Table of Content

25 September 2026, Volume 34 Issue 9 Previous Issue   

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Public-Private Partnership for Disaster Preparedness Investment, Resilience, and Economic Growth System Model Huanhuan Liu, Jingjing Ding, Liang Liang, Wanting Hu 2026, 34 (9):  1-10.  doi: 10.16381/j.cnki.issn1003-207x.2024.1067 Abstract ( 76 )   HTML ( 4 )   PDF (1806KB) ( 23 )   Save In recent years， the Chinese government has proposed the integration of development and security to build a safer and more resilient China. Strengthening emergency response capabilities and enhancing system resilience are critical for effective disaster risk management. From the perspective of maximizing social welfare through public-private partnerships （PPP）， the centralized decision-making process between the public and private sectors in addressing disaster risks is explored， particularly the trade-offs between disaster preparedness investment， economic growth， and system resilience. By integrating the Solow economic growth model with system resilience theory， this paper develops a new dynamic disaster risk management model. The model incorporates two positive feedback loops and two negative feedback loops， enabling the evaluation of social welfare and analysis of policy effects. The main results show that： （1） The optimal system capital level and social welfare in the absence of disasters； （2） The optimal investment rate， disaster preparedness investment， system resilience， and social welfare level in the event of a disaster； （3） An optimization model for maximizing social welfare under disaster probability， including the investment rate， disaster preparedness investment， and system resilience level. The solutions to the objective function are analyzed and numerical simulations are conducted to explore the impact of key parameters on optimal decision-making. The results offer valuable insights for both the public and private sectors in collaboratively managing disaster risks， enhancing system resilience， and maximizing social welfare. The contribution of this study lies in providing a framework that integrates economic growth and resilience management， offering theoretical support for policymakers to optimize disaster preparedness strategies. Figures and Tables | References | Related Articles | Metrics

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Government Public Data Openness and Commercial Bank Inclusive Loans——Empirical Analysis on Small and Micro Enterprise Loans of Commercial Banks Yue Ma, Ye Guo 2026, 34 (9):  11-20.  doi: 10.16381/j.cnki.issn1003-207x.2024.1804 Abstract ( 12 )   HTML ( 0 )   PDF (1035KB) ( 29 )   Save With the construction of Digital China and the development of the digital economy， the value of data elements is gradually gaining attention. Can government public data openness， as a key measure for digital government construction， stimulate data vitality and unleash data dividends in the field of inclusive finance？ The launch of urban government public data platforms is taken as a quasi-natural experiment， and a multi time point DID model is used to study the impact of government public data openness on the commercial bank inclusive loans. The research results indicate that： Firstly， the openness of government public data has made the loans of commercial banks more inclusive， prompting commercial banks to issue more loans to small and micro enterprises. Secondly， in terms of channels， government public data openness mainly promotes more inclusive bank loans by reducing information asymmetry and lowering service costs. Thirdly， heterogeneity analysis shows that the promotion effect of government public data openness on the commercial bank inclusive loans is greater in smaller banks， greater in banks with lower levels of digital transformation before urban government public data platform establishment， and greater in cities with lower levels of digital inclusive finance development before urban government public data platform establishment. This also indicates that government public data openness can reduce the possibility of small banks being digitally marginalized and partially bridge the digital divide between regions in the process of developing inclusive finance. Figures and Tables | References | Related Articles | Metrics

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Research on SMOTE-BO-XGBoost Ensemble Credit Scoring Model for Unbalanced Data Aihua Li, Wanxin Liu, Sifan Chen, Yong Shi 2026, 34 (9):  21-28.  doi: 10.16381/j.cnki.issn1003-207x.2023.0635 Abstract ( 19 )   HTML ( 0 )   PDF (690KB) ( 7 )   Save To handle the issues of some high-accuracy models neglecting data imbalance and other studies effectively handling imbalanced data but not achieving satisfactory accuracy， a novel ensemble learning model is constructed for credit risk assessment under imbalanced data categories—a class-imbalanced credit scoring model based on the SMOTE-BO-XGBoost ensemble algorithm. Firstly， the model tackles the sample imbalance problem through the Synthetic Minority Over-sampling Technique （SMOTE）. Secondly， Bayesian optimization （BO） is employed to obtain optimal model parameters. Finally， an optimized XGBoost ensemble classification model is constructed. Based on the home-credit-default-risk dataset， four different ensemble models are sequentially trained， and the SMOTE-BO-XGBoost model is compared with traditional models. The experimental results demonstrate that： ① Ensembling is effective， and the multi-angle fused SMOTE-BO-XGBoost model exhibits the best model performance， outperforming general ensemble learning models and traditional classification algorithms； ② It can effectively overcome the problem of imbalanced samples. This model addresses individual credit risk issues of financial institution customers from two perspectives： data augmentation and model performance enhancement， providing an effective personal credit risk assessment method for banking sectors. Figures and Tables | References | Related Articles | Metrics

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Research on Short-Term Integrated Forecasting Model of Hour-Based Load in Micro-grid Based on Long-Short-Term Memory Network Xiaohong Chen, Zeshen Wang, Chao Wu, Dongbin Hu 2026, 34 (9):  29-36.  doi: 10.16381/j.cnki.issn1003-207x.2023.1574 Abstract ( 14 )   HTML ( 0 )   PDF (2447KB) ( 28 )   Save With the goal of carbon peaking and carbon neutrality， renewable energy， represented by photovoltaic solar energy， has attracted a lot of attention. However， due to the increasing complexity of urban power systems， the short-term forecasting of time-of-use electricity load for microgrids is not high. To address this issue， a short-term forecasting model that integrates various empirical mode decomposition methods and neural network models is proposed. By grouping， normalizing， and performing empirical mode decomposition on the initial data signal， multiple sets of intrinsic mode function （IMF） subsequences are obtained. Furthermore， all subsequences and the original data are respectively fed into a Long Short-Term Memory network （LSTM） and a Backpropagation Neural Network （BPNN） to obtain the forecasting model. Finally， an empirical test is conducted using a large distributed photovoltaic power station in Shanxi Province as an example. The results indicate that， compared to single or combined methods， the proposed forecasting model based on Ensemble Empirical Mode Decomposition （EEMD） and LSTM demonstrates higher accuracy in short-term time-of-use load forecasting for microgrids， showing significant superiority. Therefore， significant application value in time-of-use load forecasting for microgrids is demonstrated and can also be applied in fields such as wind power generation to assist enterprises and managers in making informed decisions. Figures and Tables | References | Related Articles | Metrics

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Subsidy Recession Policy and Overcapacity in Strategic Emerging Industries:Evidence from Listed Photovoltaic Enterprises Dan Fang, Qiaowen Lu, Bin Chen, Saige Wang, Jiangqiang Chen 2026, 34 (9):  37-47.  doi: 10.16381/j.cnki.issn1003-207x.2023.2013 Abstract ( 65 )   HTML ( 0 )   PDF (1196KB) ( 7 )   Save China’s persistent industrial overcapacity has exacerbated market inefficiencies， resource waste， and environmental pollution， posing a challenge to industrial upgrading and high-quality economic development. As strategic emerging industries （SEIs） become a key driver of new productive forces， government subsidies have accelerated their growth but also induced excessive investment and overcapacity in sectors such as photovoltaics （PV）， wind power， new energy vehicles， and machinery manufacturing. Whether subsidy recession can effectively mitigate overcapacity during the mature stage of industrial development remains an open question. The “531” photovoltaic policy， issued on May 31， 2018， marked a major acceleration in subsidy recession within China’s PV industry. Given the industry’s severe overcapacity and complete subsidy policy cycle， the “531” policy provides a quasi-natural experiment for identifying the causal effect of subsidy recession policy on enterprise overcapacity. Using panel data from listed PV and wind enterprises from 2014 to 2023， this study estimates enterprise overcapacity based on the production function method and applies the difference-in-differences model to investigate the impact of subsidy recession on overcapacity. Heterogeneous effects across industrial chain segments and ownership types are explored， and the underlying mechanisms through R&D investment and rent-seeking behaviors are examined. In addition， product output and life-cycle carbon emission data are used to quantify the policy’s economic and environmental benefits. The results indicate that subsidy recession significantly reduces overcapacity in the PV industry， with stronger effects for downstream firms and state-owned enterprises. Mechanism analysis shows that the policy alleviates overcapacity by stimulating R&D investment and reducing rent-seeking behavior， thereby shifting firms from extensive capacity expansion toward innovation-driven development. Furthermore， the policy yielded comprehensive benefits totaling 7.493 billion CNY in 2018， equivalent to 4.92% of the PV industry’s total output value， through fiscal savings， increased corporate revenue， and carbon emission reductions resulting from replacing coal-fired electricity with PV power generation. Based on micro-level evidence from China’s PV industry， this study provides policy implications for addressing overcapacity. First， governments should establish a well-designed subsidy exit mechanism with clear timelines and dynamic evaluation systems to reduce policy dependence while sustaining technological upgrading. Second， differentiated subsidy policies should be tailored to firms with different ownership and positions along the industrial chain， with greater emphasis on innovation incentives and coordinated industrial development. Finally， market-oriented reforms should further improve subsidy allocation transparency， clarify the respective roles of government and the market， and ensure an orderly subsidy withdrawal process to facilitate a smooth policy transition. Figures and Tables | References | Related Articles | Metrics

