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Fair integer programming under dichotomous and cardinal preferences 二分偏好和万有偏好下的公平整数程序设计
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-24 DOI: 10.1016/j.ejor.2024.08.023
Tom Demeulemeester , Dries Goossens , Ben Hermans , Roel Leus
One cannot make truly fair decisions using integer linear programs unless one controls the selection probabilities of the (possibly many) optimal solutions. For this purpose, we propose a unified framework when binary decision variables represent agents with dichotomous preferences, who only care about whether they are selected in the final solution. We develop several general-purpose algorithms to fairly select optimal solutions, for example, by maximizing the Nash product or the minimum selection probability, or by using a random ordering of the agents as a selection criterion (Random Serial Dictatorship). We also discuss in detail how to extend the proposed methods when agents have cardinal preferences. As such, we embed the “black-box” procedure of solving an integer linear program into a framework that is explainable from start to finish. Lastly, we evaluate the proposed methods on two specific applications, namely kidney exchange (dichotomous preferences), and the scheduling problem of minimizing total tardiness on a single machine (cardinal preferences). We find that while the methods maximizing the Nash product or the minimum selection probability outperform the other methods on the evaluated welfare criteria, methods such as Random Serial Dictatorship perform reasonably well in computation times that are similar to those of finding a single optimal solution.
除非控制(可能有很多)最优解的选择概率,否则就无法利用整数线性程序做出真正公平的决策。为此,我们提出了一个统一的框架,当二进制决策变量代表具有偏好的代理时,代理只关心他们是否在最终解决方案中被选中。我们开发了几种通用算法来公平地选择最优解,例如,通过最大化纳什乘积或最小选择概率,或使用代理的随机排序作为选择标准(随机序列独裁)。我们还详细讨论了如何在代理具有偏好的情况下扩展所提出的方法。因此,我们将求解整数线性规划的 "黑箱 "程序嵌入到一个从头到尾都可以解释的框架中。最后,我们在两个具体应用中对所提出的方法进行了评估,即肾脏交换(二分偏好)和单机总迟到时间最小化的调度问题(红心偏好)。我们发现,在所评估的福利标准上,纳什乘积最大化或选择概率最小化的方法优于其他方法,而随机序列独裁等方法的计算时间与寻找单一最优解的计算时间相近,表现相当不错。
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引用次数: 0
A multiobjective ϵ-constraint based approach for the robust master surgical schedule under multiple uncertainties 基于多目标[公式省略]约束的多不确定性条件下鲁棒性主手术计划方法
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-23 DOI: 10.1016/j.ejor.2024.08.022
Salma Makboul , Alexandru-Liviu Olteanu , Marc Sevaux
The efficient scheduling of elective surgeries in hospitals is critical for ensuring patient satisfaction, cost-effectiveness, and overall operational efficiency. However, operating theater (OT) managers face complex and competing scheduling problems due to numerous sources of uncertainty and the impact of the proposed schedule on downstream recovery units, such as the intensive care unit (ICU). To address these challenges, this study develops a multiobjective robust planning model for the weekly Master Surgical Schedule (MSS) under multiple uncertainties. The model takes into account patient priority, assignment cost and workload balancing, while also considering the constraints of the OT, surgeon availabilities, downstream resources, and the uncertainty of surgery duration and patients’ length of stay (LOS) in the ICU. To evaluate the robust solutions, a Monte Carlo simulation is used to calculate the risk of constraint violations, and an adapted ϵ-constraint algorithm is used for the four-objective problem to compute the Pareto front and calculate the hypervolume for every degree of uncertainty. This provides a comprehensive decision tool for OT decision makers and allows for the comparison of various scenarios in terms of the number of scheduled patients, canceled patients, and the utilization rate of the OT.
