Table of Content

25 January 2026, Volume 35 Issue 1

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Theory Analysis and Methodology Study

Evolutionary Analysis of Car-sharing Regulation Policy Based on Tripartite Game Model

LUO Qingyu, BING Xue, JIA Hongfei

2026, 35(1):  1-8.  DOI: 10.12005/orms.2026.0001

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Against the backdrop of increasing urban traffic congestion and mounting environmental pressure, improving travel efficiency and optimizing resource allocation have become critical issues that urban transportation systems urgently need to address. As an emerging mobility mode, car-sharing demonstrates potential advantages in enhancing vehicle utilization and alleviating resource constraints. However, during the early stage of development, car-sharing systems typically face challenges such as insufficient supply, low user adoption rates,and unstable policy incentives. The evolution of these systems is influenced not only by market supply and demand dynamics but also by the interactions among multiple agents, including the government, operators,and travelers. The strategic decisions of these agents are interdependent and generate dynamic feedback through payoff structures, rendering the system evolution complex and path-dependent.
To systematically investigate the mechanisms through which multi-agent behavior influences the evolution of car-sharing systems, this study develops a tripartite evolutionary game model involving the government, car-sharing operators,and travelers under the framework of bounded rationality. In the model, the government, as the regulatory authority, chooses between regulation and non-regulation by comprehensively considering factors such as regulatory costs, subsidy expenditures,and environmental benefits. Operators, as service providers, decide between large-scale operations and small-scale operations, balancing the trade-off between service network coverage and operational cost inputs. Their strategic choices directly determine the service capacity and market competitiveness of the car-sharing system. Travelers, as demand-side participants, determine whether to switch from private car usage to car-sharing based on the relative travel utility between the two mobility modes, with their behavioral choices serving as a key variable on the demand side of the system. Based on these settings, this study constructs a tripartite payoff matrix, specifying the payoff expressions for each agent under different strategy combinations. The proportions of agents adopting different strategies are introduced as state variables, and replicator dynamic equations are derived to characterize the evolution of strategy proportions over time.
To further reveal the underlying mechanisms of system evolution, this study applies evolutionary stability theory to solve the equilibrium points of the system. On this basis, the Jacobian matrix is constructed to systematically analyze the stability conditions of each equilibrium point, determining whether they qualify as evolutionary stable strategies based on the signs of the eigenvalues. This process identifies possible evolutionary stable states under various parameter configurations. To examine the impact of key parameters on evolutionary trajectories, numerical simulations are conducted, focusing on core variables such as subsidy levels, cost-related parameters,and travel utility differences. By setting different parameter values, the convergence paths and stable states under various parameter combinations are systematically compared, visually presenting the dynamic adjustment process of agent strategies over time.
The findings reveal that under different parameter conditions, the system can converge to multiple evolutionary stable states, reflecting the interactive nature and dynamic feedback mechanisms among the strategies of the government, operators,and travelers. Notably, when the government adopts a regulatory strategy, operators expand their service scale, and travelers shift their travel mode, the system can reach a relatively ideal stable equilibrium. In this state, a virtuous interaction is formed among policy support, service supply,and user demand, with the strategies of the three parties aligning to collectively drive the system toward efficient operation. Under other parameter configurations, the system may converge to alternative equilibria, such as scenarios where the government refrains from regulation, operators control costs without expansion, or travelers do not shift from private cars. These outcomes correspond to varying behavioral patterns and system operation states, reflecting systemic challenges arising from insufficient policy incentives or immature market development.
From the perspective of parameter effects, subsidy levels influence both the government’s payoff structure and operators’ decision-making, thereby shaping the evolutionary trajectory of the system. When subsidy levels are maintained within a reasonable range, operators are more inclined to expand service scale to capture policy support, and the government’s net benefit from adopting a regulatory strategy remains positive, enhancing the stability of this strategy. However, when subsidy levels become excessively high, the government’s net benefits decline due to increased subsidy expenditures, weakening the stability of the regulatory strategy and potentially leading to a shift toward non-regulation. Travel utility differences directly affect travelers’ strategic choices: when the relative utility of car-sharing compared to private cars increases, travelers will be more likely to shift toward car-sharing. This change in traveler behavior further influences the strategies of operators and the government through the payoff structure: a higher proportion of travelers shifting to car-sharing expands market demand, incentivizing operators to expand service scale while also strengthening the government’s motivation to implement regulatory policies, thereby affecting the overall evolutionary direction of the system.
Based on the above analysis, this study suggests that in the process of policy formulation, subsidy levels should be reasonably determined under fiscal constraints to avoid excessive pressure on government revenues while ensuring that subsidies effectively incentivize operators to expand service scale. Furthermore, efforts should be made to improve the travel utility of car-sharing relative to private cars by enhancing service quality, optimizing pricing strategies and improving supporting infrastructure, thereby effectively guiding travelers toward mode shifts and further influencing the strategic choices of the government and operators, so as to form a positive feedback mechanism. This study provides a systematic analytical framework for understanding multi-agent interactions in car-sharing systems and offers theoretical foundations and practical references for policy design and system optimization.

Research on the Motivation of Information Sharing among MedicalInstitutions under the Condition of Service Quality Differentiation

ZHAI Yunkai, LIU Yu, WANG Yu

2026, 35(1):  9-16.  DOI: 10.12005/orms.2026.0002

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In recent years, the continuous growth of the global population and the intensification of the aging trend have increased the demand for medical resources. The emergence of new diseases and the increasing burden of chronic diseases have further challenged the medical system. To address these issues, countries have been promoting healthcare reform policies aimed at improving the quality and efficiency of medical services, ultimately safeguarding the health rights of citizens. A key aspect of this reform is the sharing of medical information, which is considered to improve the efficiency of resource utilization and reduce the imbalance in resource allocation.
Medical information sharing includes electronic medical records, inter-institutional information exchange and medical research data sharing. A unified platform facilitates information exchange across regions and institutions, enabling medical staff to access comprehensive and timely patient health information, thereby improving the accuracy of diagnosis and treatment. In addition, medical information sharing also helps to optimize the allocation of medical resources. By analyzing medical data nationwide, it is possible to better understand the distribution of diseases and medical needs in various regions, thereby allocating medical resources more rationally, improving the efficiency of resource utilization, and alleviating the problems caused by the imbalance of medical resources between regions.
However, due to concerns about privacy breaches and potential revenue losses for hospitals, hospitals and patients show limited enthusiasm for medical information sharing. To address this issue, we have constructed a multi-stage duopoly dynamic game model to explore the factors influencing the participation of hospitals and patients in information sharing. Given two competing public hospitals, A and B, patient decisions are influenced by the perceived net utility of service quality, price and travel costs. Although service prices are set by social planners, hospitals decide on service qualities to maximize their own payoffs.
Our study analyzes the service quality decisions of hospitals at multiple patient care stages, considering multi-stage treatment. At the same time, it examines the impact of information sharing on hospital decision-making, benefits and social welfare, exploring the dynamic strategic evolution of hospitals in information sharing. Key findings include: First, health examination costs significantly influence hospital decisions. Lower costs or higher marginal service costs increase the hospital’s inclination towards information sharing, indicating that reducing health examination costs can foster a more conducive economic environment for sharing. Service quality decisions depend on specific circumstances. When marginal service costs are low, hospitals participating in information sharing set higher service quality in the first stage than under non-sharing scenarios. Second, for patients not transferred in the second stage, information sharing is more likely to bring about higher service quality, while for transferred patients, not sharing is more likely to bring about higher quality. This emphasizes the complex relationship between service quality and information sharing strategies. Additionally, comparing the benefits of hospitals and social planners with and without information sharing shows that when hospitals share information, social planners tend to set higher service prices, potentially compensating hospitals for revenue losses. However, excessively high prices may dampen patient enthusiasm for sharing, hindering its development. Therefore, while ensuring the economic benefits of hospitals, it is also necessary to consider the interests of patients and find a balance. Moreover, the study shows that when marginal service costs are low or health examination fees are not too high, both social planners and hospitals are inclined to medical information sharing, at which point the interests between social planners and hospitals can be aligned.
In conclusion, medical information sharing is crucial for improving resource utilization and mitigating allocation disparities. However, limited enthusiasm from hospitals and patients hinders its progress. By understanding hospitals’ and patients’ decision-making mechanisms through a dynamic game model, social planners can implement incentive measures, fostering greater hospital cooperation to advance medical information sharing.

Strategic Investment Decision Analysis of Port Alliance Considering Carbon Trading

LIANG Chengji, GUO Yamin, SHI Jian, ZHANG Yue, WANG Yu, LU Bin

2026, 35(1):  17-23.  DOI: 10.12005/orms.2026.0003

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Ports, as critical hubs in global trade, are significant sources of greenhouse gas emissions in the shipping industry. The carbon trading market, as a key economic tool for emission reduction strategies, not only provides long-term stability but also imposes additional operational and cost pressures on ports. A port alliance, which fosters port integration and promotes sustainable development through inter-port cooperation, facilitates resource sharing and cross-port investment, thereby alleviating operational and cost pressures. With the strengthening of government controls on carbon emissions and the growing prevalence of port alliances, the decision-making environment for ports has become increasingly complex.
Ports can optimize their facilities through rational investment in development to enhance their handling capacity. However, cargo handling operations increase, so do carbon emissions. To meet government emission requirements, ports need to participate in the carbon trading market by purchasing carbon allowances, which incurs costs. Ports must make rational investment decisions to maximize revenue from both cargo handling and carbon trading activities.
Port investment decisions also affect the transportation strategies of shipping companies. After ports make investment decisions, the capacity of nodes in the transportation network changes, creating a new network. Shipping companies react to this new network by adjusting their container transport and transshipment plans to minimize costs. These shipping strategies, in turn, impact port revenue and carbon emissions, which subsequently influence decisions in the carbon trading market and affect carbon trading prices.
To respond to changes in port demand and reduce emission pressures, this paper considers the carbon trading mechanism for ports and the cooperative strategies within port alliances, establishing a bi-level programming model. In this model, the upper level focuses on optimizing port investment strategies to improve the demand satisfaction capacity of both ports and the shipping system, while reducing the carbon emission intensity of ports. Shipping companies, as one of the entities at the lower level, optimize their transport strategies to minimize shipping costs, while the carbon trading market, as another lower-level entity, sets carbon trading prices based on port carbon emission demand. The alliance cooperation strategy forms a multi-leader and dual-follower game among the parties. To achieve equilibrium in this game, we employ KKT conditions and a diagonalization algorithm to solve an Equilibrium Problem with Equilibrium Constraints(EPEC), which includes multiple single-leader and dual-follower problems. Each problem is formulated as a Mathematical Program with Equilibrium Constraints (MPEC). This ensures that each port makes optimal decisions based on the decision sets of other ports, with no single port able to unilaterally increase its revenue by changing its investment decisions.
Through five years of simulation experiments, it is found that ports with higher cargo handling volumes are more willing to invest in reducing their carbon emission intensity. Regarding trends in carbon trading prices, both a reduction in carbon allowance supply and a decrease in carbon emission intensity lead to higher carbon trading prices. Concerning the effectiveness of port alliances, the presence of a port alliance within a shipping network increases the demand satisfaction rate. The larger the alliance, the higher the demand satisfaction rate. However, when growth is too rapid or emission reduction targets are too ambitious, port alliances may struggle to ensure continued growth in demand satisfaction rates.

Research on Bundling Design and Pricing of Vertically Differentiated Products Considering Customer Choice Behavior

WANG Yana, ZHOU Guohua, JIANG Wenhui

2026, 35(1):  24-31.  DOI: 10.12005/orms.2026.0004

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Bundling refers to the marketing strategy of offering two or more products or services as a specially priced package. It is widely adopted by manufacturers and retailers, as it reduces production and transaction costs, captures more consumer surplus, achieves economies of scale, and raises entry barriers for competing firms.
This paper aims to investigate how a monopolistic firm determines the composition and pricing of multiple bundles. Component suppliers provide the retailer with m categories of components, each containing n products of distinct quality levels. The retailer selects appropriate products from the upstream component portfolio to bundle and sells to heterogeneous consumers, with the goal of maximizing profits. In this paper, we assume that each bundle must include exactly one component from each category, that is, the m categories of components are assembled in a 1∶1∶…∶1 ratio, resulting in a total of n^m technically feasible bundled products available for the retailer to choose from. Considering that consumers exhibit heterogeneous perceived quality toward bundled products, this paper explores the retailer’s optimal bundle design and pricing strategies under two scenarios: super-additive perceived quality and sub-additive perceived quality.
The customer’s demand across different bundles is developed based on the utility maximization theory, and a mixed integer non-linear program is proposed to solve this problem. Firstly, a two-step solution approach is developed to obtain the optimal decisions of the retailer: in the first stage, the optimal prices can be obtained based on the assumption that the composition and assortment of bundles are known; in the second stage, the optimal composition and assortment of bundles can be recognised using the optimal price generated in the first step. Secondly, we propose an efficient algorithm to solve the problem based on the optimal properties. Finally, the validity of the algorithm is tested and the effect of perceived quality and consumer quality valuation on the retailer’s decisions is examined by numerical analysis.
The results reveal the following key findings: (1)The optimal assortment of bundles consists of the Pareto frontier of all feasible bundles, and the components constituting the optimal bundles also lie on their respective Pareto frontiers. Additionally, the optimal set of bundles depends only on the cost/perceived quality ratios of the bundles and is independent of the distribution of consumers’ valuation for quality. (2)The optimal prices of bundles, the retailer’s market share and profits are all monotonically decreasing functions of b. Specifically, when most consumers in the market have a low marginal valuation for quality, the retailer will reduce the selling price to stimulate consumption. However, this price reduction does not lead to an increase in market share. Under the dual impact of declining marginal revenue and reduced demand, the retailer’s profits decrease. (3)The optimal prices of bundles and the retailer’s profits both increase in α, which implies that when consumers have a higher perceived quality, the retailer can appropriately raise product prices to capture more consumer surplus.
The above conclusions provide the following practical implications for retailers in bundle design and pricing: (1)In making pricing decisions, retailers should take into account not only the cost and quality of the bundles but also the distribution of consumers’ quality valuation. (2)In the design of bundles, replacing dominated components with dominant ones can either improve the qualities of the bundles or reduce their costs, thereby increasing profits. (3)For retailers, the key to securing stable future returns lies in enhancing consumers’ perceived quality of their products rather than continuously expanding the scale of their product lines.
Notably, to the best of our knowledge, this is the first study to provide practitioners with optimization approaches for the design and pricing of vertically differentiated bundles. However, this research has certain limitations that are worth noting. For instance, consumers may engage in dynamic substitution if their first-choice bundle is out of stock. Therefore, a promising direction for future research is to solve the problem of optimal composition and prices of multiple bundles under stockout-based substitution.

