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Introduction to the SI “Advances in operations research and machine learning focused on pandemic dynamics” SI“专注于流行病动力学的运筹学和机器学习进展”简介
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-12-01 DOI: 10.1016/j.orp.2023.100287
Massimiliano Ferrara , Ali Ahmadian , Soheil Salashour , Bruno Antonio Pansera
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引用次数: 0
Deep reinforcement learning based medical supplies dispatching model for major infectious diseases: Case study of COVID-19 基于深度强化学习的重大传染病医疗物资调度模型——以2019冠状病毒病为例
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-12-01 DOI: 10.1016/j.orp.2023.100293
Jia-Ying Zeng , Ping Lu , Ying Wei , Xin Chen , Kai-Biao Lin
<div><p>Stockpiling and scheduling plans for medical supplies represent essential preventive and control measures in major public health events. In the face of major infectious diseases, such as the novel coronavirus disease (COVID-19), the outbreak trend and variability of disease strains are often unpredictable. Hence, it is necessary to optimally adjust the prevention and control dispatching strategy according to the circumstances and outbreak locations to maintain economic development while ensuring the human health survival, however, many models in this scenario seldom consider the dynamic material prediction and the measurement of multiple costs at the same time. Taking the COVID-19 scenario as a case study, we establish a deep reinforcement learning (DRL)-based medical supplies dispatching (MSD) model for major infectious diseases, considering the volatility of the COVID-19 situation and the discrepancy between medical material demand and supply due to the high infectiousness of the Omicron series strains. The present model has three main components: 1) First, for the dynamic medical material prediction problem in complex infectious disease scenarios, taking the lifted COVID-19 lockdown scenario as an example, the modified susceptible-exposed-infected-recovered (SEIR) model was utilized to analyze the spread of the COVID-19, understand its characteristics, and map out the related medical supplies demand; 2) Second, to break away from the previous premise of only considering supply-demand, this study adds scheduling rules and cost function that weighs health and economic costs. An epidemic dispatching optimization model (Epi_DispatchOptim) was established using the OpenAI Gym toolkit to form an environment structure with virus transmission space, and emergency MSD while considering both human health and economic costs. This architecture interprets the balance between the supply-demand of medical supplies and reflects the importance of MSD in the balanced development of health and economy under the spread of infectious diseases; 3) Finally, the MSD strategy under the balance of health and economic cost is explored in Epi_DispatchOptim using reinforcement learning (RL) and the evolutionary algorithm (EA). Experiments conducted on two datasets indicate that the RL and EA reduce economic as well as health costs compared to the original environmental strategies. The above study illustrates how to use epidemiological models to predict the demand for healthcare supplies as the premise of scheduling models, and use Epi_DispatchOptim to explore the dynamic MSD decisions under mortality and economic equilibrium. In Shanghai, China, the economic cost of the exploration strategy is reduced by 27.36–27.07B compared to static scheduling, and deaths are reduced by 126–150 in 150 day compared to the no-intervention scenario. By integrating knowledge of epidemiology, optimal decision making, and economics, Epi_DispatchOptim further constructs epidemiologica
医疗用品的储存和调度计划是重大公共卫生事件中必不可少的预防和控制措施。面对新型冠状病毒病(COVID-19)等重大传染病,疾病毒株的爆发趋势和变异往往是不可预测的。因此,在保证人类健康生存的同时,需要根据具体情况和疫情发生地对防控调度策略进行优化调整,但这种情况下的许多模型很少同时考虑动态物质预测和多重成本的测量。以新冠肺炎疫情为例,考虑新冠肺炎疫情的波动性和欧米克隆系列菌株高传染性导致的医疗物资供需差异,建立了基于深度强化学习(DRL)的重大传染病医疗物资调度模型。该模型主要由三个部分组成:1)首先,针对复杂传染病场景下的动态物资预测问题,以新冠肺炎解除封锁场景为例,利用改进的易感暴露感染恢复(SEIR)模型分析新冠肺炎的传播情况,了解疫情特征,规划相关医疗物资需求;2)其次,打破了以往只考虑供需的前提,增加了调度规则和权衡健康成本和经济成本的成本函数。利用OpenAI Gym工具包建立疫情调度优化模型Epi_DispatchOptim,在考虑人类健康和经济成本的情况下,形成病毒传播空间和应急MSD的环境结构。这一体系结构诠释了医疗用品供需平衡,反映了传染病传播下MSD在卫生与经济平衡发展中的重要性;3)最后,利用强化学习(RL)和进化算法(EA)探讨了Epi_DispatchOptim在健康和经济成本平衡下的MSD策略。在两个数据集上进行的实验表明,与原始环境策略相比,RL和EA降低了经济和健康成本。本文以流行病学模型预测医疗物资需求为调度模型的前提,利用Epi_DispatchOptim研究死亡率和经济均衡下的动态MSD决策。在中国上海,与静态调度相比,该勘探策略的经济成本降低了27.36-27.07B,与不干预方案相比,150天内死亡人数减少了126-150人。Epi_DispatchOptim通过整合流行病学、最优决策和经济学知识,进一步构建流行病学模型、成本函数、状态-行动空间等模块,帮助公共卫生决策者在重大公共卫生事件中采取适当的MSD策略。
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引用次数: 0
Early detection of students’ failure using Machine Learning techniques 使用机器学习技术早期发现学生的失败
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-11-20 DOI: 10.1016/j.orp.2023.100292
Aarón López-García , Olga Blasco-Blasco , Marina Liern-García , Sandra E. Parada-Rico

