A New Class of Overbooking Problems in Container Shipping Industry Container carriers lose billions of dollars each year when shippers reserve slots but fail to show up with the corresponding cargo. This paper studies an online booking problem under a deposit-based mechanism designed to better align incentives and mitigate the costs of overbooking. The authors derive near-optimal online policies for two demand settings: one in which shippers’ no-show behavior is coupled through a spot market, and another in which no-shows are independent. In the coupled setting, a randomized threshold policy guarantees at least 81.9% of clairvoyant profit. In the independent setting, a simple greedy policy is shown to be asymptotically 0.5-optimal as the number of slots tends to infinity. Extensive simulations further demonstrate strong and robust practical performance.
Optimizing Warehouse Space: Algorithmic Advances in Inventory Staggering Since the mid-1960s, the inventory staggering problem has challenged supply chain experts and logisticians aiming to minimize peak storage requirements across multiple periodic replenishment policies. Despite its practical prevalence in warehousing, aerospace, and production planning, foundational computational questions have remained largely unresolved. In their newly accepted paper in Operations Research, Noga Alon and Danny Segev provide major methodological advances. They develop novel algorithmic techniques that significantly improve currently known approximation guarantees for synchronizing inventory replenishments. By leveraging combinatorics and number theory, the authors design polynomial-time approximation schemes for multiple operational settings—including nested and pairwise coprime instances—resolving several long-standing open questions. Furthermore, their research uncovers surprising impossibility results, proving that localized, groupwise synchronization strategies cannot guarantee global optimality. These findings expand the analytical toolbox for warehouse stock control, offering robust frameworks to reduce peak inventory costs.
Exact Matching from Multiple Graphs Networks often describe the same underlying objects from different viewpoints: users on social platforms, proteins across species, or maps built by collaborating robots. But when labels on the nodes of the network are hidden or scrambled, how much correlation among the networks is enough to recover the true correspondence? In “Aligning Multiple Inhomogeneous Random Graphs: Fundamental Limits of Exact Recovery,” Taha Ameen and Bruce Hajek study this question for multiple heterogeneous random graphs, where different pairs of nodes may have different connection probabilities. The paper introduces a simple principle: first obtain reliable partial pairwise matchings, then combine them through transitive closure. The authors identify conditions under which this procedure exactly matches all nodes, and show that for homogeneous Erdős–Rényi graphs these conditions are information-theoretically sharp. A key insight is that multiple graphs can succeed even when no pair of graphs alone contains enough information for exact matching. The work also develops related results on k-cores of inhomogeneous random graphs.
AI-Enhanced Monte Carlo Methodology Achieves More Reliable Testing and Efficiency Certificate for Safety-Critical Systems As artificial intelligence (AI) increasingly drives human-interacting intelligent physical systems such as self-driving vehicles, ensuring their safety against rare catastrophic events has also become a critical challenge. Traditional simulation-based testing methods are powerful in quantifying risks before real deployment. However, for black box systems that generically arise in AI-embedded applications, these methods can consistently underestimate the probabilities of rare failures and, dangerously, without diagnostically detectable signals. To address this perilous gap, the paper "Certifiable Deep Importance Sampling for Rare-Event Simulation of Black Box Systems," by Arief, Bai, Ding, He, Huang, Lam, and Zhao, introduces a framework based on an integration of neural networks into importance sampling, a variance reduction technique that has been found useful in rare-event simulation. This framework, which is called deep probabilistic accelerated evaluation (Deep-PrAE), uses deep neural network classifiers to learn rare-event geometries, which then calibrates importance samplers to estimate rare events with certifiable statistical guarantees. Moreover, these guarantees are designed to go beyond the conventional certifiable notions in rare-event simulation to effectively balance the applicability to black box settings with the required sampling efficiency gain that pertains to rare-event computation. These findings demonstrate a vital step forward in the reliable and certifiable deployment of complex autonomous technologies.
Going Beyond Single-Point Demand Forecasts in Real-Time Allocation Many companies use machine learning to forecast future demand when making real-time allocation decisions, such as deciding how many airline seats, hotel rooms, or advertising opportunities to reserve for different customer groups. Most existing approaches rely on a single demand prediction, or “point estimate.” In the paper “Online Resource Allocation with Convex-Set Machine-Learned Advice,” Negin Golrezaei, Patrick Jaillet, and Zijie Zhou develop a new framework that goes beyond point estimates by representing forecasts as a convex uncertainty set—a range of possible demand outcomes for both high-reward and low-reward customers. This richer form of machine-learned advice captures uncertainty, variability, and correlations in demand while also allowing realized demand to differ from the forecast. The authors develop adaptive online algorithms with provable theoretical guarantees, showing how to optimally balance performance when forecasts are accurate with robustness when forecasts are inaccurate or misleading. Numerical studies further demonstrate that the proposed approach outperforms methods based only on single-point predictions.
