Omega-international Journal of Management Science最新文献_第2页

Routing and charging scheduling for the electric carsharing system with mobile charging vehicles 带移动充电车的电动汽车共享系统的路由和充电调度

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-19 DOI: 10.1016/j.omega.2024.103211

Li Zhang , Tingting Chen , Baozhen Yao , Bin Yu , Yunpeng Wang

Electric carsharing systems are expected to be an optional alternative to private vehicles for decreasing the urban traffic congestion and emissions. However, the temporal and spatial imbalance of the charging demand of shared electric vehicles adds to the managerial complexity of electric carsharing systems. This paper integrates mobile charging vehicles into the electric carsharing system to address this imbalance. Mobile charging vehicles can dwell at stations to provide elastic charging capacity, and thereby decrease both the waiting time of shared electric vehicles at busy stations and the investments in fixed charging piles at suburban stations. In this paper, a mixed integer linear programming formulation is proposed based on a time-space network, in which the routes of shared electric vehicles, charging schedules of shared electric vehicles, and routes of mobile charging vehicles are optimized simultaneously. Then, an algorithm based on Lagrangian relaxation is proposed. Specifically, the proposed formulation is decomposed into three independent subproblems. We propose three exact algorithms for these subproblems, and a tailored multistep repair algorithm is designed to generate feasible solutions. A case study in Hefei, China demonstrates the performance of the proposed algorithm and the effects of the number of SEVs, the number of MCVs, the number of fixed charging piles, trip component, battery capacity, and revenue on the operation of the electric carsharing system.

电动汽车共享系统有望成为私家车的可选替代方案，以减少城市交通拥堵和废气排放。然而，共享电动汽车充电需求的时空不平衡增加了电动汽车共享系统管理的复杂性。本文将移动充电车纳入电动汽车共享系统，以解决这种不平衡问题。移动充电车可以在站点停留，提供弹性充电容量，从而减少共享电动汽车在繁忙站点的等待时间和在郊区站点固定充电桩的投资。本文提出了一种基于时空网络的混合整数线性规划方法，同时优化共享电动汽车的行驶路线、共享电动汽车的充电时间表和移动充电车的行驶路线。然后，提出了一种基于拉格朗日松弛的算法。具体来说，所提出的方案被分解为三个独立的子问题。我们针对这些子问题提出了三种精确算法，并设计了一种量身定制的多步修复算法来生成可行的解决方案。在中国合肥进行的案例研究展示了所提算法的性能，以及 SEV 数量、MCV 数量、固定充电桩数量、行程组件、电池容量和收入对电动汽车共享系统运行的影响。

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引用次数: 0

Accurate preference-based method to obtain the deterministically optimal and satisfactory fairness-efficiency trade-off 基于偏好的精确方法，获得确定性最优和令人满意的公平-效率权衡

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-18 DOI: 10.1016/j.omega.2024.103214

Liming Yao , Zerui Su , Hao-Chun Lu

The resource allocation problem is a classic multi-objective challenge, particularly when balancing the fairness-efficiency trade-off. To achieve a deterministically optimal and satisfactory solution, researchers frequently employ preference-based methods, including selecting among Pareto solutions based on the decision-maker's a posteriori preference and using deterministic models incorporating a priori preferences. In this study, we address two main challenges—specifically, (1) the limitations in measuring the abstract concepts of fairness and efficiency and (2) finding a deterministically optimal and satisfactory balance between fairness and efficiency. We apply a Gini impurity index derived from the classification and regression tree to calculate fairness, ensuring the Gini index function's differentiability. Additionally, we unify the scales of fairness and efficiency to facilitate calculation. Using accurate preference information, we employ the extended interval goal programming method to solve the model and achieve a deterministically optimal and satisfactory solution. The comparative analysis results demonstrate that our model (1) efficiently addresses the real-world water resource allocation problem concerning the fairness-efficiency trade-off; and (2) generates fewer penalties, with an average improvement ratio of 8% in the case study, using more refined penalty functions that align closer to the decision-maker's real and nonlinear preferences.

