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Simple fixes that accommodate switching costs in multi-armed bandits 适应多臂匪徒中转换成本的简单修复方法
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-19 DOI: 10.1016/j.ejor.2024.09.017
Ehsan Teymourian , Jian Yang
When switching costs are added to the multi-armed bandit (MAB) problem where the arms’ random reward distributions are previously unknown, usually quite different techniques than those for pure MAB are required. We find that two simple fixes on the existing upper-confidence-bound (UCB) policy can work well for MAB with switching costs (MAB-SC). Two cases should be distinguished. One is with positive-gap ambiguity where the performance gap between the leading and lagging arms is known to be at least some δ>0. For this, our fix is to erect barriers that discourage frivolous arm switchings. The other is with zero-gap ambiguity where absolutely nothing is known. We remedy this by forcing the same arms to be pulled in increasingly prolonged intervals. As usual, the effectivenesses of our fixes are measured by the worst average regrets over long time horizons T. When the barriers are fixed at δ/2, we can accomplish a ln(T)-sized regret bound for the positive-gap case. When intervals are such that n of them occupy n2 periods, we can achieve the best possible T1/2-sized regret bound for the zero-gap case. Other than UCB, these fixes can be applied to a learning while doing (LWD) heuristic to reach satisfactory results as well. While not yet with the best theoretical guarantees, the LWD-based policies have empirically outperformed those based on UCB and other known alternatives. Numerically competitive policies still include ones resulting from interval-based fixes on Thompson sampling (TS).
在多臂强盗(MAB)问题中加入转换成本时,由于各臂的随机奖励分布是未知的,通常需要采用与纯 MAB 完全不同的技术。我们发现,对现有的置信上限(UCB)策略进行两个简单的修正,就能很好地解决有转换成本的多臂强盗(MAB)问题(MAB-SC)。需要区分两种情况。一种情况是正差距模糊性,即已知领先臂和落后臂之间的性能差距至少为某个 δ>0。对于这种情况,我们的解决办法是设置障碍,阻止轻率的臂切换。另一种情况是零间隙模糊性,在这种情况下,我们完全不知道任何事情。对此,我们的补救措施是强迫在越来越长的时间间隔内拉动相同的臂。像往常一样,我们的固定方法的有效性是通过长时间跨度 T 的最坏平均遗憾来衡量的。当障碍固定在 δ/2 时,我们可以在正间隙情况下实现 ln(T)-sized regret bound。当时间间隔为 n 个,其中 n 个占据 n2 个周期时,我们就能在零间隙情况下实现最佳的 T1/2 大小的遗憾约束。除 UCB 外,这些修正也可以应用于边做边学(LWD)启发式,以获得令人满意的结果。基于 LWD 的策略虽然尚未获得最佳的理论保证,但在经验上已经优于基于 UCB 和其他已知替代方法的策略。在数值上具有竞争力的策略还包括基于汤普森采样(Thompson sampling,TS)的区间固定策略。
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引用次数: 0
The set team orienteering problem 集队定向越野问题
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-18 DOI: 10.1016/j.ejor.2024.09.021
Tat Dat Nguyen , Rafael Martinelli , Quang Anh Pham , Minh Hoàng Hà
We introduce the Set Team Orienteering Problem (STOP), a generalised variant of the Set Orienteering Problem (SOP), in which customer locations are split into multiple clusters (or groups). Each cluster is associated with a profit that can be gained only if at least one customer from the cluster is visited. There is a fleet of homogeneous vehicles at a depot, and each vehicle has a limited travel time. The goal of the STOP is to find a set of feasible vehicle routes to collect the maximum profit. We first formulate the problem as a Mixed Integer Linear Programming (MILP) to mathematically describe it. A branch-and-price (B&P) algorithm is then developed to solve the problem to optimality. To deal with large instances, we propose a Large Neighbourhood Search (LNS), which relies on problem-tailored solution representation, removal, and insertion operators. Multiple experiments on newly generated instances confirm the performance of our approaches. Remarkably, when tested on the SOP using benchmarks available in the literature, our B&P method achieves optimality in 61.9% of these instances. This is the first time such a large number of SOP instances are solved to optimality. Our LNS outperforms existing algorithms proposed to solve the SOP in terms of solution quality. Out of 612 considered instances, it improves 40 best-known solutions.
