Omega-international Journal of Management Science最新文献_第10页

Navigating uncertainty in human interaction: A management science approach using Bayesian games in therapy 在人际交往中导航不确定性：在治疗中使用贝叶斯游戏的管理科学方法

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-09-25 DOI: 10.1016/j.omega.2025.103430

A. Mehrabi, R. Rahimi M., A. Nikoofard

Therapy sessions are widely recognized as an effective form of treatment, with outcomes sometimes more strongly influenced by the quality of therapist–patient interaction and decision-making than by the specific methods employed, prompting extensive empirical investigation into these dynamics. Existing studies overlook individual differences and long-term effects, relying on generalized findings that miss the complexity of human interactions and therapeutic decision-making. To address these limitations, this study adopts a structured analytical approach that captures the nuanced, evolving nature of therapist–patient interactions and enables long-term insight into how individual behaviors and strategic decisions shape therapeutic trajectories.

Game theory, widely used to optimize and analyze multi-agent decision-making across various domains, provides a powerful framework for this study. By incorporating Nash equilibrium, Bayesian games, and repeated games, the proposed model captures the uncertainty and complexity inherent in real-world interactions. The model highlights the strategic merit of selecting non-cooperative policies under certain conditions and, through simulation analysis, demonstrates that patient behavior has a significantly greater impact on session outcomes compared to that of the therapist. Furthermore, the influence of cooperation becomes more pronounced as the planning horizon extends into the long term. Therapists who adapt their strategies to patient type and behavior can enhance outcomes, while rigidity may hinder progress. The model offers practical value in guiding effective, personalized strategy selection.

治疗会议被广泛认为是一种有效的治疗形式，其结果有时受到治疗师-患者互动和决策的质量的强烈影响，而不是所采用的具体方法，促使对这些动态进行广泛的实证研究。现有的研究忽视了个体差异和长期影响，依赖于广义的发现，而忽略了人类相互作用和治疗决策的复杂性。为了解决这些局限性，本研究采用了一种结构化的分析方法，捕捉了治疗师-患者互动的细微差别，不断发展的本质，并能够长期洞察个体行为和战略决策如何塑造治疗轨迹。博弈论被广泛用于优化和分析各个领域的多智能体决策，为本研究提供了一个强大的框架。通过整合纳什均衡、贝叶斯博弈和重复博弈，所提出的模型捕捉到了现实世界互动中固有的不确定性和复杂性。该模型突出了在特定条件下选择非合作策略的战略价值，并通过模拟分析表明，与治疗师相比，患者行为对会话结果的影响显著更大。此外，随着规划范围延伸到长期，合作的影响变得更加明显。根据患者类型和行为调整策略的治疗师可以提高结果，而僵化可能会阻碍进展。该模型对指导有效的、个性化的战略选择具有实用价值。

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引用次数: 0

To adopt or not? The impacts of “Try-Now-Pay-Later” on platform markets 收养还是不收养？“先试后付”对平台市场的影响

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-07-09 DOI: 10.1016/j.omega.2025.103390

Shuxiao Sun , He Liu , Jinrong Zhu , Shouyang Wang

“Try-Now-Pay-Later” (TNPL), which combines “Try Before You Pay” (TBYP) and “Buy Now, Pay Later” (BNPL), is a business model innovation launched by some platforms such as Klarna and Affirm in collaboration with retailers. It allows consumers to place an order for free and provides consumers with a free experience period to assess the product fit before finishing the payment. Under TNPL, cash flow occurs within platform markets (including platforms, retailers, and consumers), influencing purchasing decisions of consumers and operational decisions of platforms and retailers. This paper develops a game-theoretic model to investigate the impact of TNPL on platform operations in a market where a retailer sells through a platform. The retailer determines the retail price and pays a commission fee to the platform for each product sold, and either the retailer or consumers pay(s) for the return freight. The results show that (1) TNPL can increase both the retailer’s retail price and the platform’s commission rate, no matter who bears the return freight. (2) Compared to the traditional model, the retailer is most likely to benefit the most from TNPL, followed by consumers, with the platform benefiting the least. (3) If the retailer’s proficiency in handling returns is not significantly greater than that of consumers, especially when the proportion of defaulting consumers is larger and the opportunity cost of cash is lower, all three parties are better off when the return shipping cost is borne by consumers. (4) TNPL generates Pareto improvements when consumer utility enhancement is significant, the product matching rate is high, the proportion of defaulting consumers is small, and the cash opportunity cost is low. Furthermore, the impact of TNPL on competing platforms and retailers depends on the relative competitive advantages gained through consumers’ utility improvements. Our findings offer valuable insights for platforms and retailers on how to optimize their operational strategies to effectively leverage TNPL, thereby enhancing both business performance and social welfare.