资源分配问题是一个典型的多目标挑战，尤其是在平衡公平与效率之间的权衡时。为了获得确定性最优和令人满意的解决方案，研究人员经常采用基于偏好的方法，包括根据决策者的后验偏好在帕累托方案中进行选择，以及使用包含先验偏好的确定性模型。在本研究中，我们要解决两个主要难题--具体而言，(1) 衡量公平与效率这一抽象概念的局限性；(2) 在公平与效率之间找到一个确定的最佳和令人满意的平衡点。我们采用由分类和回归树推导出的基尼杂质指数来计算公平性，并确保基尼指数函数的可微分性。此外，我们还统一了公平和效率的尺度，以方便计算。利用准确的偏好信息，我们采用了扩展区间目标编程法来求解模型，并获得了确定的最优满意解。对比分析结果表明，我们的模型（1）有效地解决了现实世界中关于公平与效率权衡的水资源分配问题；（2）使用更精细的惩罚函数，更贴近决策者的真实和非线性偏好，产生的惩罚更少，案例研究中的平均改进率为 8%。

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引用次数: 0

Deliberate shortage in live-streaming commerce 直播商业的故意短缺

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-17 DOI: 10.1016/j.omega.2024.103201

Kaili Li , Song Yao , Yongjian Li , Fangcheng Tang , Zhongbin Wang

Live-streaming commerce has gained significant traction in recent years as an additional channel employed by online retailers to engage consumers in real-time interactions. However, it is essential to highlight the growing prevalence of limited sales as a popular marketing strategy within these live-streaming channels, resulting in an inability to fulfill all consumer demands. Surprisingly, this phenomenon has gone largely unnoticed in previous literature. This paper aims to bridge this gap by delving into the impact of product shortages within the realm of live-streaming commerce. To accomplish this objective, we introduce a stylized model that captures the strategic interactions between online retailers and consumers within live-streaming channels featuring rationed product availability. Our findings reveal that the online retailer’s profit exhibits a unimodal trend concerning the quantity of products offered in the live-streaming channel when the product value falls within a non-extreme range. In simpler terms, deliberately limiting product availability in live-streaming commerce can lead to significantly higher profits, incentivizing retailers to implement rationing strategies. Moreover, contrary to conventional expectations that consumers anticipate a greater supply of products than the retailer intends to provide, we uncover that consumers expect a lower quantity when the potential product value is relatively small. Finally, our research highlights that while live-streaming channels attract consumers with high patience, encouraging their engagement, impatient consumers who favor traditional online channels may face long-term adverse effects due to the retailer’s strategic pricing response. We validate the robustness of our main findings by exploring various extensions, such as the influence of strategic waiting behavior, advertising effects and enhanced perceived product value.

近年来，作为在线零售商与消费者进行实时互动的又一渠道，直播商务获得了巨大的发展。然而，有必要强调的是，在这些直播渠道中，限量销售作为一种流行的营销策略越来越普遍，导致无法满足消费者的所有需求。令人惊讶的是，这一现象在以往的文献中基本上没有被注意到。本文旨在通过深入研究直播商业领域中产品短缺的影响来弥补这一空白。为了实现这一目标，我们引入了一个风格化模型，该模型捕捉了在线零售商和消费者在产品供应配给的直播渠道中的战略互动。我们的研究结果表明，当产品价值处于非极端范围内时，在线零售商的利润与直播渠道中提供的产品数量呈单峰趋势。简单地说，在直播商务中刻意限制产品供应量可大幅提高利润，从而激励零售商实施配给策略。此外，与消费者预期产品供应量大于零售商打算提供的产品供应量的传统预期相反，我们发现，当潜在产品价值相对较小时，消费者预期产品供应量较低。最后，我们的研究强调，虽然直播渠道吸引了高耐心的消费者，鼓励了他们的参与，但由于零售商的策略性定价反应，偏爱传统在线渠道的没有耐心的消费者可能会面临长期的不利影响。我们通过探讨各种延伸问题，如战略等待行为的影响、广告效应和感知产品价值的提升，验证了我们主要结论的稳健性。

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引用次数: 0

From investigation of expressiveness and robustness to a comprehensive value-based framework for multiple criteria sorting problems 从表现力和稳健性研究到多标准排序问题的基于价值的综合框架

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-15 DOI: 10.1016/j.omega.2024.103203