The educational system determines one of the significant strengths of an advanced society. A country with a lack of culture is less competitive due to the inequality suffered by its people. Institutions and organizations are putting their efforts into tackling that problem. Nevertheless, it is not an easy task to ascertain why their students have failed or what are the conditions that affect such situations. In this work, an intelligent system is proposed to predict academic failure by using student information stored by the Industrial University of Santander (Colombia). The prediction model is powered by the XGBoost algorithm, where a TOPSIS-based feature extraction and ADASYN oversampling have been conducted. Hyperparameters of the classifier were tuned by a cross-validated grid-search algorithm. We have compared our results with other decision-tree classifiers and displayed the feature importance of our intelligent system as an explainability phase. In conclusion, our intelligent system has shown a superior performance of our prediction model and has indicated to us that economic, health and social factors are decisive for the academic performance of the students.

教育制度决定了一个先进社会的重要力量之一。一个缺乏文化的国家由于其人民遭受的不平等而缺乏竞争力。机构和组织正在努力解决这个问题。然而,要弄清楚他们的学生失败的原因或影响这种情况的条件并不是一件容易的事。在这项工作中,提出了一个智能系统,通过使用桑坦德工业大学(哥伦比亚)存储的学生信息来预测学业失败。预测模型由XGBoost算法驱动,其中进行了基于topsis的特征提取和ADASYN过采样。通过交叉验证的网格搜索算法对分类器的超参数进行了调整。我们将我们的结果与其他决策树分类器进行了比较,并显示了我们的智能系统作为可解释性阶段的特征重要性。综上所述,我们的智能系统表现出了我们预测模型的优越性能,并向我们表明,经济、健康和社会因素对学生的学习成绩具有决定性作用。
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引用次数: 0
Research on the scheduling method of ground resource under uncertain arrival time 不确定到达时间下地面资源调度方法研究
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-11-15 DOI: 10.1016/j.orp.2023.100291
Guoning Xu, Yupeng Lin, Zhiying Wu, Qingxin Chen, Ning Mao