我们引入了集群定向问题(STOP),它是集群定向问题(SOP)的一个广义变体,其中客户位置被分成多个集群(或小组)。每个群组都与利润相关联,只有访问了该群组中的至少一个客户,才能获得利润。车厂有一支由同质车辆组成的车队,每辆车的行驶时间有限。STOP 的目标是找到一组可行的车辆路线,以获取最大利润。我们首先将该问题表述为混合整数线性规划(MILP),对其进行数学描述。然后,我们开发了一种分支加价格(B&P)算法,以最优方式求解该问题。为了处理大型实例,我们提出了大型邻域搜索 (LNS),它依赖于问题定制的解决方案表示、移除和插入算子。在新生成的实例上进行的多次实验证实了我们方法的性能。值得注意的是,在使用文献中的基准对 SOP 进行测试时,我们的 B&P 方法在 61.9% 的实例中达到了最优。这是首次有如此多的 SOP 实例达到最优解。在求解质量方面,我们的 LNS 优于现有的 SOP 求解算法。在所考虑的 612 个实例中,它改进了 40 个最知名的解决方案。
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引用次数: 0
Probabilistic branch and bound considering stochastic constraints 考虑随机约束的概率分支与约束
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-17 DOI: 10.1016/j.ejor.2024.09.016
Hao Huang , Shing Chih Tsai , Chuljin Park
In this paper, we investigate a simulation optimization problem that poses challenges due to (i) the inability to evaluate the objective and multiple constraint functions analytically; instead, we rely on stochastic simulation to estimate them, and (ii) a discrete and potentially vast solution space. Rather than providing a single optimal solution, our aim is to identify a set of near-optimal solutions within a specific quantile, such as the top 10%. Our investigation covers two different problem settings or frameworks. The first framework is focused solely on a stochastic objective function, disregarding any stochastic constraints. In this context, we propose employing a probabilistic branch-and-bound algorithm to discover a level set of solutions. Alternatively, the second framework involves stochastic constraints. To address such stochastically constrained problems, we utilize a penalty function methodology in conjunction with a probabilistic branch-and-bound algorithm. Furthermore, we establish a convergence analysis of both algorithms to demonstrate their asymptotic validity and highlight their theoretical properties and behavior. Our experimental results provide evidence of the efficiency of our proposed algorithms, showing that they outperform existing approaches in the field of simulation optimization.
在本文中,我们研究了一个模拟优化问题,该问题具有以下挑战:(i) 无法分析评估目标函数和多个约束函数;相反,我们依赖随机模拟来估计它们;(ii) 离散且潜在的巨大解决方案空间。我们的目标不是提供单一的最优解,而是在特定的量级(如前 10%)内找出一组接近最优的解。我们的研究涵盖两种不同的问题设置或框架。第一个框架只关注随机目标函数,不考虑任何随机约束条件。在这种情况下,我们建议采用概率分支和边界算法来发现水平解集。另外,第二个框架涉及随机约束。为解决此类随机约束问题,我们将惩罚函数方法与概率分支边界算法结合使用。此外,我们还对这两种算法进行了收敛分析,以证明它们的渐近有效性,并突出它们的理论特性和行为。我们的实验结果证明了我们提出的算法的效率,表明它们优于模拟优化领域的现有方法。
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引用次数: 0
Optimizing extended warranty options with preventive maintenance service under multinomial logit model 在多项式对数模型下优化预防性维护服务的延保方案
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-16 DOI: 10.1016/j.ejor.2024.09.024
Anshu Dai , Xi Yang , Duo Yang , Ting Li , Xin Wang , Shuguang He
Extended warranty (EW) services have become the primary source of profit for manufacturers. How to design the appropriate EW service to balance customer user experience with the manufacturer’s profit issues has received great attention. Implementing preventive maintenance (PM) actions can not only reduce the customer’s lifecycle cost but also enhance the manufacturer’s brand image. Therefore, EW bundled with PM service has emerged in the after-sales market today. To enrich customers’ choice, we investigate the design of EW menus bundled with PM service options, and then we jointly determine EW prices and the frequency of PM actions for the provided menus. In the proposed model, we combine the multinomial logit model with prospect theory to characterize customer choice behavior when presented with different EW menu options. Based on that, with the aim of maximizing the manufacturer’s profit, we can derive sets of offers, the corresponding EW service prices, and the number of included PM actions. We also introduce two additional models that account for different customer purchase scenarios. Numerical results reveal that when the manufacturer chooses to offer a unified EW menu to all customers, it is consistently more profitable to present the menu at the point of product sales. Another interesting finding is that customized EW menus designed for various customer segments do not always outperform unified ones. Overall, this study will provide a foundation for manufacturers to make informed decisions regarding the selection and design of EW menus in various scenarios.
