacation with probability 1-q.The mixed vacation policy allows service interruptions during stock-outs, and the interrupted service can be resumed upon the completion of the replenishment of the inventory or under some other special conditions. For instance, if a server is temporarily closed due to breakdown, the service of the server will be resumed once the server is repaired. This flexible vacation policy is helpful not only for inventory management according to real-time inventory status, but also for dealing with the service interruption due to server’s breakdown or other situations. In highly dynamic and uncertain market environments, this strategy provides a flexible and effective means for companies to tackle challenges related to inventory shortages and service interruptions. The r-random order size policy dictates that an order of random sizes is placed when the inventory level falls to a threshold r. This provides a flexible mechanism to handle demand fluctuations. This is particularly crucial during periods like pandemics. When demand fluctuates sharply, this strategy significantly reduces the risk of stock-outs and enhances supply chain resilience. By combining these two strategies, companies can better manage uncertainties during unexpected events, ensuring service continuity and supply chain efficiency. This enables the companies to maintain competitiveness in a complex and volatile market environment.
In this paper, the system’s stability condition and the product form solution of the steady-state probability distribution are obtained by using the theory of the quasi-birth-and-death process. Performance measures are established to develop the expected cost function of the system. The expected cost function of the system between the random order size policyand r-random order size policy is compared by numerical examples. The impact of the threshold r, the probability q and other parameters on the expected cost function are also analyzed numerically. The integration of the mixed vacation and r-random order size policies enables the system to optimize resource usage while ensuring the quality of service, and also reduces the potential loss of the system due to service interruptions.

In recent years, with the rapid economic development of China and the further deployment of take-out services and new retail, consumers’ differentiated demands for instant delivery have driven the diversified development of the service business categories. The door-to-door delivery service and high-quality performance capabilities of instant delivery have greatly met consumers’ diverse needs for convenience, timeliness, and other aspects, enabling instant delivery services to further expand to all-time, all-scenario, and all-distance coverage. Although instant delivery is in a golden period of development, some areas still face issues that have not been properly addressed due to their unique regulatory environments. These areas often become “blind spots” and “difficult points” in the process of instant delivery operation and management. Therefore, this paper collectively refers to such areas as “delivery-challenged regions,” characterized by two types of issues: one involves areas where riders do not have permission to enter due to special regulations, requiring customers to pick up their orders at the perimeter, such as university campuses with access control and residential communities with special property management systems; the other involves areas where riders can enter but face challenges in door-to-door delivery due to the compact arrangement of buildings and high population density, necessitating local area knowledge to ensure timely delivery, such as business districts with concentrated office buildings and industrial parks. The differentiated regional regulatory environments result in weakened delivery timeliness for traditional riders in delivery-challenged regions, and in some cases, riders are unable to complete door-to-door delivery services, leading to customer dissatisfaction and reduced rider willingness to deliver. This poses significant challenges to logistics service providers in planning delivery schemes.
To address the issues in delivery-challenged regions, this paper proposes a collaborative delivery solution combining dedicated riders and crowdsourced riders. A mixed-integer programming model is established with the objective of minimizing the sum of vehicle travel costs, crowdsourced rider recruitment compensation costs, and time window violation penalty costs. Upon receiving a batch of orders with their locations and flexible time windows, the delivery platform determines the delivery tasks for dedicated and crowdsourced riders, the number of crowdsourced riders to recruit, and their respective delivery routes, enabling the two types of riders to collaboratively complete the delivery tasks. An improved variable neighborhood search algorithm is designed based on scenario characteristics, using a greedy algorithm to generate initial solutions to open vehicle routing within the region and closed vehicle routing outside the region. Local search operators are then designed based on three optimization stages: closed vehicle routing optimization outside the region, open vehicle routing optimization within the region, and interactive optimization of vehicle routing inside and outside the region, to enhance the algorithm’s global optimal search capability.
Finally, the case studies are conducted to verify the effectiveness and applicability of the model and algorithm. The results indicate that the crowdsourced collaborative delivery solution for instant delivery in delivery-challenged regions can effectively reduce total delivery costs, providing a valuable reference for improving service quality in future instant delivery operation and management.

The refining production process is characterized by uncertainty, multiple objectives, and numerous constraints, and is an NP-hard problem. In the short-term production scheduling of crude oil processing, each sub-scheduling involves a series of combined operations on equipment such as oil tankers, charging tanks, distillation towers, etc. Consequently, the quantitative relationship between each piece of equipment has a decisive impact on the feasibility of the scheduling solution. For instance, if a production plan necessitates the temporary addition of distillation towers to increase output, or if certain charging tanks require maintenance shutdowns prior to production, this will result in a shortage of charging tanks relative to distillation towers. This will cause the production system to enter a non-equilibrium state, intensifying competition for charging tank resources among related equipment such as pipelines and distillation towers. As a result, the complexity and challenges of production scheduling are significantly heightened.
Currently, there is only a feasibility analysis of crude oil short-term scheduling of non-equilibrium in existing research, without considering the optimization of related costs, and this may result in substantial financial waste during actual production. So, it is necessary to conduct multi-objective optimization research on crude oil short-term scheduling under non-equilibrium conditions between charging tanks and distillation towers. Based on the resource allocation backtracking search method, a multi-objective optimization mathematical model is constructed to find feasible schedules and minimize the five target costs including mixing cost of crude oil in the pipeline and at the bottom of charging tanks, the switching cost of charging tanks, the use cost of charging tanks and the energy consumption cost of crude oil transportation. The feasible scheduling must adhere to all constraints. However, the mathematical model constructed for the problem includes a critical constraint on crude oil residence time. Under conditions of relative equipment resource scarcity, backtracking search is prone to frequent violations of the crude oil residence time constraint, rendering the current scheduling solution infeasible. This issue triggers extensive backtracking, which significantly reduces the efficiency of solving the problem. To improve the quality and efficiency of solving this model, this paper first introduces the Parallel Long-Short Term Memory (PLSTM) module into the Pairwise Comparison Surrogate-Assisted Evolutionary Algorithm (PC-SAEA) and then proposes PLSTM-PC-SAEA. The SAEA leverages computationally efficient surrogate models to approximate optimal values with limited computing resources, showing certain advantages in solving single or multiple objective optimization problems. Within the basic framework of the Surrogate-Assisted Evolutionary Algorithm (SAEA), the surrogate model can be constructed, trained, and tested using solutions that have completed Fitness Evaluation (FE). The model is then utilized to assess the quality of candidate solutions through auxiliary FE. This method selects a portion of better candidate solutions for real FE, conserving computational resources and improving the algorithm’s solving efficiency. The PLSTM model includes a set of parallel LSTM modules with independent parameters, which can make each LSTM network more focus on learning the type features of the corresponding input and clearly distinguish the different permutations and combinations of label 1 and label 0. When the dataset is constructed, based on the principle of pairwise comparison, better and worse solutions are combined into a series of regular tuples and dual tuples according to specific rules. This strategy significantly expands the dataset size and enhances the training effectiveness of the model. Before candidate solution auxiliary evaluation is conducted, the surrogate model undergoes reliability testing, and reliability labels are obtained according to the model management strategy. Then, auxiliary FE is conducted using the corresponding strategy managed by the test result. Additionally, an energy consumption optimization Linear Programming (LP) model is designed to optimize the energy consumption cost, explicitly embedded in the encoding and decoding process of the solution chromosomes.
Finally, the PLSTM-PC-SAEA algorithm is applied to an industrial example of a real crude oil short-term scheduling problem provided in the reference. It is compared with six other comparative algorithms by comparing the metrics like CR, HV, and algorithm operation time. Experimental results demonstrate that the proposed approach achieves favorable overall performance in terms of convergence, solution diversity, and computational efficiency. This provides a valuable reference for solving crude oil short-term scheduling problems under non-equilibrium conditions between charging tanks and distillation towers.

In recent years, a continuing decline in the global fertility rate and an increase in life expectancy have made the issue of population ageing more prominent. To meet the demands brought about by the growth of the ageing population, while respecting the traditional will of the older citizens, the home-based elderly care service model is gradually taking over at this stage. As an important form of its function, the home health care aims to provide convenient medical and life care services to the older and disabled citizens through professional home care teams. It has been proven to deliver outcomes comparable to those provided by hospitals or skilled nursing facilities, while also offering greater accessibility and flexibility. However, there is currently a shortage of professional caregivers in China, and clients are usually dispersed in different regions, with the driving time of caregivers taking up a larger proportion of the overall working time. The reasonable and efficient caregiver routing and scheduling has become one of the key issues in the home health care operation and management.
There are many uncertainties in real-world environments. Therefore, gradually, studies have begun to incorporate uncertainty factors to make the research questions more relevant to real-world situations. Most current home health care studies use stochastic methods, and a few studies use robust optimization to deal with these uncertainties. Stochastic methods usually require modeling random variables and simulating their probability distributions based on historical data. However, when information is difficult to obtain or sufficient information is lacking, it is difficult to portray its probability distribution. Robust optimization, although it does not require probability distributions of uncertain parameters, is unable to deal with parameters that involve subjectivity and ambiguity. When dealing with this kind of information, it is necessary to apply fuzzy methods to determine uncertain variables based on the past experiences of experts and caregivers.
In this study, to address the home health care routing and scheduling problem with fuzzy times, a fuzzy chance-constrained programming model is established with vehicle capacity, time window, skill level, and caregiver overtime constraints. An uncertain programming theory is introduced, where the travel and service times are described as triangular fuzzy numbers. Most current studies use exact algorithms or meta-heuristic algorithms as solution methods. Although the exact algorithm can find the optimal solution to the problem, its efficiency gradually will decrease when the scale increases, making it difficult to determine the solution in a reasonable time. Meta-heuristic algorithms, although they have efficient problem-solving capabilities, may ignore high-quality routes that do not improve the solution quality or violate constraints during the search process. To combine the advantages of both methods, a matheuristic is proposed by combining hybrid variable neighborhood search and the set partitioning model. The proposed algorithm combines variable neighborhood search and late acceptance hill-climbing to enhance the local search ability when ensuring search efficiency. The set partitioning model is used to further improve the overall search performance based on the candidate feasible routes.
Finally, numerical experiments based on adjusted Solomon benchmark instances validate the performance of the proposed algorithm, and sensitivity analysis reveals the impact of the decision maker’s risk preference on the routing and scheduling plan. Decision makers may be able to develop plans with lower operating costs if their attitudes toward time window and caregiver overtime constraints are risky. However, if the decision maker is too cost-effective, it may lead to untimely service delivery and longer working hours of caregivers, which in turn may affect the long-term operation of the home health care center. Therefore, decision makers need to develop reasonable plans based on the actual situation and previous management experience. Future research could consider teamwork of caregivers and introduce methods such as machine learning to further improve the algorithm’s solution performance.

