推文作者:胡思行
编者按
在本系列文章中,我们从运筹学顶刊 Management Science 11月份发布的37篇文章中筛选出11篇文章,并介绍基本信息,旨在帮助读者快速洞察行业最新动态。
推荐文章1
双重道德风险下的动态合同设计
We consider a stylized incentive management problem over an infinite time horizon, where the principal hires an agent to provide services to customers. Customers request service in one of two ways: either via an online or a traditional offline channel. The principal does not observe the offline customers’ arrivals, nor does she observe whether the agent exerts (costly) effort that can increase the arrival rate of customers. This creates an opportunity for the agent (i) to divert cash (that is, to under-report the number of offline customers and pocket respective revenues) and also (ii) to shirk (that is, not to exert effort), thus leading to a novel and thus far unexplored double moral hazard problem. To address this problem, we formulate a constrained, continuous-time, stochastic optimal control problem and derive an optimal contract with a simple intuitive structure that includes a payment scheme and a potential termination time of the agent. We enrich the model to allow the principal to either (i) dynamically adjust the prices for the services in both channels or (ii) monitor the agent. Both tools help the principal to alleviate the double moral hazard problem. We derive respective optimal strategies for using those tools that guarantee the highest profits. We show that the worse the agent’s past performance is, the lower the prices should be set and the more the principal should monitor the agent.
我们考虑一个风格化的激励管理问题,在无限时间范围内,委托人雇佣一个代理人提供客户服务。客户通过两种方式之一请求服务:要么通过在线渠道,要么通过传统的离线渠道。委托人无法观察到离线客户的到达情况,也无法观察代理人是否付出(有成本的)努力来提高客户的到达率。这为代理人创造了两个机会:(i)转移现金(即低报离线客户数量并私吞相应的收入);以及(ii)偷懒(即不付出努力),从而导致一个新颖且迄今未被探索的双重道德风险问题。为了解决这个问题,我们构建了一个受约束的连续时间随机最优控制问题,并推导出一个具有简单直观结构的最优合同,包括支付方案和代理人可能的终止时间。我们进一步丰富了模型,允许委托人(i)动态调整两种渠道的服务价格,或(ii)监控代理人。两种手段都有助于委托人缓解双重道德风险问题。我们推导了使用这些手段的最优策略,能够确保委托人获得最高利润。我们展示了,代理人过去的表现越差,委托人应设置更低的价格并对代理人进行更多的监控。
推荐文章2
具有异构服务员和优先级客户的服务系统最优控制
We study service systems with parallel servers and random customer arrivals and focus on the waiting cost of customers. Using a Markov decision process (MDP) modeling approach, we analytically characterize the structures of the optimal dynamic server assignment policies for two important systems, one consisting of multiple homogeneous servers and two classes of customers and the other consisting of two heterogeneous servers and multiple classes of customers. Based on the obtained results, we propose a threshold-type heuristic policy for the generalized system consisting of multiple heterogeneous servers and multiple classes of customers. To design such a heuristic policy, we first develop techniques for the performance evaluation of general threshold-type policies with any given threshold values. We then construct a path to search for the optimal threshold values. We compare the performance of the best threshold-type heuristic policy with that of the optimal policy and show that our proposed heuristic policy is computationally efficient yet generates great performance. To derive additional managerial insights, we compare the system under our threshold-type dynamic server assignment policy with other commonly seen and simple systems, such as the dedicated system and the work-conserving flexible priority system. The clear performance advantage observed from extensive numerical experiments demonstrates the importance and usefulness of dynamic server assignment control for systems serving multiple classes of customer arrivals. Finally, we extend our analysis to incorporate customer-dependent service rates and sojourn-time minimization performance metrics.
