编者按：

在本系列文章中，我们梳理了运筹学顶刊Operations Research在2024年6月份发布的9篇相关文章的基本信息，旨在帮助读者快速洞察领域新动态。

推荐文章1

• 题目：Tight Guarantees for Multiunit Prophet Inequalities and Online Stochastic Knapsack 对多单位先知不等式和在线随机背包问题的严格保证
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2022.0309
• 发表日期：2024/06/03
• 作者：Jiashuo Jiang, Will Ma, Jiawei Zhang
• 摘要：
  • Prophet inequalities are a useful tool for designing online allocation procedures and comparing their performance to the optimal offline allocation. In the basic setting of k-unit prophet inequalities, a well-known procedure with its celebrated performance guarantee of $1-\frac{1}{\sqrt{k+3}}$ has found widespread adoption in mechanism design and general online allocation problems in online advertising, healthcare scheduling, and revenue management. Despite being commonly used to derive approximately optimal algorithms for multiresource allocation problems, the tightness of the $1-\frac{1}{\sqrt{k+3}}$guarantee has remained unknown. In this paper, we characterize the tight guarantee for multiunit prophet inequalities, which we show is in fact strictly greater than $1-\frac{1}{\sqrt{k+1}}$for all $k>1$. This improvement is achieved using duality for a new linear programming (LP) that is based on online contention resolution schemes (OCRS), and as a by-product, we also show the Magician’s policy (but not guarantee) to be instance optimal. We also consider the more general online stochastic knapsack problem where each individual allocation can consume an arbitrary fraction of the initial capacity. Here we introduce a new “best-fit” procedure with a performance guarantee of $\frac{1}{3+e^{-2}}\approx 0.319$, which we also show is tight with respect to the standard LP relaxation. This improves the previously best-known guarantee of 0.2 for online knapsack. Our analysis differs from existing ones by eschewing the need to split items into “large” or “small” based on capacity consumption, using instead an invariant for the overall utilization on different sample paths. Finally, we refine our technique for the unit-density special case of knapsack, and improve the guarantee from 0.321 to 0.3557 in the multiresource appointment scheduling application of Stein et al. (2020).
  • 先知不等式是设计在线分配程序和比较其性能与最优离线分配的有用工具。在k单位先知不等式的基本设置中，一个广为人知的程序及其著名的性能保证 $1-\frac{1}{\sqrt{k+3}}$ 已在机制设计和一般在线分配问题中得到广泛应用，如在线广告、医疗保健排程和收入管理。尽管它常用于推导多资源分配问题的近似最优算法，但该 $1-\frac{1}{\sqrt{k+3}}$保证的紧致性一直未知。在本文中，我们描述了多单位先知不等式的严格保证，事实上我们显示它严格大于 $1-\frac{1}{\sqrt{k+1}}$ 对所有 $k>1$。这种改进是通过为新的线性规划（LP）使用对偶性来实现的，该线性规划基于在线争用解决方案（OCRS），作为副产品，我们还展示了魔术师策略（但不是保证）在实例上是最优的。我们还考虑了更一般的在线随机背包问题，其中每个单独的分配可以消耗初始容量的任意一部分。在这里，我们引入了一个新的“最佳匹配”程序，其性能保证为$\frac{1}{3+e^{-2}}\approx 0.319$，我们还显示它与标准LP松弛相比是紧致的。这比在线背包的先前已知最佳保证0.2有所改进。我们的分析与现有分析不同，它避免了根据容量消耗将物品分为“大”或“小”的需要，而是使用不同样本路径上的整体利用率的不变量。最后，我们精炼了我们对背包单位密度特例的技术，并在Stein等人（2020）的多资源预约调度应用中将保证从0.321提高到0.3557。