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Research on Dynamic Allocation and Monitoring of Critical Chain Project Buffer from the Perspective of Investment Portfolio Dan Wan, Kaiye Gao, Xiangbin Yan 2026, 34 (9):  48-56.  doi: 10.16381/j.cnki.issn1003-207x.2024.1753 Abstract ( 6 )   HTML ( 0 )   PDF (1315KB) ( 10 )   Save Buffer management is a crucial component in critical chain project management （CCPM） as it helps address the risks and uncertainties inherent in project execution. Traditional buffer management methods primarily focus on risk characteristics and attribute factors to allocate and control the project buffer in a static manner. These approaches often fail to account for the dynamic nature of the project environment， leading to inefficient buffer configuration and excessive buffer consumption. As a result， projects may suffer from suboptimal resource allocation， increased costs， and delays due to poor responsiveness to real-time project variations. To address these challenges， a dynamic buffer allocation and monitoring method is proposed for critical chain project based on investment portfolio theory. Unlike traditional methods， the proposed approach reconceptualizes buffer allocation as an optimization problem aimed at maximizing expected buffer returns， subject to the constraint that buffer returns second-order stochastically dominate the baseline returns. To achieve this， a second-order stochastic dominance-based optimal buffer allocation model is established， explicitly incorporating buffer control costs to enhance resource utilization efficiency. Furthermore， the proposed method integrates uncertainties in project activity durations， as well as dynamic changes in activity link execution and buffer consumption patterns， to construct a buffer action matrix for adaptive buffer allocation and monitoring. By continuously updating buffer distribution based on project progress and risk fluctuations， the model ensures that buffer resources are optimally allocated where they are most needed， minimizing unnecessary buffer waste while maintaining high project completion reliability. Simulation results demonstrate that， compared with the traditional static allocation method， the proposed method offers significant improvements in several key performance indicators， including the probability of on-time project completion， average buffer consumption ratio， actual project duration， and effective project output. This enhancement in buffer efficiency not only boosts the adaptability of critical chain project scheduling but also improves project stability and risk absorption capability. The findings of this study provide valuable theoretical insights and practical strategies for advancing buffer management practices， offering meaningful contributions to the management of complex projects characterized by uncertainty and variability， with direct implications for improving project performance and ensuring timely delivery. Figures and Tables | References | Related Articles | Metrics

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A Social Network Large-scale Group Decision-making Method Based on Dynamic Conformity Behavior Yuan Xu, Haiyan Xu, Zhiwei Xu 2026, 34 (9):  57-67.  doi: 10.16381/j.cnki.issn1003-207x.2024.2043 Abstract ( 9 )   HTML ( 0 )   PDF (1280KB) ( 18 )   Save In order to reduce divergences among experts and enhance the scientific rigor of decision results， the consensus reaching process（CRP） has become a crucial stage in group decision-making. During the CRP， conformity behavior may exert a significant influence on both the decision process and its outcomes. However， most existing studies assume conformity behavior to be static， which deviates from the complex and ever-changing reality. To address this limitation， a social network large-scale group decision-making method is proposed that incorporates dynamic conformity behavior. Specifically， a K-medoids clustering algorithm is employed to partition the large group into several subgroups. A dynamic conformity degree is then defined by jointly considering individual and group factors， based on which a dynamic ideal adjustment point is introduced to model the dynamic conformity behavior. Furthermore， by dynamically adjusting the limited budget based on subgroup consensus levels， a maximum consensus model under dynamic conformity behavior is constructed. Numerical results demonstrate that the presented method not only substantially reduces decision-making costs but also effectively improves consensus levels. The presented method exhibits strong consensus efficiency and behavioral adaptability， thereby offering a novel theoretical perspective and a practical framework for modeling dynamic conformity behavior and supporting complex group decision-making under evolving environments. Figures and Tables | References | Related Articles | Metrics

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Airline Network Capability Control and Overbooking with Deep Reinforcement Learning Chunjuan Fu, Wenjie Bi, Haiying Liu 2026, 34 (9):  68-78.  doi: 10.16381/j.cnki.issn1003-207x.2024.2195 Abstract ( 9 )   HTML ( 0 )   PDF (1464KB) ( 4 )   Save The challenges of airline network capacity control and overbooking strategies in the context of a choice-based demand model is explored in this research. Traditionally， most studies in this area have relied on independent demand models， where passenger behavior is assumed to be independent and the target product for each passenger is a fixed option. However， with the rise of low-cost carriers and increasing competition， simulating the decision-making process of passengers selecting from a range of products has become a key issue. The core of the problem lies in optimizing seat （resource） allocation across multiple flight segments， with the goal of maximizing revenue while managing the potential losses caused by passenger no-shows and overbooking. At each time step， it is necessary to decide which products to offer， and as the number of product types increases， the number of possible product combinations grows exponentially， leading to a large action space. Additionally， passenger behavior is uncertain， and the state transition rules are complex. To address this problem， the research models the issue as a Markov Decision Process （MDP）， where the state represents the total booking amount of each product at each time step. The action space consists of determining which products to open at each time step， considering resource constraints and overbooking limits. To efficiently solve this problem， the research proposes a deep reinforcement learning （DRL） algorithm based on the Branching Dueling Q-Network （BDQ） framework， named Max-BDQ （MBDQ）. This algorithm significantly reduces the computational complexity by decomposing the high-dimensional action space into multiple independent subspaces. It also combines techniques such as Double Deep Q-Network （Double DQN）， prioritized experience replay， and Dueling Deep Q-Network （Dueling DQN）， which improve the stability and convergence speed of the model. MBDQ incorporates several key enhancements， including a modified Q-value calculation method， an improved neural network architecture， and hyperparameter optimization， all of which enable the algorithm to adapt to dynamic and uncertain environments. A linear programming-based revenue upper bound calculation method is proposed and extensive experiments are conducted by setting different passenger arrival patterns and load factors to evaluate the performance of the MBDQ algorithm. The experimental results show that the average revenue of the MBDQ algorithm is approximately 87% of the revenue upper bound， with the highest performance exceeding 90%. Compared to a full-product open strategy， MBDQ yields about 10% higher revenue， and its performance further improves as the load factor increases. Compared to BDQ， MBDQ yields about 6% higher revenue. These demonstrate the robustness and efficiency of MBDQ in handling large-scale， high-dimensional decision spaces. A practical solution is provided for enhancing airline revenue management and offers theoretical support for dynamic optimization in high-dimensional systems. The findings also highlight the potential of deep reinforcement learning as a powerful tool for solving complex， large-scale revenue management problems. Figures and Tables | References | Related Articles | Metrics

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Multi-Criteria Preference Learning Method Considering Context-Dependent Decision Behavior Qian Liang, Zhongquan Hu, Zhen Zhang, Haomin Wang 2026, 34 (9):  79-89.  doi: 10.16381/j.cnki.issn1003-207x.2024.1896 Abstract ( 14 )   HTML ( 0 )   PDF (1782KB) ( 10 )   Save Multi-criteria decision analysis （MCDA） often requires decision makers （DMs） to provide preference information for a subset of reference alternatives， thereby reducing their cognitive burden while capturing their underlying value functions. When a DM’s holistic preference information is inconsistent with an assumed model， either some assignments cannot be reproduced， or the DM must revise their preferences. In this study， a specific challenge is addressed： the inconsistency arising from criterion context-dependent decision behavior. As DMs gather more information about alternatives， they may adopt different evaluation strategies across various criteria contexts， leading to inconsistencies in their preference information. To tackle this issue， the DM’s preferences are modeled using a piecewise linear value function and develop a two-stage methodological framework. In the first stage， an optimization model is constructed to assess the consistency of the provided preference information and to determine the number of value functions required for an accurate reconstruction. In the second stage， leveraging the principle of parsimony， an optimization model is introduced to select a complementary set of value functions that best reconstruct the DM’s preference information. Furthermore， classification and regression tree （CART） algorithms are integrated to extract rules that correlate different criteria contexts with the corresponding value functions， thereby enhancing the interpretability and decision support of the model. The proposed approach is validated through a comprehensive case study on the evaluation of research units. Detailed numerical experiments， comparative assessments， and simulation analyses demonstrate that our method effectively captures the context-dependent decision behavior of DMs， while also improving the robustness and explanatory power of the preference model. Figures and Tables | References | Related Articles | Metrics