我们研究了具有并行服务台和随机客户到达的服务系统,并重点关注客户的等待成本。采用马尔可夫决策过程(MDP)建模方法,我们分析性地刻画了两种重要系统的最优动态服务台分配策略的结构,其中一个系统由多个同质服务台和两类客户组成,另一个系统由两个异质服务台和多类客户组成。基于所获得的结果,我们提出了一种阈值型启发式策略,适用于由多个异质服务台和多类客户组成的广义系统。为了设计这样的启发式策略,我们首先开发了针对任意给定阈值的通用阈值型策略性能评估技术。接着,我们构建了一条路径来搜索最优阈值。我们将最优策略与最佳阈值型启发式策略的性能进行了比较,并展示了我们提出的启发式策略在计算效率上具有优势,同时能够产生良好的性能。为了进一步提炼管理洞察,我们将采用阈值型动态服务台分配策略的系统与其他常见的简单系统进行了比较,如专用系统和灵活工作优先级系统。通过广泛的数值实验,我们清楚地看到,阈值型动态服务台分配控制在服务多类客户到达的系统中具有显著的性能优势,体现了其重要性和实用性。最后,我们将分析扩展到考虑客户依赖的服务率和停留时间最小化绩效指标。
推荐文章3
当客户成批到达时如何配置员工
In many different settings, requests for service can arrive in near or true simultaneity with one another. This creates batches of arrivals to the underlying queueing system. In this paper, we study the staffing problem for the batch arrival queue. We show that batches place a dangerous and deceptive stress on services, requiring a high amount of resources and exhibiting a fundamentally larger tail in those demands. This uncovers a service regime in which a system with large batch arrivals may have low utilization but will still have nontrivial waiting. Methodologically, these staffing results follow from novel large batch and large batch-and-rate limits of the multiserver queueing model. In the large batch limit, we establish the first formal connection between general multiserver queues and storage processes, another family of stochastic models. By consequence, we show that the batch scaled queue length process is not asymptotically normal and that, in fact, the fluid- and diffusion-type limits coincide. Hence, the (safety) staffing of this system must be directly proportional to the batch size just to achieve a nondegenerate probability of wait. In exhibition of the existence and insights of this large batch regime, we apply our results to data on Covid-19 contact tracing in New York City. In doing so, we identify significant benefits produced by the tracing agency’s decision to staff above national recommendations, and we also demonstrate that there may have been an opportunity to further improve the operation by optimizing the arrival pattern in the public health data pipeline.
在许多不同场景中,服务请求可能近乎同时或完全同时抵达,这使得基础排队系统出现批量到达的情况。本文对批量到达排队的人员配置问题展开研究,发现批量到达会给服务带来危险且具欺骗性的压力,需大量资源,且在需求方面呈现出更厚的尾部特征,由此揭示出一种服务机制,即存在大量批量到达情况的系统虽利用率可能较低,但仍会有不可忽视的等待现象。从方法学角度看,这些人员配置结果源于多服务台排队模型新颖的大批次以及大批次兼大速率极限,在大批次极限情况下,我们首次在一般多服务台排队与存储过程(另一类随机模型)间建立正式联系,进而证明按批次缩放的队列长度过程并非渐近正态,且流体型和扩散型极限是重合的,因此该系统的(安全)人员配置必须与批次大小成正比,才能实现非退化的等待概率。为展示大批次机制的存在及其意义,我们将研究结果应用于纽约市新冠病毒接触者追踪的数据上。通过这一应用,我们发现了追踪机构做出高于国家建议的人员配置决策所产生的显著益处,并且我们还证明了通过优化公共卫生数据管道中的信息到达模式,原本或许存在进一步改善运营情况的机会。
推荐文章4
使用参数化运营数据分析(ODA)定价设定下的报童问题
We study the data-integrated, price-setting newsvendor problem in which the price–demand relationship is described by some parametric model with unknown parameters. We develop the operational data analytics (ODA) formulation of this problem that features a data-integration model and a validation model. The data-integration model consists of a class of functions called the operational statistics. Each operational statistic maps the available data to the ordering decision. The validation model finds, among the set of candidate operational statistics, the ordering decision that leads to the highest actual profit, which is unknown because of the unknown demand parameters. This ODA framework leads to a consistent estimate of the profit function with which we optimize the pricing decision. The derived quantity and price decisions demonstrate robust profit performance even when the sample size is very small in relation to the demand variability. Compared with the conventional approach with which the unknown parameters are estimated and then the decisions are optimized, the ODA framework produces significantly superior performance in the mean, standard deviation, and minimum of the profit, suggesting the robustness of the ODA solution especially in the small-sample regime.