延长保修(EW)服务已成为制造商的主要利润来源。如何设计适当的延保服务,以平衡客户的用户体验和制造商的利润问题,已受到极大关注。实施预防性维护(PM)行动不仅能降低客户的生命周期成本,还能提升制造商的品牌形象。因此,与 PM 服务捆绑在一起的 EW 已出现在当今的售后市场上。为了丰富客户的选择,我们研究了与 PM 服务选项捆绑在一起的 EW 菜单设计,然后共同确定所提供菜单的 EW 价格和 PM 行动频率。在所提出的模型中,我们将多项式对数模型与前景理论相结合,描述了顾客在面对不同 EW 菜单选项时的选择行为。在此基础上,以制造商利润最大化为目标,我们可以推导出报价集、相应的 EW 服务价格以及所含 PM 操作的数量。我们还引入了两个额外的模型,以考虑不同的客户购买情况。数值结果表明,当制造商选择向所有客户提供统一的 EW 菜单时,在产品销售点提供菜单的利润始终更高。另一个有趣的发现是,为不同客户群设计的定制 EW 菜单并不总是优于统一菜单。总之,这项研究将为制造商在各种情况下选择和设计电子门店菜单提供决策依据。
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引用次数: 0
Mathematical models based on decision hypergraphs for designing a storage cabinet 基于决策超图的数学模型用于设计储藏柜
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-16 DOI: 10.1016/j.ejor.2024.09.022
Luis Marques, François Clautiaux, Aurélien Froger
We study the problem of designing a cabinet made up of a set of shelves that contain compartments whose contents slide forward on opening. Considering a set of items candidate to be stored in the cabinet over a given time horizon, the problem is to design a set of shelves and a set of compartments on each shelf, and select the items to insert into the compartments. The objective is to maximize the sum of the profits of the selected items. We call our problem the Storage Cabinet Physical Design (SCPD) problem. The SCPD problem combines a two-staged two-dimensional knapsack problem for designing the shelves and compartments with a set of temporal knapsack problems for selecting and assigning items to compartments. We formalize the SCPD problem and formulate it as a maximum cost flow problem in a decision hypergraph with additional linear constraints. To reduce the size of this model, we break symmetries, generalize graph compression techniques and exploit dominance rules for precomputing subproblem solutions. We also present a set of valid inequalities to improve the linear relaxation of the model. We empirically show that solving the arc-flow model with our enhancements outperforms solving a compact mixed integer linear programming formulation of the SCPD problem.