有效安排医院的择期手术对于确保患者满意度、成本效益和整体运营效率至关重要。然而,手术室(OT)管理人员面临着复杂且相互竞争的排程问题,这是因为存在许多不确定因素,而且拟议的排程对重症监护室(ICU)等下游恢复单元有影响。为了应对这些挑战,本研究开发了一个多目标稳健规划模型,用于在多种不确定性条件下制定每周主手术日程表(MSS)。该模型考虑到了患者优先级、分配成本和工作量平衡,同时还考虑到了加班、外科医生可用性、下游资源的限制,以及手术持续时间和患者在重症监护室住院时间(LOS)的不确定性。为了评估稳健性解决方案,我们使用蒙特卡罗模拟计算违反约束的风险,并针对四目标问题使用了一种适应性约束算法,以计算帕累托前沿,并计算每种不确定性程度下的超体积。这为加班决策者提供了一个全面的决策工具,可对各种情况下的计划病人数、取消病人数和加班利用率进行比较。
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引用次数: 0
Evaluation of counterparty credit risk under netting agreements 净额结算协议下的交易对手信用风险评估
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-23 DOI: 10.1016/j.ejor.2024.08.019
Ahmadreza Tavasoli, Michèle Breton

We investigate counterparty credit risk and credit valuation adjustments in portfolios including derivatives with early-exercise opportunities, under a netting agreement. We show that credit risk and netting agreements have a significant impact on the way portfolios are managed (that is, on options’ exercise strategies) and, therefore, on the value of the portfolio and on the price of counterparty risk. We derive the value of a netted portfolio as the solution of a zero-sum, finite horizon, discrete-time stochastic game. We show that this dynamic-game interpretation can be used to determine the value of the reglementary capital charges required of financial institutions to cover for counterparty credit risk and we propose a numerical valuation method. Numerical investigations show that currently used numerical approaches can grossly misestimate the value of credit valuation adjustments.

我们研究了在净额结算协议下,包括有提前行权机会的衍生品在内的投资组合中的交易对手信用风险和信用估值调整。我们的研究表明,信用风险和净额结算协议对投资组合的管理方式(即期权的行权策略)有重大影响,因此对投资组合的价值和交易对手风险的价格也有重大影响。我们将净投资组合的价值推导为一个零和、有限时间跨度、离散时间随机博弈的解。我们表明,这种动态博弈解释可用于确定金融机构为应对交易对手信用风险所需的补充资本费用的价值,我们还提出了一种数值估值方法。数值研究表明,目前使用的数值方法会严重误估信用估值调整的价值。
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引用次数: 0
Maintenance optimization for multi-component systems with a single sensor 利用单一传感器优化多组件系统的维护工作
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-22 DOI: 10.1016/j.ejor.2024.08.016
Ragnar Eggertsson , Ayse Sena Eruguz , Rob Basten , Lisa M. Maillart
We consider a multi-component system in which a single sensor monitors a condition parameter. Monitoring gives the decision maker partial information about the system state, but it does not reveal the exact state of the components. Each component follows a discrete degradation process, possibly correlated with the degradation of other components. The decision maker infers a belief about each component’s exact state from the current condition signal and the past data, and uses that to decide when to intervene for maintenance. A maintenance intervention consists of a complete and perfect inspection, and may be followed by component replacements. We model this problem as a partially observable Markov decision process. For a suitable stochastic order, we show that the optimal policy partitions in at most three regions on stochastically ordered line segments. Furthermore, we show that in some instances, the optimal policy can be partitioned into two regions on line segments. In two examples, we visualize the optimal policy. To solve the examples, we modify the incremental pruning algorithm, an exact solution algorithm for partially observable Markov decision processes. Our modification has the potential to also speed up the solution of other problems formulated as partially observable Markov decision processes.
