Omega-international Journal of Management Science最新文献

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Optimal sizing and location of energy storage systems for transmission grids connected to wind farms 与风电场相连的输电网储能系统的最佳尺寸和位置
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-22 DOI: 10.1016/j.omega.2025.103301
Arya Sevgen Misiç , Mumtaz Karatas , Abdullah Dasci
{"title":"Optimal sizing and location of energy storage systems for transmission grids connected to wind farms","authors":"Arya Sevgen Misiç ,&nbsp;Mumtaz Karatas ,&nbsp;Abdullah Dasci","doi":"10.1016/j.omega.2025.103301","DOIUrl":"10.1016/j.omega.2025.103301","url":null,"abstract":"<div><div>Although modern renewable power sources such as solar and wind are increasing their share of the world’s power generation, they need to grow faster to replace a greater share of coal and gas power generation and thus, help prevent CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and other greenhouse gas emissions to reach critical levels. Renewable energy generation must be coupled with energy storage systems, which are unfortunately expensive investments. However, substantial cost savings may be possible if a system-wide solution is sought. This paper presents such an attempt for a transmission grid that has a mixture of renewable and non-renewable sources. The particular problem is to find the type, location and size of the storage systems in the grid, as well as the structure of the transmission network, to minimize total investment and system-wide operating costs of power generation, transmission and storage. A mixed integer linear programming formulation is devised for the problem, which can be very large because various operational decisions are made at short intervals. Hence, we develop a “divide-and-conquer” type solution approach based on time decomposition, wherein the problem is first solved in monthly time segments. Subsequently, optimal or near-optimal monthly generation schedules are merged to construct the greater portion of a grand schedule for the whole year. Although still considerably large, the model can be solved effectively after another set of heuristically developed restrictions on the transmission network structure. The formulation and solution method are implemented on a series of realistic instances for a modest-sized transmission grid adapted from Sardinia Island of Italy to demonstrate the effectiveness of the approach and the insight into related design decisions.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103301"},"PeriodicalIF":6.7,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Supply chain network viability: Managing disruption risk via dynamic data and interaction models 供应链网络可行性:通过动态数据和交互模型管理中断风险
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-19 DOI: 10.1016/j.omega.2025.103303
Sha-lei Zhan , Joshua Ignatius , Chi To Ng , Daqiang Chen
{"title":"Supply chain network viability: Managing disruption risk via dynamic data and interaction models","authors":"Sha-lei Zhan ,&nbsp;Joshua Ignatius ,&nbsp;Chi To Ng ,&nbsp;Daqiang Chen","doi":"10.1016/j.omega.2025.103303","DOIUrl":"10.1016/j.omega.2025.103303","url":null,"abstract":"<div><div>This study addresses the challenge of enhancing viability of an interconnected supply chain network, particularly in the context of low-probability high-impact events that recur unpredictably. We re-examine the viability from the views of agility, resilience, and sustainability, and propose a novel hybrid approach which integrates dynamic network data and multi-echelon interaction. Diverging from traditional static approaches, we introduce a dynamic decision-making framework that strategically maintains long-term survival by coordination between timely response actions and the risk of overreaction. A data-driven hidden Markov model is built to update the risk forecasting via dynamic network data. A Bayesian network game theoretical model is developed to support collaborative risk mitigating via the multi-echelon interaction. The main findings are as follows. In the short term, we encourage enterprises to engage in collaborative risk mitigating to significantly increase the likelihood of reaching a consensus on achieving a more cost-efficient level of risk mitigation, marked by an intriguing interplay between weakened individual fairness and the tendency to mitigate network-wide risk more economically. In the long term, we advocate building a data-driven, structure-dynamic, and interaction-focused risk response timing system to enable the network to adapt to changes swiftly and achieve desired viable levels efficiently.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103303"},"PeriodicalIF":6.7,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhanced efficiency assessment in manufacturing: Leveraging machine learning for improved performance analysis 增强制造业效率评估:利用机器学习改进性能分析
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-15 DOI: 10.1016/j.omega.2025.103300
Maria D. Guillen , Vincent Charles , Juan Aparicio