Investigating the Mechanism of Phasing-out Subsidies of Energy-saving on Green Durable Product

ZHANG Wenjie, LI Zixuan, CHEN Weiwei, LU Yuyan

2026, 35(1):  32-39.  DOI: 10.12005/orms.2026.0005

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With the intensification of global energy tension, China advocates the concept of green development and provides subsidies for energy-saving products. However, the implementation of subsidy policies has also caused the following two problems. Firstly, government subsidies lead to market distortion, resulting in resource waste and low efficiency. Secondly, continuous subsidies impose a burden on government finances and even trigger financial crises. In order to effectively address these issues, the government has begun to implement subsidy reduction policies. However, how to effectively withdraw government subsidies in the field of green energy conservation, and how to design the terms for government subsidy withdrawal? How should enterprises respond to subsidy reduction policies? All these issues are worthy of in-depth research.
In fact, the government mainly considers the following two environmental performance goals when designing subsidy reduction policies. Based on the above situation, this article mainly focuses on the following issues. Firstly, how should the optimal subsidy reduction coefficient of the government be set under two environmental performance objectives? What is the difference between the two? Secondly, how can enterprises make optimal decisions under the government subsidy reduction mechanism? Thirdly, how does the subsidy reduction mechanism affect enterprises and consumers? The main marginal contributions of this study are as follows. On the one hand, considering the government decision-making under the subsidy reduction mechanism, the optimal energy-saving subsidy reduction clause is designed. On the other hand, the impact of subsidy reduction mechanisms is explored on the energy-saving index of green and durable products for enterprises under different environmental performance goals.
This research studies the mechanism of government subsidy reduction on green and durable products by constructing a three-stage game model, including the government, enterprises and consumers. On this basis, the focus is on designing the optimal terms for the energy-saving subsidy rebate mechanism for green and durable products under the two environmental performance objectives and analyzing the impact of the rebate mechanism on the decision-making of enterprises and consumers. Specifically, in the first stage, the government designs subsidy reduction clauses and decides on the optimal subsidy reduction coefficient. In the second stage, enterprises decide whether to produce ordinary products or green products based on the subsidy reduction policy and determine the energy-saving index and price of the products. In the third stage, consumers make purchasing decisions based on product type and price.
The research findings include: Firstly, the subsidy reduction coefficient is negatively correlated with the subsidy budget, and an increase in subsidy budget will promote enterprises to improve the energy-saving index of green products. Secondly, when the subsidy budget is low, there is no difference in the slope reduction clause between the two environmental performance objectives. When the subsidy budget is high, there will be differences in the optimal slope reduction clauses under the two environmental performance objectives, which are mainly related to the government budget level. Thirdly, under the subsidy rebate mechanism, enterprises will choose to produce different types of products based on the subsidy phasing-out coefficient. Only when the coefficient is low will enterprises choose to produce green products, and at this time, the optimal energy-saving index of the product is the minimum standard level stipulated by the government subsidy policy. In addition, under the objective of maximizing the overall energy-saving index, the optimal subsidy reduction clause will encourage enterprises to increase the energy-saving index of green products.

Research on Impact of Supply Chain Finance on Financing Efficiency of SMEs: Based on a Moderated Mediating Model

LI Xiangmei, YANG Huijin, QIU Jinlong, WANG Jing

2026, 35(1):  40-46.  DOI: 10.12005/orms.2026.0006

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As the capillaries of the national economy, Small and Medium-sized Enterprises(SMEs) play a key role in employment, innovation, and value creation, and are the source of vitality for high-quality economic development. However, SMEs generally face the obvious challenges, including difficult and expensive financing, insufficient credit-pricing mechanism, and low financing efficiency. Notably, financing efficiency directly restricts the sustainable development of enterprises. The existing studies mainly focus on the impact of corporate governance, information communication, macroeconomic environment, and policies on financing efficiency, but ignore the relationship between supply chain finance and financing efficiency of SMEs. Therefore, this paper deconstructs the mechanism and boundary conditions by which supply chain finance influences financing efficiency of SMEs. The findings not only provide new incremental evidence for this research field, but also offer theoretical support for enhancing the quality and efficiency of supply chain finance to serve the real economy and achieving the goal of SMEs’ high-quality development.
Based on the sample of SMEs listed on ChiNext from 2012 to 2023, this paper analyzes the impact of supply chain finance on the financing efficiency of SMEs. Based on the empirical analysis, this paper finds that supply chain finance can significantly improve the financing efficiency of SMEs. Mechanism tests show that the structure effect of supply chain finance is conducive to accurately matching the capital demand cycle of enterprises and improving the financing efficiency of SMEs by adjusting the capital term structure; the resource effect of supply chain finance is conducive to optimizing the resource allocation efficiency mechanism of enterprises and improving the financing efficiency of SMEs by alleviating financing constraints. The internal information environment strengthens the structure effect and resource effect, while the external financial environment only highlights the structure effect. Heterogeneity analysis shows that the impact of supply chain finance on the financing efficiency of SMEs is more significant in non-state-owned enterprises, as well as enterprises situated in the eastern and central regions and those in growth and maturity stage of the corporate life cycle. The economic consequence test shows that SMEs’ participation in supply chain finance can improve their viability by improving financing efficiency.
The paper’s marginal contributions are mainly embodied in three aspects. First, existing studies on financing efficiency have predominantly focused on macroeconomic policies and internal corporate governance. Based on network theory, this paper integrates supply chain finance into the analytical framework of financing efficiency, thereby offering incremental empirical evidence for researchs on the economic consequences of supply chain finance. Second, relying on the moderated mediating model, this paper explores the moderating effect of the internal and external environment on the impact of supply chain finance on financing efficiency by structure effect and resource effect, and clarifies the influence mechanism. Third, this paper investigates the heterogeneous characteristics and market response of the financing effect of supply chain finance, expands the research scope and practical application scenarios of supply chain finance, and provides decision-making support and policy enlightenment for advancing the high-quality development of SMEs and optimizing the financial service system.
This paper proposes management suggestions from the following aspects. First, SMEs should constantly optimize the digital information system, actively participate in supply chain financial activities, adjust the financing term structure, relieve financing constraints, and enhance core competitiveness. Second, the government should cooperate with SMEs to improve the policy support mechanism of enterprise digital transformation and supply chain finance development. The cooperation between government and enterprises should promote the “de-core” supply chain finance digital ecosystem transformation to balance the financing resources of SMEs.

Analysis of the Recycling Model of Renewable Resources with the Participation of Informal Organizations

LI Zhendong, SHI Lefeng, HE Weijun

2026, 35(1):  47-53.  DOI: 10.12005/orms.2026.0007

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In view of the reality that a large amount of domestic renewable resources flow into informal channels, this paper designs a model of cooperation between formal and informal organizations in the recycling of renewable resources with the goal of increasing the quantity of recycling and processing of renewable resources through formal channels, so as to facilitate the transformation of informal organizations from traditional recycling and processing organizations to full-time recycling organizations, thus giving full play to the advantages of flexibility of informal organizations and achieving the goal of “building on strengths and avoiding weaknesses”. The model is designed to facilitate the transformation of informal organizations from traditional “recycling processors” to “full-time recyclers”, thus giving full play to the flexibility of informal organizations and achieving the purpose of “making the best use of their strengths and avoiding their weaknesses”.
This study bridges the gap between formal and informal organizations in the existing research on recycling, and overcomes the shortcomings of a small amount of research focused on the negative benefits brought by the private processing of informal organizations and a lack of analysis of the causes of the advantages of recycling and the inefficiencies of the current governance strategy, so it provides ideas for the rationalization of the operation of informal organizations and expands the scope of the research on informal organizations. It also gives ideas for rationalizing the operation of informal organizations, expands the strategic options for government departments to regulate the recycling market, and reduces the negative effects of social unemployment and intensification of conflicts brought about by the over-suppression of informal organizations by relevant law enforcement departments.
In order to explore the evolution mechanism of the cooperation mode, the article constructs an evolutionary game model with government departments, formal organizations and informal organizations as the main players, and analyzes the influence of different influencing factors on the strategy choices of the three parties in the game; combined with the conclusion of the analysis, the behavioral strategies of the main players in the game are summarized, and the final numerical simulation verifies the feasibility of the proposed strategies.
The study finds that: government departments should adopt the strategy of “increasing penalties and decreasing subsidies” to guide the cooperation, and focus on the two-way strategy of resonance, and the same direction; the formal organization should follow the principle of “the main default, auxiliary acquisition” to regulate the purchase price of renewable resources and the amount of default, in order to consolidate the cooperation with the informal organization; formal organizations should follow the principle of “main default, secondary purchase” to regulate the purchase price of recycling resources and the amount of liquidated damages, so as to consolidate the cooperative relationship with informal organizations; informal organizations will be affected by the triple impact of government penalties, liquidated damages constraints and transfer of proceeds to participate in the recycling cooperation with the formal organizations; the media is an important auxiliary force to promote the government’s active participation in the early stage and smooth withdrawal in the later stage.

Cooperation Strategies between Internet Celebrities and Brands from the Perspective of Differential Games

LI Rui, CHENG Yukun, MENG Tingting

2026, 35(1):  54-60.  DOI: 10.12005/orms.2026.0008

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In the context of the digital economy, the rapid development of the live-streaming industry has significantly promoted social and economic progress. By 2023, the number of short video users in China had reached 1.012 billion, and the number of live-streaming users had stood at 751 million, making the live-streaming industry the leader in China’s social media sector. This surge in internet celebrity-driven live commerce has posed a considerable challenge to traditional direct-to-consumer e-commerce. Consequently, brand manufacturers face a crucial dilemma: how to leverage internet celebrity live-streaming channels to maximize profits, considering the impact of internet celebrities and the chosen mode of cooperation?
To explore the optimal cooperation model between internet celebrities and brand manufacturers on live-streaming platforms, while accounting for the continuous nature of live-stream traffic and time, this paper constructs a differential game system involving one internet celebrity and brand manufacturers selling similar products. By employing the Hamilton-Jacobi-Bellman equation, we analyze the optimal decisions regarding effort levels and corresponding payoffs for both internet celebrities and brand manufacturers under three cooperation models: the decentralized decision model, the centralized decision model and the fairness concern model. Through theoretical analysis of the effort levels and overall system revenue under these three cooperation models, coupled with the numerical experiment using real data from the live e-commerce analytics platform “Douchacha,” we derive the following conclusions.
(1)In the centralized decision model, both the effort levels of the internet celebrity and the brand manufacturer, as well as the level of live-streaming traffic, are maximized. This model facilitates the highest degree of cooperation and synergy between the parties, thereby significantly enhancing market promotion effectiveness and overall revenue.
(2)In the decentralized decision model, each party makes independent decisions without global cooperation and coordination, which limits the efforts of both the internet celebrities and the brand manufacturers. Consequently, the system’s overall performance is the lowest in this model due to the lack of a cohesive strategy and mutual alignment.
(3)In the fairness concern model, the system achieves the highest overall profit. By appropriately reducing the fairness concern of the internet celebrity towards each brand manufacturer or increasing the commission paid by the brand manufacturers to the internet celebrity, both the internet celebrity’s and the brand manufacturers’ profits can be effectively increased. Such coordination can ensure the maximization of the interests of all parties involved, thereby achieving a true win-win situation.
Through a comparative analysis of theoretical and numerical experiments, it is evident that the centralized decision model and the fairness concern model facilitate deeper collaboration between internet celebrities and brand manufacturers more effectively than the decentralized decision model. This approach not only yields higher returns for both parties but also supports the healthy and efficient development of the internet celebrity economy, fostering long-term growth in the industry.

