In many classification settings, the class of primary interest is underrepresented, leading to imbalanced data problems that arise in applications such as rare disease detection and fraud identification. In these contexts, identifying a potential positive instance typically triggers costly follow-up actions, such as medical imaging or detailed transaction inspection, which are subject to limited operational capacity. Motivated by this setting, we consider classification problems where data may arrive sequentially and decisions must be made under constraints on the number of instances that can be selected for further analysis. We propose a classification framework that explicitly controls the rate of positive predictions, enforcing a user-defined bound on the proportion of observations classified as belonging to the minority class while maximizing detection performance. The approach can be implemented using standard learning methods and naturally extends to online settings, where decisions are taken in real time. We show that incorporating capacity constraints leads to substantial improvements over classical approaches, including resampling techniques such as SMOTE, which do not directly control the selection rate.

Public resource allocation involves the efficient distribution of resources, including urban infrastructure, energy, and transportation, to effectively meet societal demands. However, existing methods focus on optimizing the movement of individual resources independently, without considering their capacity constraints. To address this limitation, we propose a novel and more practical problem: Collaborative Public Resource Allocation (CPRA), which explicitly incorporates capacity constraints and spatio-temporal dynamics in real-world scenarios. We propose a new framework called Game-Theoretic Spatio-Temporal Reinforcement Learning (GSTRL) for solving CPRA. Our contributions are twofold: 1) We formulate the CPRA problem as a potential game and demonstrate that there is no gap between the potential function and the optimal target, laying a solid theoretical foundation for approximating the Nash equilibrium of this NP-hard problem; and 2) Our designed GSTRL framework effectively captures the spatio-temporal dynamics of the overall system. We evaluate GSTRL on two real-world datasets, where experiments show its superior performance. Our source codes are available in the supplementary materials.

The ROC curve is widely used to assess binary classification performance. Yet for some applications such as alert systems for hospitalized patient monitoring, conventional ROC analysis cannot capture crucial factors that impact deployment, such as enforcing a minimum precision constraint to avoid false alarm fatigue or imposing an upper bound on the number of predicted positives to represent the capacity of hospital staff. The usual area under the curve metric also does not reflect asymmetric costs for false positives and false negatives. In this paper we address all three of these issues. First, we show how the subset of classifiers that meet given precision and capacity constraints can be represented as a feasible region in ROC space. We establish the geometry of this feasible region. We then define the partial area of lesser classifiers, a performance metric that is monotonic with cost and only accounts for the feasible portion of ROC space. Averaging this area over a desired range of cost parameters results in the partial volume over the ROC surface, or partial VOROS. In experiments predicting mortality risk using vital sign history on the MIMIC-IV dataset, we show this cost-aware metric is better than alternatives for ranking classifiers in hospital alert applications.

As urban aerial mobility (UAM) infrastructure development accelerates globally, cities like Shenzhen are planning large-scale vertiport networks (e.g., 1,200+ facilities by 2026). Existing planning frameworks remain inadequate for this complexity due to historical limitations in data granularity and real-world applicability. This paper addresses these gaps by first proposing the Capacitated Dynamic Maximum Covering Location Problem (CDMCLP), a novel optimization framework that simultaneously models urban-scale spatial-temporal demand, heterogeneous user behaviors, and infrastructure capacity constraints. Building on this foundation, we introduce an Integrated Planning Recommendation System that combines CDMCLP with socio-economic factors and dynamic clustering initialization. This system leverages adaptive parameter tuning based on empirical user behavior to generate practical planning solutions. Validation in a Chinese center city demonstrates the effectiveness of the new optimization framework and recommendation system. Under the evaluation and optimization of CDMCLP, the quantitative performance of traditional location methods are exposed and can be improved by 38\%--52\%, while the recommendation system shows user-friendliness and the effective integration of complex elements. By integrating mathematical rigor with practical implementation considerations, this hybrid approach bridges the gap between theoretical location modeling and real-world UAM infrastructure planning, offering municipalities a pragmatic tool for vertiport network design.

Any agents we can possibly build are subject to capacity constraints, as memory and compute resources are inherently finite. However, comparatively little attention has been dedicated to understanding how agents with limited capacity should allocate their resources for optimal performance. The goal of this paper is to shed some light on this question by studying a simple yet relevant continual learning problem: the capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem. We derive a solution to this problem under appropriate technical conditions. Moreover, for problems that can be decomposed into a set of sub-problems, we also demonstrate how to optimally allocate capacity across these sub-problems in the steady state. We view the results of this paper as a first step in the systematic theoretical study of learning under capacity constraints.

In China's competitive fresh e-commerce market, optimizing operational strategies, especially inventory management in front-end warehouses, is key to enhance customer satisfaction and to gain a competitive edge. Front-end warehouses are placed in residential areas to ensure the timely delivery of fresh goods and are usually in small size. This brings the challenge of deciding which goods to stock and in what quantities, taking into account capacity constraints. To address this issue, traditional predict-then-optimize (PTO) methods that predict sales and then decide on inventory often don't align prediction with inventory goals, as well as fail to prioritize consumer satisfaction. This paper proposes a multi-task Optimize-then-Predict-then-Optimize (OTPTO) approach that jointly optimizes product selection and inventory management, aiming to increase consumer satisfaction by maximizing the full order fulfillment rate. Our method employs a 0-1 mixed integer programming model OM1 to determine historically optimal inventory levels, and then uses a product selection model PM1 and the stocking model PM2 for prediction. The combined results are further refined through a post-processing algorithm OM2. Experimental results from JD.com's 7Fresh platform demonstrate the robustness and significant advantages of our OTPTO method. Compared to the PTO approach, our OTPTO method substantially enhances the full order fulfillment rate by 4.34% (a relative increase of 7.05%) and narrows the gap to the optimal full order fulfillment rate by 5.27%. These findings substantiate the efficacy of the OTPTO method in managing inventory at front-end warehouses of fresh e-commerce platforms and provide valuable insights for future research in this domain.