我们考虑了一个由多个组件组成的系统,在该系统中,单个传感器监测一个条件参数。监测为决策者提供了系统状态的部分信息,但并不能揭示组件的确切状态。每个组件都遵循一个离散的退化过程,可能与其他组件的退化相关。决策者从当前的状态信号和过去的数据中推断出每个组件的确切状态,并据此决定何时进行维护干预。维护干预包括一次完整、完美的检查,随后可能会进行部件更换。我们将这一问题建模为一个部分可观测的马尔可夫决策过程。对于合适的随机顺序,我们证明最优策略最多能在随机顺序线段上划分出三个区域。此外,我们还证明,在某些情况下,最优策略可以划分为线段上的两个区域。在两个例子中,我们直观地展示了最优策略。为了解决这些例子,我们修改了增量剪枝算法,这是一种针对部分可观测马尔可夫决策过程的精确求解算法。我们的修改也有可能加快以部分可观测马尔可夫决策过程形式提出的其他问题的求解速度。
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引用次数: 0
Applying fixed order commitment contracts in a capacitated supply chain 在产能供应链中应用固定订单承诺合同
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-22 DOI: 10.1016/j.ejor.2024.08.018
Christina Imdahl , Kai Hoberg , William Schmidt

Demand uncertainty can lead to excess inventory holdings, capacity creation, emergency deliveries, and stock-outs. The costs of demand uncertainty may be directly borne by upstream suppliers, but can propagate downstream in the form of higher prices. To address these problems, we investigate a practical application of a fixed order commitment contract (FOCC) in which a manufacturer commits to a minimum fixed order quantity each period and receives a per unit price discount from the supplier for the commitment. We model a FOCC as a Stackelberg game in which the supplier offers a price discount anticipating the manufacturer’s response, and the manufacturer subsequently decides on the optimal commitment quantity. We show that a FOCC can smooth the orders received by the supplier, mitigating the negative consequences of demand uncertainty for the supplier, the manufacturer, and the supply chain. We extend the current literature by solving for an endogenous price discount instead of treating it as an exogenous value, and validate our model insights with our research partner, a large international materials handling equipment manufacturer. Using data on 863 parts, we evaluate the relationships between the model parameters, contract parameters, and the contract effectiveness, and show the conditions under which the FOCC generates greater cost savings for both the manufacturer and supplier. Our results help operations managers better understand how to obtain the optimal contract parameters for a FOCC and the circumstances under which such a contract is most beneficial for the company and its supply chain.

需求的不确定性会导致库存过剩、产能过剩、紧急交货和缺货。需求不确定性的成本可能直接由上游供应商承担,但也可能以价格上涨的形式向下游传播。为了解决这些问题,我们研究了固定订单承诺合同(FOCC)的实际应用,在该合同中,制造商承诺每期的最低固定订单量,并从供应商处获得每单位的价格折扣。我们将 FOCC 建模为一个斯塔克尔伯格博弈,在这个博弈中,供应商根据制造商的反应提供价格折扣,制造商随后决定最佳承诺数量。我们的研究表明,FOCC 可以平滑供应商收到的订单,减轻需求不确定性给供应商、制造商和供应链带来的负面影响。我们通过求解内生价格折扣而不是将其作为外生值来扩展现有文献,并通过我们的研究合作伙伴--一家大型国际材料处理设备制造商--来验证我们的模型见解。利用 863 个零件的数据,我们评估了模型参数、合同参数和合同有效性之间的关系,并展示了 FOCC 为制造商和供应商节省更多成本的条件。我们的研究结果有助于运营经理更好地理解如何获得 FOCC 的最佳合同参数,以及在什么情况下这种合同对公司及其供应链最有利。
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引用次数: 0
A framework for integrated resource planning in surgical clinics 外科诊所综合资源规划框架
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-22 DOI: 10.1016/j.ejor.2024.08.021
Thomas Reiten Bovim , Anders N. Gullhav , Henrik Andersson , Atle Riise

The problem under study is based on the challenges faced by the Orthopaedic Clinic at St. Olav’s Hospital in Trondheim, Norway. Variations in demand and supply cause fluctuating waiting lists, and it is challenging to level the activities between the clinic’s two units, the outpatient clinic and the operating theater, to obtain short waiting times for all activities. Based on these challenges, we describe and present a planning problem referred to as the Long-term Master Scheduling Problem (LMSP), where the objective is to construct an integrated Long-term Master Schedule (LMS) that facilitates short waiting times in both units. The LMS can be separated into two schedules, one cyclic high-level schedule, and one non-cyclic low-level schedule. The demand for outpatient clinic consultations and surgeries is stochastic, as are the waiting lists. To account for this, we propose a planning framework consisting of an optimization model to solve the LMSP, and a two-level planning procedure. In the planning procedure, we first solve the LMSP to construct the LMS for the upcoming planning horizon. Then, to adjust to the fluctuating waiting lists, we periodically refine the low-level schedule by solving a constrained LMSP. We also develop a simulation-based evaluation procedure to evaluate the planning framework in a real-life setting and use this to investigate different planning strategies. We find that imposing flexible, dynamic and agile planning strategies improve waiting time outcomes and patient throughput. Furthermore, combining the strategies yields additive improvements.