“先试后付”（Try-Now-Pay-Later， TNPL）结合了“先试后付”（Try Before You Pay， TBYP）和“先买后付”（Buy -Now, Pay-Later， BNPL），是Klarna和Affirm等平台与零售商合作推出的一种商业模式创新。它允许消费者免费下订单，并在完成付款之前为消费者提供免费体验期，以评估产品是否合适。在TNPL下，现金流发生在平台市场（包括平台、零售商和消费者）内部，影响消费者的购买决策以及平台和零售商的经营决策。本文建立了一个博弈论模型来研究零售商通过平台进行销售的市场中TNPL对平台运营的影响。零售商确定零售价格，并为售出的每件产品向平台支付佣金，零售商或消费者支付回程运费。结果表明：(1)无论谁承担退货运费，TNPL都可以提高零售商的零售价格和平台的佣金率。(2)与传统模式相比，零售商从TNPL中获益最多，其次是消费者，平台获益最少。(3)如果零售商处理退货的熟练程度不显著大于消费者，特别是当消费者违约比例较大且现金机会成本较低时，则退货运输成本由消费者承担时，三方都更有利。(4)当消费者效用增强显著、产品匹配率高、违约消费者比例小、现金机会成本低时，TNPL产生帕累托改进。此外，TNPL对竞争平台和零售商的影响取决于消费者效用提高所获得的相对竞争优势。我们的研究结果为平台和零售商如何优化其运营策略以有效利用TNPL，从而提高业务绩效和社会福利提供了有价值的见解。

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引用次数: 0

Approximate dynamic programming-based thresholds for cargo capacity management considering postponements 基于近似动态规划的货运能力管理阈值

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-08-30 DOI: 10.1016/j.omega.2025.103416

Dhandabani Srinivasan , R.K. Amit , Atul Kumar Malik , Shao Hung Goh

We consider an airline that operates sequential flights in an origin–destination pair. Cargo products are opaque in terms of which specific transportation vessel or routing is used to carry a shipment. Hence, based on the time sensitivity, shipments can be postponed to later flight departures to accommodate the high-value requests. The objective is to assist the airline with joint capacity control and overbooking decisions, considering all the complexities associated with the cargo product. We model the master problem as an infinite-horizon dynamic program (DP) with frequent arrivals and infrequent departures, and relax the cargo divisibility assumption while computing offload costs. We decompose the master problem into several DP sub-problems, with each one focusing on individual flights considered in the study. As the proposed DP sub-problem solution becomes intractable, we resort to approximate dynamic programming to find an implementable solution. Specifically, the space of policies based on control limits or thresholds is looked upon as they are easily implementable. Hence, we use approximate policy iteration to find the implementable solution, where we prove the convergence and existence of such a solution. Numerical results illustrate that the proposed solution of the sub-problem performs 6%–9% better than the first-come, first-served policy and approximates 88%–94% of the upper bound. Additionally, about 4%–10% of revenue improvements are possible if the postponement strategy is considered. Extensions to time-dependent thresholds, aircraft selection, and policy beyond allowable limits are also discussed.

我们考虑一家航空公司在始发目的地对中运行连续航班。货物产品是不透明的，具体运输船只或路线是用来运送货物。因此，基于时间敏感性，发货可以推迟到较晚的航班出发，以满足高价值的请求。目标是帮助航空公司进行联合容量控制和超售决策，同时考虑到与货运产品相关的所有复杂性。我们将主问题建模为一个到达频繁和离港不频繁的无限视界动态规划，在计算卸载成本时放宽了货物可分性假设。我们将主问题分解为几个DP子问题，每个子问题都关注研究中考虑的单个飞行。由于所提出的DP子问题求解变得难以处理，我们采用近似动态规划来寻找可实现的解。具体来说，基于控制限制或阈值的策略空间被视为容易实现的。因此，我们使用近似策略迭代来寻找可实现的解，并证明了该解的收敛性和存在性。数值结果表明，所提出的子问题解比先到先得策略的求解效率提高6% ~ 9%，逼近上界的88% ~ 94%。此外，如果考虑延迟策略，大约4%-10%的收入改善是可能的。扩展到时间依赖的阈值，飞机的选择和政策超出允许的限制也进行了讨论。