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Optimal Online Strategy for the\mathit{k}-secretary Search Problem Based on\lambda-competitive Rate Wenming Zhang, Zhengfang Guo 2026, 34 (9):  90-98.  doi: 10.16381/j.cnki.issn1003-207x.2024.0330 Abstract ( 6 )   HTML ( 0 )   PDF (596KB) ( 2 )   Save In this study， the onlinek-secretary search problem is studied basing on the\lambda-competitive rate criterion （where，\lambdais the preference）. Firstly， a threshold-type online strategyOK{S}_{\lambda }is designed basing on a nonlinear programmingNL{P}_{\lambda }with variables\left\{{\phi }_{\lambda ,\mathrm{1}}^{\mathrm{*}},{\phi }_{\lambda ,\mathrm{2}}^{\mathrm{*}},\cdots ,{\phi }_{\lambda ,k}^{\mathrm{*}},{\gamma }_{\lambda }^{\mathrm{*}}\right\}. The steps of solving for the thresholds {\phi }_{\lambda ,\mathrm{1}}^{\mathrm{*}},{\phi }_{\lambda ,\mathrm{2}}^{\mathrm{*}},\cdots ,{\phi }_{\lambda ,k}^{\mathrm{*}}are given and it is further proved thatm\le {\phi }_{\lambda ,\mathrm{1}}^{\mathrm{*}}\le {\phi }_{\lambda ,\mathrm{2}}^{\mathrm{*}}\le \cdots \le {\phi }_{\lambda ,k}^{\mathrm{*}}\le M. The strategyOK{S}_{\lambda }is proved to be optimal in the sense of the\lambda-competitive rate and its\lambda-competitive rate is{\gamma }_{\lambda }^{\mathrm{*}}.In the special case analyses when\lambda =\mathrm{1}and\lambda =\mathrm{0}， it is found that when\lambda =\mathrm{1}the competitive rate is just the competitive ratio， which is consistent with the results of Lorenz et al.； when\lambda =\mathrm{0}the competitive rate is just the competitive difference， where the explicit expression of{\gamma }_{\lambda }^{\mathrm{*}}can be obtained. It is further proved that the threshold{\phi }_{\mathrm{0},i}^{\mathrm{*}}which is based on competitive difference is larger than the threshold{\phi }_{\mathrm{1},i}^{\mathrm{*}}which is based on the competitive ratio， implying that the online strategy based on the competitive ratio is more conservative. In the special case analyses whenk=\mathrm{1}， the onlinek-secretary search problem degenerates into the the classical online time series search problem proposed by El-Yaniv et al. and optimal online strategies based on competitive ratio and competitive difference are both presented， respectively.Finally， numerical simulation experiments reveal that： （1） the larger the preference\lambdathe smaller the threshold{\phi }_{\lambda ,i}^{\mathrm{*}}， i.e.， the larger the preference\lambdathe more conservative the strategy is， and vice versa the more aggressive it is； （2） When the expectation of a candidate's rating sequence is small， an online strategy with a large preference should be selected； when the expectation of the rating sequence is moderate， an online strategy with a moderate preference should be selected； when the expectation of the rating sequence is large， an online strategy with a small preference should be selected. Figures and Tables | References | Related Articles | Metrics

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Coordinated Decision of Extended Warranty Price and Service Level Considering Channel Preference Yuanpeng Ruan, Xin Zhen, Xianghai Ding, Xinggang Luo 2026, 34 (9):  99-108.  doi: 10.16381/j.cnki.issn1003-207x.2024.2095 Abstract ( 10 )   HTML ( 0 )   PDF (1466KB) ( 5 )   Save Extended warranty （EW） services have been regarded as a key strategy for enhancing profit growth in supply chains involving manufacturers and retailers. With the development of digital technologies， dual-channel sales， where both manufacturers and retailers sell directly to consumers， have become increasingly prevalent. In this context， critical decisions regarding the determination of EW pricing and service levels have been raised， particularly under the influence of customer channel preference shaped by individual tendencies and product characteristics. Although prior studies have examined various aspects of EW service management， such as coordinated pricing， service level decisions， and channel strategies under dual-channel settings， the joint decision-making of EW price and service level in such contexts has been largely overlooked. Specifically， the influence of customer channel preference on the strategic behaviors and profit outcomes of supply chain members has not been systematically explored. In order to solve the above problems， a dual-channel supply chain consisting of a single manufacturer and a single retailer is considered. Two models are developed in which either the manufacturer or the retailer determines the pricing and service level of the extended warranty. How customer channel preference influences the decision-making behaviors of the manufacturer and retailer， along with their respective profits and the overall supply chain profit under different decision-making structures， is explored. Finally， numerical experiments are conducted to further investigate and validate the conclusions. The findings reveal that： （1） Due to the investment threshold required to enter the extended warranty market， both manufacturers and retailers need a certain proportion of customer demand to maintain the economic viability of both parties. （2） Under high EW price sensitivity， when the manufacturer decides on the EW price and service level，as the proportion of customers purchasing EW from the manufacturer increases，the manufacturer’s profit decreases，while the retailer's profit and the overall supply chain profit increase. In this scenario，the manufacturer should lower the product wholesale price and EW price to protect its profit， while the retailer should increase the product retail price to enhance product revenue. （3） Conversely， under high EW price sensitivity， when the retailer decides on the EW price and service level， as the proportion of customers purchasing EW from the manufacturer increases， the profits of the manufacturer， retailer， and the entire supply chain all decrease. The manufacturer should lower the wholesale price to stimulate the retailer's procurement， while the retailer should raise the product retail price and EW price， and reduce the service level when product price sensitivity is low， to increase sales and EW revenue. （4） For the supply chain， the model where the retailer determines the EW service is more advantageous. The theoretical understanding of dual-channel coordinated decision is enriched， and actionable insights are provided for supply chain managers. Figures and Tables | References | Related Articles | Metrics

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Intelligent Redeployment of Electric Ambulances Considering Temporal and Spatial Uncertainty of Demand Jia Liu, Jie Cao, Yi Xiong 2026, 34 (9):  109-119.  doi: 10.16381/j.cnki.issn1003-207x.2024.2042 Abstract ( 50 )   HTML ( 0 )   PDF (1569KB) ( 12 )   Save Ambulances， as scarce resources in the Emergency Medical Service （EMS） system， require rational deployment to significantly improve EMS quality. The intelligent redeployment problem of electric ambulances-specifically， how to intelligently reselect deployment stations based on dynamically changing demand after completing emergency missions is studied， in order to address the uncertainty in call request rates （\mathit{\lambda }）. In this study， “intelligence” refers to the use of deep reinforcement learning methods to automatically optimize redeployment decisions in response to environmental uncertainties and dynamic changes. Current mainstream redeployment decision methods typically rely on precise estimation of\mathit{\lambda }. However， in highly uncertain environments， especially when \mathit{\lambda } cannot be accurately predicted， these methods perform poorly. To address this， an intelligent dynamic decision-making method for electric ambulance redeployment is proposed that considers state observation uncertainty. First， the EMS system is modeled as a Markov Decision Process （MDP）， and basis functions are introduced based on approximate dynamic programming theory to compress system state variables， thereby solving the dimensionality curse problem. Second， uncertainty is incorporated into the observation of state variables， a new policy gradient calculation formula is derived， and a robust Actor-Critic algorithm is designed to learn optimal redeployment strategies. Experimental results show that the robust Actor-Critic algorithm demonstrates significant advantages in both average response time and on-time response rate. Building on this， the impact of different charging strategies on ambulance performance is explored， management suggestions for electric ambulance redeployment is proposed， and theoretical support and practical guidance for optimizing EMS systems is provided. Figures and Tables | References | Related Articles | Metrics

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P-robust Optimization of Emergency Location-allocation Problem Considering Deprivation Cost Ling Zhang, Xiaojin Zhuo, Jing Wang 2026, 34 (9):  120-132.  doi: 10.16381/j.cnki.issn1003-207x.2024.0518 Abstract ( 10 )   HTML ( 0 )   PDF (2102KB) ( 8 )   Save Natural disasters pose a great threat to humanity. In order to improve the ability of disaster relief network， it focuses on pre-disaster facilities location and post-disaster capacity allocation and evacuation of disaster victims under uncertain demand. Considering two different types of disaster victims and deprivation costs， a scenario based robust optimization model is developed to minimize the expected total cost. Finally， taking the Sichuan earthquake as a case， numerical experiments and sensitivity analysis are performed to prove the effectiveness of the model and obtain some management insights. The results show that comparing with the deterministic model and stochastic programming model， p-robust optimization model can effectively enhance the cross-scenario robustness of decision-making. In addition， deprivation cost plays an important role in balancing economic benefits and psychological pain in decision-making. Expanding the capacity of emergency reserve warehouse can reduce the risk of shortages. Besides， emphasizing the evacuation of disaster victims can effectively control the deterioration of the disaster and reduce casualties. Figures and Tables | References | Related Articles | Metrics