推荐文章2

• 题目：Dynamic Relocations in Car-Sharing Networks 共享汽车网络中的动态调度
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2021.0062
• 发表日期：2024/06/06
• 作者：Mahsa Hosseini, Joseph Milner, Gonzalo Romero
• 摘要：
  • We propose a novel dynamic car relocation policy for a car-sharing network with centralized control and uncertain, unbalanced demand. The policy is derived from a reformulation of the linear programming fluid model approximation of the dynamic problem. We project the full-dimensional fluid approximation onto the lower-dimensional space of relocation decisions only. This projection results in a characterization of the problem as n + 1 linear programs, where n is the number of nodes in the network. The reformulation uncovers structural properties that are interpretable using absorbing Markov chain concepts and allows us to write the gradient with respect to the relocation decisions in closed form. Our policy exploits these gradients to make dynamic car relocation decisions. We provide extensive numerical results on hundreds of random networks where our dynamic car relocation policy consistently outperforms the standard static policy. Our policy reduces the optimality gap in steady state by more than 23% on average. Also, in a short-term, time-varying setting, the lookahead version of our dynamic policy outperforms the static lookahead policy slightly more than in the time-homogeneous tests.
  • 我们提出了一种新颖的动态汽车调度政策，适用于具有集中控制和不确定、不平衡需求的共享汽车网络。该政策源自动态问题的线性规划流体模型近似的重新表述。我们将完整维度的流体近似投影到仅涉及调度决策的低维空间。这种投影结果表述了问题为n+1个线性规划，其中n是网络中的节点数。该重新表述揭示了可通过吸收马尔可夫链概念解释的结构特性，并允许我们以封闭形式写出相对于调度决策的梯度。我们的政策利用这些梯度来做出动态汽车调度决策。我们在数百个随机网络上提供了广泛的数值结果，其中我们的动态汽车调度政策一致性地优于标准的静态政策。我们的政策在稳态下平均将最优化差距减少了超过23%。此外，在短期、时变环境中，我们的动态政策前瞻版本的表现略优于时齐测试中的静态前瞻政策。

推荐文章3

• 题目：Boundary Effects in the Diffusion of New Products on Cartesian Networks 笛卡尔网络上新产品扩散的边界效应
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2022.0004
• 发表日期：2024/06/10
• 作者：Gadi Fibich, Tomer Levin, Kenneth T. Gillingham
• 摘要：
  • We analyze the effect of boundaries in the discrete Bass model on D-dimensional Cartesian networks. In two dimensions, this model describes the diffusion of new products that spread primarily by spatial peer effects, such as residential photovoltaic solar systems. We show analytically that nodes (residential units) that are located near the boundary are less likely to adopt than centrally located ones. This boundary effect is local and decays exponentially with the distance from the boundary. At the aggregate level, boundary effects reduce the overall adoption level. The magnitude of this reduction scales as $\frac{1}{M^{1/D}}$, where M is the number of nodes. Our analysis is supported by empirical evidence on the effect of boundaries on the adoption of solar.
  • 我们分析了在D维笛卡尔网络上离散Bass模型中边界的效应。在二维中，该模型描述了主要通过空间同伴效应传播的新产品的扩散，例如住宅光伏太阳能系统。我们从理论上展示了靠近边界的节点（住宅单元）比位于中心的节点更不可能被采纳。这种边界效应是局部的，并且随着与边界的距离呈指数衰减。在整体层面上，边界效应降低了总体采纳水平。这种减少的幅度随着节点数量M按照 $\frac{1}{M^{1/D}}$的规模变化。我们的分析得到了关于边界对太阳能采纳影响的实证证据的支持。