In the past few years, the problem of environmental pollution in cities has become more and more serious, and the sustainable development of cities has received more and more attention. In order to alleviate the impact of urban logistics and distribution pollution on the urban environment, most city governments have implemented traffic restriction policies to limit pollution from the source. However, the long-term regional restriction leads to the obstruction of logistics transportation, which greatly reduces the efficiency of logistics operation and increases the cost of logistics transportation.
In order to address this, this paper sets up quantifiable regional access costs, so as to restrict the passage of trucks and at the same time more accurately measure the cost of transportation. At the same time, a mixed fleet is introduced to construct a mixed fleet routing optimization study considering the zone entry fee. This problem is an extension of the multi-vehicle fleet routing optimization problem. A distribution routing model is constructed with the objective of minimizing the sum of vehicle fixed cost, operation cost, zone entry fee and carbon emission cost to evaluate the optimal choice of urban distribution vehicles and distribution paths. The problem is described as follows: there are several distribution centers, and each distribution center has two types of transportation vehicles: traditional oil vehicles and electric vehicles. There are sufficient vehicles of each type in each yard. Different types of vehicles serve the customer points from each distribution center. Meanwhile, due to the battery limitation of electric vehicles, the trams will go to the charging station for recharge when they have insufficient power during the distribution process, and they will continue to perform the distribution task when they are fully charged. The total amount of customer demand in each sub-path does not exceed the vehicle load, and the vehicle returns to the nearest distribution center after completing the task. The innovation of the problem is to construct a new cost type to measure the cost of urban distribution more accurately under regional traffic restrictions.
According to the characteristics of the problem, a hybrid ant colony heuristic algorithm is designed for solving the problem, in which a decentralized search algorithm is used to optimize the initial solution and improve the solution performance of the ant colony algorithm. The steps of the algorithm are as follows: (1)The diversity initial solution is constructed by K-means clustering and improved scanning algorithm. (2)The optimal solution under the current clustering is solved using the improved ant colony algorithm. (3)Decompose the current optimal solution according to the decentralized search to generate new clusters for solving, and cycle sequentially until the stop condition is satisfied. In order to check the effectiveness of the algorithm, several MDVRP benchmark experiments are set up to let Gurobi, MACO and this paper’s algorithm be compared and analyzed, and the results show that this paper’s algorithm is significantly better than Gurobi, and can be used to solve this paper’s model.
Finally, combined with the case of an enterprise’s logistics and distribution network in the city, the simulation obtains the distribution routing results before and after considering the zone entry fee, and carries out a Fosensitivity analysis of the size of the restricted area and the zone entry fee. The experimental results show that: reasonable consideration and setting of zone entry fee in the city can greatly increase the utilization rate of EVs in the mixed fleet, and at the same time significantly reduce the carbon emissions; in cities with different restricted zones, the larger the restricted zone is, the more obvious is the impact of zone entry fee, and the more customer points and charging piles there are in the restricted zones, the more obvious is the impact of zone entry fee. The utilization of electric vehicles increases as the cost of regional access increases, and the total cost of zone entry fee increases and then decreases until all electric vehicles are used instead of oil vehicles.

The soul of high-tech zone is innovation and development. Meanwhile, high-tech zone is also the result of industrial spatial agglomeration of high-tech enterprises. The development of national high-tech zones will produce agglomeration effect, siphon effect and technological innovation effect on the high-tech industry, and in turn, the high-tech industry will affect the development of national high-tech zones through policy effect, human capital, science and technology. The action and reaction between the two can be expressed as the ability and degree of their collaborative development. In the process of rapid and high-speed development, the mutual influence and interaction between the two cannot be separated from the participation of the core subject high-tech enterprises and academic and research institutions. The joint development of national high-tech zones and high-tech industries is essentially an operation mode of innovation chain, and the operation of innovation chain cannot be separated from the dynamic game between participants. From the perspective of collaboration, the coupling of the two subsystems requires the cooperation of different participants, and whether it is a national high-tech zone or a high-tech industry, the participants are all stakeholders. When making coupled cooperative decision, the decision-making subject will consider the influence of other subject’s decision and the cost and benefit of coupling cooperation. The action process of national high-tech zones and high-tech industries is to participate in the inter-subject game process. The win-win situation and information in coupling coordination are not fully in line with the cooperation and uncertainty of the game. The behavior strategies of participants will influence each other, and the cooperation also has the characteristics of dynamic repetition. Participants make judgment according to cost and benefit in the process of coordination. From the perspective of coupling mechanism, how the core players involved in the collaborative development of national high-tech zones and high-tech industries carry out game evolution, and how to construct the selection strategy that fits the tacit understanding mechanism of the core players based on different scenarios are the core of this paper.
Depending on the coupling mechanism and under the premise of incomplete rationality, the strategies adopted by the two types of subjects can be divided into “cooperation” and “non-cooperation”. The cooperation and income of subjects under different market and government supervision mechanisms are evaluated, and its value coordination mechanism is determined in the form of contract. Due to the limited rationality and the incompleteness of contract, the cooperative cooperation between the two subjects has certain moral hazard. The evolutionary game method is widely used in the study of the dynamic process evolution of the system, and the two sides achieve a higher level of interaction, trial and error and coupling between the high-tech zone and high-tech industry through collaborative cooperation. Therefore, the coupling coordination between high-tech enterprises and research institutions is the key to studying this problem. Based on the above research objectives, this paper carries out a systematic analysis of the player’s strategy selection along the path of “basic hypothesis - different mechanism model construction - numerical analysis - random disturbance analysis”. In the conventional evolutionary game, the player’s strategy has an important impact on whether the national high-tech zone and high-tech industry can achieve a high level of coupling and collaborative development, and the player’s evolution strategy is different under different mechanisms. However, the player’s state and other factors may affect the player’s strategy choice, so it is necessary and practical to construct a stochastic evolutionary model to test the influence of uncertain factors on the evolutionary system.
The evolutionary game model is introduced into the coupling framework of the two subsystems, and the coupling coordination interest relationship of the two sub-systems is constructed from the two aspects of market mechanism and government regulation. The system stability conditions and equilibrium points are obtained by evolutionary game method, and the evolutionary stability of the factors affecting the coupling coordination dynamics of the main body under the two mechanisms is analyzed by simulation. Random interference factors are introduced to analyze the influence of game system. The results show that under the market mechanism, the benefit distribution ratio, cost allocation ratio, risk factor size and penalty for breach of contract have obvious effects on high-tech enterprises and institutions to support the coupling coordination activities of the two subsystems, but the mechanism is different. Under the supervision of the government, the behaviors of the game parties change with the change of regulation intensity. In addition to the income distribution coefficient, risk coefficient, cost allocation ratio and penalty damages, the government’s incentive, subsidy factor and tax reduction and exemption intensity of the coupling coordination mechanism will have an impact on the evolutionary game system. Considering random interference factors, random interference factors will slow down the speed of high-tech enterprises and institutions to evolve into stable strategies.

The 14th People’s Congress emphasized digitalization as a key factor to promote the development of the resilience of the manufacturing industry chain, so it is crucial to strengthen the development and application of digital technology policy support. Exploring whether digital policies can effectively promote the development of the resilience of the manufacturing industry chain has become an urgent practical problem to be solved. This paper discusses whether digitization policy can affect the development of the toughness of the manufacturing industry chain and the degree of its impact. In theory, the application scope of the theory is enriched. In terms of practical significance, the first is to optimize the design of digitization policy as a reference basis for policy formulation. The second is to provide decision support for enterprises and enhance the management ability of enterprises. Third, it is beneficial to promote the efficiency of resource allocation and improve the return rate of R&D investment. Fourth, we can strengthen the coordination between the government and enterprises and promote the cooperation mechanism between the government and enterprises. Fifth, we can promote regional economic development and make targeted policy recommendations.
By collecting and analyzing the data of 1,993 listed companies from 31 provincial administrative regions in China from 2018 to 2022, this study constructs an evaluation index system for the resilience of the manufacturing industry chain, measures and analyzes the resilience of China’s manufacturing industry chain from the perspectives of high, medium and low industry chain resilience. The digitized policy texts of each province are retrieved and quantified by means of environmental, supply and demand policy tools. The relationship model of digitalization policy on the toughness of manufacturing industry chain is established, and the regression empirical test is carried out.
The results show that the overall toughness level of China’s manufacturing industry chain is on the rise, but it is still at the medium toughness level. The digitalization policy has a significant effect on the toughness of the manufacturing industry chain, but the demand-oriented policy has a certain inhibitory effect on the toughness of the manufacturing industry chain. The digitalization policy has a more significant effect on the toughness of the high-tech manufacturing industry chain, but the demand-oriented policy has a certain limiting effect on the toughness of the high-tech manufacturing industry chain.
We suggest we promote the synergy, service and intelligence of the manufacturing industry, and emphasize the key role of policies in promoting the transformation and upgrading of manufacturing enterprises. We should strengthen the implementation of supply-oriented and environment-oriented policies, reduce the restriction of demand-oriented policies, and promote the continuous presence of the combined policy effect. We should also adopt “special policies” to enhance the flexibility of independent development and innovation of high-tech manufacturing enterprises, and provide more policy support and guidance for high-tech enterprises.

The construction of a unified national carbon emissions trading market is an important element in creating a unified market for factors and resources. The integration of the carbon market can realize lower cost carbon emission reduction, solve the“carbon leakage”between regions, improve the quality of carbon market operation, and enhance the international influence of China’s carbon market. Currently, China’s carbon market mainly consists of seven regional carbon markets, including Shanghai, Guangzhou, Tianjin, Shenzhen, Beijing, Hubei and Chongqing, and the national carbon market. However, due to regional heterogeneity and industry heterogeneity, etc., the unification of China’s carbon market cannot be achieved overnight, which greatly affects the functioning of the carbon market. Therefore, there is an urgent need to bridge the gap between carbon markets. In the process of marketization of China’s carbon market, scientifically measuring the dynamic level of China’s regional carbon market integration and analyzing the dynamic features of the integration and the obstacles can provide policymakers with dynamic detection indicators of carbon market integration as well as the basis for decision-making to enhance the integration of the carbon market.
Under the guidance of the law of one price, this paper gives a definition of carbon market integration based on the perspective of the convergence of price changes in the carbon market, and discusses the dynamic characteristics and obstacles of the integration of the Chinese carbon market in four steps. First, this study introduces a stochastic dynamic dependence correction mechanism based on dynamic principal component analysis, average dynamic correlation method and dynamic standard correlation method, constructs a series of dynamic indicators of carbon market integration, reveals the effectiveness of the indicators through the relationship between each indicator and diversification benefits, changes the width of the rolling window to analyze the robustness of the indicators, and finally determines the optimal indicators through the Granger causality test. Second, the results of the BP breakpoint test are used to analyze the impact of important policy shocks on carbon market integration and provide recommendations for carbon market integration. Third, macro variables such as output, price and air quality are used to show the correlation of economic fundamentals among the carbon market pilot regions, and then analyze the impact of economic fundamentals on carbon market integration based on the mixed-frequency Granger causality test. Fourth, the Generalized Forecast Error Variance Decomposition (GFEVD) method is used to analyze the volatility spillover effects among pilot carbon markets, find the key market and information transmission mechanisms in the risk contagion of China’s carbon market, and analyze the information connection among markets.
The research results mainly include the following three aspects.First, the 1stPC indicator based on the PCA method is the optimal carbon market integration measurement indicator, the level of carbon market integration in China is low, and the relevant major policies and conferences have had a significant impact on carbon market integration. Second, at the macro level, differences in price levels and air quality between the pilot regions have hindered the integration of the carbon market, with a significant lag effect. Third, at the micro level, cross-regional spillovers between pilot carbon markets are low. Beijing and Shanghai are typical net information spillovers, while Hubei is a net information spillover. Information spillovers between pilot carbon markets are time-varying.
Based on the conclusions of the above study, the following approaches can be considered to promote the integration of China’s carbon market. Firstly, the improvement of the carbon market operation mechanism and the unification of the policy system is the first task to promote the integration of China’s carbon market and realize the efficient operation of the carbon market, which should accelerate the unification process of the industry accounting standards, regulatory rules, trade settlement, quota allocation scheme and other regulations among the pilot regions. Secondly, as the differences in economic fundamentals in the pilot regions have led to a low degree of regional carbon market integration, accelerating the sectoral expansion of the national carbon market and speeding up the process of a unified national carbon market are the fundamental paths to realizing carbon market integration in the long term. Thirdly, poor information flow between pilot carbon markets has also led to market segmentation. Therefore, in the short term, information flow between markets can be enhanced by changing trading rules, introducing institutional investors, building a carbon derivatives market and increasing the policy flexibility, which will ultimately improve carbon market integration.