Rubinstein Bargaining Game with Prospect Theory Preference

FENG Zhongwei, LI Fangning, WU Yuping

2026, 35(1):  61-67.  DOI: 10.12005/orms.2026.0009

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Bargaining is the process in which players try to reach an agreement through alternating offers. Bargaining process usually takes a lot of time. The main problem faced by players in bargaining is that players reach an agreement on how to cooperate before truly cooperating and achieving results. On the one hand, each player hopes to reach a consensus agreement. On the other hand, each player hopes to reach an agreement that is as beneficial as possible to itself. Therefore, there are conflicts among players in the bargaining process-each player tries to reach an agreement that is as beneficial as possible to itself. As a result, after paying a high price, both players are likely to reach an agreement or fail to do so. The cost (frictions) incurred by players in the bargaining process comes from two facts: bargaining is time-consuming, while time is valuable to players. Therefore, reaching a consensus agreement between both players will pay a price (i.e., time cost).
In the Rubinstein bargaining game, the time cost of a player is reflected by the discount rate, whose impacts on subgame perfect equilibrium are investigated. It is worth noting that expected utility theory dominates the analysis of bargaining theory, despite much evidence that it fails to characterize or predict adequately human behavior. Experimental studies on economics and psychology have demonstrated that players tend to exhibit irrational behavior. It means that expected utility theory cannot accurately describe such behavior. Therefore, KAHNEMAN and TVERSKY (1992) proposed prospect theory, which is an alternative to expected utility theory. Prospect theory can explain the phenomenon that players cannot follow the principle of maximizing expected utility. Prospect theory is a modification of expected utility theory that deviate in the following three aspects: (1)Different from expected utility theory that evaluates the final wealth, prospect theory evaluates the outcomes with respect to a reference level. Deriving gains and losses are regarded as prospects. (2)The marginal utility in benefits is smaller than in losses. That is, losses loom larger than gains. (3)Probability weighting: small probabilities are overestimated, while other probabilities are underestimated. Prospect theory and its variants are currently the most commonly used behavioral decision-making models. Therefore, our work incorporates prospect theory into the classic Rubinstein bargaining game, and explores the impact of loss aversion and probability weighting in prospect theory on the subgame perfect equilibrium.
It is worth noting that some works have explored the application of prospect theory in game theory. But they mainly focus on the impact of prospect theory on static matrix games and dynamic matrix games. A few scholars have explored the impact of prospect theory on bargaining games, and they mainly focus on the impact of loss aversion behavior of players on the alternating-offer bargaining game. However, those works do not consider the weighting of risk probability by players when there is a risk of bargaining breakdown. Different from the extant literatures, we introduce prospect theory into Rubinstein bargaining games, not only analyzing the impact of loss aversion behavior on the subgame perfect equilibrium, but also exploring the influence of weighted risk probability of players.
This paper reconsiders the Rubinstein bargaining game, where players have prospect theory preferences, and their proposals depend on bargaining history. We construct a PT-subgame perfect equilibrium and prove the existence and uniqueness of the PT-subgame perfect equilibrium. The findings are shown as follows: (1)When the reference points of two players are high, the equilibrium share of players will not be related to loss aversion behavior, but only will depend on the probability weighted behavior of players; when the reference points of two players are low, the equilibrium share of players will depend on both their loss aversion behavior and probability weighted behavior. (2)If the probability of bargaining continuing is high, probability weighting is advantageous to the first-player with loss aversion behavior; otherwise, whether probability weighting is advantageous to the first-player with loss aversion behavior depends on the weight coefficient. (3)Only when the degree of loss aversion for the first-player is higher than that of the competitor and the probability of bargaining continuing is sufficiently high, prospect theory preference may have adverse effects on the first-player; otherwise, prospect theory preference is advantageous to the first-player.

Robust Optimization for Lot-sizing Problems with Remanufacturing under Yield Uncertainty

WU Peng, YANG Liqing

2026, 35(1):  68-74.  DOI: 10.12005/orms.2026.0010

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Yield uncertainty is caused by production defects in the manufacturing process. Due to factors such as the environment, machine failure and worker proficiency, the actual output of the production system often deviates from the planned output. In order to provide products that meet customer quantity and quality requirements and minimize operating costs, manufacturing companies need to decide the production batch size for each cycle. Although enterprises strive to achieve zero production defects, production defects are unavoidable in the manufacturing process, which requires enterprises to formulate production plans under the condition of accepting production defects. Additionally, China’s “14th Five-Year Plan for Green Development in Industry” has put forward a series of goals, including reducing carbon dioxide emissions per unit of industrial added value by 18% by 2025 and achieving remarkable results in the green and low-carbon transformation of industrial production methods by 2025. Attaining these goals will contribute to the green and low-carbon transformation of China’s industrial production, significantly improving energy and resource efficiency and comprehensively enhancing the level of green manufacturing. Moreover, remanufacturing as a kind of low carbon production mode, can help enterprises to increase profits and achieve energy conservation and emission reduction. This paper studies the production planning problem of a non-static multi-cycle single project under a hybrid production system that considers remanufacturing, aiming to achieve the lowest total operating cost within the planning cycle under the conditions of time-varying production costs. Therefore, in order to ensure the stability and green sustainable development of the production system, it is necessary to study the robust optimization for lot-sizing problems with remanufacturing under yield uncertainty. The research on the issue of hybrid production planning considering yield uncertainty with remanufacturing serves a dual purpose. Firstly, it offers theoretical guidance for manufacturing enterprises to judiciously organize production under yield uncertainty, thereby enhancing the stability of the production system. Secondly, through remanufacturing, it can enhance the green manufacturing level of the production system and reduce resource consumption.
First, this paper develops a kind of the robust optimization model under yield uncertainty to minimize the total operating cost of production system and satisfy the constraints of inventory cost and shortage cost under the most pessimistic yield condition. To efficiently solve this, the nonlinear robust optimization model is then transformed into an equivalent mixed-integer linear programming model according to the problem characteristics. Finally, the effectiveness of the model is verified by a real auto parts production case and a large number of randomly generated instances.
The experimental results show that: (1)To assess the advantages of robust strategies in dealing with variations in actual yield conditions, Monte Carlo simulations are conducted for each example. Each scenario is simulated 10000 times to obtain the results for expected cost and worst-case cost. Compared with the traditional model, the robust model can provide a robust production strategy for decision makers under uncertain scenarios. The average pessimistic cost decreases by 11.77%, and the gap between target cost and expected cost decreases from 7.63% to -9.88%. (2)According to the experimental requirements, we classify the quantity of returned products, startup costs and returns disposal costs to explore the preference for robust production planning strategies under different circumstances. Compared with other parameters, setup cost is highly correlated with solving efficiency, and the correlation coefficient between them is 0.999. Expanding the scale of the experiment further corroborate the findings of the small-scale experiment. (3)We analyze the cost structure of robust production planning strategies under different stockout cost conditions. Simultaneously, we study the production level and inventory level of robust strategies to further understand their performance in response to yield uncertainty. Decision makers can refer to the robust strategy of reducing production frequency and increasing inventory to cope with yield uncertainty. The numerical experiments and case studies prove that the robust optimization model proposed in this paper can provide decision makers with production planning strategies under output uncertainty. In hybrid production systems, robust strategies help decision-makers develop effective production plans under the condition of accepting production defects. On the other hand, through the research on remanufacturing production methods, the green manufacturing level of the production system is fully improved, resource utilization efficiency is improved, and greater social benefits are achieved.
Future research directions can be developed from the following two aspects: (1)The description of the hybrid production system in this article is based on a single product. In future research, the hybrid production system can be further considered in terms of different output rates of multiple products, and the robust optimization problem of multi-product production planning considering remanufacturing under output uncertainty can be studied. (2)Uncertain conditions can be extended to include demand uncertainty or return uncertainty, so that the research on this issue can be closer to reality and include a variety of scenarios.

Single-machine Multitasking Scheduling Based on Efficiency Improvement and Resource allocation

LI Mengya, MA Ran, ZHANG Yuzhong

2026, 35(1):  75-82.  DOI: 10.12005/orms.2026.0011

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Multi-task scheduling is a critical research area within operations research and management, aiming to optimize task completion times and resource consumption by effectively allocating production resources and managing task relationships. Originally proposed in the field of computer systems, multitasking primarily refers to the parallel execution of multiple processes and tasks within a specific time period. In real life, multitasking is a common phenomenon, such as doctors attending to other patients while waiting for test reports or restaurant servers tending to other guests while waiting for food preparation in the kitchen. The main motivations for studying multi-task scheduling can be summarized as follows. Firstly, diverse work styles can significantly improve work efficiency, reduce the fatigue and boredom associated with performing the same tasks for extended periods, and enhance practitioners’ sense of achievement and satisfaction. Additionally, project leaders can gain early insights by partially handling waiting tasks, thereby reducing the uncertainty of such tasks and effectively alleviating anxiety. In today’s fast-paced work environment, multitasking has become an inevitable trend. Many enterprises consider multitasking ability a crucial criterion in recruitment, underscoring the importance and urgency of studying multi-task scheduling. Therefore, in-depth exploration and optimization of multi-task scheduling models not only improve productivity but also help adapt to the complex demands of modern working environments.
In the multi-task scheduling model presented in this paper, two types of tasks are considered: primary tasks and waiting tasks. A primary task is a task selected at a particular point in time, whereas waiting tasks are other tasks that remain available but are not completed while the primary task is in progress. Since primary tasks are not allowed to be replaced, waiting tasks are not completely finished until they are transformed into primary tasks. They can only be partially processed, and these partially processed portions do not need to be reprocessed afterward. The processing of the primary task can be interrupted by the waiting task, thus involving both interruptions and switches in the multi-task scheduling model. We denote the switching time function by f(·) and the interrupting time function by g_i(·). Therefore, the processing time of the primary task consists of three components: the remaining processing time of the primary task, the interruption time caused by the partial processing of waiting tasks, and the switching time of the unprocessed task when the primary task switches with a waiting task.
The core of the multi-task scheduling problem studied in this paper is to examine the variation in job processing time within a single-computer multi-task scheduling environment. We comprehensively consider both the positive effect of the operator’s perception or cognitive level induced by multitasking, i.e., the efficiency improvement effect, and the fatigue effect caused by performing the same job for an extended period, i.e., the degradation effect. Based on these considerations, we also explore the impact of resource allocation on overall processing time. In this paper, two multi-task scheduling models are constructed. The first model considers the processing time affected by linear resource allocation, incorporating both the linear efficiency improvement effect and the degradation effect based on position change. The actual machining time of the workpiece is expressed as:公式; the second model, on the other hand, accounts for the machining time affected by the convexity of resource allocation, in addition to the linear efficiency improvement effect and the degradation effect based on position change. The actual machining time of the workpiece is represented as: 公式. The objective of these models is to minimize the total completion time and resource cost. We integrate the objective of each model into three parts: the part related to processing time, the part related to resources and the constant part. The resource-related coefficient part is first analyzed to find the optimal resource allocation rule, and then the objective function is transformed into an assignment problem to be solved. For each model, we design efficient polynomial time algorithms and provide structural properties of the optimal scheduling. We prove that such problems are polynomial-time solvable for each model and verify the feasibility and effectiveness of the algorithms through arithmetic experiments. We set the ranges of values for parameters such as p_j, a_j, b_j, v_j, etc., by researching in the context of a real industry and referring to numerous experiments in the relevant literature, and then test them using software to generate random data. We demonstrate the proposed algorithm specifically with an example containing six jobs to find the optimal solution and further verify the feasibility and effectiveness of the algorithm. The experimental results show that the total cost incurred by allocating convex resources is less than the total cost incurred by allocating linear resources.
Future research can be extended in the following aspects: Firstly, the multi-task scheduling model can be applied to more practical scenarios, such as multi-computer environments and dynamic task allocation. Secondly, the algorithm can be further optimized to enhance its computational efficiency in large-scale task scheduling problems.

A Conjugate Gradient Method with Strong Convergence and itsApplications in Image Restoration and Traffic Assignment

JIAN Dan, LUO Qiang, JIANG Xianzhen

2026, 35(1):  83-90.  DOI: 10.12005/orms.2026.0012

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Unconstrained optimization serves as the foundational basis for investigating constrained optimization problems. Moreover, numerous practical problems in fields including economics, management, engineering control, and artificial intelligence can be directly or indirectly modeled as unconstrained optimization models. Commonly used methods for solving unconstrained optimization problems include the Newton method, quasi-Newton methods, and the conjugate gradient method. Among these approaches, the conjugate gradient method eliminates the need to compute the Hessian matrix of the objective function or the inverse of its approximate matrix in each iteration. This characteristic endows the conjugate gradient method with advantages such as simple iteration steps and low memory consumption, making it one of the most competitive algorithms for solving large-scale unconstrained optimization problems.
The conjugate gradient methods include the classical conjugate gradient methods Hestenes-Stiefel (HS) method, Fletcher-Reeves (FR) method, Polak-Ribière-Polyak (PRP) method, Conjugate-Descent (CD) method, Liu-Storey (LS) method and Dai-Yuan (DY) method and their improved variants. In this paper, motivated by the single-parameter conjugate parameter proposed by DAI and YUAN (2003), an efficient conjugate gradient method is proposed by introducing a novel conjugate parameter strategy and a resrart procedure. Here, the conjugate parameter is derived from a two-parameter conjugate gradient method family generated by FR, CD, and DY. To ensure the algorithm achieves strong convergence, the denominator of the conjugate parameter is further truncated. Moreover, to enhance the computational efficiency of the algorithm, a resrart procedure related to the conjugate parameter is incorporated into the design of the search direction to accelerate the algorithm’s descent. Under conventional assumptions and the standard Wolfe line search, the strong convergence of the algorithm is established. We aim to develop an efficient conjugate gradient method for solving large-scale unconstrained optimization problems, thereby providing an effective algorithmic model for practical applications such as image restoration, machine learning, and traffic assignment.
Two notable theoretical advantages of the proposed algorithm are as follows: its generated search direction always satisfies the sufficient descent condition, independent of any specific line search strategy; and under conventional assumptions such as the Lipschitz continuity of the gradient and the boundedness below the level sets, the algorithm is proven to possess strong convergence when combined with a standard Wolfe line search for determining the step size.
To evaluate the practical performance of the proposed algorithm, this paper conducts three sets of numerical experiments. Firstly, under the same computational environment, a numerical comparison of six algorithms is carried out on 102 unconstrained optimization test problems, evaluated from three dimensions: computational time, number of iterations, and solution accuracy. The numerical results show that the numerical performance of the proposed algorithm is generally superior to other methods on the test problems. Secondly, the presented algorithm is applied to deal with the image restoration problem, which involves deblurring and denoising blurred and noisy images via a regularized least-squares formulation, which shows that the proposed method is effective on the tested images. Finally, the proposed algorithm to handle the traffic assignment problem in transportation network modeling involves solving a large-scale network equilibrium problem. Our algorithm contributes to achieving a more efficient and realistic flow distribution, and significantly reduces the runtime compared to traditional solvers.
The numerical results indicate that the newly designed algorithm is not only theoretically sound but also highly effective and versatile across different application domains. It provides researchers and practitioners in science and engineering with an effective tool for handling large-scale optimization problems.