{"title":"Enhanced efficiency assessment in manufacturing: Leveraging machine learning for improved performance analysis","authors":"Maria D. Guillen ,&nbsp;Vincent Charles ,&nbsp;Juan Aparicio","doi":"10.1016/j.omega.2025.103300","DOIUrl":"10.1016/j.omega.2025.103300","url":null,"abstract":"<div><div>This paper introduces EATBoosting, a novel application of gradient tree boosting within the Data Envelopment Analysis (DEA) framework, designed to address undesirable outputs in printed circuit board (PCB) manufacturing. Recognizing the challenge of balancing desirable and undesirable outputs in efficiency assessments, our approach leverages machine learning to enhance the discriminatory power of traditional DEA models, facilitating more precise efficiency estimations. By integrating gradient tree boosting, EATBoosting optimizes the handling of complex data patterns and maximizes accuracy in predicting production functions, thus improving upon the deterministic nature of conventional DEA and Free Disposal Hull methods. The practicality of our approach is demonstrated through its application to a PCB assembly process, highlighting its capacity to discern subtle inefficiencies that traditional methods might overlook. This methodology not only enriches the analytical toolkit available for operational efficiency analysis but also sets a precedent for incorporating advanced machine learning techniques in performance evaluation across various industries. Looking forward, the continued integration of such innovative methods promises to revolutionize efficiency analysis, making it more adaptive to complex industrial challenges and more reflective of real-world production dynamics. This work not only broadens the scope of DEA applications but also invites further research into the integration of machine learning to refine performance measurement and management.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103300"},"PeriodicalIF":6.7,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamic bus bridging strategy in response to metro disruptions integrated with routing, timetabling and vehicle dispatching 针对地铁中断的动态公共汽车桥接战略,与路线、时间安排和车辆调度相结合
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-14 DOI: 10.1016/j.omega.2025.103287
Yin Yuan , Shukai Li , Shi Qiang Liu , Andrea D’Ariano , Lixing Yang
{"title":"Dynamic bus bridging strategy in response to metro disruptions integrated with routing, timetabling and vehicle dispatching","authors":"Yin Yuan ,&nbsp;Shukai Li ,&nbsp;Shi Qiang Liu ,&nbsp;Andrea D’Ariano ,&nbsp;Lixing Yang","doi":"10.1016/j.omega.2025.103287","DOIUrl":"10.1016/j.omega.2025.103287","url":null,"abstract":"<div><div>Unplanned metro disruptions always result in severe confusion and delays, while bus bridging can provide a promising resolution by efficient evacuating stranded passengers. This article investigates the dynamic bus bridging problem under metro disruptions to generate the routing, timetabling and vehicle dispatching schemes for bus bridging services in an online fashion. Specifically, we formulate a mixed-integer non-linear programming model for each decision stage, with the objective of minimizing passenger travel times and operational costs. This model focuses on the role of multimodal transportation in improving the overall urban public transportation network’s responses to metro disruption emergencies, which involves the utilization of temporary bus bridging services and the spare capacity of unaffected metro lines, passenger transfers and path choices. To address the model complexity, we propose a two-level decomposition approach to split the original problem into the master problem and subproblem. The approach can ensure the optimal solution in finite iterations. To further improve the performance of the solution approach, we design multiple acceleration techniques (i.e., customizing integer cuts supporting parallel computation, solution adjustment, domain reduction for the master problem, warm start and bound contraction for the subproblem) without compromising optimality. Extensive experiments verify that the proposed method can effectively evacuate stranded passengers, improving passenger satisfaction and meanwhile reducing operational costs. The proposed two-level decomposition approach with multiple acceleration techniques demonstrates higher computational efficiency than the common commercial solver and standard two-level decomposition approach, facilitating timely disruption responses. Additionally, according to the computational results, we derive a series of managerial insights for decision-makers.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103287"},"PeriodicalIF":6.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint optimization of order- and rack-scheduling in KIVA picking systems KIVA拣货系统中订单和货架调度的联合优化
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-14 DOI: 10.1016/j.omega.2025.103286
Xiying Yang , Guowei Hua , Li Zhang , Tai Chiu Edwin Cheng , Tsan-Ming Choi