Fossil fuel combustion not only emits CO₂ but also releases atmospheric pollutants such as SO₂. CO₂ and these pollutants share a common origin and process. Currently, the excessive emissions of greenhouse gases and atmospheric pollutants pose a significant challenge to the international community, a problem exacerbated by the increasingly severe global climate change. The synergistic governance of pollution reduction and carbon mitigation has gradually become a mainstream trend in environmental management. It is of great significance to comprehensively explore the synergistic effects of pollution reduction and carbon mitigation within China’s carbon market for advancing international environmental governance and China’s ecological civilization. Difference-In-Differences (DID) model to evaluate the impact of China’s carbon market on the synergistic governance of carbon emissions and atmospheric pollutants. Furthermore, it innovatively identifies the driving mechanisms of the synergistic emission reduction effect of China’s carbon market from the perspective of internal constraints within the carbon market, based on both constraint and market mechanisms. This provides a new perspective for analyzing the driving mechanisms of the carbon market’s synergistic emission reduction effect. Additionally, a mediation effect model is used to analyze the transmission pathways of carbon market policies, aiming to comprehensively dissect the synergistic emission reduction effect of China’s carbon market.
The innovations of this paper are as follows: (1)Introducing internal constraint factors of the carbon market and analyzing the driving mechanisms of the synergistic emission reduction effect of the carbon market from both constraint and market perspectives, so as to provide a new perspective on constraint mechanisms for analyzing the carbon market’s synergistic emission reduction effect. (2)Including both CO₂ and SO₂ in the same analytical framework, and using a multi-period DID model to comprehensively analyze the synergistic emission reduction effect and action pathway of carbon market policies. This paper quantitatively analyzes the impacts of market and constraint mechanisms on synergistic emission reduction effect, while also exploring the action pathway of these effects.
The research findings are: (1)The implementation of the carbon market has synergistic emission reduction effect, reducing CO₂ emissions while also lowering SO₂ emissions, with the experimental results passing a series of robustness tests. (2)The constraint mechanism is the driving force for achieving synergistic emission reduction effect in carbon market policies, while the market mechanism has not yet been effective. This paper dissects the driving mechanisms of the carbon market’s synergistic emission reduction effect from the perspectives of constraint and market mechanisms. The proxy variables for the constraint mechanisms derived from the carbon market’s institutional design all have passed significance tests, while those for the market mechanisms have not. (3)Mediation effect tests further reveal that carbon market policies can promote synergistic emission reduction effect by optimizing the energy structure, but the pathways of technological innovation and industrial structure have not been evident.
Based on the research conclusions, the following three policy recommendations are proposed to further enhance the role of China’s carbon market in synergistically controlling pollution and reducing carbon emissions: (1)Scientifically set benchmarks for total quota and penalty severity, and further enhance the incentivizing effects of market mechanisms such as carbon pricing and liquidity. Based on the conclusions of this paper, the current carbon market primarily achieves carbon and synergistic emission reduction effect through constraint mechanisms like total quota and penalty severity. Therefore, it is necessary to rigorously set these constraint mechanisms to ensure the carbon market’s effectiveness in reducing pollution and carbon emissions without overburdening market participants. The market mechanisms’ synergistic emission reduction effect has not yet been fully realized, which may require the introduction of financial instruments to invigorate the carbon market and enhance the incentivizing effects of mechanisms such as carbon pricing and liquidity. (2)Synergistic development of pollution reduction and carbon mitigation should focus on promoting energy transition as a fundamental starting point. This study finds that the current carbon market in China achieves collaborative emission reduction effect through optimizing energy structure. Therefore, emphasis should be placed on the role of energy transition in driving pollution reduction and carbon mitigation. Accelerating the promotion and use of clean energy and gradually reducing reliance on fossil fuels can effectively lower emissions of atmospheric pollutants and CO₂. Promoting energy transition not only aids environmental protection but also fosters sustainable economic development. (3)Establish a unified system for synergistic pollution reduction and carbon mitigation to advance the dual goals of carbon peaking, carbon neutrality, and ecological and environmental protection. A unified system can optimize resource allocation, avoid resource waste due to fragmented policies and lack of coordination among relevant departments, and maximize the effects of pollution reduction and carbon mitigation. Moreover, a unified system can improve policy implementation efficiency, facilitating the simultaneous advancement of the dual goals of carbon peaking, carbon neutrality, and ecological and environmental protection in terms of both time and space.

In early 2020, the novel coronavirus disease (known as “COVID-19”) triggered a global public health crisis due to its highly contagious nature. The sudden outbreak of the pandemic triggered a sharp decline and shock in the securities markets, posed challenges to firms’ sustainable operations, affected firms’ external financing decisions, and increased the uncertainty about investors’ expectations for the future. This further expanded the information asymmetry between firms and investors, which was an important factor leading to IPO underpricing.
To contain the spread of the pandemic, the Chinese government implemented normalized control measures by suspending production and business operations, closing stores, and restricting resident activities. China was one of the few countries that adopted a “dynamic zero-case” policy, which lasted up to three years. More importantly, the political system and economic environment within a country, as well as the collective consciousness and customs embedded in the society and culture are basically the same. This unique context provides a distinctive perspective for researching the impact of the COVID-19 pandemic on IPO pricing in the Chinese A-share market.
Our research endeavors to answer the question: does the COVID-19 pandemic significantly influence IPO pricing, and if so, through which channels? During the pandemic, China’s A-share markets implemented registration-based reforms, removing price-earnings ratio caps and first-day trading price limits for Growth Enterprise Market (GEM, also known as ChiNext market) and Sci-Tech Innovation Board (STAR market) listings, thereby avoiding distortions to IPO pricing and investor valuations. Analyzing 409 firms listed on the ChiNext market and 415 firms listed on the STAR market, we investigate how pandemic severity has influenced IPO underpricing through the IPO process (bookbuilding, subscription, and first-day trading). The empirical evidence indicates a significant negative correlation between the severity of the COVID-19 pandemic and IPO underpricing, within the 14 days before the pricing announcement date (listing date). Channel tests show that the COVID-19 pandemic has no significant (a significant negative) impact on the offering prices in the primary market (the first-day closing price of the secondary market). The improvement of pricing efficiency reflects the negative impact on the investors’ firm value evaluations in the secondary market’s pricing. Institutional investors, due to the lock-up restriction, are more negatively affected by the COVID-19 pandemic than individual investors. Moreover, heterogeneity analysis shows that the negative impact of COVID-19 on IPO underpricing is more significant for firms listed on the ChiNext market, low intangible assets, small size, and a high proportion of largest shareholders. Finally, benefiting from the improved post-IPO performance of firms heavily impacted by the pandemic, the negative impact of the COVID-19 pandemic on cumulative abnormal return is limited to the short term.
This study has important implications for market participants and policy makers. First, the information content of institutional investors’ demand in the bookbuilding process highlights their superior valuation capabilities relative to retail investors. Second, the registration-based reform enhances pricing efficiency, with secondary markets promptly reflecting the adverse impact of the pandemic, though primary market pricing remains insensitive to such shocks. Improving the pricing efficiency of the primary market is still the focus of deepening the reform of the registration system.

For a long time, a relational transaction mode has widely existed in enterprises in China, influenced by cultural customs, imperfect laws and market systems. This leads to a high degree of customer concentration, so enterprises suffer from “reliance on key customers”, which is particularly prominent in manufacturing enterprises. However, relying too much on key customers may increase the operational risk of enterprises and erodes the profit space of enterprises. Especially since the outbreak of the epidemic, the uncertainty and complexity of the external environment have risen sharply, and the “black swan” incidents of key customers have occurred frequently. More and more enterprises begin to re-examine supply chain security, and reduce the excessive dependence on key customers as an important goal of supply chain strategy adjustment and risk control. Therefore, how to alleviate the “reliance on key customers” in manufacturing enterprises has become a practical problem to be solved urgently.
Servitization is an important strategic plan and development trend for China’s manufacturing industry to break through the low-end lock-in of global value chain and realize high-end transformation and upgrading. It is also an important way to enhance the competitiveness of manufacturing industry and achieve high-quality development. As the micro-subject of economic transformation, manufacturing enterprises realize the transformation from product supply to providing “products plus services” and solutions by integrating knowledge, technology and products. This transformation process is the innovation and reshaping of the original business model by adhering to the purpose of being “customer-oriented”. The company can dynamically respond to market demand, optimize the customer’s trading experience, and expand the “siphon” effect of customer scale by developing high value-added derivative services. Therefore, from the theoretical analysis, manufacturing enterprises can strengthen the cooperative relationship with more customers by providing in-depth embedded services, thus reducing their dependence on key customers. Based on this, this paper empirically analyzes and tests the influence and mechanism of servitization on key customer dependence in China, from the perspective of customer relationship governance, taking A-share manufacturing listed companies from 2010 to 2022 as samples. It is found that servitization is conducive to reducing the excessive reliant on key customer resources and optimizing customer resource structure, the higher the level of marketing and managerial ability, the more significant the negative relationship between them. The mechanism test shows that servitization alleviates the dependence of key customers through innovation-driven and cost optimization. Heterogeneity analysis shows that the influence of servitization on the dependence on key customer is more significant in state-owned, large-scale enterprises and enterprises in growth stage. The research conclusion not only enriches the theoretical research on servitization in manufacturing, and offers manufacturing enterprises a practical basis for the implementation of service transformation, but also provides a new solution for solving the “reliant on key customer”.
The contributions of this paper are follows. Different from the existing literature, it mainly focuses on the adverse economic results brought by the dependence on key customers, this paper discusses the role of servitization in reducing the dependence on key customers, and puts forward a new governance path to solve the dependence on key customers; the existing research on servitization effect mainly focuses on the influence of servitization on their own operating results, but this paper analyzes the value of servitization in optimizing customer resource structure from the perspective of customer relationship governance, which enriches the research on servitization effect of manufacturing enterprises to a certain extent; this paper opens the “black box” for servitization to reduce the dependence of key customers. The research shows that enterprises implementing servitization reduce the dependence on key customers through innovation-driven and cost optimization. It provides a theoretical basis for enterprises to deeply understand the potential value of servitization and an effective path for enterprises to alleviate the dependence on key customers.