Algorithm for Preemptive Multi-mode Project Scheduling Problem Based on Mode-improvement

WANG Min, LIU Guoshan

2026, 35(1):  91-98.  DOI: 10.12005/orms.2026.0013

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With the scale, complexity and randomization brought by various uncertainties in modern projects, as an important means of optimizing the allocation of project resources, project scheduling becomes increasingly important and challenging. In many actual projects, the execution of activity often presents multi-mode characteristics(different combinations of activity duration and resources), thus forming the Multi-mode Resource Constrained Project Scheduling Problem(MRCPSP). MRCPSP is a generalized version of the RCPSP, where each activity can be performed in one out of a set of modes. The objective of MRCPSP is to find a mode and a start time for each activity so that the makespan is minimized and the schedule is feasible with respect to the precedence and renewable and nonrenewable resource constraints.
However, during the execution of the project, activity is often interrupted due to uncertainties, which changes the state of resources, execution duration and so on, how to schedule the project after activity interruption becomes a new problem. So, in this paper, the multi-mode resource-constrained project scheduling problem allowing for activity preemption is studied, which is the Preemptive Multi-mode Resource Constrained Project Scheduling Problem(P-MRCPSP). The problem brings more flexibility to the project scheduling while increasing the difficulty of scheduling. In order to optimize the project duration and fully consider the relationship between resources and active duration, a three-stage scheduling algorithm for mode-improvement based on renewable resources is designed, namely, mode preprocessing stage, activity interruption transformation stage and mode-improvement scheduling stage, so that the execution mode can be dynamically adjusted according to the optimization objective of the minimum duration during the execution of the project. By calling the Project Scheduling Problem Library(PSPLIB)for experimental design, the algorithm scheduling results under different algorithms and parameters are compared and analyzed.
The computational results show that the proposed algorithm is relatively superior and provides scientific decision-making guidance for the project management practice, especially for a large-scale project. By comparing the effects of different resource parameters on scheduling results(including renewable and nonrenewable resources), the results show that the changes in renewable resource parameters RSR and RFR have a significant impact on scheduling results. And when the resource supply is sufficient or the resource demand is small, scheduling results outperform the existing algorithms in literature.
However, with the expansion of the project scale, the project uncertainty also increases. How to take various uncertainties into account in P-MRCPSP, such as the uncertainty of the activity duration and resources, are worthy of further study. And, in this study, we just assume that execution after activity interruption does not consume additional costs and resources, and switching execution modes is not allowed. However, considering the complexity of the actual project, how to consider the cost consumption, resource consumption and mode-switch of re-execution after activity interruption in stochastic preemptive project scheduling is worthy of further study. At the same time, it is worth further exploring how to effectively embed the dynamic heuristic algorithm designed in this paper into more meta-heuristic algorithms for more complex problems.

Marginality and New Characterization of Position Value for Hypergraph Games

SHAN Erfang, YU Bingxin, CUI Zeguang

2026, 35(1):  99-104.  DOI: 10.12005/orms.2026.0014

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Cooperative game theory examines how individuals cooperate with each other to achieve a common goal. In cooperative games, players cooperate with each other by integrating their efforts, resources, and skills to maximize the collective good. The transferable utility cooperative game, the TU-game, refers to a situation where any collection of players can be rewarded for cooperating to form a viable coalition, and it focuses on how the benefits (costs) of a grand coalition are shared (apportioned) among players. It is usually assumed that all players can communicate with each other, and the Shapley value is a well-known allocation rule based on this assumption. However, in the real world, cooperation between players is limited by subjective and objective factors such as differences in players’ abilities, cultural diversity, time and resources constraints. To describe this phenomenon, MYERSON (1977) introduced a class of TU-games with cooperation structures given by communication graphs on the player set, in which it is assumed that only connected players can fully cooperate, and the Shapley value of the so-called graph-restricted games induced by the graph cooperation structure is defined as a new allocation rule, i.e., the Myerson value. Subsequently, MEESSEN (1988) proposes another important allocation rule for graph-restricted games, namely the position value. This allocation rule is based on the graph structure, emphasizing the role of links in the graph. It treats the links connecting players as players themselves and allocates the Shapley value to these links, and then distributing the Shapley value obtained by each link equally to the two players connecting that link.
The Shapley value focuses on the player’s marginal contribution to each coalition. A player’s marginal contribution is the difference in value before and after that player joins each coalition. The Shapley value assigned to each player is exactly the average of all of the player’s marginal contributions. In 1985, YOUNG first introduced the concept of marginality, which states that the same player with the same marginal contribution should receive equal payments in two different games. Since then, marginality and its derived forms have gradually been applied to the characterizations of values in TU-games.
In graph-restricted games, academics introduce PL-marginality based on the axiom of marginality, which is a variant of marginality that takes into account the influence of players and their connected links. Specifically, it considers the possibility that a player joins a coalition and then communicates with that coalition. In this paper, we consider the position value for hypergraph games from the same perspective and generalize PL-marginality from graph-restricted games to hypergraph games by introducing PH-marginality. In reality, the hypergraph structure is more general and thus can model more complex communication relationships between players. Secondly, by weakening the property of partial balanced conference contributions in the hypergraph games, it applies only to necessary players. By means of efficiency, partial balanced conference contributions for necessary players, and PH-marginality, this paper provides a new characterization of the position value for hypergraph games.
Finally, applications of the position value for hypergraph games are considered. In this paper, we describe the problem of optimizing the allocation of network resources among devices in a local area network (LAN) as a hypergraph game model, and tailor network optimization solutions for different application scenarios based on the device’s position value.
In the future, a natural question is whether the inscription method of marginality can be generalized to the characterization of other allocation rules in hypergraph games.

The Monopolize Surplus Division Value and its Axiomatization

YANG Qinle, BAI Xueting

2026, 35(1):  105-111.  DOI: 10.12005/orms.2026.0015

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After obtaining the basic yield v(i), the fair and reasonable distribution of the surplus value generated by cooperation has become the focus for all players. DRIESSEN and FUNAKI (1991) proposed the ED value based on the idea of egalitarianism, which evenly distributed the surplus value of the grand coalition to all players; considering the differences in individual abilities among players, ORTMANN (2000) allocated the surplus value of the grand coalition using the ratio of individual value to the total individual value. Based on this idea, the PD value proposed belongs to a typical utilitarian solution. Afterwards, many scholars conducted extensive research on the fairness and rationality of these two solutions. Fortunately, PD value compensates for the shortcomings of ED value in completely ignoring individual differences among players in the allocation scheme of surplus value of the grand coalition, but overly relying on the individual abilities of players and neglecting their collaborative abilities. The problem of insufficient use of countermeasure information in profit distribution scheme is exposed.
TIJS (1981) adopted the ideal income vector b^v for income distribution, but there was a situation where the grand coalition’s value was not enough distributed (i.e.,v(N)b^v(N)). By defining concession vector to determine the concession values that each participant should undertake when successfully obtaining ideal values b^v_i, TIJS innovatively proposes the τ-value of the quasi-equilibrium game based on the idea of concession. We consider the selfish nature exhibited by cooperative participants in real life, especially in economic issues, when faced with the distribution of benefits. Inspired by the ideas of TIJS, this paper proposes an egoistic approach to the distribution of surplus value in the grand coalition after giving each participant individual value. This article defines the egoistic vector of cooperative games based on egoistic thinking, and proposes the Monopolize Surplus Division value (MSD value) of cooperative games based on the ratio of the egoistic demand of each player to the total egoistic demands of all players. This effectively overcomes the disadvantage of insufficient use of game information in PD value distribution of benefits, and realizes the “distribution according to work” of surplus value in grand coalition. By studying the properties of MSD value, this paper gives the first axiomatic description of MSD value by using the proportionality of egoistic income, efficiency and invariance.
CHOUDHURY et al. (2020) used algebraic theory to uniquely describe the solution of cooperative game. Inspired by the idea, this paper first presents a set of direct sum decomposition conclusions for weakly essential cooperative game spaces. Secondly, with the direct sum decomposition theory of Euclidean space, it has been proven that MSD values can also be uniquely characterized by inessential game property and individual covariance combined with the proportionality of egoistic income. Finally, by redefining the weight coefficient used to present the importance of each player in game and constructing an optimization model, the MSD value is proven to be the only optimal solution of the optimization model. Taking the issue of revenue distribution for tourism pass as an example, a comparative analysis is conducted between MSD values and other values, and the application significance of MSD value is discussed.

DEA Model of Management Goal Oriented Environmental Resource Allocation Method Based on Nash Bargaining Solution

WANG Ying

2026, 35(1):  112-118.  DOI: 10.12005/orms.2026.0016

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How to allocate environmental resources reasonably among various economic entities (Decision-Making Units, DMUs) to form an acceptable rights and responsibilities allocation scheme for environmental resources protection among all economic entities (DMUs) is a challenging issue in practical economic management. Data Envelopment Analysis (DEA) has the advantages of not needing to preset production function forms and error structures, and it is widely used in the evaluation of input-output efficiency and resource allocation. Therefore, this paper develops a goal-oriented DEA method for optimizing the allocation of environmental resources, in accordance with the principles of the Nash bargaining solution.
Firstly, this paper presents a weighted additive slack-based DEA model, which accounts for the public externalities based on the Directional Economic Environmental Distance Function (DEED), called the Adjusted Directional Economic Environmental Distance Function (ADEED). The DEED model only considers the private impact of undesirable output, whereas the ADEED model takes into account the fact that some undesirable outputs such as pollution emissions have public external effects on all economic entities (DMUs). Then, this paper constructs management Goal-Oriented ADEED (GOADEED) model by adding the objective constraint of total quantity controlling for the environmental resource into the ADEED model. Finally, by using the GOADEED model to calculate the Pareto optimal welfare under the constraint of management objectives, and by using the DEED model to calculate the disagreement points, a goal-oriented optimization allocation method for environmental resources conforming to the Nash bargaining solution is proposed.
In the empirical analysis, the environmental resources allocation method proposed in this paper is applied to address the issue of carbon reduction responsibility allocation among provinces in China, thereby demonstrating the effectiveness of the method. Each province is treated as a DMU, and each DMU has three inputs, namely, labor input, energy input and capital input. Additionally, each DMU has one desired output, which is Gross Domestic Product (GDP), and one undesirable output, which is carbon emission. The empirical data are collected from various public and authoritative institutions. Based on the collected data, the environmental resources allocation method proposed in this paper not only accurately allocates the carbon reduction tasks for each province, but also further calculates the amount of benefit compensation for each province relative to the allocation of carbon reduction responsibilities.
Overall, the environmental resource allocation method proposed in this paper can achieve equilibrium allocation of the environmental resource under the constraint of the total control goal for environmental resource set by managers, following the principle of the Nash bargaining solution. However, the DEED, ADEED, and GOADEED models require weighted information such as prices or costs of various input and output variables. In reality, this weighted information may not be available, especially for undesired outputs such as environmental pollution. Due to the absence of a trading market, it is particularly difficult to obtain information on prices or costs of undesired outputs such as environmental pollution. Therefore, it is necessary to adjust the ADEED model and GOADEED model into unweighted models, which is also a direction for further research.