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Two-stage Robust Guaranteed Delivery in Targeted Display Advertising Xin Sui, Wenqiang Dai, Ziqi Wang 2026, 34 (9):  133-141.  doi: 10.16381/j.cnki.issn1003-207x.2023.1055 Abstract ( 10 )   HTML ( 0 )   PDF (981KB) ( 2 )   Save As technology advances and the economy experiences rapid growth， the internet advertising has witnessed an unprecedented boom. Guaranteed display advertising plays a significant role in internet advertising. A successful display ad must not only offer a wide range of presentation styles but should also aim for widespread exposure. However， guaranteed delivery strategy is influenced by various factors， with the greatest challenge being the uncertainty in the online behavior of internet users. In this context， the study of guaranteed display ad delivery strategy that considers uncertainty holds practical significance. Additionally， strategy is typically determined before the arrival of internet users and advertising placements， and the effectiveness of strategy can be validated through the recourse of performance. Therefore， adopting a two-stage model to address guaranteed display ad delivery issues provides more valuable guidance. In the realm of display advertising， the publisher owns advertising platforms， where advertisers represent products. When users browse the publisher's website， impressions （random variable） are generated， with each impression corresponding to an opportunity for a user to view an ad on the webpage. As users browse web pages， the publisher can categorize them into different segments based on characteristics. Once the publisher identifies the specific target segments of advertisers， ads on ad slots can be automatically loaded and displayed to users with different characteristics. Regarding guaranteed delivery， the publisher signs contracts with advertisers in which advertisers require demands， target segments and specific period. The contract also specifies penalties for shortage and excess of demand. Based on this， a two-stage distributionally robust model is formulated from the perspective of the publisher with the objective of maximizing overall revenue， in which the mean and variance of impression supply as the only known distribution information. The objective function consists of two parts： the fairness of allocation in the first stage and the publisher's expected revenue in the second stage. To better solve the proposed model， a cutting-plane algorithm is designed. Experimental results compared with the benchmark model（Sample Average Approximation - SAA） demonstrates the delivery strategy based on the method proposed in this paper effectively mitigates the interference caused by uncertainty and exhibits robustness. At the same time， some management insights are provided for the publisher. Figures and Tables | References | Related Articles | Metrics

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Affine Adjustable Robust Optimization Strategy of Emergency Facility Location and Multi-period Allocation for Supplies Huali Sun, Yixiang Zhang, Shuo Liu 2026, 34 (9):  142-152.  doi: 10.16381/j.cnki.issn1003-207x.2024.0663 Abstract ( 8 )   HTML ( 0 )   PDF (1617KB) ( 4 )   Save Natural disasters have inflicted significant casualties and economic losses on society， with earthquakes being the most devastating. From 1993 to 2017， earthquakes in China resulted in 74，000 fatalities， 474，000 injuries， and economic losses amounting to 1.1 trillion yuan. After disasters， it is critical to strategically establish a network consisting of material supply centers and temporary distribution centers near affected areas， along with implementing timely material allocation to meet the demands of disaster-stricken regions. Furthermore， as post-disaster information evolves dynamically， emergency relief decisions must be continuously adapted to enhance operational efficiency. Efficient material transportation through both direct and indirect modes can ensure timely delivery to disaster sites. To manage risks and address uncertain demand for emergency supplies， a hybrid transportation strategy combining both modes is critical. Direct transport involves using vehicles to deliver materials directly from the supply center to the disaster site， while indirect transport first utilizes vehicles to transfer supplies to a temporary distribution center， from which helicopters transport them to the disaster area. Given the dynamic nature of available emergency resources， such as vehicles， helicopters， and material stocks， it is imperative to divide the emergency response into multiple decision-making cycles. Addressing this integrated optimization problem—encompassing the location of emergency facilities and multi-cycle distribution of materials—is vital for enhancing post-disaster relief efforts. The uncertain demand for commodities in affected areas and the changes in the availability of emergency resources are addressed. A robust optimization model is proposed for the location of emergency facilities and commodity distribution using both direct and indirect transportation modes， including vehicles and helicopters. The objective is to determine the location of supply centers and temporary distribution centers， as well as the distribution plan for each period， to maximize the fulfillment of needs at disaster sites while minimizing transportation time. The model utilizes an affine adjustable robust optimization method， where decision variables and state variables are expressed as affine functions of demand. Affine tunable robust optimization is a branch of tunable robust optimization in which uncertain parameters are represented by uncertain sets. To maintain the model's integrity， the uncertainty of material demand is described using polyhedral sets. Some variables， called “unadjustable variables”， must be determined before the implementation of uncertain parameters， while others， referred to as “adjustable variables”， can be adjusted after the uncertainty is revealed. According to affine rules， the adjustable variables are expressed as affine functions of uncertain parameters and substituted into the original model for strong dual transformation， facilitating solution computation. Case studies of the Wenchuan earthquake are conducted， and CPLEX is used to simulate and solve the model after preprocessing. The main findings of this study are as follows： （1） The affine adjustable robust optimization model outperforms both deterministic models and sample-based stochastic programming models in terms of resilience； （2） Predicting and reducing the uncertainty of information can better meet the supply demands in the disaster area； （3） Increasing the number of decision-making cycles improves the ability to meet material demand effectively； and （4） Increasing the number of rescue transport vehicles， distribution center capacity， and overall cost budget enhances material availability， though excessive quantities may lead to waste. Multiple sources of uncertainty are considered， including demand， supply， and transportation time， but the casualty evacuation problem is not addressed. Future studies will integrate the location of emergency facilities， multi-cycle casualty transport， and multi-cycle material distribution under uncertain conditions. Figures and Tables | References | Related Articles | Metrics

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Transportation Strategies Considering the Service Uncertainty of Online Freight Platforms Chenchen Yang, Xiaolong Guo, Yangguang Zhu, Wenwen Jiang 2026, 34 (9):  153-163.  doi: 10.16381/j.cnki.issn1003-207x.2024.1504 Abstract ( 26 )   HTML ( 0 )   PDF (2011KB) ( 8 )   Save The emergence of Online Freight Platforms （OFPs） has revolutionized the road freight industry by aggregating fragmented social transportation capacity， enhancing market efficiency， and promoting intensive resource utilization. However， the inherent service uncertainty of OFPs， stemming from their limited control over independent drivers， poses a critical challenge to their ability to serve high-value logistics segments. A game-theoretic model incorporating a risk-averse shipper， an OFP， and a Traditional Logistics Service Provider （TLSP） is developed to investigate the service commitment and pricing strategies of OFPs under service uncertainty. The analysis yields several counterintuitive yet insightful findings. First， while OFPs are inclined to offer service level commitments to highly risk-averse shippers to assure stability， the promised service level under commitment is actually lower than the average level provided without commitment. This paradoxical result arises from the transfer of risk responsibility： when bearing the risk themselves， OFPs are motivated to reduce costly efforts and optimize their cost structure， leading to a stable but lower service output. Second， a service commitment alone is not a sufficient condition for shippers to choose an OFP. Shippers will only opt for an OFP over a TLSP if the former possesses a significant cost advantage （i.e.， a lower cost factor for service effort）. Furthermore， by characterizing the strategic equilibrium under varying degrees of risk aversion and cost configurations， it is identified that the conjunction of low-cost advantage and high-risk aversion constitutes the critical condition under which an OFP should offer service commitment to secure the shipper’s cooperation. Substantial theoretical contributions are made by unveiling the intricate strategic interactions among participants in the digital freight ecosystem. It provides a novel theoretical explanation for the operational mechanisms of OFPs， particularly the effort adjustment and risk-transfer incentives behind service commitment. Moreover， it offers practical managerial implications for OFPs in designing their service and pricing strategies and guides shippers in making informed outsourcing decisions in the presence of service uncertainty. Figures and Tables | References | Related Articles | Metrics

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Optimization of Airport Electric Ferry Vehicle Scheduling Considering Flight Priorities Chenchen Du, Xue Han, Peixin Zhao 2026, 34 (9):  164-172.  doi: 10.16381/j.cnki.issn1003-207x.2024.1287 Abstract ( 68 )   HTML ( 0 )   PDF (1415KB) ( 6 )   Save Electrification of ground service vehicles has emerged as a new trend in airport ground operations. Insufficient number of vehicles and improper scheduling are significant contributors to flight delays. Existing research on the scheduling of airport ground support vehicles predominantly focuses on fuel-powered vehicles. The scheduling problem of airport electric ferry vehicles under the condition of limited vehicle resources is studied. Considering the flight service priorities， a bi-objective mixed-integer programming model with the objective of minimizing the flight delay cost and the vehicle idling time is constructed. To improve the solving efficiency， according to the characteristics of the model， an improved genetic algorithm is integrated within the framework of the boxed line method to solve it. The effectiveness of this algorithm compared with the ε-constraint method and the classical genetic algorithm is validated through a comparative analysis using the actual flight data from a hub airport. A theoretical foundation and practical guidance for the scheduling operations of electric ferry vehicles at airports is provided， holding significant implications for promoting the green transformation of airports， enhancing passenger satisfaction and improving operational efficiency. Figures and Tables | References | Related Articles | Metrics