In current city sanitation management, the environment is characterized by frequent natural disasters and social emergencies, and the behavior of various entities within city sanitation (residents, sanitation personnel, sanitation robots, etc.), under the attacks from environment, also has various catastrophe phenomena. Under such internal and external attacks, the layout of city waste infrastructure should not only aim at the minimum cost and pollution, but also consider the resilience of layout solutions against internal and external attacks. Thus, nowadays the waste infrastructure layout is a classical multi-objective optimization decision issue.
For this reason, this work proposes a multi-criteria decision method with the integration of optimization theory, simulation analysis and catastrophe analysis. First, a double-objective integer programming model for the waste infrastructure layout with minimum cost and environmental pollution is established, and the Pareto optimal solution set, i.e., multiple alternative solutions of infrastructure layout strategies with minimum cost and environmental pollution, is obtained by using genetic algorithm NSGA-II. Second, according to the operation of the infrastructure layout strategies, i.e., the working process of city waste cleaning and transportation, a multi-agent simulation model for city waste cleaning and transportation is developed using AnyLogic 8.8, including the whole process operations from the residents in various city areas putting out waste, to the transportation and storage at waste transfer stations, and then to the terminal disposal points (including landfills or waste-to-energy incineration plants). The performance of each layout solution is tested under various uncertainty internal and external attacks, and simulation data, e.g., the average amount of waste generation per person, the amount of waste explosion caused by emergencies, the average daily speed of waste collection vehicles, the number of collection vehicles, the average daily speed of transfer vehicles, the number of transfer vehicles, the waste processing capacity at transfer stations, the waste processing capacity at terminal disposal sites, and the total amount of city waste processed, are collected. Finally, cusp catastrophe theory is employed to build the catastrophe model, and analyze the catastrophe hazards of layout solutions under multiple uncertain attacks using the simulation data. Basing on the catastrophe model of the layout of city waste infrastructure, resilience index of each layout solution is calculated and the layout solution with the smallest resilience index is determined as the one with the largest resilience under the various attacks, which represents the multi-objective optimization solution with the minimum cost and pollution, and the maximum resilience. While the other infrastructure layouts of the Pareto optimal solution set are filtered out.
The above proposed method is applied to the case of Wuhan city’s waste infrastructure layout to perform the validation. According to the actual investigation and data collection in Wuhan city, the following data are collected, including the total population of the city, the total annual amount of waste generated in the city, number of candidate landfill sites, number of candidate transfer stations, the capacity of each landfill site and transfer station, the annual fixed cost of landfill site and transfer station, unit transportation cost between population centers and transfer stations and unit transportation cost from transfer station to landfill site. The thirteen double-objective optimization layouts with the minimum cost and pollution are calculated by using genetic algorithm NSGA-II. The simulation analysis is conducted for each layout. The data of input and output of simulation are used to build the catastrophe model and calculate the resilience index. The layout solution 5, i.e., the most resilient layout, is obtained. The comparison of resilience index calculation process with other solutions is performed. It is found that the resilience is related to the number of transfer stations, disposal plants and transportation vehicles. Too much infrastructure can easily be suffered from attacks of multiple concurrent points. The hazards are amplified. While, too lack of infrastructure can lead to the limited capability of processing wastes. When the two pressures accumulate to a certain degree in the system, it will cause the system to be in a highly unstable state that catastrophe may happen at any time.
The integrated innovative method proposed in this work, combining operations research optimization, simulation analysis, and catastrophe analysis, has academic value for multi-objective optimization of infrastructure layout with resilience consideration. The research results have important theoretical and practical significance for the infrastructure layout problem of smart cities, as well as city resilience management under frequent serious environmental and social attacks.
In the next works, optimization models can not only consider minimizing cost and pollution, but also other objectives such as social minimizing dissatisfaction and transportation time. In addition to the nine factors of catastrophe analysis considered in this work, more city sanitation operation factors can also be considered. The proposed method requires further validation through case studies from more cities.

Heterogeneous GPU clusters have become a core support in the field of high-performance computing, providing essential computational power for deep learning, scientific computing, and other batch processing tasks. However, batch jobs exhibit significant diversity in resource requirements, meaning that jobs within the same batch may have vastly different GPU and CPU demands. This heterogeneity and diversity in resource requirements significantly increase the complexity of resource allocation, resulting in low overall resource utilization (only 25%~50%), prolonged job waiting times, and worsening load imbalance, which severely constrain the improvement of Service Quality (QoS). Traditional resource allocation strategies, such as random allocation (Random), Round-Robin scheduling (RR), and Shortest Job First (SJF), primarily rely on static rules or heuristic methods, making them ineffective adapt to the complexity and dynamic nature of heterogeneous computing resources. These approaches often lead to resource wastage, unbalanced scheduling, and decreased system throughput. To address these challenges, this paper proposes a multi-objective optimization-based resource allocation method for heterogeneous GPU clusters, aiming to improve resource utilization, reduce job waiting time, and optimize overall load balancing, thereby enhancing cluster computing efficiency and QoS.
This study formulates the batch job resource allocation problem in heterogeneous GPU clusters as a multi-objective optimization problem, considering GPU/CPU resource utilization, job waiting time, and load balancing as key optimization objectives. To enable efficient decision-making, this paper constructs a Markov decision process framework that includes state space, action space, and reward functions. Furthermore, a multi-objective optimization-based resource allocation strategy is proposed using deep reinforcement learning techniques. Specifically, the paper adopts the Deep Q-Network (DQN) for decision-making optimization, leveraging Deep Neural Networks (DNN) to learn optimal scheduling policies. Additionally, a dual-parameter threshold linear decay strategy is incorporated to dynamically balance exploration and exploitation, ensuring efficient scheduling strategy optimization in complex heterogeneous environments.
This study builds an experimental platform using Python and TensorFlow and simulates a heterogeneous cluster environment with three types of GPU nodes: T1, T2, and T3. The experimental data is sourced from a real Alibaba Cloud dataset, and systematic evaluations are conducted under various job loads and resource configurations. Furthermore, to conduct a comprehensive analysis of model performance, this study performs a sensitivity evaluation of six different DNN architectures (with fixed input and output layers), focusing on the impact of the number of hidden layers and activation functions. To systematically assess the effectiveness of the dual-parameter threshold linear decay strategy in optimizing the exploration-exploitation trade-off, three comparative experiments are designed: the first adopts a fixed exploration rate, the second employs a dual-parameter exponential decay strategy, and the third utilizes a single-parameter threshold linear decay strategy. These experiments provide a comparative analysis of different exploration strategies and their influence on model learning performance.
The experimental results demonstrate that the proposed method effectively stabilizes GPU and CPU utilization at 65%~70% and 70%~75%, respectively, while significantly reducing the average job waiting time from over 10 seconds to approximately 4 seconds. Additionally, it improves load balancing across nodes. A generalization evaluation is conducted across different batch job sizes (200, 500, and 1000 tasks) and heterogeneous cluster configurations (with 1 to 3 types of GPUs), revealing that the proposed method consistently outperforms traditional resource allocation algorithms (Random, RR, SJF) in overall performance, demonstrating strong generalization capability and robustness. Compared to single-objective optimization strategies, the proposed multi-objective optimization model achieves an average improvement of 9.52% in resource utilization, a 131.78% reduction in average job waiting time, and a 16.66% reduction in load imbalance variance, effectively optimizing both scheduling efficiency and fairness in heterogeneous cluster environments. In terms of computational overhead, the DQN-based deep reinforcement learning algorithm not only requires lower training costs but also offers faster decision-making, outperforming common deep reinforcement learning approaches such as DDQN, PPO, and A3C.
Although the proposed method exhibits outstanding performance in multi-objective optimization, future research can explore dynamic weight adjustment mechanisms and scalability for large-scale clusters. Potential directions include integrating federated learning to achieve distributed scheduling and supporting preemptive job scheduling scenarios.

Inspired by some existing research and based on the background of the order production intelligent manufacturing system, this paper develops a N-policy M/G/1 multiple vacation queueing model with Bernoulli interruption vacation and random start-time. In this model, the server takes a random length of vacation once there is no customer in the system. If customers arrive during this vacation, then the server interrupts vacation immediately with probability p(0≤p≤1) and activates the system. Otherwise, he/she will not interrupt the vacation with probability 1-p until the end of this vacation before returning to the system and starting it. If no customers arrive during this vacation, then the server immediately begins another vacation and repeats this in this way. Meanwhile, it takes a random length of time to start the system. When the system startup is completed, if the number of customers waiting in the system is greater than or equal to a given integer threshold value N(N≥1), then the server begins service immediately until the system becomes empty again. Otherwise, he/she keeps idle but on duty until the number of customers waiting in the system reaches N and immediately begins serving the waiting customers. The queueing model studied in this paper is more in line with the actual situation and this Bernoulli interruption vacation is more flexible, which can be used for modeling and analysis of intelligent manufacturing systems that produce orders.
Firstly, we apply the total probability decomposition technique to obtain the steady probability distribution of queue-length at the beginning of the server’s busy period. Secondly, we obtain the probability generating function of the steady queue-length by applying the stochastic decomposition theorem of the steady queue-length. Meanwhile, some algebraic calculations are used to derive some other queueing performance indicators, such as the average queue-length and the probability distribution of the additional queue-length. Finally, the expression of the long-run expected cost per unit time of the system is obtained by establishing a cost structure model and employing the renewal reward theorem that depends on the update process. Furthermore, the system cost optimization problems with(without) the expected waiting time constraints are respectively discussed.
As is known to all, although setting the threshold N can reduce the cost of the system due to frequent startup, it also increases the customer’s waiting time. As a result, it increases the cost of customer stay, reduces customer satisfaction, and even leads to customer loss. In this issue, the long-term benefits of the system are affected. Therefore, it is of great theoretical importance and application value to consider the optimal control policy and cost optimization problem of the system under the waiting time constraints. Inspired by the above, we characterize the factory’s order processing as the queueing model studied in this paper. Numerical examples are provided to investigate the one-dimensional optimal control policy N^* for economizing the system cost as well as the two-dimensional optimal control policy (N^*, T^*) when the vacation time is a fixed time length T, which provides ideas and theoretical support for the decision-makers to achieve the maximization of the economic benefits. The results show that the optimal control policy N^* of starting the service without the waiting time constraints is larger than that of starting the service under the waiting time constraints, and the smaller the constraint threshold of waiting time is, the smaller the optimal control policy N^* of starting the service is and the larger the corresponding minimum expected cost is. Thus, if the system manager expects to reduce customer’s waiting time and increase customer satisfaction, it needs to start the system earlier and pay more costs. Such a consideration is helpful for balancing the interests of the manager and customer and makes the innovation of this paper clear and the theoretical analysis results have more practical application value.
Therefore, the main innovations of this article are as follows: (1)Based on the background of the order production manufacturing system, this paper develops a new queueing model - a N-policy M/G/1 multiple vacation queueing model with Bernoulli interruption vacation and random start-time,which is more flexible and also is more in line with the actual situation. (2)We use the stochastic decomposition theorem of the steady queue-length to obtain the probability generating function of the steady queue-length, and derive some queueing performance measures such as the average queue-length and so on. (3)In depth, we investigate the cost optimization and the optimal control policy of the system, which will make the theoretical analysis results of this paper have better practical applications.

In the digital age, data centers have emerged as the cornerstone of modern information systems. However, the distribution of data centers in China is highly uneven, with a significant concentration on economically prosperous eastern regions such as the Beijing-Tianjin-Hebei area, the Yangtze River Delta, and the Guangdong-Hong Kong-Macao greater bay area. Despite their economic advantages, these regions face substantial challenges in hosting data centers. High land prices, power shortages, and unsuitable climates that necessitate energy-intensive cooling systems all contribute to the rise of operational costs. Whereas, western China offers substantial potential for data center development, characterized by low land costs, abundant power resources, and a more favorable climate. To address this imbalance and achieve coordinated regional development, China has introduced the “Eastern Data and Western Computing” strategy.
The strategic location and resource allocation of data centers are complex decision-making processes that involve multiple factors, including geographical location, climate, energy supply, and land cost. Existing research in this area is limited. Many studies focus only on partial factors and lack precision in optimizing data center locations. Additionally, there is a significant void in research that comprehensively considers carbon emissions and overall resource utilization. This study aims to address the multi-objective location and resource allocation problem of naturally cooled data centers under the “Eastern Data and Western Computing” strategy.
A multi-objective optimization model centered on natural cooling technology is proposed, which integrates economic, environmental, and social benefits. The model defines parameters for user demand nodes and resource endowment nodes, such as the number of existing cabinets, power generation structure, and energy utilization efficiency, and determines decision variables related to data center construction and node connections. By combining integer and linear programming techniques, the model solves complex problems in data center location and scale configuration and employs the Multi-Objective Genetic Algorithm (MOGA) for optimization. MOGA, based on the principle of natural selection, can simultaneously optimize multiple objectives, such as minimizing costs and maximizing carbon emission reduction.
Data for this study come from a wide range of reliable sources, including statistical yearbooks, national economic development bulletins, operator data, meteorological datasets, and information from local development and reform commissions. The improved K-means clustering method is used as an analytical technique. It standardizes data to eliminate dimensional differences, determines the optimal number of clusters through the elbow method and silhouette coefficient, and classifies data center construction areas according to user demands and resource endowments.
Theoretical analysis validates the effectiveness of the proposed model, which optimizes the layout of data centers to achieve the lowest cost and minimal environmental impact, thereby effectively reducing carbon emissions. The empirical results show that different natural cooling technologies significantly impact data center location, cost, and environmental performance. For example, liquid-cooling technology, despite its high initial investment, offers high energy efficiency, leading to lower long-term operating costs and better environmental performance. In practical applications, the integration of cluster analysis and multi-objective optimization generates a scientific layout plan. In the case studies of different cooling scenarios, the model provides guidance for rational resource allocation. This study offers practical guidance for data center operators to optimize layout and resource allocation, for policymakers to formulate relevant policies, and for equipment suppliers to develop suitable products. It serves as a crucial reference for data center planning and management under the “Eastern Data and Western Computing” strategy, facilitating the green transformation and energy-saving efforts of the data center industry.