Application Research

Will Knight Uncertainty Cause Stock Market Liquidity to Dry up? Evidence from Chinese A-share Listed Companies

WANG Chunfeng, LIU Zhuoran, CUI Xin, YAO Shouyu, FANG Zhenming

2026, 35(1):  119-124.  DOI: 10.12005/orms.2026.0017

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Uncertainty is an inherent attribute of capital markets. Knight distinguishes the concepts of risk from uncertainty, pointing out that risk is a situation in which the probability distribution of profits and losses is known, while the situation in which the probability distribution of profits and losses is unknown is the real uncertainty. Later, economists defines it as “the Knight uncertainty.” In recent years, the global economy has faced downward pressure, leading to increased instability and uncertainty in economic development. Numerous unknown micro (such as corporate bankruptcies and legal issues) and macro (such as the Saudi Aramco oil attack, the novel coronavirus outbreak and the Russia-Ukraine war) uncertain events have exacerbated economic uncertainty and have a negative impact on financial markets in various countries.
Liquidity, as a feature of market quality, is a sign of market efficiency. In a market with sufficient liquidity, investors can quickly trade stocks at low cost, asset prices can reflect market information in a timely manner, and resource allocation efficiency is high. From a micro point of view, liquidity is at the forefront of the capital market, has an incentive effect on technological innovation of enterprises, and helps to increase the long-term value of enterprises. In addition, liquidity has a positive effect on boosting corporate profits. From a macro perspective, once the market is illiquid or even dried up, asset prices will plummet in a short period of time, triggering a financial crisis.
Based on the data of Chinese A-share listed companies from February 2015 to December 2019, this study explores the impact of the Knight uncertainty on stock market liquidity. The results show that an increase in the Knight uncertainty significantly reduces stock market liquidity. The mechanism analysis shows that the Knight uncertainty has a negative impact on stock market liquidity by affecting investors’ trading behavior. On the one hand, with the rise in the Knight uncertainty, some investors tend to sell assets, resulting in the imbalance of market buying and selling pressure, thus reducing the liquidity of the stock market. On the other hand, with the rise in the Knight uncertainty, some investors stop trading or even withdraw from the market, resulting in the reduction in overall market participation and the decline of stock market liquidity. Heterogeneity analysis shows that the negative impact of the Knight uncertainty on stock market liquidity is more significant for companies with weak ability to resist risks (such as small market capitalization, short listing years and non-state-owned nature) and low governance level (such as less institutional shareholding and using non-Big four auditors), as well as in the market environment with low overall investor sentiment.
This paper enriches the research on the relationship between the Knight uncertainty of China’s capital market and the liquidity of the stock market, explores whether the conclusions drawn from the mature capital market are applicable to the emerging capital market, and provides some enlightenment for the smooth operation of China’s capital market. Secondly, the Knight uncertainty directly affects investor behavior, which currently focuses more on mathematical models. Following previous studies, this paper explores the internal impact of the Knight uncertainty on stock liquidity from the perspective of investor trading behavior through empirical methods on the basis of theoretical analysis. In order to explain investor behavior, this paper innovatively uses order book data to construct an index of “abnormal trading volume” to measure stock market participation in a quantitative way, and further explores its role in the relationship between the Knight uncertainty and stock market liquidity. This provides some significance for understanding the operation law of China’s stock market and improving market efficiency. Finally, the conclusions of this paper have practical significance for investors, enterprises and regulators.

Time-Varying Correlation and Volatility Spillover between Chinese Crude Oil Futures and Chinese and American Stock Markets: Research Based on TVP-VAR-DY Model

ZHAO Shuran, WANG Yuanxi, FAN Lishuang, LIU Yan

2026, 35(1):  125-132.  DOI: 10.12005/orms.2026.0018

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As one of the most important commodities, crude oil is very important in promoting the stable development of national economy. China officially launched The Shanghai International Energy Exchange (INE) as the country’s first international crude oil futures in 2018. Under the background of financial integration, the liquidity of capital and the efficiency of information transmission are constantly improving, and the correlation between China and the international financial market, especially the US financial market, is gradually increasing. The uncertainty of the US financial system has made the imported financial risks in China’s energy market increasingly great. In this context, the study on the time-varying linkage and volatility spillover effect of China’s crude oil futures market and Sino-US stock markets is helpful to establish and improve the risk supervision system in line with the characteristics of China’s crude oil futures market.
Through the sorting and research of relevant literature, it is found that the research objectives of the existing research are mostly focused on WTI and Brent crude oil futures, and the multivariate volatility models such as BEKK and DCC are mostly used in the research methods, and most of the volatility as a whole is taken as the research object. However, with the frequent occurrence of special events such as Sino-US trade frictions and public outbreaks, it is necessary to analyze the co-movement of China’s oil market and domestic and foreign stock markets under the impact of “black swan” events. Therefore, this paper selects Shanghai crude oil futures as the representative of China’s oil market to explore the characteristics of time-varying linkage and volatility spillover effect between China’s oil market and Chinese and American stock markets.
Firstly, the paper uses the five-minute high-frequency data of Shanghai crude oil futures, SP500 and Shanghai Composite Index to calculate the corresponding daily realized volatility, the paper adopts C_TZ test method to achieve the decomposition of volatility, and the volatility is decomposed into continuous volatility and jump volatility. Secondly, the TVP-VAR model is established for the continuous volatility and jump volatility of the three types of markets, and the time-varying linkage effect is analyzed under different time intervals and different time points. Finally, based on the forecast error variance decomposition (DY) method, the volatility spillover effect between continuous volatility and jump volatility is analyzed. In this paper, the Shanghai crude oil futures (INE), the Standard & Poor’s 500 index (SP500) and the Shanghai Composite Index (SH) are selected as the research objects to describe the Chinese oil market and the Chinese and American stock markets. The sample period is from March 26, 2018, to November 30, 2021, including a total of 853 trading days during the white-hot and staged easing period of China-US trade frictions, the period of frequent geopolitical conflicts and the outbreak of COVID-19. All data are obtained from the Wind database. (http://www.wind.com.cn/En).
The paper has obtained the following conclusions: first of all, Shanghai crude oil futures have the most jump days, indicating that it is more vulnerable to extreme fluctuations. Secondly, the impact of the extreme shock of Shanghai crude oil futures on SP500 and Shanghai Composite Index has the same trend in different lag periods, which indicates that the long-term linkage effect between China’s crude oil futures and Chinese and American stock markets is obvious in both conventional and extreme cases. Thirdly, whether in the normal state or in the occurrence of extreme events, the degree of linkage between China’s crude oil futures and the US stock market is greater than that of the Chinese stock market. That is, China’s crude oil futures are easy to impact the external market, but also vulnerable to the impact of the external market which to some extent proves that its pricing power in the international crude oil market has increased. Moreover, the volatility linkage effect of oil market and stock market will be time-varying. Finally, under normal conditions, the continuous spillover effect between the crude oil market and the US stock market is significantly stronger than that between the crude oil market and the Chinese stock market. However, under extreme shocks, jump volatility is more uncertain, and the spillover effect of jump volatility among markets is weak. Overall, there are time-varying linkage and volatility spillover effects between the Chinese crude oil futures market and the Chinese and American stock markets.

Optimization of Two-stage Liner Container Slot Allocation Considering Booking Cancellation in Spot Market

LI Yingqi, JIN Zhihong, XU Shida

2026, 35(1):  133-138.  DOI: 10.12005/orms.2026.0019

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Fluctuations in container liner shipping rates are the norm in the industry, with different lines on the same route charging different rates, and even the same line on the same route charging different rates at different booking stages. As a result, cargo owners are naturally always concerned about container liner shipping rates. At the same time, due to the dynamic price play between lines, this often leads to customers engaging in booking cancellation-rebooking behavior. How to determine the relationship between pricing and slot allocation of liner companies has also become a key decision problem for liner companies in competitive markets.
Although the construction of a slot allocation optimization model based on revenue management can effectively solve the static slot allocation problem, most current studies divide customers into long-term contract customers and spot customers, ignoring the market segmentation differences between spot customers in the liner shipping market, such as differences in booking cancellation rates. And, of course, the differences in booking cancellation rates between spot customers at different booking stages are not taken into account.
This paper attempts to fill the gaps in existing research from both of the above perspectives. Given the uncertainty of the spot customer market and the withdrawal behavior of customers, a further segmentation of customers in the spot market based on big data of customer booking and withdrawal information, as well as the consideration of the impact of different booking phases to improve the slot utilization rate and the revenue of liner shipping companies, can provide a decision basis for liner shipping companies to formulate reasonable slot allocation and pricing strategies.
To address the problem of liner space allocation in the spot market, where customers frequently withdraw their bookings, a two-step space allocation method based on the division of customer credibility is proposed. First, based on the big data analysis of customers’ historical bookings, a method for predicting customers’ withdrawal rate based on different booking periods is proposed. On this basis, a two-stage slot allocation optimization model based on customer credibility in the spot market is constructed with the objective of maximizing the liner’s revenue, and an equivalent implementation of opportunity constraints is carried out. The empirical analyses are conducted on the example of a Dalian liner’s short sea route to verify the effectiveness and practicality of the model. The results show that, compared with the existing slot allocation strategy, the two-stage slot allocation strategy considering customer credibility can significantly improve the slot utilization rate and the company’s revenue.
The two-stage slot allocation optimization model based on customer reputation proposed in this article provides a new decision-making tool for shipping companies in fierce market competition. This model can not only improve slot utilization and reduce cancellation risk, but also flexibly adjust pricing strategies according to market changes to achieve maximum revenue. With the development of network technology and the continuous improvement of online booking systems, the application of this model will bring greater competitive advantages to shipping companies and promote the healthy development of the container shipping market. Future research can conduct an in-depth analysis of customer competition behavior among shipping companies, in order to optimize the model through more accurate pricing strategies and enhance its practicality and efficiency in practical applications.

Intelligent Scheduling of Wind Turbine Extrusion Plate Production Considering Fuzzy Lead Times

YANG Xin, YANG Xiaoying

2026, 35(1):  139-144.  DOI: 10.12005/orms.2026.0020

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Wind power is a cost-effective, clean and mature energy source, offering a sustainable alternative to fossil fuels. Wind turbine extrusion plates, critical structural components of turbine blades, are manufactured through a continuous, order-driven and flexible production process to meet diverse market needs. However, the Wind Turbine Extrusion Plate Production Scheduling Problem (PSP-WTEP) is highly complex and falls into the NP-hard category, as it must consider constraints such as mold replacements, sequential flush sets and operational limitations. PSP-WTEP can be divided into three sub-problems: assigning production areas for orders, allocating processing equipment within those areas and sequencing components on machines. These challenges require a multi-objective optimization model to balance equipment load, maximize customer satisfaction, and minimize mold changeover times, all while adhering to fuzzy delivery deadlines. Effectively solving PSP-WTEP is essential for improving production efficiency, reducing costs and promoting innovation in the wind power industry.
To tackle this issue, the study develops the Enhanced Multi-Objective CrayfishOptimization Algorithm (EMOCOA), an improvement over the Crayfish Optimization Algorithm (COA). EMOCOA incorporates advanced strategies such as non-dominated sorting, refractive inverse learning for population initialization, nonlinear convergence factors, sub-swing perturbations and dynamic step adjustments. The algorithm employs a two-layer coding system for components and regions, converting continuous variables into discrete codes using Ranked Order Value (ROV) encoding. It adopts a “backward-repair-optimize” decoding strategy to resolve fuzzy delivery constraints and improve solution feasibility. These enhancements allow EMOCOA to effectively balance global exploration and local exploitation, handle the coupling of PSP-WTEP sub-problems, and deliver diverse and high-quality solutions that meet production goals. The algorithm’s hybrid learning strategies ensure fast convergence and robust performance, even in complex scenarios.
Extensive experiments highlight the superiority of EMOCOA over the Multi-Objective Crayfish Optimization Algorithm (MOCOA) and Multi-Objective Whale Optimization Algorithm (MOWOA). EMOCOA consistently outperforms its counterparts, generating 10 Pareto solutions compared to 7 by MOCOA and 8 by MOWOA, with better results on key evaluation metrics such as IGD and HV. These metrics indicate that EMOCOA provides improved solution diversity and convergence, making it more practical for real-world application. Production managers can use methods such as hierarchical analysis and entropy weight to rank and select Pareto solutions for implementation. By solving various scenarios and demonstrating its adaptability, EMOCOA proves to be a powerful tool for optimizing production scheduling, reducing costs, and increasing efficiency. The algorithm supports intelligent upgrades in wind turbine extrusion plates manufacturing, facilitating the sustainable growth and technological advancement of the wind power industry.

Site Selection and Capacity Determination for Nucleic Acid Testing Facilities in the Presence of Large-scale Outbreaks

MA Zujun, WANG Qiuyue

2026, 35(1):  145-152.  DOI: 10.12005/orms.2026.0021

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Many epidemic outbreaks have occurred worldwide in recent years, which have not only seriously jeopardized people’s health and life safety, but also caused significant losses to the country’s economic and social development. Public health emergencies have become one of the most critical concerns of the public due to their suddenness, urgency, harmfulness and epidemic. The increase in large-scale epidemic outbreaks, for example, the COVID-19 epidemic, has significantly impacted society. The research on optimizing the siting of emergency facilities in the field of public health has gradually increased. However, much is on focused on the planning of the siting of medical institutions and the optimization of the emergency logistic network, and there is insufficient research on the siting of the testing institutions for large-scale epidemic outbreaks. Diagnostic testing is essential for controlling an epidemic, and nucleic acid testing, as a standard pathogen detection method, has been widely used in various outbreaks. In an outbreak, the scientific design of the site selection of nucleic acid testing facilities, the design of testing capacity and the distribution strategy of testing samples are crucial for curbing the spread of the virus. Therefore, this paper investigates the siting and capacity decision-making of nucleic acid testing facilities in large-scale outbreaks, intending to provide a reference for similar outbreaks that may occur in the future.
In this paper, we consider the location, capacity and allocation decisions for nucleic acid testing facilities in a region under the government’s provision of subsidized funding for nucleic acid testing capacity building in the event of an outbreak, including determining the capacity expansion plan for medical institutions with testing capacity and existing testing facilities, the location and capacity level of the additional testing facilities and the allocation of testing samples. It is assumed that (1)the location of nucleic acid sampling sites in the region and the number of samplers are known; (2)the location and initial testing capacity of healthcare facilities with nucleic acid testing capacity and existing nucleic acid testing facilities in the region are known; (3)the location of candidate additional nucleic acid testing facilities is known; (4)different mixing methods are used for different types of samplers; (5)samples collected at each sampling site can be allocated to multiple nucleic acid testing facilities for testing, and each nucleic acid testing facility can receive samples from multiple sampling sites for testing. The ultimate goal is to achieve the two objectives of minimizing government subsidy expenditure and minimizing time spent on nucleic acid testing.
A mixed integer programming model is developed to solve the problem. By introducing the cost preference weights of government subsidy expenditures and adopting the weighting method based on the membership function, the multi-objectives are transformed into a single objective for the solution. The solution is then performed using the Gurobi solver and the designed genetic algorithm. A capacity reduction step is added to the genetic algorithm to reduce the waste caused by excess capacity. Moreover, the fitness value calculation introduces a penalty function for violating the time constraint. We first verify the validity of the model and algorithm through numerical analysis. Then, we use the designed genetic algorithm to study the optimization problem of nucleic acid testing organization layout in 12 municipal districts of Chengdu with the background of the new coronary pneumonia epidemic. The information on nucleic acid testing sampling points and nucleic acid testing organizations in the region is obtained through the Health Commission of Chengdu. The layout of nucleic acid testing organizations in 12 municipal districts of Chengdu is finally given. The effects of different values of cost preference weights for government subsidy expenditures on the final cost are analyzed. With the gradual increase in cost preference weights, the government subsidy cost shows a decreasing trend, while the total testing time shows an increasing trend. Roughly, the results can correspond to the early, middle and late stages of a large-scale outbreak. In the future, decision-makers can choose different weighting schemes for various periods. In addition, the influence of time limits and government budgets on the results is also analyzed.
There are some shortcomings in this paper. Although we have identified issues such as the expansion of existing nucleic acid testing facilities, the location of additional nucleic acid testing facilities and the allocation of sampling points, we have only investigated the optimization of the layout of a single cycle in various parameter determination scenarios. In the case of an actual outbreak, data such as the number of people sampled at a sampling point is constantly changing. Therefore, future research can further explore the problem of optimizing the layout of multi-period dynamic nucleic acid testing facilities under the uncertainty of the sampling population to better adapt to the complex reality.