推荐文章4

• 题目：Pricing Optimal Outcomes in Coupled and Non-convex Markets: Theory and Applications to Electricity Markets 耦合与非凸市场中最优结果定价：理论及其在电力市场的应用
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2023.0401
• 发表日期：2024/06/11
• 作者：Mete Şeref Ahunbay, Martin Bichler, Johannes Knörr
• 摘要：
  • In many real-world markets, participants have non-convex preferences, and the allocation problem needs to consider complex constraints. Electricity markets are a prime example, but similar problems appear in many markets, which has led to a growing literature on market design. Competitive equilibrium does not generally exist in such markets. Today, power markets use heuristic pricing rules based on the dual of a relaxed allocation problem. With increasing levels of renewables, these rules have come under scrutiny as they lead to high out-of-market side payments to some participants and inadequate congestion signals. We show that existing pricing heuristics optimize specific design goals that can be conflicting. The tradeoffs can be substantial, and we establish that the design of pricing rules is fundamentally a multiobjective optimization problem addressing different incentives. In addition to traditional multiobjective optimization techniques that involve weighting individual objectives, we introduce a novel parameter-free pricing rule that minimizes incentives for market participants to deviate locally. Our theoretical and experimental findings show how the new pricing rule capitalizes on the upsides of existing pricing rules under scrutiny today. It leads to prices that incur low make-whole payments while providing adequate congestion signals and low lost opportunity costs. Our suggested pricing rule does not require weighing objectives, it is computationally scalable, and balances tradeoffs in a principled manner, addressing a critical policy issue in electricity markets.
  • 在许多现实世界的市场中，参与者具有非凸偏好，且分配问题需要考虑复杂的约束。电力市场是一个典型的例子，但类似的问题在许多市场中都有出现，这促使市场设计的文献不断增长。在这样的市场中，竞争均衡通常不存在。如今，电力市场使用基于放松分配问题的对偶的启发式定价规则。随着可再生能源水平的增加，这些规则受到了审查，因为它们导致对某些参与者的高额市场外侧支付以及不充分的拥堵信号。我们展示了现有定价启发式如何优化可能冲突的特定设计目标。这些权衡可能是实质性的，我们确定定价规则的设计本质上是一个处理不同激励的多目标优化问题。除了涉及对个别目标加权的传统多目标优化技术外，我们还引入了一种新颖的无参数定价规则，该规则最小化市场参与者的局部偏离激励。我们的理论和实验发现显示了新定价规则如何利用当前受审查的现有定价规则的优势。它导致的价格产生低额的全额支付，同时提供充分的拥堵信号和低失去机会成本。我们建议的定价规则不需要权衡目标，它具有计算可扩展性，并以原则性方式平衡权衡，解决了电力市场中的一个关键政策问题。

推荐文章5

• 题目：Optimal Dynamic Mechanism Under Customer Search 顾客搜索下的最优动态机制
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2022.0136
• 发表日期：2024/06/11
• 作者：Zhenyu Hu, Yangge Xiao
• 摘要：
  • This paper investigates the seller’s revenue-maximizing mechanism in the face of a customer who searches for outside alternatives over a finite horizon. The customer’s utility from searches is modeled as a general function—referred to as the recall function—of the past search outcomes. Without observing the customer’s valuation of the product or any realization of search outcomes, the seller can propose and commit to a contract with the customer before the search process begins. Under a general recall function, we show that the optimal strategy for the seller is to offer a menu of American options consisting of deposits and strike prices. In the case in which the customer can only recall a few recent outside alternatives, we further establish that, under the optimal mechanism, customers with low valuation search for outside alternatives without engaging with the seller, whereas high-valuation customers exercise the option immediately, effectively turning the option into an exploding offer. Customers with intermediate valuation only exercise the option, if ever, at the end of the search horizon. Whereas a longer search horizon or smaller search cost both increase the customer’s utility from searches, they have different impacts on the seller’s revenue. More search opportunities lead to an exponential decrease in the seller’s revenue, and in the limit, the optimal mechanism converges to a posted price mechanism. In contrast, as the search cost increases, the seller’s revenue may initially decrease and then increase. In the extreme case in which the search cost exceeds the average value of outside alternatives, the customer’s sequential search problem reduces to strategically timing purchases of the seller’s product. Our optimal mechanism, in this case, reduces to making a single exploding offer with a monopoly price.
  • 本文探讨了在顾客在有限期限内寻找外部替代品的情况下，卖方如何实现收入最大化的机制。顾客从搜索中获得的效用被建模为一个一般函数——称为回忆函数——基于过去搜索结果。在不观察顾客对产品的估值或任何搜索结果的实现的情况下，卖方可以在搜索过程开始前与顾客提出并承诺一个合同。在一般回忆函数下，我们展示了卖方的最优策略是提供一个由存款和执行价格组成的美国期权菜单。在顾客只能回忆几个最近的外部替代品的情况下，我们进一步确定，在最优机制下，低估值的顾客会在不与卖方互动的情况下搜索外部替代品，而高估值的顾客则会立即行使期权，有效地将期权变为即时爆炸性报价。具有中等估值的顾客只会在搜索期限结束时才行使期权（如果有的话）。虽然更长的搜索期限或更小的搜索成本都会增加顾客从搜索中获得的效用，但它们对卖方收入的影响不同。更多的搜索机会导致卖方收入呈指数级下降，在极限情况下，最优机制收敛为一个公开价格机制。相反，随着搜索成本的增加，卖方的收入可能最初会下降然后上升。在极端情况下，搜索成本超过外部替代品的平均价值，顾客的连续搜索问题减少为策略性地定时购买卖方的产品。在这种情况下，我们的最优机制简化为提出一个单一的带有垄断价格的即时爆炸性报价。