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A Dynamic Scheduling and Preventive Maintenance Method Based on Product-machine Assignment Yang Yang, Bin Zhang, Chenghung Wu 2026, 34 (9):  173-183.  doi: 10.16381/j.cnki.issn1003-207x.2024.1431 Abstract ( 47 )   HTML ( 0 )   PDF (1643KB) ( 17 )   Save A joint production dispatching and preventive maintenance problem in multi-product， heterogeneous-machine manufacturing is addressed through a Product-Machine Assignment （PMA） framework. The assignment is formulated as a mixed-integer linear program that matches product types to machines and controls per-machine variety through a penalty parameter \kappa， achieving a balance between throughput and machine specialization. The assignment decomposes the system into independent multi-product single-machine subproblems， each solved as a continuous-time Markov decision process to coordinate dispatching and preventive maintenance. Combining these yields a near-optimal system policy with computational complexity growing approximately linearly in the number of machines. Numerical experiments on 30 instances， compared with C\mu， First-Come-First-Served， and Round-Robin under throughput and cycle-time metrics， show that PMA maintains throughput while notably reducing cycle time. Additional tests under non-Markovian inter-event times and a real semiconductor workstation dataset exhibit consistent performance. The results indicate that PMA provides a scalable and interpretable approach for real-time joint dispatching and maintenance decisions in large heterogeneous manufacturing systems. Figures and Tables | References | Related Articles | Metrics

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Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply in Same-Day Delivery Jianhua Xiao, Liang Chen, Liujiang Kang, Xujiang Lou 2026, 34 (9):  184-196.  doi: 10.16381/j.cnki.issn1003-207x.2024.2034 Abstract ( 122 )   HTML ( 0 )   PDF (1972KB) ( 71 )   Save The demand for same-day delivery （SDD） has increased rapidly over the past few years and has become a popular delivery option for customers. In this paper， the Autonomous Vehicle Assisted Delivery Problem with Dynamic Resupply （AVADDR） is proposed to address the challenge of high-frequency， time-sensitive stochastic requests in same-day delivery. Throughout the day， customers place requests for same-day delivery （SDD） services without prior knowledge of the exact timing or delivery locations. The dispatcher then dynamically allocates the courier with autonomous vehicle resupply to fulfill these requests. It is assumed that the autonomous vehicle performs multiple trips from the warehouse to replenish the courier at any required time while the courier delivers the orders. The AVADDR is decomposed into two stages： routing optimization and dynamic resupply. A mathematical programming model is developed for AVADDR to minimize the delivery time. An adaptive large neighborhood search algorithm （ALNS） is designed to solve the routing optimization problem， and myopic and adaptive resupply strategies are proposed to address the dynamic resupply issue. Comprehensive testing and analysis demonstrate the superior effectiveness of our approach compared to benchmarks. The approach can provide effective decision-making support for same-day delivery companies with high time-sensitivity requirements. In the end， several managerial implications are obtained through sensitivity analysis experiments. （i） It is advisable to select the distribution center within the service area in SDD. （ii）The sorting time is an important factor influencing the total time required to complete same-day deliveries. If enterprises can conduct sorting in advance before dispatching for delivery， it can effectively reduce the total delivery completion time. Figures and Tables | References | Related Articles | Metrics

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Home Health Care Scheduling for Clustered Residents Jie Zhou, Kai Wang 2026, 34 (9):  197-208.  doi: 10.16381/j.cnki.issn1003-207x.2024.2240 Abstract ( 24 )   HTML ( 0 )   PDF (1404KB) ( 68 )   Save With the rapid economic growth and accelerated urbanization in China， there is an increasing demand for health management and long-term disease treatment. Home health care （HHC） is a type of medical service where professional caregivers， such as nurses， therapists， or doctors， provide in-home care for patients. It mainly serves the elderly， people with chronic illnesses， or those recovering from surgery. It focuses on a novel home health care routing and scheduling problem for clustered residents in this paper. Unlike residents in Western countries who often live dispersedly， urban residents in China typically cluster together in communities， inevitably leading to a large number of requests for home healthcare services in the same area during the same period. The traditional “one caregiver per vehicle” service model， where each caregiver travels alone to visit patients， is simple to schedule but incurs high operational costs when patient locations are spatially clustered. To address this challenge， a novel team-based “multiple caregivers per vehicle” service model is proposed. In this model， multiple medical staff travel together on a bus， disembark at designated stops simultaneously， and individually provide personalized care to patients in the surrounding area. To minimize the total cost of home healthcare centers， a mixed-integer programming model is established， which simultaneously determines team composition， vehicle routes， and the sequence of patient visits for nurses. Given the NP-hardness of the studied problem， an improved adaptive large neighborhood search algorithm （IALNS） is developed to generate solutions. Considering the two-echelon routing structure arising from the team-based mode， a total of seven destroy operators and seven repair operators are specifically designed. To further improve the solution quality， a penalizing strategy is applied to handling infeasible solutions. Computational results on small-sized and large-sized test instances are conducted. For small-sized instances， IALNS performs better than CPLEX in terms of both solution quality and computation time. For large-sized instances， IALNS outperforms the simulated annealing （SA）， variable neighborhood search （VNS）， and ALNS allowing infeasible solutions. In addition， sensitivity analysis of key parameters is conducted to provide managerial insights to home healthcare centers. Most importantly， the team-based service model provides greater cost advantages compared to the traditional individual-caregiver model. Figures and Tables | References | Related Articles | Metrics

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Multi-Objective Routing Optimization of Takeout Delivery Considering Rider Rewards and Penalties of Distribution Timeliness Hao Xiong, Xiaodie Chen, Huili Yan 2026, 34 (9):  209-224.  doi: 10.16381/j.cnki.issn1003-207x.2024.2209 Abstract ( 12 )   HTML ( 0 )   PDF (2215KB) ( 31 )   Save Presently， the takeaway industry continues to demonstrate robust growth， with takeaway services becoming increasingly entrenched in people's daily lives. Nevertheless， given the differences in focal points of platforms， consumers， and riders， a pronounced discord of interests has emerged among the three parties， even hindering the development of the industry. Distribution timeliness， a pivotal factor， impacts not only customer satisfaction and platform profits but also directly influences the rewards and punishments for riders. To address these challenges， a multi-objective routing optimization problem is proposed for takeout delivery， considering the rewards and punishments for riders based on the perspective of distribution timeliness. The primary aim of this study is to further balance the interests of all parties dynamically. A soft time window concept is adopted to portray customer expectations and tolerance of delivery time， and a linear time satisfaction function is constructed to assess customer satisfaction. Concurrently， the rider's rewards and penalties are designated， encompassing the rider's overtime penalty cost based on on-time rate， the order overtime penalty cost in step-pricing style， and the performance reward based on satisfaction. The functions of rider revenue， driving cost， waiting cost， and platform revenue are then combined to establish a complex objective optimization model for maximizing customer satisfaction， rider revenue， and platform profit. Secondly， an enhanced NSGA-II algorithm based on KNN classification is proposed. The proposed algorithm first allocates orders based on geographic distance and time window， generates high-quality and diverse initial populations， and subsequently outputs a Pareto solution using the enhanced NSGA-II algorithm. To assess the efficacy of the proposed algorithm， two ordinary region examples and one commercial region example are utilized for testing purposes. It then compares this algorithm with the traditional NSGA-II and MOPSO algorithms for validation purposes. The convergence of the algorithm and the diversity of the solution set are further verified by analyzing the iterative convergence curves of each objective function as well as the indicators of spacing and maximum spread of the solution set. Finally， a comparative analysis of customer satisfaction， rider revenue， and platform profit under different reward and punishment rules is conducted. It is indicated that the platform's punishment measures can enhance delivery efficiency， foster customer satisfaction and augment platform revenue. Equitable sanctions have the potential to engender a mutually beneficial scenario for all three parties. While the incentive mechanism may temporarily reduce platform revenue， it can enhance delivery efficiency and rider revenue. Consequently， a theoretical foundation is offered for the coordination of interests among multiple parties in the future of takeaway services and the establishment of a platform's reward and punishment mechanism for riders. Figures and Tables | References | Related Articles | Metrics

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Model and Algorithm for Parallel Batch-processing Machines Scheduling Problem in Aerospace Composite Materials Manufacturing Shaoxiang Zheng, Naiming Xie, Qiao Wu 2026, 34 (9):  225-236.  doi: 10.16381/j.cnki.issn1003-207x.2023.1745 Abstract ( 40 )   HTML ( 0 )   PDF (793KB) ( 14 )   Save The autoclave molding scheduling problem in aerospace composite materials manufacturing is investigated and identified as the parallel batch-processing machines scheduling problem with two-dimensional constraints. A novel compact mathematical formulation that eliminates symmetry and minimizes the makespan is developed to define the problem with incompatibility and linear batch setup times. An iterative approximation search algorithm is proposed to handle the problem： heuristic and exact algorithms are combined in the algorithm to find a feasible solution with a better objective value through an iterative process which employs an exact method so that the problems are solved with efficiency and effectiveness. In terms of the execution on different randomly generated instances， the results show that： （1） the presented model is much more efficient than the classic one； the efficiency and effectiveness of the model and the algorithm are compared to demonstrate the superiority in solving the problem； and both the developed model and algorithm outperform the compared method in a statistical sense. In the end， the properties and performance of the model and algorithm are concluded based on the simulation experiments， and the specific managerial implications are provided. Figures and Tables | References | Related Articles | Metrics