We present a two-stage scheduling approach including proactive and reactive scheduling to solve the ground resource scheduling problem with uncertain arrival time. In the first stage, an integer programming model is constructed to minimize the delay and transfer costs. After solving this model, we obtain a baseline scheduling plan that considers the service arrival time uncertainty. In the second stage, the feasibility of the subsequent benchmark plan is evaluated based on the current state of the services and resources. The reactive scheduling model is enabled when trigger conditions are met. Moreover, an improved adaptive large neighborhood search is designed to solve the proactive scheduling model effectively. Real data from an international airport in South China is used as a test case to compare different scheduling strategies. The results show that it is difficult to handle the uncertainty of the problem with the benchmark plan that simply considered buffer time. Compared with rolling time-domain scheduling, the average transfer cost of the scheduling strategy proposed in this paper increased slightly, but the average service delay cost can be reduced significantly. Algorithm-wise, instances of different scales are designed to verify the effectiveness of the improved adaptive large neighborhood search algorithm. The efficiency of the algorithm scheme is better than that of the Gurobi solver scheme in medium to large-scale problems. Therefore, the forward and reactive strategies can better handle the uncertainty of airport ground protection services as they can simultaneously guide the allocation and utilization of airport ground protection resources.

针对地面资源到达时间不确定的调度问题,提出了一种主动和被动两阶段调度方法。在第一阶段,构造一个整数规划模型,以最小化延迟和转移成本。求解该模型后,得到了考虑服务到达时间不确定性的基线调度方案。在第二阶段,根据服务和资源的当前状态评估后续基准计划的可行性。当满足触发条件时,启用响应式调度模型。此外,设计了一种改进的自适应大邻域搜索算法,有效地解决了主动调度问题。本文以华南某国际机场的真实数据为例,比较不同的调度策略。结果表明,单纯考虑缓冲时间的基准方案难以处理问题的不确定性。与滚动时域调度相比,本文提出的调度策略的平均转移成本略有增加,但平均服务延迟成本可以显著降低。在算法方面,设计了不同尺度的实例来验证改进的自适应大邻域搜索算法的有效性。在大中型问题中,该算法方案的求解效率优于Gurobi方案。因此,正向策略和被动策略可以同时指导机场地面保护资源的配置和利用,可以更好地处理机场地面保护服务的不确定性。
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引用次数: 0
Effects of variable prepayment installments on pricing and inventory decisions with power demand pattern and non-linear holding cost under carbon cap-and-price regulation 碳限额-价格管制下电力需求模式和非线性持有成本下可变预付分期对定价和库存决策的影响
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-11-11 DOI: 10.1016/j.orp.2023.100289
Md. Al-Amin Khan , Leopoldo Eduardo Cárdenas-Barrón , Gerardo Treviño-Garza , Armando Céspedes-Mota , Imelda de Jesús Loera-Hernández , Neale R. Smith

Regulators’ increasingly stringent carbon rules to protect the environment are encouraging practitioners to modify their operational activities that are accountable for releasing emissions into the atmosphere. Thereby, practitioners dealing with product inventory planning are seeking proper management strategies not only to increase profits but also to reduce released carbons from operations. In addition, increasing uncertainty in supply operations has motivated suppliers to impose prepayment mechanisms in recent decades. This study examines the best prepayment installment policy for a practitioner for the first time, where the consumption behavior of consumers changes as a result of the combined effects of unit selling price and storage time. Moreover, to make the present inventory planning more realistic, the unit holding cost function is adopted as a power function of the inventory unit's storage period. The goal of this study is to provide the best combined installment for advance payment, price, and replenishment strategies for a practitioner under cap-and-price, cap-and-trade, and carbon tax environmental guidelines by ensuring maximum profit. For this purpose, an algorithm is created by combining all derived theoretical results from the analytical study, whereas the efficacy of the algorithm is assessed through the examination of five illustrative numerical instances. A plethora of noteworthy management insights for the practitioner are obtained by investigating the dynamic shifts in optimal strategies resulting from fluctuations in system parameters. The results reveal that if the demand is low in the nascent phases of the business cycle, then the prudent approach for the practitioner entails procuring a comparatively smaller lot-size using a modest number of payment frequencies and then setting a relatively small unit selling price to increase profits.