The photolithography area is a critical component of the chip manufacturing process and is constrained by various factors such as low equipment utilization, extended waiting time for chip processing, and limitations related to photomasks. These constraints create bottlenecks in the production scheduling of the photolithography area, ultimately impacting chip yield and manufacturing costs. With the continuous advancement of chip technology and increasing market demand, there is a growing need for resources in the photolithography area. Researchers have turned their attention to optimizing the production scheduling problem in the photolithography area to enhance operational efficiency and capacity, thus improving chip yield and reducing manufacturing costs. Existing production scheduling models for the photolithography area are primarily based on single-objective optimization, which fails to comprehensively balance and consider the interrelationships among various factors in actual production. This study aims to propose an innovative chip production scheduling model for the photolithography area based on multi-objective optimization, aiming to significantly reduce equipment idling and minimize total chip processing waiting time. In this way, the lithography chip can be produced in the shortest time and with the highest efficiency.
Drawing from multi-objective scheduling optimization theory and specific enterprise examples, a multi-objective optimization model for the production scheduling of photolithography area chips has been developed. The model also includes the optimization of chip weights, enhancing its scientific foundation. To solve this model, the study has designed a multi-strategy improved multi-objective sparrow algorithm, incorporating the Halton sequence chaotic improved initial value, external archive update mechanism, non-dominant sorting, discoverer polynomial mutation, and population self-adaptive control. In the process of solving large datasets, the multi-strategy improved sparrow search algorithm demonstrates the best performance. The research integrates the actual production scenario in the photolithography area and simulates data based on real workshop data.
Through experimental analysis of the multi-strategy improved multi-objective sparrow search algorithm, it is observed that the algorithm exhibits the best performance in problem-solving. Even with changes in chip weights, the algorithm maintains good stability and reliability. The optimized scheduling model demonstrates clear advantages in multiple aspects. Compared with the existing scheduling model, the optimized model effectively addresses the allocation scheme of the photolithography area, significantly reducing production time. By accurately analyzing the matching relationship between the photolithography area and the machine stage, and considering factors such as the state and work efficiency of the machine stage, the photolithography area can be allocated to the machine stage more reasonably, thereby enhancing production efficiency.
The study holds significant importance in the field of chip production, providing a practical method to optimize chip production scheduling in the photolithography area. Future research can explore further multi-objective optimization algorithms and consider additional constraint conditions to further enhance the production scheduling effect in the photolithography area. This is of great significance for improving the production efficiency and competitiveness of the manufacturing industry.

Under the background of a strong push for the Extended Producer Responsibility (EPR) system, the government has issued a series of measures to encourage supply chain enterprises to take extended responsibility; in addition to bearing the responsibility for the production and distribution of products, product manufacturers should also change the production mode, introduce ecological design from the production source, and share the recycling responsibility with other responsible groups in the Closed Loop Supply Chain (CLSC), so as to realize the prevention of pollution sources and the assumption of environmental responsibility. At the same time, in the era of digital economy, enterprises responsible for EPR should change their business model, accordingly, introduce a digital marketing mode to promote their own products, improve consumers’ preference for eco-design and remanufacturing products, and realize the integrated development of enterprise digital transformation and environmental responsibility fulfilment. Therefore, under the EPR system, through relevant policies the government supervises enterprises responsible for EPR producing eco-designed products and digitally marketing their products to consumers in the positive link of CLSC, and in the reverse link, through the best recycling channel jointly built by all members of the supply chain, recycling end-of-life products from consumers and re-manufacturing into a new round of product cycle. The government, closed-loop supply chain enterprises and consumers playing the three parties, are of great significance for the realization of the all-round development of the extended responsibility of producers in the era of digital economy.
Based on the Stackelberg Game Theory and nonlinear programming method, this paper explores the best recycling channels for CLSC under the background of EPR, and the government encourages enterprises to fulfil their responsibilities through regulatory subsidy policies. Then, through digital enabling CLSC, the optimal digital marketing mode based on the best recycling channel is achieved. Firstly, according to different recycling issues, three kinds of recycling channel decision models are designed: manufacturer-built recycling, e-commerce platform recycling and two-party joint recycling. The influence trend of government EPR regulation factor, ecological design factor and recycling impact factor on the model equilibrium result and the income of all parties is explored, and the best recycling channel is selected from the perspective of EPR fulfillment degree and the profit of supply chain members, respectively. Secondly, based on the establishment of the best reverse recovery channel, and further considering the influence of digital marketing on EPR performance, two digital marketing decision models are each designed: third-party digital marketing and e-commerce platform digital marketing. The influence of digital marketing on the operational efficiency of the closed-loop supply chain and the performance of EPR is studied, and the best digital marketing method is selected from the perspective of EPR performance and benefits to supply chain members.
The main conclusions are: From the perspective of recycling channel selection, we should diversify the recycling channels. By comparing the recovery rate, ecological design level, market sales volume and members’ profits of the decision model of manufacturer recycling, e-commerce platform recycling and joint recycling, the optimal decision and members’ profits are optimal under the joint recycling channel. From the perspective of the best BDM cooperation method, manufacturers and internal e-commerce platforms in the supply chain achieve better EPR compliance and members’ profits by sharing marketing costs than by cooperating with third-party data companies. The investment level of BDM and the marketing efficiency of manufacturers are influenced by the unit marketing payment fees when BDM is outsourced to third parties. From the perspective of the government’ s best EPR system, the level of ecological design, the recovery rate and the profits of both sides will decrease with an increase in the basic environmental tax on unit products and increase with an increase in the recovery subsidies on unit products, which indicates that the government’s composite strategy of rewards, punishments and subsidies can simultaneously regulate and support enterprises in CLSC and promote the development of the EPR system. From the perspective of environmental benefits, enterprises should choose the best cooperation mode of introducing big data to promote marketing according to product types. When the ratio of the environmental impact of the front and back ends of the products produced is small, only the introduction of the third-party data marketing cooperation mode can improve the environmental benefits; when the ratio is in the middle level, the introduction of e-commerce platforms or third-party BDMs can improve the environmental benefits; when the ratio is high, the cooperation between producers and e-commerce platforms can improve the environmental benefits. The recycling channel and big data marketing system of CLSC under the EPR system are studied in this paper.
In the future, we will further study the impact of uncertain market demand on the establishment of CLSC recycling channel and the selection of big data marketing scheme.

As a concentrated manifestation of information technology development and service model innovation, cloud computing has become an important foundation for the digital transformation of enterprises, and the cloud service industry has gradually formed an ecosystem oriented to user needs. Cloud user requirements mainly include cost control, resilience, reliability, security, and data privacy. Cost control, resilience and reliability are closely related to the number of user requirements. Acquiring demand quantity information can ensure that cloud service providers offer stable and reliable cloud services. In the cloud service supply chain, cloud platform operators possess an advantage in acquiring demand information because of their proximity to users. However, the impact of information acquisition and disclosure behaviors on the entire cloud service supply chain remains inadequately explored. In addition, the special cost structure and replicability of cloud products make it unnecessary for downstream enterprises to order products and manage inventory in advance, and upstream enterprises do not need to arrange production in advance, so the signals for conveying demand information in traditional supply chains are invalid in cloud service supply chains. Revenue-sharing contract is the main mode of cooperation between upstream and downstream of cloud service supply chain, and there is limited research on using revenue distribution ratio as a signal to address the problem of asymmetric demand information in cloud service supply chain.
Based on the above background, this study focuses on a cloud service supply chain consisting of a cloud application developer and a cloud platform operator, who cooperate under a revenue-sharing contract. By considering varying information structures based on user demand, this study constructs three models: complete information, incomplete information, and information asymmetry. A comparative analysis is conducted on the optimal decisions and profits for both the cloud platform operator and the cloud application developer under these three models. The analysis reveals the value of acquiring and sharing demand information. The main conclusions are as follows:
Firstly, the cloud platform operator does not always benefit from information acquisition behavior, which could be worsened by profit losses stemming from the upward distortion of the revenue distribution ratio. Secondly, when the investment coefficient of cloud service product performance is in a certain range and the retained profit of cloud application developers is at a high level, the cloud platform operator’s information acquisition behavior can lead to win-win outcomes. Thirdly, the cloud platform operator should choose information sharing. Conversely, for the cloud application developer, such sharing does not necessarily enable it to make profit. It only enhances its profit when retained profits are below the threshold. Lastly, when retained profits are low, information sharing leads to higher expected price, expected performance, and expected demand for cloud service products, and disclosure by cloud platform operators is beneficial to both parties.
In terms of theoretical contributions, firstly, this paper innovatively takes the income distribution ratio as the signal, considers the unique cost structure of information products, and uses the signaling game method to explore the problem of information asymmetry of user demand, which provides the basis for the decision-making process of the involved parties. Secondly, unlike previous studies that only focus on the impact of demand information disclosure on upstream and downstream profits, this paper emphasizes the value of information acquisition by the cloud platform operator through historical data and prediction models in the context of big data, which makes up for the limitations of the existing studies concerning information acquisition strategies and the value of demand information. Lastly, the paper thoroughly considers the implications of diverse information strategies on the members, measuring the value of information and selecting appropriate strategies for information disclosure. This allows for a better understanding of the nature of information value and the factors that influence it.
This paper can be further extended. Future research could explore scenarios where participants in the cloud service supply chain have access to different information simultaneously or examine competition among multiple participants.