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The Operation Decision of Service Providers Based on Extra Waiting Area Value-added Service Wentao Zhan, Minghui Jiang, Xuchuan Yuan, Yi Zhao, Chengzhang Li, Chencan Lin 2026, 34 (9):  237-247.  doi: 10.16381/j.cnki.issn1003-207x.2023.1707 Abstract ( 11 )   HTML ( 1 )   PDF (1205KB) ( 6 )   Save The rapid development of the service industry plays a significant role in driving economic growth. To attract customers， many service providers not only offer base services but also introduce premium paid services such as Extra Waiting area value-added Service （EWS）. These extra value-added services have become critical in the current service industry landscape. Not only do service providers offer EWS themselves， but third-party service companies also participate through collaborative modes. This raises challenges for service providers， such as how to make optimal decisions when operating both base services and EWS， and how to collaborate with third-party companies to maximize overall benefits.Therefore， it focuses on the following questions in this study： First， in a centralized operational mode， how should service providers determine the optimal EWS level and its pricing？ Second， when EWS is provided by third-party companies， how should the optimal EWS level be set， and how should service providers adjust the pricing strategy for base services？ Finally， what are the differences in EWS levels， pricing strategies， and profit performance between centralized and decentralized modes？Based on customer utility in service， the M/M/1 queuing model is used to characterize customer behavior in queues. On this basis， both a centralized mode for service providers and a collaborative mode involving third-party companies are constructed， allowing us to analyze the optimal decisions and profit performance of service providers and third-party companies. The findings reveal that　（1） As customers place greater importance on EWS， indicated by increased sensitivity， the provider of EWS does not need to continuously raise the EWS level to achieve optimization. （2） In the short term， under centralized operations， EWS has an insignificant impact on the pricing of base services. However， in the long term， service providers need to moderately lower the price of base services to achieve higher profits. （3） Under decentralized operations， whether service providers and third-party companies can achieve higher unit profits in the long term compared to the short term depends on customer conversion rates. （4） Whether in short-term or long-term operations， centralized operations enable service providers to achieve higher profits from both base services and EWS. However， for service providers with limited funds and difficulties in independently operating EWS， decentralized operations may be a better strategic choice. Figures and Tables | References | Related Articles | Metrics

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Optimal Logistics Outsourcing Mode Selection of Fresh Cold Chain Transport Platform Jun Chen, Hailong Liu, Xin He 2026, 34 (9):  248-257.  doi: 10.16381/j.cnki.issn1003-207x.2024.0018 Abstract ( 15 )   HTML ( 0 )   PDF (1241KB) ( 22 )   Save At present， the mismatch between supply and demand of cold chain transport is quite prominent in China. On the demand side， it is difficult for cargo owners to find cars， slow to find cars. Multi-stage transportation and non-standardized temperature control frequently cause a lot of food loss and waste. On the supply side， the distribution of agricultural products is not balanced， and the drivers are often caught in the shortage of goods and the high cost of empty driving. In the face of industry pain points， SF Express cold transport， etc.， actively explore and practice the platform operation mode by integrating dispersed social cold transport resources and provide customers with whole-process cold transport integration services. However， in actual operation， the cold transport enterprises of different sizes on the platform are limited by their own fresh-keeping capacity， and often can only complete half-way of the cold transportation. This specific freight market environment presents a new challenge for logistics platforms to choose logistics outsourcing modes.Different from　normal logistics outsourcing， the development of cold chain logistics in China is not long， the number of logistics enterprises that can undertake cold chain transport business is small and the core business is concentrated in trunk road transport， the fresh transport capacity is different. More prominently， the “first kilometer” transportation is mostly completed by local small and medium-sized logistics enterprises， the thermal insulation performance of the carriage is poor， and the temperature control technology is relatively backward. In such a realistic environment， it is contrary to objective facts for platform vendors to independently determine the freshness-keeping level and require carriers to achieve it. Therefore， a new strategic decision-making mechanism is proposed in which platform operators can influence the freshness-keeping decision-making of carriers through outsourcing price. Figures and Tables | References | Related Articles | Metrics

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Posterior Price Matching of a Retailer Based on Consumers' Waiting Behavior Xingzheng Li, Jinpeng Xu, Tianfang Zan, Gengzhong Feng 2026, 34 (9):  258-271.  doi: 10.16381/j.cnki.issn1003-207x.2024.0106 Abstract ( 10 )   HTML ( 0 )   PDF (1488KB) ( 2 )   Save With the evolution of e-commerce platforms， it has become common for consumers to delay purchases， anticipating future discounts. Posterior price matching policies help reduce this waiting behavior， especially before major sales events （e.g.， Double 11 shopping festival）. Under such a policy， consumers can request compensation from a retailer if they find a lower price for the same product within a specified period after purchase. The optimal strategy for a retailer to make scientific pricing and price matching decisions， considering consumer waiting behavior， remains unclear. The following questions are addressed： How should a retailer set prices without and with the posterior price matching policy？ How does this policy influence the retailer's optimal pricing and profitability？ What impact do factors such as consumer characteristics and future market size have on the retailer’s decision to adopt the policy？To address these questions， a market consisting of two consumer types is modeled： waiting and immediate purchase. A two-period framework for a retailer's pricing and price matching decisions is developed， analyzing two scenarios： non-adoption （Scenario N） and adoption （Scenario M） of the posterior price matching policy.The findings indicate that the potential market size in the second period significantly impacts the retailer's optimal pricing decision. The presence of waiting consumers prompts retailers without the price matching policy to lower prices in the second period. Conversely， retailers with the policy may maintain or increase prices due to compensation claims， though price reductions cannot be entirely ruled out. Additionally， the policy can lower overall price levels and increase profits under certain conditions， benefiting both retailers and consumers. The mechanisms and conditions under which a retailer adopts the posterior price matching policy from the perspective of consumer structure are examined. In other words， the main contribution of this study is to examine the retailer's optimal pricing strategies with and without the posterior price matching policy， and to analyze the mechanisms by which the policy affects optimal pricing and profitability as well as the conditions under which the retailer can benefit from the policy. It enriches theoretical research on price matching policies and offers practical guidance for retailers in this study. Specifically， retailers should fully investigate the utility loss and proportion of waiting consumers， the rate of compensation claims， and the potential market size of the second period in order to scientifically decide on the posterior price matching policy. At the same time， retailers should endeavor to create the image that they will not reduce prices when they adopt the posterior price matching policy in order to increase their profits. Market administrators are encouraged to promote the policy under suitable conditions， as it benefits both retailers and consumers. In addition， Individual consumers should utilize the policy judiciously and monitor post-purchase prices. Figures and Tables | References | Related Articles | Metrics

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Consumer Credit Service Strategy of E-commerce Platform with Product Returns Long Ding, Xinyi Bian, Shan Chang 2026, 34 (9):  272-281.  doi: 10.16381/j.cnki.issn1003-207x.2024.0688 Abstract ( 15 )   HTML ( 0 )   PDF (1229KB) ( 11 )   Save With the standard development of the e-commerce and consumer credit business， many e-commerce platforms have launched consumer credit services. While at the same time， the phenomenon of high returns is particularly prominent. Considering the endogeneity strategy of e-commerce platforms to launch or not launch consumer credit service， a stylized model is conducted， which shows the interaction between product return and consumer credit service strategy by establishing the product return utility decision-making model affected by the coefficient of pain buffering. Then how product return rate and coefficient of pain buffering influence on optimal product pricing， demand， and corporate profits.It is found that 1） Considering product return， it is not always beneficial for e-commerce platform to launch consumer credit service. When the expected return value loss rate is low， it is beneficial for the platform to launch consumer credit service. When the expected return value loss rate is high， it is harmful for the platform to launch consumer credit service； 2） When launching consumer credit service， demand could probably drop. Although the pain buffering effect of consumer credit service could increase consumer purchase intention， its disutility also reduces their purchase intention. At this time， manufacturers also seek opportunities to increase product prices， which may ultimately reduce consumer purchase intention， and this leads to a decrease in product demand； 3） When the expected return value loss rate is low enough， only when the e-commerce platform launches consumer credit services can it achieve a “triple win” for the interests of the platform， manufacturer and bank. Figures and Tables | References | Related Articles | Metrics