我们研究的问题是设计一个由一组货架组成的橱柜,这些货架上的隔间在打开时会向前滑动。考虑到在给定的时间范围内橱柜中要存放的一组候选物品,问题是设计一组货架和每个货架上的一组隔间,并选择要放入隔间的物品。目标是使所选物品的利润之和最大化。我们将这一问题称为存储柜物理设计(SCPD)问题。SCPD 问题将一个用于设计货架和隔间的两阶段二维背包问题与一组用于选择和分配物品到隔间的时间背包问题结合在一起。我们将 SCPD 问题形式化,将其表述为决策超图中的最大成本流问题,并附加了线性约束。为了缩小该模型的规模,我们打破了对称性,推广了图压缩技术,并利用优势规则来预先计算子问题的解决方案。我们还提出了一系列有效的不等式,以改进模型的线性松弛。我们的经验表明,用我们的改进方法求解弧流模型优于求解 SCPD 问题的紧凑型混合整数线性规划公式。
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引用次数: 0
Attention-based dynamic multilayer graph neural networks for loan default prediction 基于注意力的动态多层图神经网络用于贷款违约预测
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-14 DOI: 10.1016/j.ejor.2024.09.025
Sahab Zandi , Kamesh Korangi , María Óskarsdóttir , Christophe Mues , Cristián Bravo
Whereas traditional credit scoring tends to employ only individual borrower- or loan-level predictors, it has been acknowledged for some time that connections between borrowers may result in default risk propagating over a network. In this paper, we present a model for credit risk assessment leveraging a dynamic multilayer network built from a Graph Neural Network and a Recurrent Neural Network, each layer reflecting a different source of network connection. We test our methodology in a behavioural credit scoring context using a dataset provided by U.S. mortgage financier Freddie Mac, in which different types of connections arise from the geographical location of the borrower and their choice of mortgage provider. The proposed model considers both types of connections and the evolution of these connections over time. We enhance the model by using a custom attention mechanism that weights the different time snapshots according to their importance. After testing multiple configurations, a model with GAT, LSTM, and the attention mechanism provides the best results. Empirical results demonstrate that, when it comes to predicting probability of default for the borrowers, our proposed model brings both better results and novel insights for the analysis of the importance of connections and timestamps, compared to traditional methods.
传统的信用评分往往只采用单个借款人或贷款层面的预测指标,而借款人之间的联系可能会导致违约风险在网络中传播,这一点早已得到认可。在本文中,我们提出了一个信用风险评估模型,该模型利用了由图神经网络和循环神经网络构建的动态多层网络,每一层都反映了不同的网络连接来源。我们使用美国抵押贷款金融公司房地美提供的数据集,在行为信用评分的背景下测试了我们的方法,其中借款人的地理位置和他们对抵押贷款提供商的选择会产生不同类型的联系。建议的模型考虑了这两种类型的联系以及这些联系随时间的演变。我们通过使用自定义关注机制来增强模型,该机制可根据不同时间快照的重要性对其进行加权。在对多种配置进行测试后,一个包含 GAT、LSTM 和注意力机制的模型取得了最佳结果。实证结果表明,在预测借款人违约概率方面,与传统方法相比,我们提出的模型在分析连接和时间戳的重要性方面既能带来更好的结果,又能带来新的见解。
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引用次数: 0
An indifference result for social choice rules in large societies 大社会中社会选择规则的冷漠结果
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-12 DOI: 10.1016/j.ejor.2024.09.018
Dezső Bednay , Balázs Fleiner , Attila Tasnádi
Social choice rules can be defined or derived by minimizing distance-based objective functions. One problem with this approach is that any social choice rule can be derived by selecting an appropriate distance function. Another problem comes from the computational difficulty of determining the solution of some social choice rules. We provide a general positive indifference result when looking at expected average distances by showing that on ‘average’ each social choice rule performs equally well with respect to a very large class of distance functions if the number of voters is large. Our result applies also to the frequently employed Kendall τ, Spearman rank correlation and Spearman footrule ‘distance functions’.