Miłosz Kadziński , Michał Wójcik , Mohammad Ghaderi

We adopt an experiment-oriented perspective to investigate two essential characteristics – expressiveness and robustness – of multiple criteria sorting methods. We focus on the approaches from the family of UTADIS, learning the parameters of a value-driven threshold-based model from the Decision Maker’s assignment examples. Even if the considered properties are crucial for the methods’ reliability and usefulness in real-world scenarios, their verification through explicit numerical tests has been so far neglected. On the one hand, expressiveness captures the models’ flexibility to reproduce different preferences, including simple and complex ones, meaningfully and accurately. On the other hand, robustness reflects the ability to deliver valid recommendations and ensure proper conclusiveness given the multiplicity of compatible preference model instances. We consider different variants of UTADIS, from assuming monotonic and preferentially independent criteria to more advanced settings that relax the monotonicity constraints or represent interactions. The experimental results capture the trade-off between the considered quality dimensions, indicating that richer models are characterized by greater expressiveness and lesser robustness. We also formulate a comprehensive framework indicating when some variant should be used, given the nature of supplied preferences or problem characteristics. These findings aid decision analysts in making robust recommendations in different contexts and help refine preference modeling assumptions. The framework’s practical use is illustrated in a case study involving sorting mobile phone models into pre-defined preference-ordered classes.

我们采用面向实验的视角来研究多重标准排序方法的两个基本特征--表现力和稳健性。我们将重点放在UTADIS系列方法上，从决策者的分配示例中学习基于值驱动阈值模型的参数。尽管所考虑的特性对于这些方法在现实世界中的可靠性和实用性至关重要，但迄今为止，通过明确的数值测试来验证这些特性却一直被忽视。一方面，表达性体现了模型的灵活性，可以有意义地、准确地再现不同的偏好，包括简单偏好和复杂偏好。另一方面，鲁棒性反映了提供有效建议的能力，以及在兼容偏好模型实例众多的情况下确保适当结论的能力。我们考虑了UTADIS的不同变体，从假定单调性和优先独立标准，到放宽单调性约束或表示交互作用的更高级设置。实验结果反映了所考虑的质量维度之间的权衡，表明更丰富的模型具有更强的表现力和更低的鲁棒性。我们还制定了一个全面的框架，指出根据所提供偏好的性质或问题特征，何时应使用某些变体。这些发现有助于决策分析师在不同情况下提出稳健的建议，并有助于完善偏好建模假设。该框架的实际应用在一个案例研究中得到了说明，该案例研究涉及将手机模型排序到预定义的偏好排序类别中。

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引用次数: 0

Brand extension strategy in the presence of carbon tax regulation policy and social influence 碳税监管政策和社会影响下的品牌延伸战略

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-11 DOI: 10.1016/j.omega.2024.103210

Pin Zhou , He Xu , Xu Liu , Dan Gao

Brand extension is a common marketing strategy used to capture a competitive advantage in the fashion industry and often causes social influence between the parent and sub-brands. On the one hand, sub-brand consumers are more willing to buy products when the parent brand sells well. On the other hand, the parent brand consumers’ purchase intention decreases when the sub-brand product sells too much. The fashion industry also contributes considerably to global carbon emissions. To reach sustainable development goals, governments impose carbon taxes. This paper analyzes how social influence and carbon tax regulations can affect a monopolistic firm’s brand extension strategy. The analytical results show that the firm extends from the parent brand to the sub-brand when the magnitude of social influence is not strong in the absence of a carbon tax, as the market expansion effect dominates the cannibalization effect. When the regulator imposes a carbon emissions tax, the range is further narrowed of the social influence that allows the firm to benefit from brand extension strategy because of the cost effect. Counterintuitively, the brand extension strategy can force the regulator to lower the tax price. Moreover, our findings reveal that social influence exerts an inverse impact on the regulator’s tax pricing decisions, contingent upon the extent of the parent brand’s brand power advantage. Carbon tax regulation hurts the firm and consumer surplus, but benefits the environment and social welfare. Additionally, we reaffirm the robustness of our findings under conditions of asymmetry in the intensity of social influence and different pollution damage functions. Intriguingly, we find that the firm can mitigate the negative cannibalization effect by selling its sub-brand products through a downstream retailer.

品牌延伸是时尚产业为获取竞争优势而常用的营销策略，往往会在母品牌和子品牌之间产生社会影响。一方面，当母品牌销售良好时，子品牌消费者更愿意购买产品。另一方面，当子品牌产品销量过高时，母品牌消费者的购买意向就会下降。时尚产业对全球碳排放也有很大贡献。为实现可持续发展目标，各国政府纷纷征收碳税。本文分析了社会影响和碳税法规如何影响垄断企业的品牌延伸战略。分析结果表明，在不征收碳税的情况下，当社会影响力不大时，由于市场扩张效应主导了蚕食效应，企业会从母品牌向子品牌延伸。当监管机构征收碳排放税时，由于成本效应，使企业从品牌延伸战略中获益的社会影响范围进一步缩小。与直觉相反，品牌延伸战略可以迫使监管机构降低税价。此外，我们的研究结果表明，社会影响力对监管机构的税收定价决策具有反向影响，这取决于母品牌的品牌力优势程度。碳税监管损害了企业和消费者剩余，但有利于环境和社会福利。此外，在社会影响强度不对称和污染损害函数不同的条件下，我们再次证实了研究结果的稳健性。耐人寻味的是，我们发现企业可以通过下游零售商销售其子品牌产品来缓解负面蚕食效应。