推荐文章6

• 题目：Learning to Persuade on the Fly: Robustness Against Ignorance 现场学习说服技巧：对无知的鲁棒性
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2021.0529
• 发表日期：2024/06/18
• 作者：You Zu, Krishnamurthy Iyer, Haifeng Xu
• 摘要：
  • Motivated by information sharing in online platforms, we study repeated persuasion between a sender and a stream of receivers, where, at each time, the sender observes a payoff-relevant state drawn independently and identically from an unknown distribution and shares state information with the receivers, who each choose an action. The sender seeks to persuade the receivers into taking actions aligned with the sender’s preference by selectively sharing state information. However, in contrast to the standard models, neither the sender nor the receivers know the distribution, and the sender has to persuade while learning the distribution on the fly. We study the sender’s learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the distribution. To do this, we first propose and motivate a persuasiveness criterion for the unknown distribution setting that centers robustness as a requirement in the face of uncertainty. Our main result is an algorithm that, with high probability, is robustly persuasive and achieves $O(\sqrt{T\log T})$ regret, where T is the horizon length. Intuitively, at each time, our algorithm maintains a set of candidate distribution and chooses a signaling mechanism that is simultaneously persuasive for all of them. Core to our proof is a tight analysis about the cost of robust persuasion, which may be of independent interest. We further prove that this regret order is optimal (up to logarithmic terms) by showing that no algorithm can achieve regret better than $\Omega (\sqrt{T})$.
  • 受在线平台上信息共享的启发，我们研究了发送者与一系列接收者之间的重复说服过程，在该过程中，每次发送者观察到一个从未知分布中独立同分布抽取的与收益相关的状态，并与接收者共享状态信息，接收者随后选择一个行动。发送者通过选择性共享状态信息，试图说服接收者采取与发送者偏好一致的行动。然而，与标准模型不同的是，发送者和接收者都不知道这一分布，发送者必须在实时学习分布的同时进行说服。我们研究了发送者的学习问题，即如何做出有说服力的行动推荐，以对知道分布的最优说服机制实现低遗憾。为此，我们首先提出并激励了一个针对未知分布设置的说服力标准，该标准将鲁棒性作为面对不确定性时的一个要求。我们的主要成果是一个算法，该算法以高概率具有鲁棒的说服力，并实现了 $O(\sqrt{T\log T})$ 的遗憾，其中T是时间范围的长度。直观上，每次我们的算法都维护一组候选分布，并选择一个对所有这些分布同时具有说服力的信号机制。我们证明的核心是关于鲁棒说服成本的严密分析，这可能具有独立的兴趣。我们进一步证明了这种遗憾的顺序是最优的（直到对数项），通过展示没有算法能实现比 $\Omega (\sqrt{T})$ 更好的遗憾。