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引用次数: 0

Fixed cost and minimum compensation allocations in two-stage systems: A DEA-dual game framework 两阶段系统的固定成本和最小补偿分配：DEA-dual博弈框架

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-05-27 DOI: 10.1016/j.omega.2025.103373

Zixuan Lyu, Lin Wang, Quanbo Zha

Though data envelopment analysis (DEA) is widely utilized in two-stage systems for fixed cost allocation, it often overlooks the payoffs of decision-making units (DMUs) deriving from undertaking the cost and receiving compensation. This paper puts forward a dual game approach to determine the Nash equilibrium-based fixed cost and minimum total compensation allocations in two-stage systems. The dual game involves the competition game among DMUs engaging in cost and compensation allocations and the non-cooperation and cooperation games between two stages. The Nash equilibrium allocation under the non-cooperation game maximizes the payoffs of DMUs' two stages sequentially, while the Nash equilibrium allocation under the cooperation game maximizes the payoffs of DMUs' two-stage systems simultaneously. To ensure all DMUs are efficient in the Nash equilibrium allocations, the possible sets of allocations under both cooperation and non-cooperation games between two stages maximizing both the payoffs and efficiencies of all DMUs are proved to be always non-empty. Furthermore, minimum total compensation allocations are obtained from these possible sets respectively. Finally, an application case study is conducted to demonstrate the practical application and benefits of the proposed approach.

虽然数据包络分析（DEA）被广泛应用于两阶段固定成本分配系统，但它往往忽略了决策单元（dmu）承担成本和获得补偿所产生的收益。本文提出了一种确定两阶段系统中基于纳什均衡的固定成本和最小总补偿分配的双博弈方法。双重博弈包括参与成本和补偿分配的dmu之间的竞争博弈和两个阶段之间的不合作与合作博弈。非合作博弈下的纳什均衡分配使两阶段决策单元的收益顺序最大化，而合作博弈下的纳什均衡分配使两阶段决策单元的收益同时最大化。为了保证所有决策单元在纳什均衡分配中都是有效的，在两个阶段之间的合作博弈和非合作博弈中，最大化所有决策单元的收益和效率的可能分配集总是非空的。进而分别从这些可能集合中求得最小的总补偿分配。最后，通过一个应用案例研究来说明该方法的实际应用和效益。

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引用次数: 0

A trailer-detention-constrained multi-trailer drop-and-pull container drayage problem with flexible service starting time and time windows 具有灵活服务启动时间和时间窗口的多拖车拖运集装箱拖运问题

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-09-04 DOI: 10.1016/j.omega.2025.103422

Decheng Wang , Zhihui Fan , Yarong Liu , Ilkyeong Moon

Trailer detention at delivery locations, frequently caused by the time-consuming (un)packing process, presents a significant challenge in container drayage. Despite extensive research on container drayage, the specific issues stemming from trailer detention remain relatively underexplored. This study addresses a trailer-detention-constrained multi-trailer drop-and-pull container drayage problem, incorporating flexible service starting times and time windows. The detained trailers differ from standard trailers as they require only a single pickup operation within the planning horizon, rather than the typical two-step delivery and subsequent pickup. These pickup operations must be completed within specified time windows due to their potential to disrupt logistics efficiency and often require time-sensitive handling. Furthermore, time windows are imposed on normal trailer deliveries, as these operations initiate the (un)packing process, which can impact the operational efficiency of customer activities. The problem involves tractors capable of towing multiple trailers, utilizing the drop-and-pull method for detachment and reattachment. Tractors possess the flexibility to select their service starting times. To address the inherent complexity of this problem, a mixed-integer programming model is developed alongside a tailored heuristic algorithm. The algorithm leverages a modified Clarke-and-Wright algorithm to generate both rapid and high-quality initial solutions. It strategically integrates the mathematical model, ensuring solution quality is maintained without compromising computational efficiency. To further enhance solution efficiency, a route-based release-fix-optimize method is implemented. Extensive computational experiments validate the efficacy of the proposed methods and examine the impact of time windows and detained inbound and outbound requests on transportation plans, offering valuable insights for effectively managing logistics systems.