{"title":"Joint optimization of order- and rack-scheduling in KIVA picking systems","authors":"Xiying Yang ,&nbsp;Guowei Hua ,&nbsp;Li Zhang ,&nbsp;Tai Chiu Edwin Cheng ,&nbsp;Tsan-Ming Choi","doi":"10.1016/j.omega.2025.103286","DOIUrl":"10.1016/j.omega.2025.103286","url":null,"abstract":"<div><div>We study the order processing operations in KIVA robot-assisted warehouses, where racks are delivered to multiple workstations by robots so that pickers at each workstation just focus on retrieving items from the racks to fulfill the orders. In this context, the order- and rack-scheduling, including their assignment and sequencing decisions, should be considered integrally as they are closely related and can enhance systemic efficiency by leveraging their synergy. We thus consider the comprehensive problem of jointly allocating orders and racks to workstations under workload balancing and sequencing their interlinked processing flows. We formulate it as a mixed-integer programming model to minimize the total number of rack visits. To tackle this model, we present a simulated annealing search framework, which builds on a relaxation model and a best-first-search heuristic exploiting the problem structure. Computational studies show that our proposed approach performs well on small-sized instances. On a large scale, it outperforms both the rule-based policy and two other state-of-the-art algorithms in terms of solution quality. We also conduct sensitivity analysis to generate some managerial insights for real-world warehouse operations.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"135 ","pages":"Article 103286"},"PeriodicalIF":6.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IoT-driven dynamic replenishment of fresh produce in the presence of seasonal variations: A deep reinforcement learning approach using reward shaping 在季节变化的情况下,物联网驱动的新鲜农产品动态补充:一种使用奖励塑造的深度强化学习方法
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-12 DOI: 10.1016/j.omega.2025.103299
Zihao Wang , Wenlong Wang , Tianjun Liu , Jasmine Chang , Jim Shi
{"title":"IoT-driven dynamic replenishment of fresh produce in the presence of seasonal variations: A deep reinforcement learning approach using reward shaping","authors":"Zihao Wang ,&nbsp;Wenlong Wang ,&nbsp;Tianjun Liu ,&nbsp;Jasmine Chang ,&nbsp;Jim Shi","doi":"10.1016/j.omega.2025.103299","DOIUrl":"10.1016/j.omega.2025.103299","url":null,"abstract":"<div><div>Internet of things (IoT) has been transforming inventory management disruptively by linking and synchronizing inventory products together. It is one of the driving forces for the prevailing innovation of AgriTech. For fresh produce replenishment in the presence of its inherent seasonal variations, not only can IoT devices capture bidirectional seasonal information of lead time and demand, but also detect fresh produce loss and waste (FPLW) caused by deterioration. With the aid of the massive data collected by IoT, we propose a data-driven deep reinforcement learning (DRL) approach using reward shaping, called DQN-SV-RS, to optimize the dynamic replenishment policy for a fresh produce wholesaler, specifically addressing the challenge posed by seasonal variations. Experimental results show that our DQN-SV-SR approach yields significant improvements for fresh produce supply chain (FPSC) inventory management, especially achieving a remarkable reduction in FPLW. As a core innovation in our DQN-SV-SR approach, the introduced reward shaping can significantly mitigate lost sales and inventory holding, thereby lowering the total cost. Furthermore, with numerical experiments based on real business data, our proposed approach is demonstrated with plausible robustness and scalable applicability.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103299"},"PeriodicalIF":6.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Acknowledgement to Reviewers 审稿人致谢
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-12 DOI: 10.1016/S0305-0483(25)00022-2
{"title":"Acknowledgement to Reviewers","authors":"","doi":"10.1016/S0305-0483(25)00022-2","DOIUrl":"10.1016/S0305-0483(25)00022-2","url":null,"abstract":"","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"133 ","pages":"Article 103296"},"PeriodicalIF":6.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variable range measure: A new range measure for super-efficiency model based on DDF in presence of nonpositive data 变量程测量:一种基于DDF的非正数据超效率模型的量程测量方法
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-02-05 DOI: 10.1016/j.omega.2025.103295
Hsuan-Shih Lee
{"title":"Variable range measure: A new range measure for super-efficiency model based on DDF in presence of nonpositive data","authors":"Hsuan-Shih Lee","doi":"10.1016/j.omega.2025.103295","DOIUrl":"10.1016/j.omega.2025.103295","url":null,"abstract":"<div><div>In order to handle the nonpositive data and increase the discrimination power, we propose a new DDF super-efficiency model called variable range measure (VRM). VRM is translation-invariant and unit-invariant. VRM is feasible when data set contains zero or negative data. The super-efficiency obtained by VRM is less than or equal to two. Range adjusted measure (RAM) makes input contraction and output expansion along the direction vector in a balanced way, but it is target-invariant. The range directional model (RDM) for super-efficiency might be infeasible, but it is target-variant. We combine the advantages of RAM and RDM into VRM so that VRM is target-variant and feasible under super-efficiency. Output vector of the direction vector proposed by Lin and Liu (2019) (LL model) might be zero for some DMUs. VRM overcomes the shortcomings of the LL model. We show that the VRM direction vector is a good proxy of the RAM direction vector by examples.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"134 ","pages":"Article 103295"},"PeriodicalIF":6.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A mixed integer programming approach to address cumulative threats in multi action management plans for biodiversity recovery 生物多样性恢复多行动管理计划中累积威胁的混合整数规划方法