监管机构为保护环境而制定的日益严格的碳排放规定,正鼓励从业者修改对排放到大气中的气体负责的经营活动。因此,处理产品库存计划的从业者正在寻求适当的管理策略,不仅要增加利润,还要减少运营中释放的碳。此外,近几十年来,供应业务日益增加的不确定性促使供应商实施预付机制。本文首次探讨了在单位销售价格和储存时间共同作用下,消费者消费行为发生变化的最佳提前付款分期付款政策。此外,为了使现有的库存规划更具有现实性,采用了单位持有成本函数作为库存单元存贮期的幂函数。本研究的目的是提供在限额与价格、限额与交易和碳税环境指导下,为从业者提供最佳的预付款、价格和补充策略组合,以确保利润最大化。为此,通过结合分析研究的所有推导出的理论结果来创建算法,而通过检查五个说明性数值实例来评估算法的有效性。通过研究由系统参数波动引起的最优策略的动态变化,从业者获得了大量值得注意的管理见解。结果表明,如果在商业周期的初期阶段需求较低,那么对于从业者来说,谨慎的方法需要使用适度数量的付款频率采购相对较小的批量,然后设置相对较小的单位销售价格以增加利润。
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引用次数: 0
Prescriptive price optimization using optimal regression trees 使用最优回归树的规定性价格优化
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-11-10 DOI: 10.1016/j.orp.2023.100290
Shunnosuke Ikeda , Naoki Nishimura , Noriyoshi Sukegawa , Yuichi Takano

This paper is concerned with prescriptive price optimization, which integrates machine learning models into price optimization to maximize future revenues or profits of multiple items. The prescriptive price optimization requires accurate demand forecasting models because the prediction accuracy of these models has a direct impact on price optimization aimed at increasing revenues and profits. The goal of this paper is to establish a novel framework of prescriptive price optimization using optimal regression trees, which can achieve high prediction accuracy without losing interpretability by means of mixed-integer optimization (MIO) techniques. We use the optimal regression trees for demand forecasting and then formulate the associated price optimization problem as a mixed-integer linear optimization (MILO) problem. We also develop a scalable heuristic algorithm based on the randomized coordinate ascent for efficient price optimization. Simulation results demonstrate the effectiveness of our method for price optimization and the computational efficiency of the heuristic algorithm.

本文关注的是规定性价格优化,它将机器学习模型集成到价格优化中,以最大化多个项目的未来收入或利润。规定性的价格优化需要准确的需求预测模型,因为这些模型的预测准确性直接影响到以增加收入和利润为目标的价格优化。本文的目标是利用最优回归树建立一种新的规定性价格优化框架,该框架可以在不失去可解释性的前提下获得较高的预测精度。我们使用最优回归树进行需求预测,然后将相关的价格优化问题表述为混合整数线性优化(MILO)问题。我们还开发了一种基于随机坐标上升的可扩展启发式算法,用于有效的价格优化。仿真结果验证了该方法的有效性和启发式算法的计算效率。
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引用次数: 1
The effect of an uncertain commission rate on the decisions of a capital-constrained developer 不确定的佣金率对资金受限的开发商决策的影响
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-11-10 DOI: 10.1016/j.orp.2023.100288
Tal Avinadav, Priel Levy

This study investigates a green supply chain consisting of a capital-constrained developer who sells a product via a platform. The parties interact via an agency contract, in which the platform charges a fixed proportion of the revenue gained from each sold unit and the developer receives the remaining sum. Since the development process is relatively protracted, at the early stages of this process, the commission rate to be charged by the platform is random from the developer’s perspective. Upon receiving information about the amount of capital the developer has committed to investing in greenness from his own resources, an external investor offers the developer a loan at a certain interest rate (to further enhance the developer’s investment in greenness), based on which the developer sets the product’s greenness level and selling price. The study provides a game-theoretic analysis of this model and compares its equilibrium solution with the optimal solution of a fully self-financing developer. The innovative feature of the study lies in its comparison between the case of a developer who might not be able to repay the loan, because his revenue from selling the product might be lower than the amount he is required to repay the investor (the loan plus interest), and the case in which it is certain that the developer will be able to repay any debt to the investor. Our study shows that, in the case where the investor takes on the financing risk, the customers benefit from a higher greenness level (albeit at a higher price), resulting in greater demand for the product.