Deep Reinforcement Learning Based on Multi-source Information Fusion Solving Vehicle Path Planning Problem

SU Jiman, LU Yuming, LI Zhengxiu, HONG Lianhuan, JIE Lilin

2026, 35(1):  153-159.  DOI: 10.12005/orms.2026.0022

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Vehicle routing problem is a combinatorial optimization model widely used in the field of modern logistics and transportation, involving many fields such as resource allocation, process optimization, network planning, logistics and transportation. It is a typical NP-hard combinatorial optimization problem with high complexity and many constraints. The traditional vehicle routing problem solving methods include exact algorithm, heuristic algorithm and approximate algorithm, but it is difficult to obtain the optimal solution under multi-objective and multi-constraint conditions. In recent years, the deep reinforcement learning method has been gradually applied in the field of vehicle routing problem solving, through the construction of neural network models to autonomously learn the characteristics of problems and optimize in complex scenarios. However, the existing methods based on deep reinforcement learning usually face the problems with long time, slow solving speed and difficulty to obtain accurate solutions in practical applications. To solve them, this paper proposes an improved multi-objective vehicle path planning method based on deep reinforcement learning.
This method uses a variety of encoders to dig into multi-source information, and introduces a context-based multi-scale information decoder structure to construct an accurate decision sequence. In the encoder part, each sub-problem in the multi-objective combinational optimization problem is encoded to realize the deep mining and comprehensive capture of multi-source information. The decoder constructs an accurate and coherent decision sequence based on the context multi-scale interaction space. During the model training phase, the Greedy Rollout baseline method in the REINFORCE algorithm is adopted to improve the solving quality and stability of the model and accelerate the convergence process.
To verify the validity of the proposed method, experimental data are obtained from classical vehicle routing problem datasets and evaluated by generating problem sets of different sizes through simulation. Through experiments on problems of different scales and comparison with existing deep reinforcement learning algorithms, the results show that the proposed algorithm is superior to existing deep reinforcement learning algorithms in solution quality and speed, and shows excellent robustness and generalization in generalization experiments. Specifically, in terms of solution quality, the proposed algorithm can solve the multi-objective combinatorial optimization problem accurately, and the result quality is significantly improved. In terms of solving speed, the learning stability of the model is improved with the REINFORCE algorithm based on the Greedy Rollout baseline, the convergence process is accelerated, and the efficiency is significantly improved. In terms of generalization, the excellent robustness and efficiency of the algorithm in dealing with complex, and high and multi-variable interaction problems are verified by generalization experiments.
The improved model and algorithm proposed in this paper provide a new solution to the multi-objective vehicle path planning problem, which has important theoretical and practical significance. In future studies, we can further optimize the model structure, expand its application in dynamic VRP problems and try to combine with other optimization methods to improve the model performance.

Analysis of Timing and Intensity of Government Intervention in Public Health Emergencies

LYU Yunxiang, LIU Dehai

2026, 35(1):  160-166.  DOI: 10.12005/orms.2026.0023

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In recent years, a series of pandemics, including Mpox and Avian influenza, have not only severely impacted public health but also resulted in substantial economic losses worldwide. Consequently, governments across the globe are confronted with the critical challenge of effectively managing potential public health emergencies. In the practices of pandemic prevention, it is evident that the timely implementation of appropriate intervention measures is crucial for controlling the spread of such emergencies. Therefore, it is imperative for governments to develop an effective dynamic intervention scheme for modulating population mobility. Despite its importance, there is scarce research exploring this critical scheme. To account for the dynamic of government intervention measures,public mobility,and the characteristics of pandemics, this paper develops a differential game framework including the government and the public.
To capture the changing trends of the pandemic, we incorporate the Susceptible-Infective-Susceptible (SIS) epidemic model into the framework. We analyze the optimal levels of government intervention measures intensity and public mobility under both baseline and pandemic containment scenarios and then research the timing of implementing intervention measures from the perspectives of the cost of pandemic prevention and public behavior. We then discuss the correlation between the intensity of government intervention measures and the level of public mobility. Furthermore, we conduct an extensive numerical analysis to thoroughly examine the findings derived from our theoretical model. We collect the experimental data from the documents of authoritative organizations like WHO and the literature on epidemic containment to conduct numerical experiments. In extended model, we discuss the interaction between the intensity of government intervention measures and the level of public mobility in a societal epidemic prevention and control system.
Our findings show that the government should implement intervention measures as soon as possible from the perspective of the cost of pandemic prevention. Specifically, the correlation between the pandemic trends and the cost of pandemic prevention is not a linear relationship. Increasing the intensity of intervention measures incurs a higher cost. From the perspective of public behavior, facing a major public health emergency with high transmission rates, governments must implement intervention measures to control the pandemic. Facing general public health emergencies with low transmission rates, the government should not implement intervention measures too early to avoid social panic. As a result, the government should comprehensively determine the timing of implementing intervention measures, taking into account the cost of prevention and public behavior. Second, intense intervention measures are not always better. The results indicate that the appropriate relationship between the level of public activity and the intensity of government intervention is influenced by various factors. Consequently, the government should focus on the coordination between intervention strategies and public behavioral responses and further adjust the intensity of intervention measures within an appropriate range based on the needs and risks of the public, to avoid causing more serious social problems. Finally, a higher risk of infection does not necessarily deter the public from engaging in outdoor activities. Infected individuals may still require outdoor medical visits. As the epidemic situation deteriorates and public mobility increases, the government must escalate intervention measures in response to heightened infection risks.
Although this paper provides several important findings and management implications, there are still some limitations. First, future research can discuss the impact of virus mutation. Second, the infected public has different clinical manifestations. In the future, the multi-compartment epidemic model should be used to classify the public and design intervention measures for different public groups. Finally, the government can also take drug interventions. Hence, further research could study how to optimize the combination of government intervention measures.

Analysis of Green Transformation Strategies for Steel Enterprises under External Environmental Regulations and Internal Incentives

RUAN Sumei, WANG Shaoxin

2026, 35(1):  167-173.  DOI: 10.12005/orms.2026.0024

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The steel industry is a pillar of China’s national economy and forms a critical foundation for achieving low-carbon transformation within the industrial sector. However, much of China’s steel production capacity stems from low-level and repetitive construction, characterized by large output volumes and the use of high-carbon production processes. This dual factor has led to persistently high carbon emissions in the Chinese steel industry. Driving the green transition of steel enterprises and reducing their carbon emissions have thus become pressing challenges that require immediate attention. Effectively leveraging external regulations and internal incentives to promote the green transition of steel enterprises represents a crucial breakthrough in addressing this issue. It holds significant practical implications for facilitating the green transformation of the steel industry and mitigating its carbon emissions.
The corpus of scholarly research, both nationally and internationally, has primarily centered on the mechanisms and efficacy of external environmental regulatory mechanisms in spurring the green transformation of steel enterprises. The effective utilization of internal incentives to facilitate the green transformation of steel enterprises remains an area that merits further investigation. There is a contentious debate regarding the ability of environmental regulatory measures to effectively incentivize steel enterprises to engage in green transformation, with existing methodologies falling short in effectively explicating the intrinsic mechanisms by which internal incentives propel the green transformation of steel enterprises. Given the pivotal role of governments and banks as economic agents in driving the green transformation of steel enterprises, this study incorporates steel enterprises into an evolutionary game framework. It constructs a tripartite dynamic evolutionary game model involving “government-banks-steel enterprises,” analyzing the strategic choices and evolutionary trajectories of these tripartite players under the dual constraints of external environmental regulation and internal incentives. It explores the policy intensity of the green transformation of steel enterprises under the dual constraints of external regulation and internal incentives.
To validate the effectiveness of the model construction and related conclusions, this study derives benchmark parameter values for the numerical simulation section by referring to relevant literature and real-world economic data. Using MATLAB software, we conduct simulated analysis to visualize the evolutionary impact of various parameters on the green transformation system. The results show that: (1)An increase in carbon prices, a decline in green credit interest rates, and government reward and punishment mechanisms can promote the green transformation of steel enterprises. Further research reveals that the guiding effect of market-based environmental regulations, including the carbon market, on green transformation diminishes, while the constraining effect of command-and-control environmental regulations, including green credit and government rewards and punishments, does not exhibit a significant marginal change trend. (2)Increasing internal incentive investment can stimulate employees’ innovative efforts, thereby encouraging steel enterprises to implement green transformation.
Based on the aforementioned conclusions, this paper proposes three policy recommendations for government policy implementation regarding the real issues of green transformation in the steel industry. First, the government should flexibly adjust carbon allowances according to different circumstances to influence carbon prices, thereby refining the mechanisms of the carbon market. Second, banks should adopt differentiated green credit management practices, raising the entry threshold for non-green transformation steel enterprises while relaxing access for those undergoing green transformations, and actively supporting the development of green projects. Third, steel enterprises should increase their investment in internal incentive costs, innovate in the forms of internal incentives, and stimulate employee participation and green innovation. This study provides theoretical and empirical references for coordinating external environmental regulations with internal incentives to promote the green transformation and upgrading of steel enterprises.

Analysis of Disaster Network Dynamic Evolution and Multi-agent Collaborative Rescue Effect: A Case Study of the 2023 Shulan Rainstorm

LEI Ting, HUI Xiaojing

2026, 35(1):  174-181.  DOI: 10.12005/orms.2026.0025

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In recent years, rainstorm disasters in China have exhibited increasing trends of suddenness and recurrence, posing significant threats to economic development, the safety of human lives, and property. Furthermore, extreme rainstorm events often exhibit spatiotemporal dynamic coupling relationships with social and economic activities, leading to cascading effects that are challenging for single disaster response organizations to manage effectively. To recognize the systematic requirements for addressing rainstorm disasters, it is essential to establish an integrated response model encompassing “multiple disaster events, multiple stages, multiple emergency tasks, and multiple response entities,” as well as to develop a rational emergency task allocation mechanism to enhance the adaptability of collaborative networks within emergency organizations and improve the precision of disaster prevention and relief measures.
This article focuses on the 2023 Shulan rainstorm as a case study. Data are collected from news reports disclosed by mainstream media, laws, regulations, and emergency plans published on government websites at various levels. Based on these materials, the study first identifies representative disaster events frequently triggered by typhoons or rainstorms and constructs a rainstorm disaster network topology diagram using the interrelationships among these events. The overall network attributes, node characteristics, and edge vulnerabilities are analyzed in depth to summarize the primary features of this rainstorm disaster. Subsequently, the content of emergency tasks is extracted. If an emergency task co-occurs with a specific disaster event in the same source material, a connection is established between them, and a “disaster event - emergency task” two mode network is constructed. A “core-periphery” structural analysis is then performed to identify key disaster events and emergency task contents. Next, “emergency task - response entity” two mode networks are constructed for statistical units T1 through T4. Connections are established if a response entity executes a specific emergency task during the corresponding period. Finally, the collaborative rescue effectiveness of this rainstorm disaster is analyzed from the perspectives of disaster events, emergency tasks, and response entities.
The main findings of this paper are as follows: (1)The control windows for different disaster events vary. For instance, typhoons and rainstorms are primarily managed during the warning response, personnel search, rescue, clearance, and resettlement stages, whereas crop damage is addressed during the clearance, resettlement, recovery, and reconstruction stages. During these stages, the number of disaster events, the chains controlled by each response entity, the reduction in vulnerability of disaster chain edges, and the clustering coefficient of the disaster network can serve as indicators to evaluate their collaborative performance. (2)Across the stages of rainstorm disaster response, there are both similarities and differences in the prioritization of emergency tasks. It is crucial to ensure the stable execution of cross-stage emergency tasks, such as consultation, judgment, command, and coordination. (3)In these stages, response entities with larger effective scales and greater opportunities for “structural holes” are predominantly government organizations that align with the key emergency tasks of the stage. However, to enhance societal resilience and cohesion, it is necessary to further leverage the flexibility advantages of enterprise and social organizations and address issues related to insufficient participation. Additionally, the structural characteristics of the collaborative network exhibit temporal variations: during the warning response stage, the nature of disaster response entities is relatively homogeneous; during the personnel search and rescue stage, information barriers exist among multiple entities; during the clearance and resettlement stage, entities gradually adapt to complex environments; and during the recovery and reconstruction stage, the focus of emergency tasks requiring collaborative execution becomes more prominent.
Based on the findings of this study, the criteria for evaluating the collaborative rescue effectiveness of multiple entities demonstrate diverse and intricate features. However, relying solely on a single case study to assess this effectiveness has certain limitations. Future research could consider incorporating additional samples of extreme disaster emergency management and conducting more in-depth analyses from the perspective of the dynamic evolution of disaster networks to further validate the generalizability of the conclusions presented in this paper.