我们研究了数据集成的定价报童问题,该问题中价格与需求的关系由含未知参数的参数模型描述,为此我们构建了具备数据集成模型和验证模型特点的运营数据分析(ODA)公式,其中数据集成模型由一类名为运营统计量的函数组成,每个运营统计量会将可用数据映射到订货决策上,验证模型则在候选运营统计量集合中找出能带来最高实际利润(因需求参数未知所以该利润未知)的订货决策,这一 ODA 框架能对利润函数进行一致估计并借此优化定价决策,所推导出的数量和价格决策即便在样本量相对于需求可变性极小的情况下也展现出稳健的利润表现,与先估计未知参数再优化决策的传统方法相比,ODA 框架在利润的均值、标准差和最小值方面表现出显著优势,尤其体现出其在小样本情形下解决方案的稳健性。
推荐文章5
在具有高维数据的广义线性模型下的在线学习和决策制定
We propose a minimax concave penalized multiarmed bandit algorithm under the generalized linear model (G-MCP-Bandit) for decision-makers facing high-dimensional data in an online learning and decision-making environment. We demonstrate that in the data-rich regime, the G-MCP-Bandit algorithm attains the optimal cumulative regret in the sample size dimension and a tight bound in the covariate dimension and the significant covariate dimension. In the data-poor regime, the G-MCP-Bandit algorithm maintains a tight regret upper bound. In addition, we develop a local linear approximation method, the two-step weighted Lasso procedure, to identify the minimax concave penalty (MCP) estimator for the G-MCP-Bandit algorithm when samples are not independent and identically distributed. Under this procedure, the MCP estimator can match the oracle estimator with high probability and converge to the true parameters at the optimal convergence rate. Finally, through experiments based on both synthetic and real data sets, we show that the G-MCP-Bandit algorithm outperforms other benchmarking algorithms in terms of cumulative regret and that the benefits of the G-MCP-Bandit algorithm increase in the data’s sparsity level and the size of the decision set.
我们针对处于在线学习和决策环境中面临高维数据的决策者,在广义线性模型(G-MCP-Bandit)下提出了一种极小极大凹惩罚多臂老虎机算法。我们证明了,在数据丰富的情形下,G-MCP-Bandit 算法在样本量维度上能达到最优累积遗憾值,并且在协变量维度以及显著协变量维度上能达到较紧的边界。在数据匮乏的情形下,G-MCP-Bandit 算法能维持较紧的遗憾上界。此外,我们还开发了一种局部线性近似方法,即两步加权Lasso程序,用于在样本并非独立同分布的情况下,为 G-MCP-Bandit 算法确定极小极大凹惩罚(MCP)估计量。在此程序下,MCP 估计量大概率能与最优估计量相匹配,并能以最优收敛速度收敛到真实参数。最后,通过基于合成数据集和真实数据集的实验,我们表明 G-MCP-Bandit 算法在累积遗憾方面优于其他基准算法,而且 G-MCP-Bandit 算法的优势会随着数据稀疏程度以及决策集规模的增加而增大。
推荐文章6
Motivated by blockchain applications in the fresh produce industry, we consider a newsvendor problem in which a retailer faces stochastic and freshness-dependent consumer demand. The retailer can adopt blockchain technology to have more transparent information on the freshness of supply. We quantify the value of blockchain-enabled freshness transparency by deriving closed-form expressions for the retailer’s expected profit growth and food waste reduction brought by blockchain adoption. Using publicly available data, we provide a numerical example illustrating that for Walmart’s strawberry business in the United States (which is about only 4% of Walmart’s fresh produce sales), blockchain can increase annual profit by $60 million while eliminating 23 million pounds of food waste annually through operational improvements. Despite this substantial value for the retailer, blockchain adoption can decrease the expected profit of the retailer’s supplier. We design a family of threshold-type smart contracts contingent on a blockchain-based freshness consensus and examine when such contracts offer a win-win proposition to the retailer and the supplier. Moreover, when the retailer offers freshness-based price discounts, we find that less fresh supply leads to less food waste. In contrast, when the supplier adjusts the wholesale price based on freshness, less fresh supply causes more food waste. We also generalize our findings to the cases of (i) dual sourcing, (ii) noisy measurements in the Internet of Things sensors feeding data into blockchain, and (iii) the retailer’s culling processes.