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-01-28 DOI: 10.1016/j.omega.2025.103282
José Salgado-Rojas , Eduardo Álvarez-Miranda , Virgilio Hermoso
{"title":"A mixed integer programming approach to address cumulative threats in multi action management plans for biodiversity recovery","authors":"José Salgado-Rojas ,&nbsp;Eduardo Álvarez-Miranda ,&nbsp;Virgilio Hermoso","doi":"10.1016/j.omega.2025.103282","DOIUrl":"10.1016/j.omega.2025.103282","url":null,"abstract":"<div><div>Traditionally, most of the prioritization models used by researchers and practitioners, rely on spatially dichotomous settings for threats, for species and for actions’ benefit; i.e., threats and species are present with equal intensity in some territorial units (while in the other units are not present at all), and actions have impact only on those units where they are applied. However, when dealing with ecological phenomena on large and complex territories, characterized by different areas (such as multiple realms or large river basins) and different spatial connectivity patterns among them, such a dichotomous setting does not capture the spatial (cumulative) diffusion of threats and thus actions’ benefits. Hence, common conservation planning tools are likely to misestimate the benefits of actions and the impact of threats, yielding less effective solutions. In order to address this issue, we develop a framework for designing multi-action prioritization plans featuring threats and actions’ benefit spatial diffusion. Our framework relies on a mathematical programming model that identifies priority areas for the implementation of management actions for multiple threats across a complex and large landscape. We consider the particular case an ecological setting characterized by different realms, multiple threats, and multiple species. We use the Tagus River (Iberian Peninsula) as a case study, including four realms (terrestrial, freshwater, estuary, and marine), where we integrate three different types of spatial connectivity: longitudinal along rivers, and multidimensional in the estuary and marine realms. We simulate the spatial diffusion of threats across the study area using four types of decay models (dispersal kernels): one exponential kernel, two negative triangular kernels (medium and high), and no dispersal. The results show how the MIP-based methodology offers a flexible and practical strategy for incorporating the cumulative effects of threats into action management planning. Furthermore, the primal-MIP heuristic was demonstrated to be a noteworthy alternative for finding good bounds of the original MIP model.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"133 ","pages":"Article 103282"},"PeriodicalIF":6.7,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Homing strategies for asymmetric sellers on differentiated platforms 差异化平台上非对称卖家的归巢策略
IF 6.7 2区 管理学
Omega-international Journal of Management Science Pub Date : 2025-01-27 DOI: 10.1016/j.omega.2025.103284
Xiang Li, Meiqi Wang
{"title":"Homing strategies for asymmetric sellers on differentiated platforms","authors":"Xiang Li,&nbsp;Meiqi Wang","doi":"10.1016/j.omega.2025.103284","DOIUrl":"10.1016/j.omega.2025.103284","url":null,"abstract":"<div><div>With the flourishing development of e-marketplace platforms, sellers’ homing strategies have attracted considerable attention and require careful evaluation of the market environment, especially considering platform competition. This study explores two asymmetric sellers' homing and pricing strategies on two asymmetric platforms. The platforms and sellers are differentiated in their credits and boast varied consumers’ willingness to pay. We identify the competition-mitigating effects of utilizing an inferior platform and adopting single-homing strategies. We indicate that such effects should be carefully considered in balance with the valuation-enhancing effect of choosing a superior platform and the market-expanding effect of adopting multi-homing strategy. Moreover, in some situations, the benefits of seller prioritization of platform occupancy and implementation of an “either-or” policy (i.e., mandatory single-homing policy for sellers) can be less than expected. These results enhance our understanding of homing strategy optimization in the face of competition between sellers and platforms.</div></div>","PeriodicalId":19529,"journal":{"name":"Omega-international Journal of Management Science","volume":"133 ","pages":"Article 103284"},"PeriodicalIF":6.7,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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