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引用次数: 0

Embracing market dynamics in the post-COVID era: A data-driven analysis of investor sentiment and behavioral characteristics in stock index futures returns 后 COVID 时代的市场动态：股指期货收益中的投资者情绪和行为特征的数据驱动分析

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-11 DOI: 10.1016/j.omega.2024.103193

Jie Gao, Chunguo Fan, Ting Liu, Xiuran Bai, Wenyong Li , Huimin Tan

This paper aims to enhance the understanding and prediction of stock market behavior during unexpected events like the COVID-19 pandemic, with a specific focus on the role of market attention, social media sentiment indicators, and the development and evolution of unexpected events. We highlight that the common trading and technical indicators used in forecasting the stock index futures prices often overlook investor sentiment and pandemic-related data, which can be instrumental in predicting stock market behavior during significant emergencies. In response, we propose a multi-faceted approach that incorporates these overlooked factors. First, we enhance the predictive index system by integrating investor sentiment, derived from stock message board commentary, and investor behavior influenced by the development and evolution of the pandemic. This innovative approach refines our model's predictive capabilities and is validated through comparative analysis. Second, we introduce a hybrid framework for predicting stock index futures closing prices. By decomposing the closing price series into long-term trends, cyclical variations, and random fluctuations, we create a more nuanced forecast. Each component is predicted separately using appropriate time-series algorithms, improving the overall predictive accuracy and offering generalizability and scalability. Third, we devise a dynamic trading strategy that recognizes pandemic-related data, evolving over time, as a pivotal factor. This strategy is adaptable to evolving market conditions, and our experimental evidence demonstrates its effectiveness in yielding higher returns and reducing associated risks. Our findings underline the importance of incorporating investor sentiment and pandemic-related data into stock market predictions, thus offering a more comprehensive and accurate approach to market forecasting and risk management.

本文旨在加强对 COVID-19 大流行等突发事件期间股市行为的理解和预测，特别关注市场关注度、社交媒体情绪指标的作用以及突发事件的发展和演变。我们强调，用于预测股指期货价格的常用交易和技术指标往往忽略了投资者情绪和大流行病相关数据，而这些数据有助于预测重大突发事件期间的股市行为。为此，我们提出了一种多方面的方法，将这些被忽视的因素纳入其中。首先，我们整合了从股票留言板评论中得出的投资者情绪以及受大流行病发展和演变影响的投资者行为，从而增强了预测指数系统。这种创新方法完善了我们模型的预测能力，并通过比较分析得到了验证。其次，我们引入了预测股指期货收盘价的混合框架。通过将收盘价序列分解为长期趋势、周期性变化和随机波动，我们创建了一个更细致的预测。使用适当的时间序列算法分别预测每个组成部分，从而提高整体预测准确性，并提供通用性和可扩展性。第三，我们设计了一种动态交易策略，将随时间演变的大流行病相关数据视为关键因素。该策略可适应不断变化的市场条件，我们的实验证据证明了它在获得更高回报和降低相关风险方面的有效性。我们的发现强调了将投资者情绪和大流行病相关数据纳入股市预测的重要性，从而为市场预测和风险管理提供了一种更全面、更准确的方法。

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引用次数: 0

Live streaming channel and product assortment with both national and store brand products 直播频道和产品种类包括国家品牌和商店品牌产品

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-10 DOI: 10.1016/j.omega.2024.103212

Qiuyan Chen , Xin Yan , Yiwen Bian , Xiaohua Han

To counteract the fierce competition in the online retailing market, retailers are increasingly adopting live streaming selling model and introducing store brand product to enhance their competitiveness. In this context, we attempt to examine whether and when a retailer should launch a live streaming channel. If launched, we further investigate how the retailer should assort both national and store brand products across available channels. To delve into these questions, we consider a supply chain consisting of a manufacturer and an online retailer, where the retailer resells the manufacturer's national brand product and also sells a store brand product. We examine the retailer's optimal channel strategy and product assortment strategy by considering six scenarios, differentiated by whether introducing the live streaming channel and various product assortment tactics. Our findings indicate that as long as the fixed setup cost of the live channel is relatively low, the retailer will always introduce a live streaming channel. The retailer's optimal assortment of both products across channels highly depends on the consumers’ additional value derived from the live streaming channel and the perceived quality of the store brand product. We also find that, the retailer's optimal channel strategy and product assortment may not always benefit the manufacturer, but there exist conditions that can create win-win situations for both players. Our study further shows that if the retailer launches the live streaming channel at the start, it may not always be necessary to introduce the store brand product under certain conditions.