受区块链在生鲜农产品行业应用的启发,我们考虑了一个报童问题,在该问题中,零售商面临着随机且依赖新鲜度的消费者需求。零售商可以采用区块链技术来获取有关供应品新鲜度的更透明信息。我们通过推导出零售商采用区块链后预期利润增长以及食品浪费减少的封闭式表达式,对区块链带来的新鲜度透明度的价值进行了量化。利用公开可得的数据,我们给出了一个数值示例,该示例表明,对于美国沃尔玛的草莓业务(其仅占沃尔玛生鲜农产品销售额的约 4%)而言,通过运营改进,区块链每年可增加 6000 万美元的利润,同时每年减少 2300 万磅的食品浪费。尽管对零售商来说这一价值颇为可观,但采用区块链可能会降低零售商供应商的预期利润。我们设计了一系列基于区块链新鲜度共识的阈值型智能合约,并研究了这类合约何时能为零售商和供应商提供双赢方案。此外,当零售商提供基于新鲜度的价格折扣时,我们发现新鲜度较低的供应品会导致更少的食品浪费。相反,当供应商根据新鲜度调整批发价格时,新鲜度较低的供应品会造成更多的食品浪费。我们还将我们的研究结果推广到了以下几种情况:(i)双重采购;(ii)向区块链提供数据的物联网传感器存在测量噪声;(iii)零售商的挑选流程。
推荐文章7
Agricultural open burning, that is, the practice of burning crop residue in harvested fields to prepare land for sowing a new crop, is well recognized as a significant contributor to CO2 and black-carbon emissions, and long-term climate change. Low-soil-tillage practices using an agricultural machine called the Happy Seeder, which can sow the new seed without removing the previous crop residue, have emerged as the most effective alternative to open burning. However, given the limited supply of Happy Seeders from the government, and the fact that farmers incur a significant yield loss if they delay sowing the new crop, farmers are often unwilling to wait to be processed by the Happy Seeder and, instead, burn their crop residue. We study how the government can use effective information-disclosure policies in the operation of Happy Seeders to minimize open burning. A Happy Seeder is assigned to process a group of farms. The government knows, but does not necessarily disclose, the Happy Seeder’s schedule at the start of the sowing season. We propose a class of information-disclosure policies, called dilatory policies, that provide no information to the farmers about the schedule until a prespecified switch period and then reveal the entire schedule afterward. We show that an optimal dilatory policy can significantly lower the number of farms burnt compared with that under the full-disclosure and the no-disclosure policies. Using data from the rice-wheat crop system in northwestern India, we demonstrate that the optimal dilatory policy can reduce CO2 and black-carbon emissions by 17% on average. We also examine the impact of the government’s policy on the trade-off between environmental damage and farmers’ welfare.
农业露天焚烧,即在收获后的田地里焚烧农作物残留物以备新作物播种的做法,被广泛认为是导致二氧化碳和黑碳排放以及长期气候变化的重要贡献者。使用一种名为“快乐播种机”(Happy Seeder)的农业机械进行低土壤耕作实践,该机械可以在不移除前一作物残留物的情况下播种新种子,已成为替代露天焚烧的最有效方法。然而,鉴于政府提供的“快乐播种机”数量有限,以及农民如果延迟播种新作物将遭受显著的产量损失,农民通常不愿意等待“快乐播种机”的处理,而是选择焚烧他们的作物残留物。我们研究了政府如何使用有效的信息披露政策来操作“快乐播种机”,以最小化露天焚烧。一个“快乐播种机”被分配去处理一组农场。政府知道,但不一定披露,“快乐播种机”在播种季节开始时的时间表。我们提出了一类信息披露政策,称为拖延政策,这些政策在预设的转换期之前不向农民提供关于时间表的任何信息,然后在之后透露整个时间表。我们展示了与完全披露和不披露政策相比,一个最优的拖延政策可以显著减少被焚烧的农场数量。利用印度西北部水稻-小麦作物系统的数据,我们展示了最优的拖延政策平均可以减少17%的二氧化碳和黑碳排放。我们还检验了政府政策在环境损害和农民福利之间的权衡影响。
推荐文章8
We isolate the causal effect of changing the riskiness of choices on the gender gap in real-world outcomes. We do so by exploiting a national reform to the regrade system of Norwegian universities that generated exogenous variation in the probabilities of the outcome of regrade requests. Using unique individual-level administrative data, we show that both the expected value of a regrade request, as well as the downside risk, increased substantially as a result of the policy. We then show how the ostensibly gender-neutral policy substantially increased gaps between men and women because they differed in their risk preferences and beliefs. Specifically, the exogenous change in the riskiness of requesting a regrade augmented the gender gap in regrade requests by 90%. We demonstrate that this has important implications for students through its impact on their grades. We disentangle the relative importance of mechanisms through auxiliary reduced-form analyses, structural estimation, and a supplemental laboratory experiment. Taken together, our mechanism analyses suggest that gender differences in risk preferences and loss aversion are not sufficient to explain the increased gender gap after the policy change, and that gender differences in confidence or beliefs are necessary to rationalize the data and more broadly consistent with the patterns we observe.