所研究的问题基于挪威特隆赫姆圣奥拉夫医院骨科诊所面临的挑战。需求和供应的变化会导致候诊名单的波动,而要使门诊部和手术室这两个部门的活动均衡,从而缩短所有活动的候诊时间,则是一项挑战。基于这些挑战,我们描述并提出了一个规划问题,即长期总日程安排问题(Long-term Master Scheduling Problem,LMSP),其目标是构建一个综合的长期总日程安排(Long-term Master Schedule,LMS),以缩短两个单元的等候时间。长期总排班表可分为两个排班表,一个是周期性的高级排班表,另一个是非周期性的低级排班表。门诊咨询和手术需求是随机的,候诊名单也是随机的。为此,我们提出了一个规划框架,其中包括一个用于求解 LMSP 的优化模型和一个两级规划程序。在规划程序中,我们首先求解 LMSP,为即将到来的规划期构建 LMS。然后,为了适应不断波动的候补名单,我们通过求解受约束的 LMSP 来定期完善低层次计划。我们还开发了一种基于仿真的评估程序,用于评估真实环境中的规划框架,并以此研究不同的规划策略。我们发现,实施灵活、动态和敏捷的规划策略可以改善等待时间结果和病人吞吐量。此外,将这些策略结合起来还能产生叠加改善效果。
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引用次数: 0
Portfolio default losses driven by idiosyncratic risks 特异性风险导致的投资组合违约损失
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-21 DOI: 10.1016/j.ejor.2024.08.015
Shaoying Chen , Zhiwei Tong , Yang Yang
We consider a portfolio of general defaultable assets with low individual default risk and study the probability of the portfolio default loss exceeding an arbitrary threshold. The latent variables driving defaults are modeled by a mixture structure that combines common shock, systematic risk, and idiosyncratic risk factors. While common shocks and systematic risk have been found by many studies to contribute significantly to portfolio losses, the role of idiosyncratic risks is often found to be negligible. Such conclusions are usually established under the assumption that the portfolio size tends to infinity and idiosyncratic risk factors are not dominant. We study under-investigated scenarios where the portfolio size is fixed and the idiosyncratic risk factors are heavy-tailed, exploring two distinct scenarios: an independence scenario and an asymptotic dependence scenario. The former is standard in the literature, while the latter is motivated by recent studies that have found the inadequacy of relying solely on common factors to capture default clustering. This consideration also reflects the possibility that idiosyncratic reasons can trigger contagion among firms with liabilities to each other. In the independence scenario, even with heavy-tailed idiosyncratic risk factors, the probability of a substantial portfolio loss remains low unless a single asset carries a disproportionately large weight. Conversely, in the asymptotic dependence scenario, the primary drivers of increased exceedance probability are the dependent idiosyncratic risk factors.