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Whether to Open up Live E-commerce Channels? Analysis of the Dynamic Influence of Market Expansion, Cannibalization and Free-rider Effects Chi Zhou, Yong Qian, Linlin Zhang 2026, 34 (9):  282-292.  doi: 10.16381/j.cnki.issn1003-207x.2024.1683 Abstract ( 102 )   HTML ( 0 )   PDF (1159KB) ( 22 )   Save As a retail model driven by live streaming content and brands， live e-commerce channels possess both pricing and experiential advantages， creating a competitive relationship with traditional e-commerce channels. A traditional and live-streaming dual-channel sales system is examined， comprising a brand and a streamer. The brand operates two e-commerce sales channels： the traditional channel and the live-streaming channel. In the traditional channel， the brand enhances its brand reputation through online advertising investments. Simultaneously， the brand engages a streamer to sell products through the live-streaming channel. The popularity of live-streaming is influenced by both the brand's reputation and the streamer's effort level. Therefore， the brand considers whether to establish a live-streaming channel， modeling a differential game for both the traditional and dual-channel （traditional plus live-streaming） scenarios. Using Pontryagin Maximum Principle， equilibrium solutions for brand reputation， live-streaming popularity， and the brand's profit are derived， enabling a dynamic analysis of pricing strategies， advertising investment strategies， and live-streaming strategies. It is revealed that brand reputation changes monotonically regardless of whether a live-streaming channel is established. After introducing the live-streaming channel， changes in live-streaming popularity are related to the initial brand reputation level. Market cannibalization exhibits two critical thresholds impacting demand in both traditional and live-streaming channels， boosting product demand in the live-streaming channel while encroaching upon market share in the traditional channel. Furthermore， upon establishing a live-streaming channel， the brand reduces product prices to alleviate competition between the traditional and live-streaming channels. When brand reputation has a minor impact on product demand， introducing a live-streaming channel increases advertising investment and brand reputation levels. However， as brand reputation's influence grows， establishing a live-streaming channel can damage brand reputation， prompting brands to refrain from doing so. When fees are low， a lesser impact of brand reputation on product demand leads to higher advertising investment and brand reputation levels， encouraging brands to establish live-streaming channels. If slot fees are moderate， an appropriate level of brand reputation's influence on product demand and live-streaming popularity can ensure that establishing a live-streaming channel benefits the brand. Otherwise， profits from the live-streaming channel may not compensate for losses in the traditional channel， leading brands to abandon the idea of establishing a live-streaming channel. A bargaining model between traditional and live-streaming channels is established， revealing a unique negotiated market cannibalization coefficient that achieves Nash bargaining equilibrium for both channels Figures and Tables | References | Related Articles | Metrics

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Supply Chain Decision Considering Capacity Constraints and Option Contracts under Presales and Customer Returns Yue Hu, Chong Wang, Xingyu Chen, Dan Wu 2026, 34 (9):  293-303.  doi: 10.16381/j.cnki.issn1003-207x.2024.1265 Abstract ( 12 )   HTML ( 0 )   PDF (1554KB) ( 5 )   Save In recent years， the pre-sale model has emerged in the e-commerce sector， becoming increasingly favored by retailers and consumers， and gradually becoming a regular sales model. Major e-commerce platforms have launched discounted pre-sale activities to stimulate consumption and boost sales. However， behind the high turnover， retailers are also faced with the problem of returns triggered by products that fail to meet consumer expectations， a problem that is becoming increasingly prominent. For the production side， the prevailing capacity constraint problem is one of the major factors restricting business development. Moreover， due to the limited capacity of suppliers， some retailers with market advantages are unable to meet the market demand promptly， which will inevitably affect the optimal decision-making of the upstream and downstream enterprises in the supply chain and may result in the loss of profits of the supply chain as a whole. To effectively solve the “double marginalization” problem caused by the suppliers and retailers in the supply chain only pursuing their own profit maximization under the above conditions， option contracts can be used to hedge the risks related to supply chain uncertainty.Based on the analysis above， a supply chain consisting of a supplier and a retailer is considered， where the supplier is a Stackelberg leader offering both wholesale price and put option contracts to the retailer. The retailer facing stochastic demand and customer returns sells its products at a discounted price in the pre-sale period and at a normal price in the on-sale period. The optimal wholesale ordering and option ordering strategies of the retailer and the optimal option ordering and strike pricing strategies of the supplier are investigated by constructing the newsvendor model with and without supplier capacity constraints， respectively. Finally， the main findings and important parameters of the paper are numerically verified and additional managerial insights are provided.It is shown that the supplier's capacity level affects both the supplier and retailer's decisions， and the profitability of both can be optimized only when the capacity reaches a critical value. The retailer's optimal wholesale order quantity and option order quantity， the supplier's optimal option order price and strike price， and their expected profits are all decreasing functions of the customer return rate. Consequently， when higher customer returns occur in the market， suppliers need to adjust their pricing decisions to promote retailers to order more products； and retailers need to focus on consumers' needs and preferences and improve the sales process to enhance consumers' satisfaction with their products. The retailer's presale influences both the retailer's ordering and the supplier's pricing decisions and affects the retailer more significantly. As a follower in the supply chain， retailers should increase the price of pre-sale products when adopting the pre-sale strategy， which will benefit their profits. Figures and Tables | References | Related Articles | Metrics

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Welfare Effects Analysis of Quality Certification for Vertically Differentiated Products in Supply Chains Sai Zhao, Hongbo Duan 2026, 34 (9):  304-314.  doi: 10.16381/j.cnki.issn1003-207x.2024.1488 Abstract ( 15 )   HTML ( 0 )   PDF (1139KB) ( 17 )   Save Certain quality attributes of products are often difficult for consumers to identify or verify， leading to confusion between products of different quality levels. By disclosing quality information， product label certification helps consumers make more accurate purchase decisions. From the perspective of the supply chain， the impact of product certification （quality information disclosure） in the end market on supply chain firms and heterogeneous consumers is explored. A sequential game-theoretic model involving supplier（s）， duopoly manufacturers， and heterogeneous consumers is established， while considering different supply chain structures （monopoly supplier vs. competing suppliers） and product cost structures （variable quality cost vs. fixed quality cost）. It is found that for production-oriented products with variable quality costs， when product differentiation and consumers’ willingness to pay are low， product label certification may reduce overall supply chain revenue. In contrast， for design-oriented products with fixed quality costs， product certification always enhances supply chain revenue. The impact of product certification on consumer welfare depends on the specific supply chain structure： when there is a monopoly supplier in the raw materials market， product certification increases consumer welfare； however， when duopoly suppliers compete in the upstream market， product certification decreases consumer welfare. The analysis provides certain managerial insights for implementing product label certification policies in practice. Figures and Tables | References | Related Articles | Metrics

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Research on Coordination Mechanism of Time-Dependent Supply Chain under Procurement Price Fluctuations Jianbin Li, Yunjing Dai, Shuiyin Zhou, Xiyang Hou 2026, 34 (9):  315-325.  doi: 10.16381/j.cnki.issn1003-207x.2023.0184 Abstract ( 11 )   HTML ( 0 )   PDF (1659KB) ( 5 )   Save In the face of the continuously growing demand for customization， many enterprises are focusing on assembling components， outsourcing high-cost production tasks to specialized original equipment manufacturers， who are responsible for procuring the corresponding raw materials. However， influenced by various factors such as the unstable international political situation and the recurring outbreaks of the COVID-19 pandemic， prices of certain raw materials fluctuate frequently， directly impacting the prices and demand for the final products. Against this backdrop， a two-tier supply chain composed of a retailer （i.e.， assembly enterprise） and a supplier （i.e.， original equipment manufacturer） is considered. Geometric Brownian Motion （GBM） is introduced to depict the volatility in procurement prices. A joint procurement quantity and procurement timing decision model， based on the fluctuation of procurement prices， is established， using centralized decision-making as a benchmark. Two novel contracts are designed： the time-dependent wholesale price contract （TWP） and the time-dependent revenue-sharing contract （TRS）. Unlike traditional wholesale price contracts （WP） and revenue-sharing contracts （RS）， TWP and TRS contracts fully take into account the retailer's procurement time. Research results indicate that the TWP contract fails to achieve supply chain coordination， while the TRS contract can coordinate the supply chain under specific conditions. Further research results suggest that in the TRS contract， the wholesale price factor and revenue allocation ratio are closely related to the retailer's ordering time. By comparing TWP and TRS contracts， it is found that when the product selling price is relatively high and the procurement price is trending upward （or downward）， retailers tend to place orders later （or earlier） under the TRS contract. Finally， through numerical analysis of the profits of suppliers and retailers under TRS and TWP contracts， it is discovered that retailers and suppliers can achieve both Kaldor-Hicks and Pareto improvements under the TRS contract. It enriches the theoretical framework of supply chain coordination mechanisms and is beneficial for supply chain enterprises to establish more self-interested and mutually beneficial relationships in a complex and dynamic market environment. Figures and Tables | References | Related Articles | Metrics