With the ongoing advancement and integration of digital technology in society, and improved medical experiences of patients, Internet hospitals, a novel healthcare model that amalgamates digital and information technologies, are promoting a significant transformation in the medical sector. Concurrently, the demand for such services is on the rise. The expansion of Internet hospitals represents a critical initiative aimed at promoting the integration of urban and rural healthcare systems in our country. However, the widespread adoption of digital technology poses substantial barriers to the elderly population in rural areas, which often lacks digital literacy. This digital divide significantly hampers its access to Internet-based medical services. Therefore, addressing the issue of making Internet hospitals more accessible and user-friendly for the elderly population in rural regions has become a pressing concern.
In response to these challenges, this paper investigates the roles of government and Internet hospitals in enhancing the demand for Internet medical services among the rural elderly. The study explores optimal cooperation models and the appropriate allocation of government subsidies, employing numerical simulations to derive optimal strategies. The research further provides policy recommendations based on these findings.
Firstly, the paper underscores the beneficial impact of government subsidies. It then develops three distinct decision-making models for expanding the demand for Internet hospitals among the rural elderly population: a decentralized model without government subsidies, a decentralized model with government subsidies, and a centralized model. Using differential game theory and Bellman’s continuous dynamic programming, the study derives equilibrium strategies for these scenarios. Numerical examples are used to examine variations in demand and benefits across the three models, as well as the influence of parameters such as costs on demand, using the decentralized and centralized models as reference points.
The findings reveal that, compared to the decentralized model without subsidies, the centralized model can significantly increase the demand for Internet hospitals and generate greater social benefits and profits for both the government and Internet hospitals. Under specific conditions, government subsidies can effectively guide Internet hospitals toward optimal decision-making, thereby mitigating the double marginalization effect inherent in decentralized models and resulting in enhanced demand expansion and benefits. Moreover, the analysis of demand parameter impacts indicates that the sensitivity of the rural elderly to age-friendly platform modifications has a more substantial effect on demand than digital technology training. When selecting Internet hospitals, rural elderly patients prioritize the age-friendliness of online platforms over their own digital proficiency. However, when the costs associated with adapting platforms for elderly use are prohibitively high, the efficacy of government subsidies in increasing demand will be limited.
The conclusions of this study are as follows: In the decentralized decision-making model without government subsidies, Internet hospitals usually have a low level of effort due to the lack of government subsidies. Hospitals will decide whether to carry out aging-friendly transformation based on their own cost-effectiveness ratio. The government’s effort level is also limited, mainly focusing on policy supervision and technical training. In the decentralized decision-making model with government subsidies, the government will provide a certain proportion of subsidies, so its effort level depends on its fiscal expenditure capacity and its guiding role in Internet hospitals. Government subsidies reduce the transformation costs of Internet hospitals and stimulate their enthusiasm for aging-friendly transformation, so their effort level will be higher than that of the non-subsidized decision-making model. In the centralized decision-making model, the government has high requirements for public health benefits and hopes to fully lead the aging-friendly transformation of Internet hospitals. When the demand for Internet medical care among the elderly in rural areas increases significantly and Internet hospitals face greater technical and financial challenges in the transformation process, the centralized decision-making model can maximize the government’s leading role and resource coordination effect. At this time, the effort level of the government and Internet hospitals reaches the highest level. The government leads the entire transformation process through policy enforcement, full subsidies or technical support, and Internet hospitals cooperate with the government’s centralized decision-making to implement relevant plans.

The contract-farming platform is increasingly central to the digital and green transformation of modern agriculture. By enhancing traceability and transparency, blockchain technology presents a significant opportunity to add value to this model, meeting a growing consumer demand for trustworthy agricultural products. However, the widespread adoption of blockchain is confronted by a critical paradox: its potential benefits are counterweighed by blockchain energy consumption and high costs. This duality creates a complex decision-making environment for supply chain partners. Existing research has not fully addressed this challenge, particularly failing to balance economic objectives with environmental concerns under conditions of information asymmetry and fluctuating consumer trust. This paper, therefore, seeks to answer three core questions: (1)Under what specific conditions should a platform adopt blockchain technology? (2)How do key factors such as energy costs, consumer skepticism, and operational expenses influence the strategic decisions and profitability of both the platform and the farm? (3)How can the inherent conflicts of interest between the platform and the farm be effectively mitigated to achieve synergistic outcomes?
To address these questions, this paper constructs a game-theoretical framework for a two-echelon contract farming supply chain, comprising a platform and a farm. Utilizing a Stackelberg game model, we analyze and compare the optimal strategies, including pricing, carbon reduction investment, and production scale, across two scenarios: non-adoption and adoption of blockchain. The analysis moves beyond a singular focus on profit maximization to incorporate a multi-objective perspective that also considers environmental benefits, thereby offering a more comprehensive evaluation of blockchain’s systemic impact.
The results have several crucial findings. First, we identify the precise conditions for blockchain adoption, revealing that the platform’s adoption threshold is notably stricter than the farm’s preference, with energy cost emerging as the most critical determinant. When energy costs are below a specific threshold, adoption can create a “quadruple-win”, benefiting the platform, the farm, consumers, and the environment. Second, the achievement of a mutual “win-win” state for both economic and environmental goals is highly conditional, requiring not only low energy costs but also low levels of consumer skepticism towards carbon reduction efforts. Third, our model identifies a distinct zone of conflict between the platform and farm. We further propose and validate clear pathways to alleviating this conflict: improving carbon reduction technology is effective when training costs are low, while stabilizing crop yield volatility proves to be another viable strategy for enhancing cooperation and encouraging platform adoption.
This research offers significant contributions by being one of the first ones to model the impact of blockchain’s energy consumption on adoption decisions within a dual-objective contract farming framework. From a real-world perspective, this paper provides clear managerial implications. Platforms are advised to adopt low-energy consensus mechanisms and build robust certification systems to foster consumer trust. We recommend that policymakers implement a combination of short-term subsidies and long-term support for technological innovation to facilitate a smoother transition. Moreover, this paper provides a theoretical foundation and practical guidance for stakeholders to navigate the complexities of blockchain adoption, fostering a more sustainable and efficient agricultural ecosystem.

In recent years, the large-scale borrowing of local financing platforms and the hidden debt risks of local governments have become more and more prominent, and the transformation of financing platforms has become an important topic in China’s current social system reform. In previous studies, the theoretical research on financing platform transformation mainly focuses on qualitative analysis and empirical research, while there are few studies on quantifying relevant measures and establishing game models to analyze the dynamic decision-making relationship among relevant subjects, and even less evolutionary game studies on financing platform transformation. Moreover, most of them are pairwise games among local governments, financing platforms and financial institutions, and rarely put these three parties in a game framework for systematic research. Therefore, it is necessary to systematically study the interactive decision-making mechanism and strategy evolution path of local governments, financing platforms and financial institutions in the process of financing platform transformation under the framework of tripartite evolutionary game, which is of great theoretical and practical significance for understanding the financing platform transformation mechanism, optimizing government policy design, and promoting risk control and sustainable development.
This paper mainly studies the following questions: (1)Does Evolutionarily Stable Strategy (ESS) exist in the three-dimensional dynamical system composed of local governments, financing platforms and financial institutions? Is it possible that “ideal equilibrium is the system ESS”? What conditions are needed? (2)What impact does the initial strategy have on the strategy choice of all parties and the system ESS? (3)Will random disturbance factors change the system ESS, and what influence does it have on the attraction domain of ESS? In order to answer the above research questions, a tripartite evolutionary game model among local governments, financing platforms and financial institutions is constructed based on the replication dynamic equation. In terms of model analysis, according to Friedman’s research method and Lyapunov’s first method, the evolutionary stability of game systems is emphatically discussed, and a sufficient condition that “ideal equilibrium is the system ESS” is given. In terms of simulation research, a set of examples are designed according to the actual situation, and the influence of the initial strategy on the strategy selection of all parties and the system ESS is simulated by Matlab R2017b software. By introducing random disturbance factors, the influence of random disturbance factors on the system ESS and its attraction domain is discussed with simulation.
This paper mainly draws the following conclusions: (1)No matter whether local governments guide platform transformation or not, traditional financing platforms can’t get loan support from financial institutions for a long time, and transformation is an inevitable choice for financing platforms. Moreover, the first prerequisite for the successful transformation of financing platforms is to obtain financial support from local governments, and the policy guidance and regulatory restriction of local governments during the transition period are indispensable. (2)The more positive the attitude of local governments and financial institutions towards platform transformation, the more likely and accelerated it is to achieve the ideal equilibrium. Compared with the initial willingness of financing platforms to “transform”, the initial willingness of local governments to “guide” and financing platforms to “lend” is more important, and the negative attitude of either party of the latter will eventually lead to the failure of platform transformation. (3)Random disturbance will increase the uncertainty of the strategic choices of local governments, financing platforms and financial institutions, and aggravate the irregular movement of the strategies of all parties. Although it will not change the system ESS, it will reduce the possibility of realizing the ideal state that local governments and financial institutions fully support platform transformation and financing platforms themselves are willing to transform.
It should be pointed out that this paper only focuses on the interactive decision-making behavior of local governments, financing platforms and financial institutions. However, there are many stakeholders involved in the transformation of financing platforms, and the interest relationship between local governments and financing platforms is complicated. Therefore, more systematic and comprehensive research can be carried out on the basis of introducing more stakeholders and fully clarifying the multi-interest relationship in the future.

In October 2023, General Secretary Xi Jinping stressed at the Central Financial Work Conference that the financial sector was a lifeblood of a nation’s economy and crucial component of a country’s core competitiveness. Cross-industry risk contagion refers to the process of spreading and diffusing risks among different industries, and it has become an important factor affecting China’s financial stability. At present, the deep mosaic of the industrial chain, mixed operation of enterprises and investment diversification have intensified the interdependence of industries, and the risks of industries are easily transmitted through multiple channels in time of crisis, forming systemic risks.
This paper responds positively to the initiative of preventing cross-industry risks and analyzes the time-varying risk spillover among Chinese stock industries and its affecting factors from a structural perspective. In this paper, by applying the complex network method and the time-varying weighted directed network method, we construct the total volatility spillover index and directional volatility spillover index between the financial industry and real economy industry to reflect the volatility spillover mechanism between industries. This paper deeply analyzes the characteristics of the cross-industry network structure, and uses unsupervised learning methods to classify industries with similar characteristics and reveal the similarities and differences of industry segments. Then, this paper innovatively extends the risk topology network framework to realize the effective screening of risk spillover structure and its similarity in different periods. Finally, this paper combines multiple regression measures and machine learning methods to analyze the impact of the operating conditions of China’s real economy on the risk linkages among Chinese stock industries, which provides an important perspective and tool for building a robust financial market environment.
It is found that the cross-industry risk linkage effect is significantly enhanced under large risk event shocks, and the structural change in the spillover effects of each industry is particularly drastic under the impact of the COVID-19 epidemic. In terms of the structural characteristics of cross-industry spillovers, the industrials and consumer discretionary industries form a closely linked core and are the main net exporters of risk. In addition, the consumer staples, health care and information technology industries, as well as the energy, real estate and financial industries, share similar risk characteristics and spillover capabilities. Maintaining economic growth, expanding domestic demand, and stabilizing production are important ways to effectively reducing risk linkages across industries. These measures can enhance the resilience of the economic system and reduce the sensitivity of external shocks to cross-industry risk transmission.
This paper suggests that structured regulation should be highly emphasized in preventing and controlling financial risks across industries. At the same time, the momentum of financial stabilization measures should be fully stimulated, especially the growth of production capacity and the level of economic activity in industrials. Product price stability should be promoted through price monitoring, market regulation and policy guidance; and the stability of consumption growth should be promoted by raising income levels, strengthening consumer rights protection and improving market information disclosure, thereby enhancing the stability of the financial system and reducing the risk linkage effect among industries.