为了应对在线零售市场的激烈竞争，零售商越来越多地采用直播销售模式，并推出商店品牌产品，以增强竞争力。在此背景下，我们试图研究零售商是否应该以及何时推出直播渠道。如果推出，我们将进一步研究零售商应如何在现有渠道中对全国品牌和商店品牌产品进行分类。为了深入探讨这些问题，我们考虑了一条由制造商和在线零售商组成的供应链，其中零售商转售制造商的全国品牌产品，同时也销售商店品牌产品。我们通过考虑六种情况来研究零售商的最优渠道战略和产品分类战略，这六种情况因是否引入直播渠道和各种产品分类策略而有所不同。我们的研究结果表明，只要直播渠道的固定设置成本相对较低，零售商总是会引入直播渠道。零售商在不同渠道中对两种产品的最优分类在很大程度上取决于消费者从直播渠道中获得的附加价值以及对商店品牌产品的感知质量。我们还发现，零售商的最佳渠道策略和产品种类不一定总是有利于制造商，但存在着能为双方创造双赢局面的条件。我们的研究进一步表明，如果零售商一开始就推出直播流媒体渠道，在某些条件下可能并不一定需要引入商店品牌产品。

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引用次数: 0

Finding robustly fair solutions in resource allocation 在资源分配中寻找稳健公平的解决方案

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-09 DOI: 10.1016/j.omega.2024.103208

Özlem Karsu, İzzet Egemen Elver, Tuna Arda Kınık

In this study, we consider resource allocation settings where the decisions affect multiple beneficiaries and the decision maker aims to ensure that the effect is distributed to the beneficiaries in an equitable manner. We specifically consider stochastic environments where there is uncertainty in the system and propose a robust programming approach that aims at maximizing system efficiency while guaranteeing an equitable benefit allocation even under the worst scenario. Acknowledging the fact that the robust solution may lead to high efficiency loss and may be over-conservative, we adopt a parametric approach that allows controlling the level of conservatism and present the decision maker alternative solutions that reveal the trade-off between efficiency and the degree of conservatism when incorporating fairness. We obtain tractable formulations, leveraging the results we provide on the properties of highly unfair allocations. We demonstrate the usability of our approach on project selection and shelter allocation applications.

在本研究中，我们考虑了资源分配环境，在这种环境下，决策会影响多个受益人，而决策者的目标是确保以公平的方式将效果分配给受益人。我们特别考虑了系统中存在不确定性的随机环境，并提出了一种稳健编程方法，旨在最大限度地提高系统效率，同时即使在最坏的情况下也能保证公平的收益分配。考虑到稳健方案可能会导致较高的效率损失，也可能过于保守，我们采用了一种参数化方法，允许控制保守程度，并为决策者提供了替代方案，揭示了在考虑公平性时效率与保守程度之间的权衡。利用我们提供的关于高度不公平分配特性的结果，我们获得了可行的公式。我们在项目选择和住房分配应用中展示了我们方法的可用性。

引用次数: 0

On the bullwhip behaviour of a hybrid manufacturing and remanufacturing system under autocorrelated demand and returns 论需求与回报自相关条件下混合制造与再制造系统的牛鞭行为

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-05 DOI: 10.1016/j.omega.2024.103209

Yan Lu , Junyi Lin , Shupeng Huang , Jianghang Chen

This study explores the bullwhip behaviour of a hybrid manufacturing-remanufacturing system, replenished by the order-up-to policy, under auto-correlated autoregressive and integrated moving average (ARIMA) demand and corrected returns. The phenomena of demand auto-correlation are common in various industries such as automobile, beverage, and fruit and vegetables industries. However, only first-order vector autoregressive (VAR(1)) and independent and identically distributed (i.i.d.) process have been studied in the context of closed loop supply chains (CLSCs) system dynamics. Therefore, by using

z

-transform and discrete-time simulation, we explore bullwhip and inventory variance under i.i.d, AR (1), first-order moving average (MA(1)) and first-order autoregressive and moving average (ARMA(1,1)) demand processes. It is found that, for products that have autoregressive demand characteristics, bullwhip decreases with the autoregressive demand parameter, while autoregressive return parameter has a U-shaped impact on the bullwhip. For those with moving average demand patterns, bullwhip increases with the moving average demand parameter and decreases with the moving average return parameter. Also, system parameters including return rate, inventory proportional controller and forecasting smoothing not only directly impact on bullwhip and inventory variance, but also act as the moderator in influencing the relationship between demand processes and bullwhip/inventory variance. These findings imply important managerial implication to control the bullwhip costs associated with products characterised by both autoregressive and moving average demand processes.