Study on Contagion of Panic Sentiment among Chinese and U.S. Investors during the COVID-19 Pandemic

GAO Jie, MO Shuwei, LI Helong, YUAN Yichen

2026, 35(1):  182-189.  DOI: 10.12005/orms.2026.0026

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In recent years, infectious disease has caused strong external shocks to the modern society, leading to the spread of global market panic. Therefore, people from all fields in the world need to learn from historical experience and summarize it to jointly face future public health events. As investor panic sentiment infectivity is also vulnerable to public health events at different time scales, those investment or regulatory strategies that take into account investor sentiment need to be modified somewhat. This paper studies the contagion of investor panic under the background of the COVID-19 epidemic, explores the impact of the COVID-19 epidemic on market sentiment, provides a basis for investors and regulators to face similar major public health events in the future, breaks through the traditional single time scale, and explores the emotional contagion effect between markets in more detail from the three time scales of long-term, medium-term and short-term. Moreover, it integrates the research findings into the policy environment for analysis, offering significant theoretical and practical implications for investors, governments and regulatory bodies to stabilize financial markets and effectively mitigate investment risks.
This paper uses CIVIX and VIX to measure panic sentiment in the Chinese and US markets, respectively. Because the SSE50 ETF Volatility Index (iVX) ceased publication in February 2018, the study simplifies the calculation method for the SSE50 ETF Volatility Index by using implied volatility to construct the panic sentiment index (CIVIX). The panic indices for both markets are based on daily data from 883 overlapping trading days, sourced from the Wind database. Subsequently, the paper applies Variational Mode Decomposition (VMD) to decompose the VIX and CIVIX into multiple Intrinsic Mode Functions (IMFs) and calculates the dominant period of each IMF component through Wavelet Analysis (WA). Based on the dominant period characteristics of the IMFs, the components are classified and reorganized to ultimately derive the long-term, medium-term and short-term components of the indices. Using traditional econometric models, this paper investigates the impact of the COVID-19 pandemic on the contagion of panic sentiment across the three time scales: long-term, medium-term and short-term.
It is found that by comparing the curve changes in the impulse response graph between the long-term panic in China and US before and after the epidemic, it can be seen that in the long run, the COVID-19 epidemic will hinder the contagion of panic between the Chinese and American markets, resulting in a decrease in the intensity and duration of infection. By comparing the curve changes in the impulse response chart between the medium-term terms of Sino-US panic before and after the epidemic, it can be seen that in the medium term, after the COVID-19 epidemic, the process of panic contagion from the Chinese market to the US market becomes more rapid, violent and unstable, and when the panic in the US market changes, the contagion of the US market to the Chinese market will be positive and then negative before the epidemic, in turn, negative and then positive after the epidemic. By comparing the dynamic correlation coefficient between Chinese and US panic before and after the epidemic, it can be seen that in the short term, the COVID-19 epidemic will strengthen the contagion of panic between China and US, but it will also make panic contagion more uncertain.
Based on the results, the paper provides relevant recommendations to investors and regulators. Different types of investors should adopt targeted strategic adjustments in the face of major health events to improve their ability to judge information. Long-term investors can focus on the panic in the Chinese market. Medium-term investors should pay attention to the risks caused by the rise of panic in the later period when modifying the investment strategy of the Chinese market target, and should adopt defensive strategies in time when modifying the investment strategy of the US market target to avoid the risks caused by the rapid contagion of panic. Short-term speculators should study and train to understand the characteristics of their trading psychological deviations and reduce the constraints of psychological factors. Among them, short-term and medium-term investors need to develop different trading strategies to avoid losses. For governments and financial regulatory bodies, it is crucial to ensure the effectiveness and adaptability of economic and public health policies. This includes providing precise financial support to industries and groups heavily affected, implementing flexible fiscal and monetary policies to respond to market demand changes, and utilizing advanced technology to enhance economic data monitoring and early warning systems. Additionally, governments should strengthen international cooperation, share policy experiences, coordinate economic recovery measures, and ensure the overall stability of global markets.

Management Science

Third-party Logistics Guarantor Financing vs. Bank Financing: Optimal Supply Chain Operations and Financing Decisions

BI Gongbing, XIE Yinhua, LIU Yinghui

2026, 35(1):  190-196.  DOI: 10.12005/orms.2026.0027

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Capital shortage is a significant factor constraining the development of supply chains. Since the COVID-19 outbreak in 2020, many firms have faced cash flow constraints and the risk of bankruptcy due to production disruptions and declining revenues, which has exacerbated the problem of funding shortages for SMEs. Due to strict credit history and collateral requirements, it is difficult for SMEs to access bank financing. As a result, Third-Party Logistics(3PL)firms are helping SMEs ease their financial pressures by providing guarantor financing services, which are becoming increasingly popular. For example, large Chinese logistics providers such as Eternity Asia and SF Express have been offering such services for many years. The popularity of 3PL guarantor financing raises several questions worth exploring: How do different financing schemes affect the retailer’s purchasing decision? What is the optimal decision for supply chain members under 3PL guarantor financing, and when should the 3PL firm offer guarantor financing rather than allowing the retailer to use bank financing directly? These questions remain pressing issues in practice.
This paper explores two financing schemes: traditional bank financing and 3PL guarantor financing to analyze the efficacy of 3PL guarantor financing. In the traditional scheme, the retailer obtains a loan directly from the bank, while the 3PL firm only provides transportation services. In the 3PL guarantor financing scheme, on the other hand, the 3PL firm guarantees the retailer’s loan in addition to transport, and the 3PL firm is required to bear the loss of the bank’s loan if the retailer defaults due to demand fluctuations. By constructing a Stackelberg game model involving the 3PL firm and financially constrained retailer, this paper analyzes the equilibrium order quantity of the retailer and the equilibrium logistics price of the 3PL firm. Comparing 3PL guarantor financing with bank financing, the study also explores the financing preferences of both parties in the supply chain and concludes as follows: Firstly, the optimal order quantity is higher under 3PL guarantor financing than under bank financing. This indicates that risk-sharing by the 3PL firm in guarantor financing incentivizes the retailer to order more, thereby enhancing supply chain efficiency. Additionally, 3PL guarantor financing enables supply chain coordination at a given procurement cost. Secondly, the optimal logistics price is higher in 3PL guarantor financing than in bank financing. This suggests that the 3PL firm should control the retailer’s default risk by increasing the price, which may have a negative impact on the retailer and supply chain. Thirdly, the retailer consistently prefers bank financing, while the 3PL firm prefers 3PL guarantor financing when the procurement cost is not too high, and the retailer prefers to use bank financing otherwise. Finally, 3PL guarantor financing can be a consistent choice for both parties due to its Pareto improvement when the purchasing cost is at a lower level. The findings of this paper also give some managerial insights. First, 3PL firms can provide logistics and guarantor financing services to increase retailers’ order quantity and enhance their own profits. Second, competition from external banks can motivate 3PL firms to maintain a competitive edge in logistics pricing, making their provided guarantor financing services a common choice for both parties, thus improving efficiency and fairness.
This paper considers a case where a 3PL firm provides guarantor financing service to only one retailer. Exploring the efficiency of 3PL guarantor financing for multiple capital-constrained retailers would be interesting. Additionally, it is of practical interest to explore the impact of supply chain firms’ risk attitudes and information asymmetry on equilibrium operational and financing decisions of supply chain participants.

Research on Strategy of Limited-time Free Knowledge Service Offering under Duopoly Competition

KUANG Lini, YAN Zhijun

2026, 35(1):  197-203.  DOI: 10.12005/orms.2026.0028

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Amidst escalating societal competition and improving living standards, there is an increasing demand for various paid knowledge services, leading to the thriving development of online knowledge service markets. However, this development also faces challenges, such as the varying quality of knowledge services, making it difficult for consumers to identify high-quality service providers. As an intangible product, it is challenging for consumers to judge the quality or intrinsic utility of knowledge services based on their external characteristics. Serious information asymmetry exists between consumers and service providers, with consumers only able to reduce uncertainty about the quality of knowledge services after experiencing them. Therefore, many knowledge service providers reduce this uncertainty by offering a limited duration of free services to attract consumers to purchase paid knowledge services.
This “limited-time free service” strategy may impact the profitability of knowledge service providers in several ways. Firstly, offering limited-time free knowledge services can help reduce consumers’ perceived uncertainty about service quality, enhance perceived utility and attract more consumers to purchase paid knowledge services. Secondly, providing time-limited free knowledge services may cannibalize consumers who initially intend to purchase paid knowledge services. For instance, if consumers find that free knowledge services meet their consultation needs, they may not continue to purchase paid knowledge services. Finally, if competing knowledge service providers offer free knowledge services, there is a possibility of potential consumers attracted by competitors’ free service strategies, resulting in loss of consumers for themselves. Therefore, in a competitive environment, knowledge service providers may adopt strategies with a certain duration of free services or purely paid service. This paper poses two research questions under duopoly competition: What is the optimal pricing for knowledge service providers under different strategic scenarios? Under what conditions is the strategy of limited-time free knowledge services superior to the strategy of purely paid knowledge services?
Regarding the decision-making problems of service providers offering limited-time free services and purely paid services, this paper studies the strategic choice game process of service providers under duopoly competition and analyzes equilibrium prices and profits under four scenarios. Nash equilibria under different scenarios are derived using backward induction.
The study finds that: First, the optimal pricing of service providers under the free service strategy is influenced by consumers’ mismatched costs, the duration of free services provided, the difference between the actual service quality of service providers and consumers’ perceived service quality before the free trial, the difference between competitors’ actual service quality and consumers’ perceived service quality before the free trial, and the unit service costs of both competitors. Second, the longer the duration of free services provided by service providers, the higher the optimal pricing for their paid knowledge services; when the duration of free services exceeds a certain threshold, the optimal pricing of competitors’ paid knowledge services decreases with increasing duration of free services. Third, when the service cost of service providers is low, they tend to choose the strategy of offering limited-time free services.
This paper makes the following theoretical contributions. Firstly, unlike previous literature on information products, this paper considers the service provider’s service cost when providing services in the theoretical model. Secondly, this study explores the free service strategy choices and paid service pricing strategies of service providers under competitive situations, complementing research related to the “free trial” strategy of individual service providers under monopoly situations.

Three-party Evolutionary Game of Takeaway Food Safety Regulation Considering Customer Participation Behaviors

ZHU Yan, DONG Yucheng, WANG Fang, ZHANG Hengjie

2026, 35(1):  204-211.  DOI: 10.12005/orms.2026.0029

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Food safety, as a significant issue concerning public health and social stability, has always garnered extensive attention from various sectors of society. In recent years, with the rapid development of information technology and the acceleration of life pace, the takeout catering industry has emerged as a formidable force, becoming an indispensable part of urban life. However, the rapid expansion of this industry has been accompanied by frequent exposures of food safety issues in takeouts, such as unknown sources of ingredients, unsanitary processing environments and food contamination during delivery. These issues have severely infringed upon consumers’ rights and interests, triggered deep concerns among the public regarding food safety and prompted unprecedented attention from the government and various sectors of society. In the field of food safety regulation, although academia has conducted extensive research, much of this has focused on traditional offline catering industries and online food sales platforms. In contrast, there is a lack of in-depth and systematic exploration of the emerging regulatory mechanisms for takeout food safety. This research gap not only limits our comprehensive understanding of takeout food safety issues but also hampers the government’s ability to formulate effective regulatory policies. Therefore, this study aims to construct a multi-agent interaction mechanism model for takeout food safety regulation, thoroughly analyzing the strategic choices and dynamic interaction processes among government regulatory departments, takeout platforms and takeout merchants. Additionally, it examines the potential impact of consumer participation on takeout food safety regulation.
This study innovatively introduces the theory of tripartite evolutionary game, regarding government regulatory departments, takeout platforms and takeout merchants as game entities with autonomous decision-making capabilities, while fully considering the role of consumers as an external supervisory force. By constructing an evolutionary game model incorporating these three entities and their interactions, we analyze the stability conditions of each entity under different strategic choices and utilize numerical simulation techniques to delve into the impact of key parameters,such as regulatory costs, reward and punishment intensities and consumer participation, on the evolutionary process of the game. The research results indicate that within the complex dynamic system of takeout food safety regulation, there exist three distinct stable states. The first state involves government regulatory departments adopting strict regulatory measures, while takeout platforms relatively relax their oversight, leading takeout merchants to choose unsafe production due to the lack of effective constraints. The second state is characterized by government regulatory departments relaxing their oversight, with takeout platforms actively assuming the responsibility of strict regulation, and yet takeout merchants still opting for unsafe production. The third state, which is the most ideal, features government regulatory departments maintaining strict oversight, takeout platforms moderately relaxing their supervision (as the platforms’ regulatory responsibilities are relatively reduced under the government’s strict oversight), and takeout merchants choosing safe production under regulatory pressure. For this third stable state, this study further discovers that by increasing the rewards and penalties for takeout merchants, as well as enhancing consumer participation and supervisory capabilities, takeout merchants can be effectively incentivized to improve their safety production standards. This finding not only provides a theoretical basis for the government to formulate more precise regulatory policies but also points in the direction for takeout platforms and merchants to enhance their food safety management levels.
In summary, this study not only enriches the theoretical system in the field of food safety regulation and provides new perspectives and methods for takeaway food safety regulation, but also provides valuable theoretical references and practical guidance for the government, takeaway platforms and merchants in their strategic choices in food safety management. With the continuous development of the takeaway food and beverage industry, the results of this research are expected to contribute significantly to the construction of a safer, healthier and more sustainable takeaway market environment.