我们探讨了选择风险性变化对现实世界中性别差距的因果效应。具体来说,我们利用挪威大学重新评分系统的全国性改革,该改革引入了外生性变化,导致重新评分请求结果的概率发生了变化。利用独特的个体级行政数据,我们展示了政策实施后,复议请求的期望值和下行风险都显著增加。我们进一步展示了这一表面上性别中立的政策如何因为男女在风险偏好和信念上的差异而大幅增加了性别间的差距。具体来说,复议请求风险的外生变化将性别差距扩大了90%。我们证明了这对学生的学业成绩有重要影响。我们通过辅助的简化形式分析、结构估计和补充的实验室实验来区分机制的相对重要性。综合来看,我们的机制分析表明,性别在风险偏好和损失厌恶方面的差异并不足以解释政策变化后性别差距的增加,而性别在信心或信念上的差异是解释数据所必需的,并且与我们观察到的模式更为一致。
推荐文章9
We study the classic divide-and-choose method for equitably allocating divisible goods between two players who are rational, self-interested Bayesian agents. The players have additive values for the goods. The prior distributions of those values are common knowledge. We consider both the cases of independent values and values that are correlated across players (as occurs when there is a common-value component). We describe the structure of optimal divisions in the divide-and-choose game and identify several cases where it is possible to efficiently compute equilibria. An approximation algorithm is presented for the case when the distribution over the chooser’s value for each good follows a normal distribution, along with a randomized approximation algorithm for the case of uniform distributions over intervals. A mixture of analytic results and computational simulations illuminates several striking differences between optimal strategies in the cases of known versus unknown preferences. Most notably, given unknown preferences, the divider has a compelling “diversification” incentive in creating the chooser’s two options. This incentive leads to multiple goods being divided at equilibrium, quite contrary to the divider’s optimal strategy when preferences are known. In many contexts, such as buy- and-sell provisions between partners, or in judging fairness, it is important to assess the relative expected utilities of the divider and chooser. Those utilities, we show, depend on the players’ levels of knowledge about each other’s values, the correlations between the players’ values, and the number of goods being divided. Under fairly mild assumptions, we show that the chooser is strictly better off for a small number of goods, whereas the divider is strictly better off for a large number of goods.
我们研究了经典的分割与选择方法,用于在两个理性、自利的贝叶斯代理之间公平分配可分割的物品。玩家对物品有加性价值,并且这些价值的先验分布是公开的。我们考虑了独立价值和玩家之间的相关价值(当存在公共价值成分时)的情况。我们描述了分割与选择游戏中最优分配的结构,并确定了几个可以高效计算均衡的情况。对于选择者对每个物品的价值遵循正态分布的情况,我们提出了一种近似算法,同时对于在区间上均匀分布的情况,我们也提出了一种随机近似算法。通过分析结果和计算模拟的结合,我们揭示了已知与未知偏好之间最优策略的几个显著差异。最为显著的是,给定未知偏好时,分割者在创建选择者的两个选择时有强烈的“多样化”动机。这一动机导致在均衡状态下多个物品被分割,这与当偏好已知时,分割者的最优策略完全相反。在许多情境中,比如合伙人之间的买卖条款,或者判断公平性时,评估分割者和选择者的相对预期效用是非常重要的。我们表明,这些效用依赖于玩家对彼此价值的知识水平、玩家间价值的相关性以及被分割物品的数量。在相对宽松的假设下,我们表明对于少量物品,选择者的效用明显更好,而对于大量物品,分割者的效用明显更好。
推荐文章10
We introduce the click-based MNL choice model, a framework for capturing customer purchasing decisions in e-commerce settings. Specifically, we augment the classical Multinomial Logit choice model by assuming that customers only consider the items they have clicked on before they proceed to compare their random utilities. In this context, we study the resulting assortment optimization problem, where the objective is to select a subset of products, made available for purchase, to maximize the expected revenue. Our main algorithmic contribution comes in the form of a polynomial-time approximation scheme (PTAS) for this problem, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. To establish this result, we develop several technical ideas, including enumeration schemes and stochastic inequalities, which may be of broader interest. Using data from Alibaba’s online marketplace, we fit click-based MNL and latent class MNL models to historical sales and click data in a setting where the online platform recommends a personalized six-product display to each user. We propose an estimation methodology for the click-based MNL model that leverages clickstream data and machine learning classification algorithms. Our numerical results suggest that clickstream data are valuable for predicting choices and that the click-based MNL model can outperform standard logit-based models in certain settings.