推荐文章7

• 题目：Asymptotically Optimal Clearing Control of Backlogs in Multiclass Processing Systems 多类处理系统中积压清理控制的渐进最优性
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2022.0570
• 发表日期：2024/06/20
• 作者：Lun Yu, Seyed Iravani, Ohad Perry
• 摘要：
  • We consider a dynamic scheduling problem for a processing system facing the problem of optimally clearing a large backlog of unsatisfied demand from several classes of customers (or jobs). We formulate the problem as a multiclass queueing model with a large initial queue and arrival rates that approximately equal the system’s processing capacity. The goal is to find a scheduling policy that minimizes a holding-and-abandonment cost during the transient period in which the system is considered congested. Because computing an exact solution to the optimal-control problem is infeasible, we develop a unified asymptotic approximation that covers, in particular, the conventional and the many-server heavy-traffic regimes. In addition to the generality and flexibility of our unified asymptotic framework, we also prove a strong form of asymptotic optimality, under which the costs converge in expectation and in probability. In particular, for the special two-class case, we prove that a static priority policy, which follows a discounted $c\mu /\theta$ rule, is asymptotically optimal. When there are more than two classes of customers, we show that any admissible control that follows the best-effort rule, which gives the lowest priority to one of the classes according to the discounted $c\mu /\theta$ ordering, becomes asymptotically optimal after some relatively short time period. Finally, using heuristic arguments and insights from our analyses, we propose scheduling policies that build on the best-effort rule. An extensive numerical study shows that those proposed policies are effective and provides guidance as to when to use either policy in practice.
  • 我们考虑一个处理系统的动态调度问题，该系统面临着从几个类别的客户（或工作）中优化清理大量未满足需求的积压问题。我们将该问题构建为一个具有大初始队列和到达率近似等于系统处理能力的多类排队模型。目标是找到一种调度策略，以最小化在系统被认为拥堵的过渡期间的持有和放弃成本。因为计算最优控制问题的精确解是不可行的，我们开发了一个统一的渐进近似，特别涵盖了常规和多服务员重流量制度。除了我们统一渐进框架的普遍性和灵活性外，我们还证明了一种强形式的渐进最优性，在该形式下，成本在期望和概率中收敛。特别是对于特殊的两类案例，我们证明了一个静态优先权政策，该政策遵循一个折扣的 $c\mu /\theta$ 规则，是渐进最优的。当有超过两类客户时，我们显示任何遵循最佳努力规则的可接受控制，该规则根据折扣的 $c\mu /\theta$ 排序给其中一类最低优先权，在一段相对较短的时间后变得渐进最优。最后，使用启发式论证和我们分析的见解，我们提出了建立在最佳努力规则上的调度政策。广泛的数值研究表明，这些提议的政策是有效的，并提供了何时在实践中使用任一政策的指导。