本文研究了一个绿色供应链,由一个资金受限的开发商通过平台销售产品组成。双方通过代理合同进行互动,根据该合同,平台从每台售出的游戏中收取固定比例的收益,而开发商则获得剩余的收益。由于开发过程相对较长,在此过程的早期阶段,平台收取的佣金率从开发者的角度来看是随机的。外部投资者在收到开发商从自身资源中承诺投入的绿色资金信息后,以一定的利率向开发商提供贷款(以进一步提高开发商的绿色投资),开发商据此确定产品的绿色水平和销售价格。本文对该模型进行了博弈论分析,并将其均衡解与完全自负盈亏的开发商的最优解进行了比较。该研究的创新之处在于,它比较了两种情况,一种是开发商可能无法偿还贷款,因为他销售产品的收入可能低于偿还投资者所需的金额(贷款加利息),另一种是开发商肯定能够偿还投资者的任何债务。我们的研究表明,在投资者承担融资风险的情况下,客户受益于更高的绿色水平(尽管价格更高),从而导致对产品的更大需求。
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引用次数: 0
Variable Neighborhood Search Algorithm for the Single Assignment Incomplete Hub Location Problem with Modular Capacities and Direct Connections 具有模块化容量和直接连接的单分配不完全集线器定位问题的变邻域搜索算法
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-07-20 DOI: 10.1016/j.orp.2023.100286
Raed AL Athamneh , Moayad Tanash , Dania Bani Hani , Mustafa Rawshdeh , Abdallah Alawin , Zaid Albataineh

In distribution systems such as airlines and express package delivery, the use of hub-and-spoke networks is common, and flow consolidation at hub facilities is essential for cost reduction. While a constant discount factor is typically used to model cost reduction in interhub links, this paper explores an extension of the incomplete hub location problem with modular capacity that enables direct connections between non-hub nodes. The modified approach, called MHLPDC, aims to locate a set of hub facilities, connect each non-hub node to a hub, and activate hub facility links, access arc links, and direct links between non-hub nodes to minimize network costs. The MHLPDC integrates link activation decisions into the decision-making process and utilizes modular arc costs to model the flow dependence of transportation costs in all arcs. To solve the problem, the paper presents a mixed-integer mathematical programming formulation and heuristic algorithm based on a greedy randomized adaptive search and variable neighborhood search approach. The proposed algorithm produces high-quality solutions, as demonstrated through computational experiments on benchmark instances with up to 40 nodes. Furthermore, a sensitivity analysis of the optimal network structure indicates that increasing the discount factor, by varying hub and access arc capacities as well as the associated variable costs, results in fewer hubs being established and more direct shipments between non-hub nodes being permitted.

在航空公司和快递等分销系统中,轮辐网络的使用很普遍,枢纽设施的流量整合对于降低成本至关重要。虽然通常使用恒定折扣因子来模拟集线器间链路的成本降低,但本文探讨了不完全集线器位置问题的扩展,该问题具有模块化容量,可以实现非集线器节点之间的直接连接。改进后的方法称为MHLPDC,旨在定位一组集线器设施,将每个非集线器节点连接到一个集线器,并激活集线器设施链路、接入弧链路和非集线器节点之间的直接链路,以最大限度地降低网络成本。MHLPDC将链路激活决策集成到决策过程中,并利用模块化弧线成本对所有弧线中运输成本的流量依赖性进行建模。为了解决这一问题,本文提出了一种混合整数数学规划公式和基于贪婪随机自适应搜索和可变邻域搜索的启发式算法。通过在多达40个节点的基准实例上的计算实验证明,所提出的算法产生了高质量的解决方案。此外,对最优网络结构的敏感性分析表明,通过改变枢纽和通道容量以及相关的可变成本来增加折扣因子,可以减少建立枢纽的数量,并允许在非枢纽节点之间进行更多的直接运输。
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引用次数: 0
Interventions in demand and supply sides for vaccine supply chain: An analysis on monkeypox vaccine 疫苗供应链供需双方干预措施:对猴痘疫苗的分析
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-06-28 DOI: 10.1016/j.orp.2023.100285
Hamid R. Sayarshad