拖车滞留在交货地点，往往是由耗时（非）包装过程造成的，这对集装箱运输提出了重大挑战。尽管对集装箱拖曳进行了广泛的研究，但拖车滞留的具体问题仍未得到充分探讨。本研究解决了拖车滞留受限的多拖车装卸集装箱拖运问题，结合了灵活的服务启动时间和时间窗口。被扣留的拖车与标准拖车不同，因为它们只需要在计划范围内进行一次取货操作，而不是典型的两步交付和随后的取货。这些取货操作必须在规定的时间内完成，因为它们可能会破坏物流效率，并且通常需要对时间敏感的处理。此外，正常的拖车运输需要时间窗口，因为这些操作会启动（非）包装过程，这会影响客户活动的运营效率。该问题涉及能够牵引多个拖车的拖拉机，利用拉放方法分离和重新附着。拖拉机具有灵活选择其服务启动时间的能力。为了解决这个问题固有的复杂性，我们开发了一个混合整数规划模型和一个定制的启发式算法。该算法利用改进的clark - wright算法生成快速且高质量的初始解。它战略性地集成了数学模型，确保在不影响计算效率的情况下保持解决方案的质量。为了进一步提高求解效率，实现了基于路径的释放-修复-优化方法。大量的计算实验验证了所提出方法的有效性，并检查了时间窗口和滞留的入境和出境请求对运输计划的影响，为有效管理物流系统提供了有价值的见解。

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引用次数: 0

Water losses: A productivity analysis of the water supply in Portugal 水的损失：葡萄牙供水的生产力分析

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-09-30 DOI: 10.1016/j.omega.2025.103431

P. Ravelojaona , A. Abad , P.N. Alves Junior , F.S. Pinto , I. Costa-Melo

Environmental concerns have increasingly influenced production processes, particularly in recent years, as natural resources become progressively scarce. Among these, water remains the most critical resource, further exacerbated by climate change and its associated challenges, such as frequent droughts, especially in warm and mild-climate regions like Southern Europe. This study analyzes the performance of the Portuguese water supply sector, focusing on a sample of 116 water utilities between 2013 and 2021, representing diverse geographic and management structures. The production process is conceptualized as a non-linear joint-production process, incorporating water losses as an undesirable output within performance evaluations. By applying exponential Hicks-Moorsteen and Malmquist indices within a non-parametric Data Envelopment Analysis framework, this study provides an assessment of the efficiency and productivity trends in the sector. The findings offer insights into how Portuguese water utilities manage resources under environmental and infrastructural constraints, with a focus on reducing water losses and enhancing sustainable practices.

环境问题日益影响到生产过程，特别是近年来，因为自然资源日益稀少。其中，水仍然是最关键的资源，气候变化及其相关挑战（如频繁干旱）进一步加剧了这一问题，尤其是在南欧等温暖和温和气候地区。本研究分析了葡萄牙供水部门的表现，重点关注2013年至2021年间116家水务公司的样本，代表了不同的地理和管理结构。生产过程被定义为一个非线性联合生产过程，将失水作为不希望的产出纳入绩效评估。通过在非参数数据包络分析框架内应用指数Hicks-Moorsteen和Malmquist指数，本研究提供了该部门效率和生产力趋势的评估。调查结果为葡萄牙水务公司如何在环境和基础设施限制下管理资源提供了见解，重点是减少水损失和加强可持续实践。

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引用次数: 0

Content moderation and creator incentives mechanism amidst controversial content surges 争议内容激增中的内容审核与创作者激励机制

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-09-17 DOI: 10.1016/j.omega.2025.103427

Ruixiao Dong , Xu Guan , Xiaohua Han , Yuan Jiang

The content platforms usually offer monetary rewards to creators to encourage the creation of high-quality content to attract views. This would motivate some creators to incorporate controversial content to generate engagement, which causes the platform’s reputation cost. Therefore, in practice, the platform actively conducts content moderation through various methods. In this paper, we consider two content moderation formats, Pre-Moderation format and Post-Moderation format, depending on whether the moderation takes place before or after the content’s publication. Under Pre-Moderation format, the platform reviews each content before it is released, which makes it less likely to suffer from a high reputation cost. However, the drawback is the potential for mistakenly blocking of high quality content. The platform has the incentive to reward creators to exert effort to attract views only when the platform’s payoff from each view of high-quality content is relatively high. Moreover, a more rigor moderation mechanism may not necessarily benefit the platform and hurt the low-type creators, and a high proportion of controversial-content fans may also not necessarily benefit the low-type creators. Conversely, Post-Moderation format proves more creator-friendly, as it enables each content published without check, though this comes at the expense of a higher reputation cost. Compared to Pre-Moderation format, the platform becomes more likely to provide monetary reward under Post-Moderation format only when the proportion of controversial-content fans is low. The platform’s profit and the creators’ profits can be higher under either moderation format, depending on the monetary reward strategy and the dissemination of low-quality content.