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Interaction between Channel Selection and Supply Chain Transparency under Varying Power Structures Xingfen Liu, Zhongbao Zhou, Feimin Zhong 2026, 34 (9):  326-336.  doi: 10.16381/j.cnki.issn1003-207x.2023.1490 Abstract ( 103 )   HTML ( 0 )   PDF (1471KB) ( 27 )   Save In recent years， frequent product safety incidents have significantly undermined consumers’ trust in product quality， shifting their attitudes from assuming safety by default to adopting a more skeptical stance. Against this backdrop， firms have increasingly attached importance to information disclosure， making the improvement of supply chain transparency a key strategic choice. However， information disclosure not only incurs costs， but its optimal level is not necessarily the highest possible. Its effectiveness may be jointly influenced by the interaction among supply chain power structure， channel strategy， and technological means. Yet， these mechanisms have not been systematically studied. To fill this gap， a two-echelon supply chain model consisting of a manufacturer and a retailer is developed， in which the manufacturer can decide whether to open a direct-sales channel. Under different power structures， the interaction between channel choice and transparency improvement is analyzed， and further blockchain technology is incorporated to enhance the reliability of information disclosure， exploring its impact on the behavior of supply chain members and profit distribution. The results show that the manufacturer’s decision on supply chain transparency is not affected by the power structure， while its wholesale pricing decision increases as its bargaining power rises. In contrast， the retailer’s optimal pricing strategy is highly dependent on its relative power： when weaker， it tends to set lower prices to maintain competitiveness； when stronger， it prefers higher prices to obtain greater profits. Improving supply chain transparency facilitates the manufacturer’s adoption of a direct-sales channel， but this effect exhibits different characteristics under different power structures. As the manufacturer’s power increases （from Retailer-led to equal power to Manufacturer-led）， both its willingness to open a direct-sales channel and the impact of transparency on channel choice first weaken and then strengthen. When direct-sales costs are high， the manufacturer prefers to maintain a single-channel structure， allowing the retailer to earn stable profits， while the manufacturer can profit only if traceability costs are low. Conversely， when direct-sales costs are low， the manufacturer is inclined to open a direct-sales channel and exclusively capture the benefits brought by improved transparency， leaving the retailer unable to profit. Therefore， although the optimal transparency level under a dual-channel structure may be lower when consumers’ online acceptance is low， the manufacturer is always more likely to profit from enhancing supply chain transparency in a dual-channel setting. Further analysis reveals that the retailer’s adoption preference for blockchain technology depends on the manufacturer’s channel choice， whereas the manufacturer’s adoption preference is mainly determined by blockchain’s efficiency in improving the reliability of information disclosure. Figures and Tables | References | Related Articles | Metrics

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Corporate Social Responsibility, Carbon Audit Efficiency, and Supplier Compliance Emissions Reduction Hongyong Fu, Ting Zhou, Bin Dan, Shuguang Zhang 2026, 34 (9):  337-348.  doi: 10.16381/j.cnki.issn1003-207x.2023.1117 Abstract ( 73 )   HTML ( 0 )   PDF (2583KB) ( 21 )   Save Under the constraints of China's dual-carbon goals， firms must unwaveringly pursue green， low-carbon， and high-quality development. Actively fulfilling carbon reduction responsibilities has become a core source of competitive advantage for firms seeking sustainable growth. However， despite the proactive efforts of supply chain core enterprises to encourage upstream suppliers to reduce carbon emissions， noncompliant behaviors such as carbon greenwashing and excessive emissions by suppliers remain widespread.Motivated by the regulatory practices of Walmart in addressing suppliers' non-compliant carbon reduction behaviors， how a manufacturing-oriented retailer—as the core enterprise in a supply chain—can leverage corporate social responsibility practices and carbon auditing as an environmental regulatory tool to manage suppliers' carbon reduction noncompliance is investigated. Whether retailers' CSR engagement always facilitates suppliers' compliance with carbon reduction requirements is examined.To address these questions， a static game model involving a supplier and a retailer is developed to explore how key factors—especially the retailer's CSR level—influence carbon audit efficiency and suppliers' compliance levels. The results show that： （1） Retailers' CSR engagement can effectively enhance carbon audit efficiency， and such efficiency exhibits a multiplier effect as the CSR level increases. （2） Retailers' carbon-reduction-oriented CSR does not necessarily promote suppliers' compliance； when CSR exceeds a certain threshold within the feasible region， excessive CSR may instead hinder suppliers' compliant carbon reduction. （3） purchase price premium and reputation loss of the supplier can amplify the impact of CSR on both carbon audit efficiency and compliance. However， retail price premium may trap retailers in a price dilemma ultimately undermining compliant carbon reduction； adopting a small profit， quick turnover pricing strategy can mitigate this risk and better support suppliers' compliance. Overall， theoretical insights and decision support for retailers aiming to utilize carbon auditing to regulate suppliers' noncompliant carbon reduction behaviors are provided. It also contributes to promoting green， high-quality development of supply chains and advancing the realization of China's dual-carbon goals. Figures and Tables | References | Related Articles | Metrics

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Final-offer Arbitration with Rewards and Penalties Jia Liu, Xianjia Wang 2026, 34 (9):  349-358.  doi: 10.16381/j.cnki.issn1003-207x.2024.1047 Abstract ( 13 )   HTML ( 0 )   PDF (542KB) ( 5 )   Save Final offer arbitration （FOA） is a common binding third-party conflict resolution mechanism. In this paper， reward and penalty mechanisms are introduced into a two-player FOA model， and the role of reward and penalty mechanisms in mitigating or resolving the conflict between the parties involved in the arbitration is considered. Unlike the traditional FOA model， the final offer arbitration model with reward and penalty mechanisms is a two-player non-zero-sum game model. The equilibrium bids of the arbitrators are analyzed and sufficient conditions are obtained for the existence of local equilibrium and the convergence of equilibrium bids. In this paper， it is shown that reward and punishment mechanisms have significant contribution to conflict mitigation， and can effectively promote the convergence of equilibrium bids when the rewards and punishments are sufficiently strong. the subsidy mechanism and the bid-cost mechanism are special reward-punishment mechanisms. In subsidy mechanisms with utility transfers， the mean of the equilibrium bids is the median of the distribution of fair settlements between the parties with respect to the arbitrator. In the winner-loser subsidy mechanism， the presence of subsidies is detrimental to the convergence of equilibrium bids. Under the loser-to-winner subsidy mechanism， the equilibrium bids converge when the subsidy is more than half of the difference between the equilibrium bids in the FOA without incentives or penalties. In the symmetric case， the loser-to-winner subsidy mechanism is twice as effective in converging equilibrium bids as the reward or penalty mechanism alone. The fixed bid cost does not affect the equilibrium bid， but when the bid cost function is a linear function of the bid difference， the equilibrium bid converges if the cost coefficient is not less than 0.5. References | Related Articles | Metrics

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Research on the Game Mechanism and Strategy of Enhancing Ecosystem Carbon Sink through Land Sea Cooperation Yixiong He, Dongdong Qiu, Chunlin Li 2026, 34 (9):  359-368.  doi: 10.16381/j.cnki.issn1003-207x.2025.0576 Abstract ( 28 )   HTML ( 0 )   PDF (2149KB) ( 12 )   Save Land carbon sinks and marine carbon sinks are both important parts of the global carbon cycle， so they should be taken into account and coordinated to promote sink enhancement measures in order to achieve optimal results. Focusing on water pollution governance as the core linkage bridging these two ecosystems， the dynamics of the overall land-sea ecosystem’s biodiversity is modeled using a stochastic differential equation. This approach comprehensively captures the positive impacts of pollution governance efforts from both terrestrial and marine ecosystems， the natural degradation of biodiversity over time， and the continuous random disturbances caused by climate change or human interference. To study the decision-making of carbon sinks in collaborative land sea ecosystems， a stochastic differential game model is established to analyze the best strategies and benefits of three modes： decentralized decision-making for cost sharing， decentralized decision-making for pollution compensation， and centralized decision-making for collaborative governance. The impact of random factors in the model is identified by the changes of the biodiversity level of the entire land sea ecosystem， and virtual simulation analysis is conducted. By constructing and solving the Hamilton-Jacobi-Bellman equations for continuous time， the optimal effort levels， as well as the expected values and variances for biodiversity under each specific scenario are derived to find the Nash equilibrium.Research has shown that　1） Under the collaborative governance mode， the total carbon sink benefits of land sea ecosystems are the highest， followed by the cost sharing mode， and the pollution compensation mode is the lowest， which may be negative at high compensation prices. 2） The level of biodiversity under the pollution compensation mode is positively correlated with the compensation price. At high compensation prices， the pollution compensation mode has the highest level of biodiversity， but its stability is poor and the system's carbon aggregation benefits are low. 3） Improving the benefit allocation coefficient can significantly enhance the biodiversity level and the total carbon sink revenue of terrestrial and marine ecosystems under the cost-sharing model. However， for the pollution discharge compensation model， increasing the benefit allocation coefficient will lead to a decline in both.4） Although the total carbon sink benefits of land sea ecosystems are highest under the collaborative governance mode， the stability of biodiversity levels and total benefits is worse under this mode， requiring greater risk to be borne. And when the random interference factor increases， the volatility of the system carbon aggregate return under all modes increases significantly.The marginal contributions are in threefold　First， it expands carbon sink research by exploring coordinated land-sea ecosystem management. Second， it applies stochastic differential game models to identify synergy strategies， broadening methodological applications. Third， it reveals how stochastic disturbances affect biodiversity and carbon sequestration， offering insights for achieving the "dual carbon" goals. Figures and Tables | References | Related Articles | Metrics