本研究探讨了在自相关自回归综合移动平均（ARIMA）需求和校正收益的情况下，由订购到补货政策补充的混合制造-再制造系统的牛鞭行为。需求自相关现象在汽车、饮料、果蔬等多个行业中普遍存在。然而，在闭环供应链（CLSCs）系统动力学背景下，只有一阶向量自回归（VAR(1)）和独立同分布（i.i.d.）过程得到了研究。因此，通过使用 z 变换和离散时间模拟，我们探讨了 i.i.d、AR(1)、一阶移动平均（MA(1)）和一阶自回归移动平均（ARMA(1,1)）需求过程下的牛鞭效应和库存方差。研究发现，对于具有自回归需求特征的产品，牛鞭随自回归需求参数的增加而减少，而自回归收益参数对牛鞭的影响呈 U 型。对于具有移动平均需求模式的产品，牛鞭随移动平均需求参数的增加而增加，随移动平均回报参数的增加而减少。此外，包括退货率、库存比例控制器和预测平滑等系统参数不仅直接影响牛鞭和库存方差，而且在影响需求过程与牛鞭/库存方差之间的关系方面起着调节作用。这些发现对控制与自回归和移动平均需求过程相关的产品牛鞭成本具有重要的管理意义。

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引用次数: 0

Adjustable robust optimization approach for SVM under uncertainty 不确定条件下 SVM 的可调整稳健优化方法

IF 6.7 2区管理学 Q1 MANAGEMENT

Omega-international Journal of Management Science

Pub Date : 2024-10-04 DOI: 10.1016/j.omega.2024.103206

F. Hooshmand, F. Seilsepour, S.A. MirHassani

The support vector machine (SVM) is one of the successful approaches to the classification problem. Since the values of features are typically affected by uncertainty, it is important to incorporate uncertainty into the SVM formulation. This paper focuses on developing a robust optimization (RO) model for SVM. A key distinction from existing literature lies in the timing of optimizing decision variables. To the best of our knowledge, in all existing RO models developed for SVM, a common assumption is that all decision variables are decided before the uncertainty realization, which leads to an overly conservative decision boundary. However, this paper adopts a different strategy by determining the variables that assess the misclassification error of data points or their fall within the margin post-realization, resulting in a less conservative model. The RO models where decisions are made in two stages (some before and the rest after the uncertainty resolution), are called adjustable RO models. This adjustment results in a three-level optimization model for which two decomposition-based algorithms are proposed. In these algorithms, after providing a bi-level reformulation, the model is divided into a master-problem (MP) and a sub-problem the interaction of which yields the optimal solution. Acceleration of algorithms via incorporating valid inequalities into MP is another novelty of this paper. Computational results over simulated and real-world datasets confirm the efficiency of the proposed model and algorithms.

支持向量机（SVM）是解决分类问题的成功方法之一。由于特征值通常会受到不确定性的影响，因此将不确定性纳入 SVM 的表述非常重要。本文的重点是为 SVM 开发鲁棒优化 (RO) 模型。与现有文献的关键区别在于优化决策变量的时机。据我们所知，在所有为 SVM 开发的现有 RO 模型中，一个共同的假设是所有决策变量都在不确定性实现之前决定，这导致决策边界过于保守。然而，本文采用了不同的策略，即在实现后确定评估数据点的误分类误差或其落差的变量，从而使模型不那么保守。分两个阶段（部分在不确定性解决之前，其余在不确定性解决之后）做出决策的 RO 模型称为可调整 RO 模型。这种调整会产生一个三级优化模型，为此提出了两种基于分解的算法。在这些算法中，在提供两级重构后，模型被划分为一个主问题（MP）和一个子问题，两者相互作用产生最优解。通过将有效不等式纳入 MP 来加速算法是本文的另一个新颖之处。对模拟和真实世界数据集的计算结果证实了所提模型和算法的效率。

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引用次数: 0