内容平台通常会向创作者提供金钱奖励，以鼓励他们创作高质量的内容来吸引浏览量。这将促使一些创作者加入有争议的内容来提高参与度，从而导致平台的声誉成本。因此，在实践中，平台通过多种方式积极进行内容审核。在本文中，我们考虑了两种内容审核格式，即Pre-Moderation格式和Post-Moderation格式，这取决于审核是发生在内容发布之前还是之后。在Pre-Moderation模式下，平台会在内容发布前对其进行审核，这样就不太可能遭受高声誉成本的影响。然而，缺点是可能会错误地阻止高质量的内容。只有当高质量内容的每次观看给平台带来的收益相对较高时，平台才有动力奖励创作者努力吸引观看。此外，更严格的审核机制不一定有利于平台而伤害低类型创作者，高比例的争议内容粉丝也不一定有利于低类型创作者。相反，Post-Moderation格式证明对创作者更友好，因为它允许发布的内容无需检查，尽管这是以更高的声誉成本为代价的。与Pre-Moderation相比，Post-Moderation只有在争议内容粉丝比例较低的情况下，平台才更有可能提供金钱奖励。在任何一种适度模式下，平台的利润和创作者的利润都可能更高，这取决于金钱奖励策略和低质量内容的传播。

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引用次数: 0

Distributionally robust master surgery scheduling with duration uncertainty and specialty parallelism 具有持续时间不确定性和专科并行性的分布式鲁棒主手术调度

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-08-25 DOI: 10.1016/j.omega.2025.103417

Jinfeng Li , Songzheng Zhao , Salma Makboul , Zhongping Zhang , Yang Wang , Mingjun Huang

This study investigates master surgery scheduling at the tactical decision-making level of operating room (OR) management, addressing uncertainty in surgeons’ surgery durations and parallelism in surgical specialties. The goal is to optimize OR time block types within the scheduling cycle, allocate them efficiently to surgical specialties and surgeons, and determine the appropriate number of surgeries to schedule. Given the limited historical data on surgery durations, we employ a distributionally robust optimization (DRO) approach to address the uncertainty in the distribution. To address the needs of different OR managers, we develop a distributionally robust chance-constrained model to manage overtime that extends beyond the designated OR time blocks. Meanwhile, we construct a distributionally robust bi-objective optimization model with the goals of minimizing the expected total duration of overtime and maximizing the number of surgeries scheduled. These optimization models are reformulated into computationally tractable forms using dual theory. We validate the proposed methods with real hospital data, finding that the DRO approach offers greater stability in scheduling solutions compared to the sample average approximation approach.

本研究探讨了手术室管理策略决策层面的主手术安排，以解决外科医生手术时间的不确定性和外科专科的并行性。目标是在调度周期内优化手术室时间块类型，将其有效地分配给外科专科和外科医生，并确定适当的手术调度数量。鉴于手术持续时间的历史数据有限，我们采用分布鲁棒优化（DRO）方法来解决分布中的不确定性。为了满足不同手术室经理的需求，我们开发了一个分布式健壮的机会约束模型来管理超出指定手术室时间块的加班。同时，我们构建了一个分布式鲁棒的双目标优化模型，以最小化预期总加班时间和最大化手术计划数量为目标。利用对偶理论将这些优化模型重新表述为可计算的形式。我们用真实的医院数据验证了所提出的方法，发现与样本平均近似方法相比，DRO方法在调度解决方案中提供了更大的稳定性。

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引用次数: 0

Distributionally robust optimisation approach for aircraft sequencing and scheduling with learning-driven arrival and departure time predictions 基于学习驱动的到达和离开时间预测的飞机排序和调度的分布式鲁棒优化方法

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-08-20 DOI: 10.1016/j.omega.2025.103415