社会选择规则可以通过最小化基于距离的目标函数来定义或推导。这种方法的一个问题是,任何社会选择规则都可以通过选择一个适当的距离函数推导出来。另一个问题来自于确定某些社会选择规则解的计算难度。在研究预期平均距离时,我们提供了一个一般的正冷漠结果,表明如果选民人数很多,"平均 "而言,每种社会选择规则在很大一类距离函数上都表现得同样好。我们的结果也适用于经常使用的肯德尔(Kendall)、斯皮尔曼等级相关性(Spearman rank correlation)和斯皮尔曼脚尺(Spearman footrule)"距离函数"。
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引用次数: 0
An evaluation of common modeling choices for the vehicle routing problem with stochastic demands 对具有随机需求的车辆路由问题的常见模型选择进行评估
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-11 DOI: 10.1016/j.ejor.2024.09.007
Y.N. Hoogendoorn, R. Spliet
We investigate three common modeling choices for the vehicle routing problem with stochastic demands: (i) the total expected demand of customers on a route may not exceed the capacity of the vehicle, (ii) the number of routes is fixed, and (iii) demand is distributed with a support that contains negative-valued realizations. We prove that modeling choices (i) and (ii) result in an arbitrarily large increase of the optimal objective value in the worst case. Additionally, we provide lower and upper bounds on the change of the optimal objective value following from (iii) in case the actual distribution of demand is censored, truncated or folded. We also evaluate the consequences of these choices numerically, by employing a state-of-the-art integer L-shaped method to solve the vehicle routing problem with stochastic demands to optimality, which we modify to deal with the alternative choices. We find that restricting the expected demand of a route to the vehicle’s capacity has a limited effect on the optimal objective value for most, but not all, benchmark instances from the literature, while drastically reducing the computation times of the integer L-shaped method. When restricting the number of routes, a similar effect occurs when the total expected demand on a route is not restricted. Otherwise, the computation time decreases only slightly, and even increases for some benchmark instances. For instances from the literature, despite admitting negative realizations, the normal distributions used to model demand are an adequate approximation for censored, truncated and folded normal distributions that have nonnegative supports.
我们研究了具有随机需求的车辆路线问题的三种常见建模选择:(i) 路线上客户的总预期需求不得超过车辆的容量,(ii) 路线数量固定,(iii) 需求分布的支持包含负值实现。我们证明,建模选择(i)和(ii)会导致最优目标值在最坏情况下任意大幅增加。此外,我们还提供了在实际需求分布被删减、截断或折叠的情况下,(iii) 所导致的最优目标值变化的下限和上限。我们还采用了最先进的 L 型整数方法来求解随机需求下的车辆路由问题,从而对这些选择的后果进行了数值评估。我们发现,对于文献中的大多数(而非全部)基准实例,将路线的预期需求限制在车辆的运载能力范围内对最优目标值的影响有限,同时大大减少了整数 L 型方法的计算时间。在限制路线数量时,如果不限制路线上的总预期需求量,也会产生类似的效果。否则,计算时间只会略微减少,在某些基准实例中甚至会增加。对于文献中的实例,尽管允许负实现,但用于需求建模的正态分布是对具有非负支持的删减、截断和折叠正态分布的适当近似。
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引用次数: 0
Condition-based switching, loading, and age-based maintenance policies for standby systems 备用系统基于状态的切换、负载和基于年龄的维护政策
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-10 DOI: 10.1016/j.ejor.2024.09.014
Xian Zhao , Rong Li , He Han , Qingan Qiu
Standby techniques are widely incorporated in structural design to enhance the inherent reliability of systems. To further leverage the system performance during operation, decision-makers can adopt operational policies to manage system degradation. Specifically, at the system level, unit switching that dynamically determines the online unit contributes to avoiding unexpected shutdowns. At the unit level, adjusting load levels to manage the trade-off between condition degradation and revenue accumulation is crucial for maximizing profit. Additionally, adopting age-based maintenance as a tactical decision, which effectively facilitates the integration of maintenance resources, can be implemented to restore a degraded system. For instance, maintenance is typically scheduled at fixed moments for multi-generator power systems located in remote areas. In between maintenance moments, the proactive switching of generators can ensure uninterrupted output, and the adjustment of load levels for online generators helps to maximize output. Motivated by such engineering practices, this paper investigates condition-based switching, loading, and age-based maintenance policies for standby systems to maximize the expected profit rate in the long-run horizon. The problem is formulated as a Markov decision process. The structural properties of the control-limit switching and monotone loading policies are analyzed for easy policy implementation and efficient problem solutions. For comparative purposes, several heuristic policies are proposed and evaluated. Finally, numerical examples are presented to validate theoretical results and illustrate the superiority of the proposed risk control policy.