我们引入了基于点击的多项式Logit(MNL)选择模型,这是一个用于捕捉电子商务环境中顾客购买决策的框架。具体而言,我们通过假设顾客只考虑他们之前点击过的商品,然后再比较这些商品的随机效用,来扩展经典的多项式Logit选择模型。在这个背景下,我们研究了由此产生的产品组合优化问题,目标是选择一组产品进行销售,以最大化预期收入。我们主要的算法贡献是为这个问题提供了一个多项式时间近似方案(PTAS),证明了可以在任何精度下有效地逼近最优的预期收入。为了建立这一结果,我们提出了几个技术性思路,包括枚举方案和随机不等式,这些思路可能具有更广泛的应用价值。通过使用阿里巴巴在线市场的数据,我们将基于点击的MNL模型和潜在类别MNL模型应用于历史销售和点击数据的拟合,研究了一个在线平台为每个用户推荐个性化的六个产品展示的场景。我们提出了一种基于点击流数据的MNL模型估计方法,结合了机器学习分类算法。我们的数值结果表明,点击流数据对预测顾客选择有很大价值,而且在某些场景下,基于点击的MNL模型的表现优于标准的Logit模型。
推荐文章11
In portfolio optimization, the computational complexity of implementing almost stochastic dominance has limited its practical applications. In this study, we introduce an optimization framework aimed at identifying the optimal portfolio that outperforms a specified benchmark under almost second-degree stochastic dominance (ASSD). Our approach involves discretizing the return range and establishing both sufficient and necessary conditions for ASSD. We then propose a three-step iterative procedure: first, identifying a candidate portfolio; second, assessing its optimality; and third, refining the discretization scheme. Theoretical analysis guarantees that the portfolio identified through this iterative process improves with each iteration, ultimately converging to the optimal solution. Our empirical study, utilizing industry portfolios, demonstrates the efficacy of our approach by consistently identifying an optimal portfolio within a few iterations. Furthermore, comparative analysis against other decision criteria, such as mean-variance, second-degree stochastic dominance, and third-degree stochastic dominance, reveals that ASSD generally leads to portfolios with higher out-of-sample average excess returns but also entails increased variations and risks.
在投资组合优化中,实现几乎随机优势(almost stochastic dominance)的计算复杂性限制了其实际应用。在本研究中,我们引入了一个优化框架,旨在在几乎二阶随机优势(ASSD)下识别出优于特定基准的最优投资组合。我们的方法包括对收益范围进行离散化,并建立ASSD的充分和必要条件。随后,我们提出了一个三步迭代过程:第一步,识别候选投资组合;第二步,评估其最优性;第三步,优化离散化方案。理论分析保证了通过这一迭代过程识别的投资组合在每次迭代中都有所改进,最终收敛于最优解。我们的实证研究利用行业投资组合,证明了我们方法的有效性,能够在几次迭代内稳定地识别出最优投资组合。此外,与其他决策标准(如均值-方差、二阶随机优势和三阶随机优势)进行的比较分析表明,ASSD通常能带来更高的样本外平均超额收益,但也伴随着更大的波动性和风险。
「运筹OR帷幄」原创的《鲁棒优化入门》电子书正在GitHub更新中,欢迎复制链接阅读
https://github.com/Operations-Research-Science/Ebook-An_introduction_to_robust_optimization
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