我们考虑了单个违约风险较低的一般可违约资产组合,并研究了组合违约损失超过任意阈值的概率。驱动违约的潜在变量由一个混合结构建模,该结构结合了共同冲击、系统风险和特异风险因素。许多研究发现,共同冲击和系统风险对投资组合损失的影响很大,而特异风险的作用往往可以忽略不计。这些结论通常是在投资组合规模趋于无穷大且特异风险因素不占主导地位的假设下得出的。我们研究了投资组合规模固定且特异性风险因素为重尾的未充分调查情景,探讨了两种不同的情景:独立性情景和渐进依赖性情景。前者是文献中的标准情景,而后者则是近期研究的结果,这些研究发现仅仅依靠共同因子来捕捉违约集群是不够的。这种考虑也反映了特异性原因可能引发相互有负债的公司之间的传染。在独立情况下,即使存在重尾特异风险因素,除非单一资产所占权重过大,否则投资组合遭受重大损失的概率仍然很低。相反,在渐近依赖情景下,超额概率增加的主要驱动因素是依赖性特异风险因素。
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引用次数: 0
Exact and heuristic approaches for the ship-to-shore problem 船到岸问题的精确方法和启发式方法
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-19 DOI: 10.1016/j.ejor.2024.08.017
M. Wagenvoort , P.C. Bouman , M. van Ee , T. Lamballais Tessensohn , K. Postek

After a natural disaster such as a hurricane or flooding, the navy can help by bringing supplies, clearing roads, and evacuating victims. If destinations cannot be reached over land, resources can be transported using smaller ships and helicopters, called connectors. To start aid on land as soon as possible this must be done efficiently. In the ship-to-shore problem, trips with their accompanying resources are determined while minimising the makespan. Limited (un)loading capacities, heterogeneous connector characteristics and constraints posed by priority of the resources and grouping of the resources (resource sets) all require that the connector trips are carefully coordinated. Despite the criticality of this coordination, existing literature does not consider resource sets and has only developed heuristics. We provide a formulation that incorporates resource sets and develop (i) an exact branch-and-price algorithm and (ii) a tailored greedy heuristic that can provide upper bounds. We find that 84% of our 98 practical instances terminate within an hour in on average 80 s. Our greedy heuristic can find optimal solutions in two-thirds of these instances, mostly for instances that are very constrained in terms of the delivery order of resources. When improvements are found by the branch-and-price algorithm, the average gap with the makespan of the greedy solution is 40% and, in most cases, these improvements are obtained within three minutes. For the 20 artificial instances, the greedy heuristic has consistent performance on the different types of instances. For these artificial instances improvements of on average 35% are found in reasonable time.

飓风或洪水等自然灾害发生后,海军可以通过运送物资、清理道路和疏散灾民来提供帮助。如果陆路无法到达目的地,可以使用小型船只和直升机(称为连接器)运输资源。为了尽快在陆地上展开援助,必须高效地完成这项工作。在 "船到岸 "问题中,在确定行程及其所附资源的同时,要尽量减少时间跨度。有限的(非)装载能力、不同的连接器特性以及资源优先级和资源分组(资源集)所造成的限制,都要求对连接器的行程进行仔细协调。尽管这种协调至关重要,但现有文献并未考虑资源集,而只是开发了启发式方法。我们提供了一个包含资源集的公式,并开发了 (i) 精确的分支-价格算法和 (ii) 一个可提供上限的定制贪婪启发式。我们发现,在 98 个实际实例中,有 84% 的实例能在平均 80 秒内于一小时内结束。我们的贪婪启发式能在三分之二的实例中找到最优解,其中大部分是在资源交付顺序方面非常受限的实例。当通过分支-价格算法找到改进方案时,与贪婪解决方案的平均差距为 40%,而且在大多数情况下,这些改进方案都能在三分钟内完成。在 20 个人工实例中,贪婪启发式在不同类型的实例上表现一致。在合理的时间内,这些人工实例的平均改进幅度为 35%。
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引用次数: 0
Optimal payoffs under smooth ambiguity 平稳模糊条件下的最优回报
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-17 DOI: 10.1016/j.ejor.2024.08.008
An Chen , Steven Vanduffel , Morten Wilke
We study optimal payoff choice for an investor in a one-period model under smooth ambiguity preferences, also called KMM preferences as proposed by Klibanoff et al. (2005). In contrast to the existing literature on optimal asset allocation for a KMM investor in a one-period model, we also allow payoffs that are non-linear in the market asset. Our contribution is fourfold. First, we characterize and derive the optimal payoff under KMM preferences. Second, we demonstrate that a KMM investor solves an equivalent problem to an investor under classical subjective expected utility (CSEU) with adjusted second-order probabilities. Third, we show that a KMM investor with exponential ambiguity attitude implicitly maximizes CSEU utility under the ‘worst-case’ second-order probabilities determined by his ambiguity aversion. Fourth, we reveal that optimal payoffs under ambiguity are not necessarily monotonically increasing in the market asset, which we illustrate using a log-normal market asset under drift and volatility uncertainty.