备用技术被广泛纳入结构设计中,以提高系统的固有可靠性。为了进一步发挥系统在运行期间的性能,决策者可以采用运行策略来管理系统故障。具体来说,在系统层面,动态决定在线机组的机组切换有助于避免意外停机。在机组层面,调整负荷水平以管理状态退化和收入积累之间的权衡,对于实现利润最大化至关重要。此外,将基于机龄的维护作为一种战术决策,可有效促进维护资源的整合,从而恢复性能下降的系统。例如,对于位于偏远地区的多发电机电力系统,通常会在固定的时间进行维护。在两次维护之间,主动切换发电机可确保不间断输出,而调整在线发电机的负载水平则有助于最大限度地提高输出。受此类工程实践的启发,本文研究了备用系统基于状态的切换、负载和基于年龄的维护政策,以实现长期预期利润率的最大化。该问题被表述为一个马尔可夫决策过程。分析了控制极限切换和单调加载政策的结构特性,以便于政策的实施和问题的有效解决。为了便于比较,提出并评估了几种启发式政策。最后,介绍了一些数值示例,以验证理论结果,并说明所提出的风险控制策略的优越性。
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引用次数: 0
A newsvendor model with multiple reference points: Target-setting for aspirational newsvendors 具有多个参考点的新闻供应商模式:为有抱负的新闻供应商设定目标
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2024-09-10 DOI: 10.1016/j.ejor.2024.09.015
Tian Bai , Gengzhong Feng , Meng Wu , Stuart X. Zhu
Prospect theory posits that the determination of an outcome as a gain or loss hinges upon the reference points, thereby exerting a substantial influence on the decision-making processes of individuals. These reference points can encompass both external targets and internal aspirations (self-goals), forming two potential candidates. Despite a growing body of evidence showcasing the concurrent impact of multiple reference points on decision-makers’ choices, scant attention has been accorded to this phenomenon within the realm of operations management literature. In light of this, the present study delves into the influence wielded by an external target, functioning as a reference point, on the decisions and profitability of newsvendors who also harbor a well-defined aspiration (self-goal) reference point. The study introduces two distinct archetypes of newsvendors: the balanced newsvendors, adept at harmonizing personal needs with target attainment and thus navigating decisions influenced by dual reference points; and the focused newsvendors, singularly fixated on target realization and thereby governed by a sole target reference point. Our findings reveal that the effects of target-setting in boosting expected profits on both categories of newsvendors are contingent upon the specific value attributed to their self-goal. The implications of target-setting can either yield advantages or drawbacks, contingent upon the self-goal. This asymmetry in outcomes holds true for both balanced and focused newsvendors, with the former exhibiting a higher likelihood of deriving benefits from target-setting. Moreover, an exploration of scenarios wherein a newsvendor’s self-goal may undergo updates underscores the potential for further enhancement in the performance of balanced newsvendors.
前景理论认为,决定结果的得失取决于参考点,从而对个人的决策过程产生重大影响。这些参照点既可以是外部目标,也可以是内部愿望(自我目标),从而形成两个潜在的候选目标。尽管越来越多的证据表明,多重参考点对决策者的选择同时产生影响,但在运营管理文献中却很少关注这一现象。有鉴于此,本研究深入探讨了作为参照点的外部目标对同时拥有明确愿望(自我目标)参照点的新闻销售商的决策和盈利能力的影响。研究介绍了两种不同的新闻销售者原型:一种是平衡型新闻销售者,他们善于协调个人需求与目标实现之间的关系,从而在双重参照点的影响下做出决策;另一种是专注型新闻销售者,他们只专注于目标实现,从而受单一目标参照点的支配。我们的研究结果表明,目标设定在提高两类新闻销售者预期利润方面的效果取决于其自我目标的具体价值。根据自我目标的不同,目标设定的影响既可能产生优势,也可能产生劣势。这种结果的不对称性对平衡型和聚焦型新闻供应商都适用,前者更有可能从目标设定中获益。此外,对新闻供应商的自我目标可能会发生更新的情况进行探讨,强调了进一步提高平衡型新闻供应商绩效的潜力。
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引用次数: 0
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European Journal of Operational Research
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