推荐文章8

• 题目：Establishing Convergence of Infinite-Server Queues with Batch Arrivals to Shot-Noise Processes 建立具有批量到达的无限服务队列向射击噪声过程的收敛性
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2023.0353
• 发表日期：2024/06/28
• 作者：Andrew Daw, Brian Fralix, Jamol Pender
• 摘要：
  • Across domains as diverse as communication channels, computing systems, and public health management, a myriad of real-world queueing systems receive batch arrivals of jobs or customers. In this work, we show that under a natural scaling regime, both the queue-length process and the workload process associated with a properly scaled sequence of infinite-server queueing systems with batch arrivals converge almost surely, uniformly on compact sets, to shot-noise processes. Given the applicability of these models, our relatively direct and accessible methodology may also be of independent interest, where we invoke the Glivenko–Cantelli theorem when the Strong Law of Large Numbers fails to hold for the queue-length batch scaling yet then, exploit the continuity of stationary excess distributions and the classic strong law when the Glivenko–Cantelli theorem fails to hold in the workload batch scaling. These results strengthen a convergence result recently established in the work of de Graaf et al. [de Graaf WF, Scheinhardt WR, Boucherie RJ (2017) Shot-noise fluid queues and infinite-server systems with batch arrivals. Performance Evaluation 116:143–155] in multiple ways, and furthermore, they provide new insight into how the queue-length and workload limits differ from one another.
  • 在如通信渠道、计算系统和公共卫生管理等多样化领域中，众多现实世界的排队系统接收批量到达的工作或客户。在这项工作中，我们展示了在一个自然的缩放机制下，与批量到达的无限服务队列系统的适当缩放序列相关的队列长度过程和工作负载过程几乎必然地、在紧凑集上一致地收敛到射击噪声过程。鉴于这些模型的适用性，我们相对直接和易于获取的方法论也可能具有独立的兴趣，其中我们在队列长度批量缩放的强大数定律失效时，调用了Glivenko-Cantelli定理，然后，在工作负载批量缩放中Glivenko-Cantelli定理失效时，利用了平稳超额分布的连续性和经典的强大数定律。这些结果以多种方式加强了de Graaf等人近期建立的收敛结果 [de Graaf WF, Scheinhardt WR, Boucherie RJ (2017) Shot-noise fluid queues and infinite-server systems with batch arrivals. Performance Evaluation 116:143–155]，并且，它们还提供了新的见解，说明队列长度和工作负载极限之间的差异。

推荐文章9

• 题目：Optimal Regularized Online Allocation by Adaptive Re-Solving 通过自适应重求解的最优正则化在线分配
• 期刊：Operations Research
• 原文链接：https://doi.org/10.1287/opre.2022.0486
• 发表日期：2024/06/28
• 作者：Wanteng Ma, Ying Cao, Danny H. K. Tsang, Dong Xia
• 摘要：
  • This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially nonconcave cumulative rewards, hard resource constraints, and a nonseparable regularizer. Under a strategy of adaptively updating the resource constraints, the proposed framework only requests approximate solutions to the empirical dual problems up to a certain accuracy and yet delivers an optimal logarithmic regret under a locally second-order growth condition. Surprisingly, a delicate analysis of the dual objective function enables us to eliminate the notorious log-log factor in regret bound. The flexible framework renders renowned and computationally fast algorithms immediately applicable, for example, dual stochastic gradient descent. Additionally, an infrequent re-solving scheme is proposed, which significantly reduces computational demands without compromising the optimal regret performance. A worst-case square-root regret lower bound is established if the resource constraints are not adaptively updated during dual optimization, which underscores the critical role of adaptive dual variable update. Comprehensive numerical experiments demonstrate the merits of the proposed algorithm framework.
  • 本文介绍了一个基于对偶的算法框架，用于解决正则化在线资源分配问题，这些问题可能具有非凹形的累积奖励、严格的资源约束和非可分的正则项。在自适应更新资源约束的策略下，所提出的框架仅要求对经验对偶问题进行近似解决到一定的精度，但在局部二阶增长条件下仍能实现最优对数遗憾。令人惊讶的是，对偶目标函数的精细分析使我们能够消除遗憾界中臭名昭著的对数对数因子。该灵活框架使得著名且计算速度快的算法可以立即应用，例如对偶随机梯度下降。此外，提出了一种不频繁的重求解方案，显著减少了计算需求，而不影响最优遗憾性能。如果在对偶优化期间资源约束未自适应更新，则建立了最坏情况下的平方根遗憾下界，这强调了自适应对偶变量更新的关键作用。全面的数值实验展示了所提算法框架的优点。