我们研究的是平滑模糊偏好下单期模型中投资者的最优报酬选择,也就是克利巴诺夫等人(2005)所提出的。与现有关于 KMM 投资者在单期模型中的最优资产配置的文献相比,我们还允许市场资产的报酬是非线性的。我们的贡献有四个方面。首先,我们描述并推导了 KMM 偏好下的最优收益。其次,我们证明了 KMM 投资者解决的问题与(CSEU)下的投资者解决的问题是等价的,且具有调整后的二阶概率。第三,我们证明了具有指数模糊态度的 KMM 投资者在其模糊厌恶所决定的 "最坏情况 "二阶概率下隐含地最大化了 CSEU 效用。第四,我们揭示了在模糊性条件下,市场资产的最优报酬并不一定是单调递增的,我们用漂移和波动不确定性条件下的对数正态市场资产来说明这一点。
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引用次数: 0
Customer and provider bounded rationality in on-demand service platforms 按需服务平台中的客户和供应商有界理性
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-08-17 DOI: 10.1016/j.ejor.2024.08.013
Danna Chen , Yong-Wu Zhou , Xiaogang Lin , Kangning Jin

The growing literature on operations management in the context of the sharing economy typically assumes that both customers and providers are fully rational. In contrast, we consider an on-demand service platform (e.g., Didi and Uber) with boundedly rational customers and providers that sets a price charged to customers and a wage paid to providers. Both customers and providers are sensitive to the payment terms set by the platform and also to congestion in the system (given by the relative numbers of available customers and providers in the market). We capture bounded rationality using a model in which customers and providers are incapable of accurately estimating the congestion level. We examine the impact of bounded rationality on the platform profit, consumer surplus, and labor welfare. We find that both customers’ and providers’ bounded rationalities may benefit the platform. Specifically, when customers’ or providers’ bounded rationality level and service valuation are relatively large or the valuation is relatively small, more irrational customers or providers increases the platform’s profit. Moreover, we find that the platform can exploit the bounded rationality differences between customers and providers to gain profit. Counterintuitively, we also demonstrate that the high bounded rationality of customers or providers may increase consumer surplus and/or labor welfare. Finally, bounded rationality on one side (e.g., customer side) can make bounded rationality on the other side (e.g., provider side) more likely to increase the platform’s profit, consumer surplus, or labor welfare under certain conditions.

有关共享经济背景下运营管理的文献越来越多,这些文献通常假设客户和供应商都是完全理性的。相比之下,我们考虑的是一个按需服务平台(如滴滴和优步),它的客户和提供者都是有界理性的,平台会设定向客户收取的价格和向提供者支付的工资。客户和提供商都对平台设定的付款条件以及系统拥堵(由市场上可用客户和提供商的相对数量决定)很敏感。我们使用一个客户和提供商都无法准确估计拥堵程度的模型来捕捉有界理性。我们研究了有界理性对平台利润、消费者剩余和劳动力福利的影响。我们发现,客户和提供商的有界理性都可能使平台受益。具体来说,当客户或供应商的有界理性水平和服务估值相对较大或估值相对较小时,更多的非理性客户或供应商会增加平台的利润。此外,我们还发现,平台可以利用客户和供应商之间的有界理性差异来获取利润。与直觉相反,我们还证明,客户或供应商的高度有界理性可能会增加消费者剩余和/或劳动福利。最后,在某些条件下,一方(如客户方)的有界理性会使另一方(如提供商方)的有界理性更有可能增加平台的利润、消费者剩余或劳动福利。
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引用次数: 0
期刊
European Journal of Operational Research
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