Chenliang Zhang , Zhongyi Jin , Kam K.H. Ng , Tie-Qiao Tang , Rong Tang

As air traffic demand grows, some airspace systems are nearing capacity. Optimising runway utilisation is a key strategy for increasing capacity. To enhance efficiency and robustness in aircraft sequencing and scheduling under uncertainty, we introduce two prescriptive analytics approaches. First, the estimate-then-optimise (ETO) approach uses a machine learning method to estimate probability distributions, which inform a stochastic programming (SP) model for the aircraft sequencing and scheduling problem (ASSP). However, prediction and sampling errors may affect decision quality. To mitigate this, we replace the SP model with a distributionally robust optimisation (DRO) model, proposing the estimate-then-distributionally-robust-optimise (ETDRO) approach. Given the complexity of solving DRO models, we develop decomposition methods to improve computational efficiency. Numerical experiments show that ETDRO consistently delivers high-quality decisions, outperforming benchmark optimisation approaches. Meanwhile, the proposed inexact decomposition methods significantly improve computational performance, enabling the real-world implementation of ETDRO.

随着空中交通需求的增长，一些空域系统已接近饱和。优化跑道利用率是增加运力的关键策略。为了提高不确定条件下飞机排序和调度的效率和鲁棒性，我们引入了两种规范分析方法。首先，估计-然后优化（ETO）方法使用机器学习方法来估计概率分布，从而为飞机排序和调度问题（ASSP）的随机规划（SP）模型提供信息。然而，预测和抽样误差可能会影响决策质量。为了缓解这一问题，我们用分布鲁棒优化（DRO）模型取代SP模型，提出了估计-然后分布鲁棒优化（ETDRO）方法。鉴于求解DRO模型的复杂性，我们开发了分解方法来提高计算效率。数值实验表明，ETDRO始终如一地提供高质量的决策，优于基准优化方法。同时，提出的不精确分解方法显著提高了计算性能，使ETDRO能够在现实世界中实现。

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引用次数: 0

Two-Stage robust optimization approach for supplier selection, development, and order allocation under uncertainty 不确定条件下供应商选择、开发和订单分配的两阶段鲁棒优化方法

IF 7.2 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2026-01-01 Epub Date: 2025-08-11 DOI: 10.1016/j.omega.2025.103413

Guyu Dai , Xicai Zhang , Ren-Qian Zhang

Effective supplier management in competitive markets involves more than selecting the most capable suppliers. It requires a comprehensive approach that combines supplier selection with long-term development efforts to ensure competitive advantages. However, traditional models often emphasize short-term efficiency and overlook supplier development as a critical strategy for achieving sustained performance improvement. This study proposes a novel two-stage robust optimization framework that unifies strategic and operational decisions to address this limitation. Different from traditional approaches, the proposed model strategically integrates supplier development programs (SDPs) with supplier selection in the first stage to minimize total costs, followed by order allocation in the second stage under the realization of worst scenarios. To capture the inherent uncertainty associated with supplier development, a budgeted uncertainty set is constructed to characterize potential variations in performance improvement. Methodologically, a multi-cut version of the column-and-constraint generation (C&CG) algorithm is developed to accelerate convergence by generating multiple cutting planes per iteration and linearizing nonconvex dual subproblems. Numerical experiments verify the computational advantages of the proposed algorithm, which achieves superior efficiency in solving large-scale instances compared to the standard C&CG algorithm. Furthermore, a procurement case study is conducted to demonstrate the practical applicability of the proposed model. The findings reveal a nonlinear relationship between uncertainty and supplier development, and highlight significant differences in management strategies for domestic and foreign suppliers.

在竞争激烈的市场中，有效的供应商管理不仅仅是选择最有能力的供应商。它需要一种综合的方法，将供应商选择与长期发展努力相结合，以确保竞争优势。然而，传统模式往往强调短期效率，而忽视了供应商发展作为实现持续绩效改进的关键战略。本研究提出了一种新的两阶段鲁棒优化框架，该框架将战略和运营决策统一起来，以解决这一限制。与传统方法不同的是，该模型将供应商发展计划与供应商选择在第一阶段进行战略整合，以实现总成本最小化，然后在第二阶段实现最坏情景下的订单分配。为了捕捉与供应商发展相关的内在不确定性，构建了一个预算不确定性集，以表征绩效改进的潜在变化。在方法上，开发了一种多切割版本的列约束生成（C&；CG）算法，通过每次迭代生成多个切割平面和线性化非凸对偶子问题来加速收敛。数值实验验证了该算法的计算优势，与标准C&；CG算法相比，该算法在求解大规模实例时具有更高的效率。此外，通过采购案例研究，验证了所提出模型的实用性。研究结果揭示了不确定性与供应商发展之间的非线性关系，并突出了国内外供应商管理策略的显著差异。

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