After a pandemic, all countries experience a shortage in vaccine supply due to limited vaccine stocks and production capacity globally. One particular problem is that it is hard to predict demands for vaccines during the global crisis. On the other hand, vaccines are usually made and packaged in different places, raising logistical issues and concerns that can further delay distribution. In this paper, we propose an optimization formulation model to link infectious disease dynamics and supply chain networks considering a one-to-one relationship between demand and supply for vaccines. We focus on designing a vaccine coordination system using government subsidy that considers the equilibrium behaviors of manufacturers under an actual demand for the vaccine. This study evaluates vaccine manufacturers and government behaviors that help the vaccine market to reach the socially optimal. Different decisions, such as vaccine demands and vaccine production and distribution are investigated. A study of the monkeypox pandemic in the U.S. is performed to validate our model and its results. The obtained results from testing the proposed system problem revealed that the vaccine coverage increased by up to 35%, while the unmet demand reduced by up to 60%, in comparison to when vaccine manufacturers act individually.

在大流行之后,由于全球疫苗库存和生产能力有限,所有国家都经历了疫苗供应短缺。一个特别的问题是,很难预测全球危机期间对疫苗的需求。另一方面,疫苗通常在不同的地方制造和包装,这引发了物流问题和担忧,可能会进一步推迟分发。在本文中,考虑到疫苗的需求和供应之间的一对一关系,我们提出了一个连接传染病动力学和供应链网络的优化配方模型。我们重点设计了一个使用政府补贴的疫苗协调系统,该系统考虑了制造商在疫苗实际需求下的均衡行为。本研究评估了疫苗制造商和政府帮助疫苗市场达到社会最优的行为。调查了不同的决策,如疫苗需求、疫苗生产和分发。对美国猴痘疫情进行了一项研究,以验证我们的模型及其结果。对拟议系统问题的测试结果显示,与疫苗制造商单独行动相比,疫苗覆盖率增加了35%,而未满足的需求减少了60%。
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引用次数: 3
A real-time balancing market optimization with personalized prices: From bilevel to convex 具有个性化价格的实时平衡市场优化:从双层到凸面
IF 2.5 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2023-01-01 DOI: 10.1016/j.orp.2023.100276
Koorosh Shomalzadeh , Jacquelien M.A. Scherpen , M. Kanat Camlibel

This paper studies the static economic optimization problem of a system with a single aggregator and multiple prosumers in a Real-Time Balancing Market (RTBM). The aggregator, as the agent responsible for portfolio balancing, needs to minimize the cost for imbalance satisfaction in real-time by proposing a set of optimal personalized prices to the prosumers. On the other hand, the prosumers, as price taker and self-interested agents, want to maximize their profit by changing their supplies or demands and providing flexibility based on the proposed personalized prices. We model this problem as a bilevel optimization problem. We first show that the optimal solution of this bilevel optimization problem can be found by solving an equivalent convex problem. In contrast to the state-of-the-art Mixed-Integer Programming (MIP)-based approach to solve bilevel problems, this convex equivalent has very low computation time and is appropriate for real-time applications. Next, we compare the optimal solutions of the proposed personalized scheme and a uniform pricing scheme. We prove that, under the personalized pricing scheme, more prosumers contribute to the RTBM and the aggregator’s cost is less. Finally, we verify the analytical results of this work by means of numerical case studies and simulations.

研究了实时平衡市场中具有单个聚合器和多个产消者系统的静态经济优化问题。聚合器作为负责组合平衡的代理,需要通过向产消者提出一组最优的个性化价格,实时地将不平衡满足的成本最小化。另一方面,生产消费者作为价格接受者和自利的代理人,希望通过改变自己的供给或需求,并根据提出的个性化价格提供灵活性来最大化自己的利润。我们将这个问题建模为一个双层优化问题。我们首先证明了通过求解一个等价的凸问题可以找到这个双层优化问题的最优解。与解决双层问题的最先进的基于混合整数规划(MIP)的方法相比,这种凸等效具有非常低的计算时间,适合于实时应用程序。其次,我们比较了个性化方案和统一定价方案的最优解。我们证明了在个性化定价方案下,更多的生产消费者对RTBM做出了贡献,聚合器的成本更小。最后,通过数值算例和仿真验证了本文的分析结果。
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引用次数: 0
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