Study on Impact of Blockchain Technology on Recycling Model Selection and Coordination Mechanism

CHENG Yanpei, XIA Xiqiang, ZHANG Yanliang, ZHANG Jingrui

2026, 35(1):  212-218.  DOI: 10.12005/orms.2026.0030

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Amid escalating environmental challenges, reverse supply chain management has received considerable attention in industrial production. The recycling of discarded products, positioned at the forefront of the reverse supply chain, represents a critical vulnerability in advancing the circular economy. At present, ambiguities surrounding responsible recycling entities and the inefficiencies of recycling channels result in the quantity and quality of recycled products remaining below optimal levels. Moreover, remanufactured products derived from discarded materials can attain performance and quality levels comparable to those of new products. However, information asymmetry erodes consumer confidence, thereby limiting the effective market demand for remanufactured products. As a result, addressing information asymmetry in the recycling and remanufacturing process has emerged as a central focus of academic research. Blockchain technology, acting as a catalyst within the digital economy, effectively improves information transparency in the production process of remanufactured products through its decentralized and traceable features. Despite the substantial advantages that blockchain technology provides in the field of recycling and remanufacturing, the success of remanufacturing operations remains critically dependent on the efficient execution of recycling processes. Currently, several typical recycling channels are utilized in the business sector, including original equipment manufacturer recycling, remanufacturer recycling and retailer recycling. Each of these recycling channels offers distinct advantages. However, the rationale behind manufacturers’ choices to pursue independent recycling or to collaborate with supply chain partners remains unclear, particularly given the rapid growth of the digital economy.
This study aims to examine the adoption strategies for blockchain in various recycling channels and its impact on channel selection. Specifically, we analyze game models that encompass three recycling channels: OEM recycling, remanufacturer recycling and retailer recycling. The analysis considers whether the recycler opts to invest in blockchain technology within the outsourced remanufacturing model, and we employ the Shapley value method to address the reasonable distribution of value-added gains derived from blockchain investment.
The study reveals the following key findings: (1)The adoption of blockchain technology in the supply chain becomes viable when the associated costs remain below a specific threshold, resulting in Pareto improvements in profitability for OEMs, remanufacturers and retailers. This outcome persists even if consumer demand transitions from new products to remanufactured products. (2)OEMs and remanufacturers consistently prefer their direct recycling channels, regardless of the adoption of blockchain technology. However, when the recycling scale factor of used products is within a certain range, the adoption of blockchain technology shifts retailers’ preference from retailer recycling to remanufacturer recycling. (3)Whether blockchain technology is adopted or not, the remanufacturer recycling channel consistently reduces environmental impacts and increases consumer surplus when consumers have a stronger preference for remanufactured products, or when the low-carbon advantage of remanufactured products becomes more evident. OEM recycling is more effective at optimizing both utilities compared to retailer recycling. (4)The Shapley value method offers an effective means for profit allocation based on the respective contributions of supply chain participants. This method helps mitigate marginal losses and promotes coordination of the outsourced remanufacturing supply chain.

Data and Knowledge Driven Ensemble Credit Default Prediction

SHAO Yuanhai, LIU Wenzheng, SONG Yiwei

2026, 35(1):  219-225.  DOI: 10.12005/orms.2026.0031

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Credit default prediction, which is important in credit business, refers to an assessment of whether a borrower is likely to default. However, with the low threshold of online lending accompanied by the high risk of investment returns, platforms often lack financial data and find it difficult to use domain knowledge to guide prediction. It is challenging to achieve high accuracy for traditional machine learning methods. To tackle this challenge, it is imperative to devise a method capable of proficiently harnessing the available knowledge embedded within the existing data to augment model training. This will aid in accurately and efficiently identifying loan users who are at risk of defaulting on their loans.
This paper proposes a novel credit default prediction method called Ensemble Statistical Invariants Learning (ESIL), which integrates the ideas of Learning Using Statistical Invariants (LUSI) and ensemble learning. It first applies financial domain expertise to construct predicates and form the statistical invariants in order to utilize credit default domain knowledge, which will accelerate the convergence of the expectation function in admissible function set based on the using of weak mode of convergence. Furthermore, it leverages ensemble learning to choose the most suitable domain knowledge, and it can be demonstrated that computing the corresponding thresholds leads to the selection of predicates, resulting in a decrease in the objective function by selecting suitable predicates from a predefined set. This strategy ensures that ESIL effectively optimizes the model during the iterative process. Besides, to maintain the integrity of the sampled data structure, easily classifiable samples are added to the existing imbalanced samples to correct the data distribution. By combining the statistical invariants and the ensemble learning obtained from the credit domain, ESIL achieves the data and is knowledge dual-driven in the domain of credit default prediction, offering a new approach for conducting credit assessment in the era of online platforms, particularly in scenarios with insufficient samples.
Subsequently, a series of experiments are conducted to validate the effectiveness of the EUSI by using real credit data from UCI, Kaggle, Tianchi and DataFoutain. In this paper, ten predicates are constructed according to the data imbalance in credit default issues, customer-specific attributes, anomalous default samples and some commonly used predicates. The following conclusions are drawn from the experiments. First, through comparative experiments on three indicators commonly used in credit default, the experimental results show that the ESIL model demonstrates excellent performance on AUC,F1 measure and G-means indicators. Especially on small datasets, the improvement can exceed 8% compared to the benchmark methods. Second, Friedman test and Nemenyi test demonstrate that ESIL is significantly superior to other models on the results of the comparison experiments. Third, this study explores the prediction effect of the ESIL model and analyzes the relevant properties on credit data. The results reveal that the ESIL model is still able to maintain a high prediction accuracy compared to other models when the size of data is small. Meanwhile, the enhancement in accuracy resulting from the combination of various statistical invariants finds that the prediction accuracy of the model is improved accordingly with the increase in the number of predicate matrices, and proves its acceleration in convergence on small datasets. Finally, taking Chinese Taiwan dataset as an example, it analyses the interpretability of ESIL in credit default prediction.
The proposed ESIL provides new ideas for the theoretical development of credit default prediction by integrating multiple statistical invariants utilizing domain knowledge. It shows that ESIL improves the accuracy and provides new strategies for the practical application of financial risk management. In the future, developing different ensemble learning techniques and comparing various ensemble methods will contribute to optimizing the performance of ESIL in credit risk assessment. Distinct ensemble strategies may be more suited for specific data distributions and types of problems, allowing us to choose the most appropriate ensemble approach to enhance the predictive prowess of ESIL. It is also interesting to investigate the applicability of ESIL beyond the credit default prediction. Expanding ESIL to diverse domains through experiments on various datasets would underscore its adaptability and performance across a wide array of scenarios.

UGC Media Platform Compensation and Investment Strategy Considering the Scale of Content Creators

MENG Xiuli, ZHOU Lin, LI Chenyang

2026, 35(1):  226-232.  DOI: 10.12005/orms.2026.0032

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With the growth of internet users and the improvement of user experience on online video platforms, video platforms have now become a frequently used product in people’s online lives. At present, mainstream video platforms can be seen as multilateral platforms composed of platform operators, platform users, content providers and advertisers. The video content generally comes from three sources: copyrighted videos, User Generated Content (UGC) and platform made content. Among them, the UGC media platform, such as Tiktok and Bilibili, provides space for excellent content creators and attracts a large number of audience fans. The operating model of this platform is to provide users with free videos and earn advertising revenue by placing advertisements in the videos. Due to users’ innate aversion to advertising, their perception of videos on the platform is influenced by the proportion of advertising and content allocation in the video and the degree of compatibility between the two. In order to attract more users to join the platform, on the one hand, the platform can adopt compensation strategy to motivate content creators to create higher quality videos; on the other hand, investing in value-added services for users can increase their stickiness to the platform. Users may choose to watch videos on one or more platforms for entertainment or pursuit of high-quality videos, resulting in different attribution behaviors, namely, single attribution and multiple attribution. At this time, different attribution behaviors of users may affect platform compensation and investment decisions. In addition, the advertising revenue of the platform is closely related to the scale of content creators on the platform. The larger the scale of content creators, the more they can attract more users to join the platform, thereby generating more advertising revenue. Different sizes of content creators can lead to differences in platform profits, so the decision faced by platforms is how to determine the optimal compensation and investment strategy based on the size of content creators.
Considering the different attribution of consumers, a monopoly model and a duopoly competition model are constructed to discuss how the scale of content creators affects the decision-making and profits of platform and content creators. Additionally, an in-depth analysis is conducted on how the influencing factor of content creator size affects platform, content creator decision-making and profits through numerical examples. The research has found that whether in a monopolistic market or a competitive market, the platform should compensate content creators with the same commission level, and in an equilibrium state, the investment level of value-added services on the platform, the proportion of content in the video creation of content creators and the fit between content and advertising depend on the scale of content creators. Due to the larger scale of content creators in a monopolistic market compared to a competitive market, platform should provide more investment in value-added services, and content creators should make more efforts to increase the proportion of content and the compatibility between content and advertising. The profits of platform and content creators in the monopolistic market are not always greater than those in the competitive market, which depends on the scale of content creators; in the competitive market, when the scale of content creators is greater than a certain threshold, the platform profits under the user multi-attribution model are greater than those under user single attribution model; both platform and content creators are communities of interest in competitive and monopolistic markets.


Quality Acquisition and Disclosure Strategies of the Refurbisher under Manufacturer Competition

LIU Wenping, LI Bangyi, WANG Zhe, CHENG Yongbo

2026, 35(1):  233-239.  DOI: 10.12005/orms.2026.0033

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Refurbishment is the most common form of product recycling, which can effectively alleviate the environmental pollution caused by waste and generate revenue by its low-cost advantage. However, refurbished products come from used products, which makes the quality of refurbished products more difficult to control, and even refurbishers themselves cannot recognize the exact quality of refurbished products. The refurbished product quality acquisition and disclosure have become a key strategy to influence consumers’ purchasing decisions. The quality acquisition methods are generally categorized into two different quality disclosure modes: voluntary disclosure mode and mandatory disclosure mode. Under the voluntary mode, the refurbisher can decide whether or not to disclose the quality. For example, Apple’s refurbisher in China, Foxconn, and Huawei’s refurbishment factory have invested in repair and testing equipment to obtain accurate quality of refurbished products. However, in some cases, refurbishers do not have the autonomy to decide whether or not to disclose quality. For example, the second-hand refurbished product sales platform “Paipai” has launched a “blockchain quality traceability system”. Once a refurbished product is recorded in the chain, the information will be passed on to the consumer regardless of the quality of the refurbished product. In addition, some small-scale refurbishers test the quality and sell refurbished products through the BackMarket refurbishment sales platform, and the test results are categorized into “Fair”, “Good” and “Excellent” for mandatory disclosure to consumers.
This study explores the quality acquisition and disclosure strategy for refurbishers introducing new product competition. The innovations of this study are as follows: (1)Based on the imperfect characteristics of refurbished products, consumers’ psychological cognitive attitudes towards refurbished products are introduced to explore their influence on quality acquisition and disclosure strategies of refurbishers. (2)By introducing the competition of manufacturer’s perfect new products, this study compensates for the insufficient consideration of the influence of market structure in the previous studies on the quality acquisition and disclosure strategy.(3)In the context of circular economy, the strategy of quality acquisition and disclosure is formulated to address the uncertainty of refurbished products’ quality, which provides useful guidance for the realization of economic value of refurbished products.
The main conclusions are shown below: (1)The incentive for refurbishers to acquire quality is greater in the voluntary disclosure mode than in the mandatory disclosure mode. (2)As competition becomes more intense, the refurbisher’s willingness to acquire quality becomes weaker under the voluntary disclosure mode. However, it first increases and then decreases under the mandatory disclosure mode. (3)After acquiring quality, the more negative the consumers’ attitudes are towards refurbished products, the stronger the refurbisher is willing to disclose quality. (4)When the quality acquisition cost is determined, the refurbisher should choose the voluntary disclosure mode when cost is small, but select the mandatory mode when it is large. However, when the cost is indeterminate, the refurbisher should proceed with the mandatory disclosure model for quality acquisition. (5)The effect of new product competition on the refurbisher’s choice of disclosure mode is related to consumers’ psychological cognitive attitudes towards refurbished products.
There are shortcomings in the study: the manufacturer’s quality acquisition and disclosure strategy has been neglected and the potential effect of “free riding” on refurbished products is not introduced, which is worth exploring in future research.