The development of a new-type energy system necessitates transitioning toward cleaner, lower-carbon, and diversified energy resources. The increasing randomness, intermittency, and volatility of new energy output, coupled with the growing complexity of user-side energy demand, pose greater challenges to the safe and stable operation of the new power system. Demand Response(DR), as an important means to improve system flexibility, economy, security, and sustainability, achieves a coordinated balance between supply and demand by incentivizing users to proactively adjust their energy consumption behavior. However, current demand response practices still suffer from insufficient demand-side resource exploration, low accuracy in response potential assessment, and inadequate utilization of adjustable resources. Especially for high-energy-consuming industrial enterprises, accurately quantifying their demand response potential is of significantly theoretical and engineering application value for formulating response strategies, aggregating flexible resources, assisting market transaction decisions, and optimizing system operation.
To address these issues, this paper proposes a comprehensive demand response potential calculation model for high-energy-consuming industrial enterprises. This model mainly includes four core analytical steps: First, the K-Medoids clustering algorithm is used to cluster the enterprise load curves, accurately representing different energy consumption patterns by identifying typical load characteristics. Second, Discrete Wavelet Transform (DWT) is used to decompose the load data into multiple scales, effectively separating stable loads from adjustable loads, thereby uncovering potential adjustable resources. Third, based on the load step analysis method, the theoretical load reduction potential under ideal response conditions is calculated. Finally, combined with the actual production and operation characteristics and energy constraints of the enterprises, the theoretical load reduction potential is corrected to obtain demand response potential results that better reflect actual operating conditions.
This paper selects historical load data from typical high-energy-consuming enterprises in industries such as calcium carbide, carbon, and ferroalloys for case analysis. Through data mining methods such as cluster analysis, wavelet decomposition, and load step calculation, the accuracy and reliability of the demand response potential assessment results are improved. The actual case verification results show that there are significant differences in the demand response potential of enterprises in different industries. Among them, calcium carbide enterprises demonstrate high responsiveness, with one calcium carbide enterprise’s average demand response potential accounting for 35.67% of its peak load; carbon enterprises have a relatively moderate demand response potential, with the highest reduction potential reaching 19.11%; and ferroalloy enterprises have relatively low response potential, with the highest reduction potential reaching 8.39%.
The research results indicate that enterprises with large peak-to-valley differences, stable load step variations, and low load rates typically possess higher demand-side adjustment potential. Therefore, in the process of demand response resource exploration, priority should be given to high-energy-consuming industries with obvious load step characteristics, fully leveraging their flexible load adjustment capabilities to improve the power system’s supply-demand balance and safe operation.

With the rapid development of the Internet, online complaints regarding automobile quality have emerged as an efficient and convenient means for automotive enterprises to gather user feedback. Consequently, this trend has necessitated the exploration of effective methods to leverage these online complaints in order to mine and monitor issues pertaining to automobile quality. Given that the frequency of online complaints is influenced by numerous factors, including automobile quality, sales, the development of the Internet, and public awareness of rights protection, it exhibits significant autocorrelation and dynamics. However, the existing methods, which are often premised on the assumption that the in-control processes remain unchanged and adhere to models with fixed parameters and constant control limits, have proven to be unreliable in practical applications for delivering dependable monitoring and timely warnings.
In this context, the motivation behind our research stems from the urgent need for automotive enterprises to effectively harness the wealth of data contained in online complaints. The problem we aim to address is how to develop an adaptive monitoring system that can dynamically capture and analyze these complaints, accurately identifying trends and potential quality issues in real-time. By doing so, enterprises can take proactive measures to address concerns, enhance product quality, and ultimately improve customer satisfaction.
To this end, we propose a dynamic method for automobile quality monitoring, denoted as the SDINAR chart, based on the sliding window Integer-valued Autoregressive (INAR) model. Firstly, we incorporate the sliding window technique, a concept that allows us to analyze data in segments over time. The maximum entropy principle is used to select the optimal window period, ensuring that we capture the most informative and representative data slices. Within each window, an INAR model is fitted to the data, and the model parameters are obtained through conditional maximum likelihood estimation. As the sliding window moves forward, the model parameters are adjusted accordingly, resulting in the establishment of a variable coefficient INAR model, which realizes the dynamic fitting of the automobile quality online complaint data. Subsequently, the conditional probability of the one-step-ahead prediction residuals is calculated, and given a specific confidence level, a confidence interval for the residuals is obtained through Monte-Carlo simulation. This leads to the development of a time-varying control limit monitoring method. This method enables us to set dynamic thresholds that can trigger alerts when the quality of automobile complaints deviates from expected norms, thereby facilitating prompt and informed decision-making.
We select “Volkswagen Sagitar” as the subject of our case study, a car brand that has consistently maintained high sales figures in recent years. To gather relevant data, we source complaint texts pertaining to Volkswagen Sagitar from “Automobile Quality Website” (http://www.12365auto.com), a national platform dedicated to receiving and addressing consumer complaints related to automobiles. Utilizing the proposed SDINAR chart, we conduct an in-depth and dynamic analysis and monitoring of the complaint data concerning the defect topic of “abnormal brake noise” from January 2015 to June 2023. To evaluate the efficacy of the proposed method, we compare its performance with traditional monitoring approaches. The results of this comparison underscore the effectiveness of the SDINAR chart in dynamic monitoring and early warning.
This research not only provides automotive enterprises with a novel tool to evaluate the dynamic state of automobile quality, but also supports decision-making based on monitoring and alert feedback. However, there are still opportunities for further exploration. In future studies, we plan to investigate the correlations between multiple complaint topics and establish a network model to comprehensively monitor the overall state of automobile quality. Additionally, we aim to incorporate additional monitoring indicators beyond complaint frequency, such as the time interval between complaints and textual features extracted from the complaints, to develop a more efficient monitoring chart from various perspectives. We believe that these enhancements will further strengthen the effectiveness and comprehensiveness of our approach in monitoring and assessing automobile quality.

With the rapid development of e-commerce, the volume of express business has increased sharply, which puts forward higher requirements for the operation efficiency of express enterprises. The effective mining of urban network node information is very important for understanding and predicting the express business volume. However, traditional prediction models often ignore the importance of urban network nodes and the complexity of express business data, resulting in insufficient prediction accuracy. In order to effectively mine the node information of the urban network and improve the prediction accuracy of the average daily express business volume, a daily express business volume prediction model based on Convolution-Bidirectional Long Short-Term Memory Neural Network and Autoregressive Integrated Moving Average (Attention-CNN-BiLSTM-ARIMA, AC-BiLSTM-ARIMA) is proposed.
Firstly, the feature derivation strategy is introduced to construct the importance ranking index of city nodes in the urban network from multiple perspectives, and the PCA-entropy weight TOPSIS model is used to analyze the city importance ranking decision, in order to help express enterprises rationally plan the allocation of resources such as manpower and equipment. Secondly, the comprehensive feature extraction method is used to capture the relevant features of the express business volume time series data: the CNN is used to extract the nonlinear features of express business data, the BiLSTM network to extract the bidirectional time series features of express business data, the ARIMA to extract the linear features of express business data, and the Attention mechanism to assign the weights to the corresponding features. Then, AC-BiLSTM-ARIMA daily express business volume prediction model is established for different node cities in the urban network. Finally, according to the real desensitization data of an express enterprise, the simulation experiment is carried out, and the performance of the model is evaluated by calculating the statistical indicators such as Explained Variance Score (EVS), Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and R². It is found that the proposed method can be effectively applied to the actual express business volume prediction and the performance is better than the comparison algorithms.
This paper constructs the city importance index, and combines machine learning and statistics knowledge to provide an improved method for forecasting express business demand. The optimization model has good generalization ability, and the innovation is mainly reflected in the following two points: first, considering factors such as city activity, contribution rate and growth potential, the feature derivation strategy is introduced to construct the city importance index, which provides a new perspective for express enterprise resource planning; the second is to combine the advantages of CNN, BiLSTM and ARIMA to improve the model’s ability to capture linear, nonlinear and time series features, and to improve the accuracy of prediction through weight allocation.
The model can be applied to the daily operation of express enterprises to help them rationally plan human and resource allocation, optimize distribution routes and improve distribution efficiency according to the prediction results.

With the continuous improvement of information technology such as the Industrial Internet, the development of capacity-sharing platform has increased steadily in China. According to the “Analysis and Prospects Research Report on the Current Situation and Development Potential of China’s Shared Manufacturing Industry from 2026 to 2032”, the scale of China’s capacity sharing market increased to 1,290.8 billion yuan in 2024.This shows that capacity-sharing platform has huge room for growth and deserves more researches for providing advices for the manufacturer.
This paper studies the pricing strategies of two duopoly capacity-sharing platforms in a competitive market. The service levels of the two platforms are different. We establish the Hotelling models and discuss the pricing strategies of the two platforms in three different cases: both platforms adopt the registration-fee model, both platforms adopt the commission model, and two platforms adopt the registration fee model and the commission model, respectively. By backward induction, we obtain the optimal solutions and profits of two platforms in three different cases, respectively. Then, we analyze the pricing strategies of two platforms by calculating the first derivatives of two platforms’ profits with respect to the relevant parameters and comparing two platforms’ profits in each case.
Firstly, we find that no matter which pricing model two platforms adopt simultaneously, the impacts of two-sided users’ service sensitivity coefficients on two platforms’ profits are not always the same. The impacts are associated with the difference in two platforms’ service levels. We take the difference value of both the first platform’s service level and the second platform’s service level as a basis. In the first case, when this value is greater than zero and no more than a threshold, two-sided users’ service sensitivity coefficients have positive impacts on the profits, respectively. Otherwise, two-sided users’ service sensitivity coefficients have negative impacts on the profits. In the second one, when this value is greater than zero and no more than the other threshold, two-sided users’ service sensitivity coefficients have positive impacts on their profits, respectively. Otherwise, two-sided users’ service sensitivity coefficients have negative impacts on their profits, respectively.
Secondly, there are profit differences between two competing capacity-sharing platforms. In the first case, when the platform’s service cost coefficient is smaller than a threshold, the platform which has higher service level can gain more profits. Otherwise, the platform which has lower service level has a competitive advantage. Similarly, in the second one, when the platform’s service cost coefficient is smaller than the other threshold, the platform which has higher service level can gain more profits. Otherwise, the platform which has lower service level has a competitive advantage. This means that the platform with low service cost coefficient and high service level has higher operational efficiency. Such platform maintains a higher service level at a lower service cost, so that the platform has more flexibility in available funds and can further improve its service level or other functions which are beneficial to platform operation, such as supervision services for two-sided users. As a result, the platform will remain at a certain level that can provide high-quality service, which can attract more bilateral users who have higher requirements for platform services to join the platform. In other words, at this time, such platform can obtain more bilateral users to achieve the improvement of profits without increasing the service cost input, that is, the platform with a higher service level has more competitive advantages. The analysis about the contrary condition is the same.
Thirdly, two-sided users’ service-sensitivity coefficient and the platform’s service cost coefficient affect the profit difference between two competing capacity-sharing platforms. No matter which pricing model two platforms adopt simultaneously, the platforms’ profit difference is positively correlated with two-sided users’ service sensitivity coefficients, and negatively correlated with the platform’s service cost coefficient when the difference is positive. Otherwise, the profit difference is negatively correlated with two-sided users’ service sensitivity coefficients, and positively correlated with the platform’s service cost coefficient. This means that in a competitive market, the platform should judge whether to improve its service level to expand its competitive advantage according to its own service cost. At the same time, the platform which is in a weak competitive position can also narrow the competitive gap by improving technology to reduce the service cost coefficient and distinguish target two-sided users. Capacity-sharing platform needs to consider such factors when making pricing decisions.
This paper focuses on the capacity-sharing platforms’ pricing decisions in a competitive market and the influence of platform’s service level on their pricing decisions. But we do not consider this parameter as a decision variable or endogenous parameter. What’s more, the optimal solutions are too complicated for us to make a detailed analysis in the third case. In the future, we will try to establish a new model by considering platform’s service level as a decision variable or endogenous parameter, and optimize our model to obtain more analyzable results.

Product quality information disclosure is widely regarded as an effective means to alleviate the asymmetry of product quality information, but in reality, enterprises often use false quality information. TerraChoice’s investigation report shows that even if the quality is not up to standard, 95% products still make false statements in the process of product quality information transmission. Different from the traditional methods such as ERP and EDI to realize product quality information disclosure, blockchain has become a new way to solve various problems such as information recording, tracking and verification due to its remarkable characteristics such as decentralization, tamper-proof information and consensus mechanism, and has been widely used in supply chain. Although product quality information disclosure based on blockchain technology can effectively improve the authenticity of information disclosure, considering the imperfection of blockchain technology as a solution for false disclosure of product quality information, opportunistic information disclosure behavior of enterprises still exists. Due to the information gap between the physical account book and the electronic account book, enterprises are prone to opportunistic errors in the process of processing the original quality information data into observable information and uploading it to the blockchain. Such opportunistic behaviors are difficult to identify under the cover of the blockchain policy value, and it is easy to establish long-term and improper trust. Therefore, it is of great significance to study the opportunistic information disclosure behavior of suppliers under the background of blockchain technology application.
This paper constructs a tripartite evolutionary game model involving suppliers, government regulators and consumers, and discusses the following questions: (1)What impact will the imperfection of blockchain technology as a solution to false disclosure of product quality information have on the information disclosure balance strategy? When will suppliers choose to implement opportunistic information disclosure? (2)How can the government supervision department improve the information disclosure policy and design the incentive mechanism to correct the opportunistic information disclosure behavior of enterprises to the maximum extent and protect the rights and interests of consumers? (3)For consumers, is it good to have more product quality information? How will “information noise” affect consumer surplus?
The study shows that: while blockchain technology improves supply chain visibility, it may also trigger the risk of information leakage and reduce consumer surplus. Under the premise of “information noise”, blockchain technology will become an important tool for coordinating and maintaining opportunistic behavior, and responding to external information disclosure policies. The difference in the degree of information disclosure between mandatory information disclosure policies and voluntary information disclosure policies has a negative impact on the standardization of product quality information disclosure behavior of enterprises, while positively affecting the formulation of mandatory information disclosure policies. Based on the research findings, this article provides countermeasures and suggestions from multiple aspects such as strengthening trust and recognition of blockchain technology, improving information disclosure policies, etc., in order to provide reference for blockchain adoption decisions.
This paper assumes that the product quality information comes from a single supplier, and when the quality information comes from multiple subjects, it will be worth further exploring the information disclosure decision of enterprises based on different supply chain structures. In addition, it is also valuable to further study the opportunistic information disclosure behavior of enterprises under the background of blockchain application through empirical research methods such as questionnaires and interviews, and to reveal its formation mechanism.

The supply chain structure caused by changes in green industries, consumption formats and sales channels has shifted from a single enterprise, a single product and a single channel to a competition for mutually alternative products produced by different manufacturers in multiple sales channels, and the decision-making strategies of the traditional supply chain have been unable to adapt to the continuous evolution of the diversified supply chain. Therefore, this paper takes the three-channel two-level supply chain composed of green brand manufacturers, traditional brand manufacturers and a retailer as the research object, based on the horizontal power structure relationship between competitive manufacturers, and comprehensively considers the influence of product substitution degree and consumer preference factors such as green, brand and channel, to construct a game model when the power position of competitive manufacturers is equal and green brand manufacturers unilaterally occupy a dominant market position. This paper explores how on-chain entities influence other relevant entities with different degrees of resource allocation, and how enterprises can make rational decisions to protect their own interests under the influence of product substitution and consumer preference factors. This is a practical study that explores the mechanism of power structure and reveals the competitive logic of alternative products.
The main conclusions of the study are as follows: (1)The higher the level of consumers’green preference and the degree of product substitution, the more the green brand manufacturers will be encouraged to implement green technology research and development to improve the level of product greenness. At the same time, consumers’preference for offline channels will enhance the sensitivity of greenness to the degree of product substitution and the degree of consumers’green preference, while the sensitivity of consumers’traditional brand preference to the two is not always favorable. (2)When the green brand manufacturer occupies a dominant position in the market alone, a higher market power position will be helpful for it to carry out green technology research and development and improve the level of product greenness, and competitive manufacturers can obtain a higher profit level under this model. Affected by the changes in upstream wholesale prices, retailers are closely related to the degree of consumer channel preference and the efficiency coefficient of product greening under which mode they obtain higher profits. (3)In order to maintain the demand and profit of their DTC channels to occupy a leading position in the supply chain, green brand manufacturers prefer the MGT model, and need to maintain a low level of product substitution to avoid being overtaken by the demand for alternative products and the profits obtained by related entities.
The management implications of this study are as follows: (1)To obtain more consumers’recognition of product environmental protection attributes and green brands, reduce the number of consumer groups that prefer traditional products, and improve consumers’green preference. In addition, green brand manufacturers are encouraged to actively implement green technology research and development, improve the level of product greenness, and continuously improve the profit level of related enterprises in the supply chain and the environmental protection benefits of the supply chain. (2)Green brand manufacturers should carry out targeted research and development, increase the irreplaceability of green products and ordinary products, control the degree of product substitution within the profit exceeding threshold under different power structure models, and then maintain the profit level obtained by green brand manufacturers to occupy a leading position in the supply chain. In this way, traditional brand manufacturers can be forced to adapt to market changes and the development of the times to green transformation, and to drive downstream retail transformation with the transformation of upstream manufacturing sources, and accelerate the process of traditional consumption substitution. (3)Green brand manufacturers should actively take advantage of the favorable trends in the general environment such as consumption and policies to consolidate their unilateral dominance in market power, inhibit the bargaining level and decision-making ability of traditional brand manufacturers and downstream retail enterprises of competing enterprises, and continue to grasp the initiative to obtain more profits.
Future research can construct a demand function based on the characteristics of demand time-variability, and comprehensively consider the horizontal and vertical power structure relationship between supply chain firms.

In the context of increasing global attention to sustainable development and the continuous growth of the remanufacturing industry, remanufacturing businesses face numerous challenges. Among them, the quality uncertainty of waste products and patent licensing issues are particularly prominent. When faced with these uncertainties, remanufacturers usually exhibit risk-averse attitudes. This paper focuses on the remanufacturing supply chain under patent licensing and explores the impact of risk aversion on supply chain decision-making and coordination. We mainly address the following issues: What impact does risk aversion have on the production and price of new and remanufactured products, as well as the recovery rate and unit patent licensing fees? What are the impacts of risk aversion from the perspectives of consumers, the environment, and social welfare? How to coordinate the remanufacturing supply chain considering risk aversion under patent licensing?
This paper constructs a single-period decision making model for a two-level remanufacturing supply chain consisting of a manufacturer and a remanufacturer. In this model, the manufacturer is responsible for the production and sales of new products and charges a remanufacturing patent license fee from the remanufacturer. The remanufacturer is responsible for recycling, remanufacturing, and then selling the products in the market. The model takes into account the fact that the quality of recycled products follows a random distribution within a specific interval, which makes the unit cost of remanufacturing uncertain. Meanwhile, a risk-aversion coefficient is introduced, and the mean-variance method is used to measure the risk-averse utility of the remanufacturer. It is assumed that there is a Stackelberg game between the manufacturer and the remanufacturer, and the information between them is completely symmetric.
This paper analyzes two scenarios: risk-neutral and risk-averse. In the risk-neutral scenario, the optimal solutions for the quantity of new products, the quantity of remanufactured products, the unit patent license fee, and the recycling rate are derived. In the risk-averse scenario, the corresponding equilibrium solutions are also obtained. By comparison, it is found that as the risk-aversion coefficient increases, the quantity of new products increases, while the quantity of remanufactured products and the recycling rate decrease. In terms of prices, the price of new products remains unchanged, the price of remanufactured products rises, and the unit patent license fee decreases. This is because the risk-averse remanufacturer would reduce recycling and remanufacturing activities to maintain its utility, thus affecting the quantity and price decisions of the total supply chain.
The impact of risk aversion is further examined from the perspectives of consumers, the environment, and social welfare. The results show that risk aversion reduces consumer surplus. This is because of a decrease in the quantity and an increase in the price of remanufactured products. Although the quantity of new products increases, it still cannot compensate for the losses of consumers. In terms of environmental impact, due to an increase in the quantity of new products and a decrease in the quantity of remanufactured products, as well as an increase in the quantity of waste products, the environmental impact increases. However, under a certain condition (when the environmental impact of waste products is not considered and the unit carbon emissions of new products are lower than a certain threshold), risk-averse behavior may reduce the environmental impact. Social welfare also decreases due to a reduction in the utilities of manufacturers and remanufacturers, a decrease in consumer surplus, and an increase in environmental impact.
Additionally, a two-part tariff contract is designed to coordinate the remanufacturing supply chain. We find that when the unit license fee and the fixed transfer fee meet certain conditions, this contract can achieve supply chain coordination, enabling the recycling rate and the total utility of the remanufacturing supply chain to reach the level of centralized scenario, while increasing consumer surplus and social welfare and reducing environmental impact.

With the advancement of China’s “dual carbon” goals, environmental protection concepts are gradually integrated into consumers’ daily lives. Manufacturing enterprises are devoting themselves to the development and production of green and low-carbon products in order to fulfill their social responsibilities, as well as their own brands and economic interests. For example, BMW has partnered with companies such as Shougang and Hegang to create low-carbon automotive steel, vigorously promoting supply chain carbon reduction, and cooperation among supply chain enterprises to reduce emissions is becoming increasingly common. Enterprises engaging in green and low-carbon production will inevitably lead to the internalization of external costs of carbon emissions, and the financial constraints of upstream and downstream enterprises in the supply chain will continue to intensify. To address the financial constraints of low-carbon supply chains, especially bilateral financial constraints, forms such as green finance financing and commercial credit financing have become important approaches. Therefore, it is of great significance to explore low-carbon supply chain emission reduction cooperation decision-making and financing strategy selection methods under financial constraints, especially bilateral financial constraints.
This paper focuses on a low-carbon supply chain consisting of a supplier and a manufacturer, where the supplier engages in carbon reduction production of semi-finished products such as components, while the manufacturer further engages in carbon reduction production of finished products. Due to the large amount of emission reduction funds required for green emission reduction production, the supplier and manufacturer often face financial constraints. When considering supply chain cooperation to reduce emissions under bilateral financial constraints, the following combination financing model is adopted to solve the problem of insufficient funds for the enterprise: (1)the “bilateral bank loan” combination financing model, in which both the supplier and manufacturer solve their funding problems through bank loans; (2)the combination financing model of “manufacturer bank loan plus advance payment” means that the downstream manufacturer solves its financial constraints through bank loans, and solves the problem of insufficient funds for the upstream supplier by paying part of the goods in advance.
First of all, the paper solves the equilibrium solution of the game through the backwards-induction under the financing model without financial constraints and with bilateral financial constraints. Then, it analyzes the impact of consumer low-carbon preferences, and emission reduction cost factors on the decisions and profits of each member. Finally, it explores the preferences of various entities for different financing models under different market conditions. The research results show that: (1)Without financial constraints, the emission reduction levels of the supplier and manufacturer are the same. Under the “manufacturer bank loan plus advance payment” combination financing model, the emission reduction level of supplier is higher than that of the manufacturer. However, under the “bilateral bank loan” combination financing model, the carbon emission reduction levels of supplier and manufacturer are influenced by the bank loan interest rates. (2)The profits of the supplier and the supply chain under combination financing models are lower than those under no financial constraints, but the profits of the manufacturer may be higher than those under no financial constraints. (3)Under bilateral financial constraints, the manufacturer and the supply chain prefer to choose the “manufacturer bank loan plus advance payment” model. However, for the supplier, when the sensitivity coefficient of advance payment wholesale price is relatively low, it prefers to choose the “manufacturer bank loan plus advance payment” model. Otherwise, it prefers to choose the “bilateral bank loan” financing model.
Further research can be extended to the stochastic demand environments and the situation where enterprises have risk aversion, analyzing the impact of market demand fluctuations and risk aversion behaviors on emission reduction decisions and financing strategy choices of various entities in the supply chain.