A total of more than 3400 public shootings have occurred in the United States between 2016 and 2022. Among these, 25.1% of them took place in an educational institution, 29.4% at the workplace including office buildings, 19.6% in retail store locations, and 13.4% in restaurants and bars. During these critical scenarios, making the right decisions while evacuating can make the difference between life and death. However, emergency evacuation is intensely stressful, which along with the lack of verifiable real-time information may lead to fatal incorrect decisions. To tackle this problem, we developed a multi-route routing optimization algorithm that determines multiple optimal safe routes for each evacuee while accounting for available capacity along the route, thus reducing the threat of crowding and bottlenecking. Overall, our algorithm reduces the total casualties by 34.16% and 53.3%, compared to our previous routing algorithm without capacity constraints and an expert-advised routing strategy respectively. Further, our approach to reduce crowding resulted in an approximate 50% reduction in occupancy in key bottlenecking nodes compared to both of the other evacuation algorithms.

Keywords: scheduling, RCPSP, bottlenecks, constraint relaxation Abstract: In realistic production scenarios, Advanced Planning and Scheduling (APS) tools often require manual intervention by production planners, as the system works with incomplete information, resulting in suboptimal schedules. Often, the preferable solution is not found just because of the too-restrictive constraints specifying the optimization problem, representing bottlenecks in the schedule. To provide computer-assisted support for decision-making, we aim to automatically identify bottlenecks in the given schedule while linking them to the particular constraints to be relaxed. In this work, we address the problem of reducing the tardiness of a particular project in an obtained schedule in the resource-constrained project scheduling problem by relaxing constraints related to identified bottlenecks. We develop two methods for this purpose. The second method identifies potential improvements in relaxed versions of the problem and proposes targeted relaxations. Surprisingly, the untargeted relaxations result in improvements comparable to the targeted relaxations. 1 INTRODUCTION In the modern manufacturing industry, Advanced Planning and Scheduling (APS) tools are used to schedule production automatically. However, not all parameters and information are available to the APS systems in practice.

We study online learning with oblivious losses and delays under a novel ``capacity constraint'' that limits how many past rounds can be tracked simultaneously for delayed feedback. Under ``clairvoyance'' (i.e., delay durations are revealed upfront each round) and/or ``preemptibility'' (i.e., we have ability to stop tracking previously chosen round feedback), we establish matching upper and lower bounds (up to logarithmic terms) on achievable regret, characterizing the ``optimal capacity'' needed to match the minimax rates of classical delayed online learning, which implicitly assume unlimited capacity. Our algorithms achieve minimax-optimal regret across all capacity levels, with performance gracefully degrading under suboptimal capacity. For $K$ actions and total delay $D$ over $T$ rounds, under clairvoyance and assuming capacity $C = \Omega(\log(T))$, we achieve regret $\widetilde{\Theta}(\sqrt{TK + DK/C + D\log(K)})$ for bandits and $\widetilde{\Theta}(\sqrt{(D+T)\log(K)})$ for full-information feedback. When replacing clairvoyance with preemptibility, we require a known maximum delay bound $d_{\max}$, adding $\smash{\widetilde{O}(d_{\max})}$ to the regret. For fixed delays $d$ (i.e., $D=Td$), the minimax regret is $\Theta\bigl(\sqrt{TK(1+d/C)+Td\log(K)}\bigr)$ and the optimal capacity is $\Theta(\min\{K/\log(K),d\}\bigr)$ in the bandit setting, while in the full-information setting, the minimax regret is $\Theta\bigl(\sqrt{T(d+1)\log(K)}\bigr)$ and the optimal capacity is $\Theta(1)$. For round-dependent and fixed delays, our upper bounds are achieved using novel scheduling policies, based on Pareto-distributed proxy delays and batching techniques. Crucially, our work unifies delayed bandits, label-efficient learning, and online scheduling frameworks, demonstrating that robust online learning under delayed feedback is possible with surprisingly modest tracking capacity.

Many real-world sequential repair problems can be effectively modeled using monotonic Markov Decision Processes (MDPs), where the system state stochastically decreases and can only be increased by performing a restorative action. This work addresses the problem of solving multi-component monotonic MDPs with both budget and capacity constraints. The budget constraint limits the total number of restorative actions and the capacity constraint limits the number of restorative actions that can be performed simultaneously. While prior methods dealt with budget constraints, including capacity constraints in prior methods leads to an exponential increase in computational complexity as the number of components in the MDP grows. We propose a two-step planning approach to address this challenge. First, we partition the components of the multi-component MDP into groups, where the number of groups is determined by the capacity constraint. We achieve this partitioning by solving a Linear Sum Assignment Problem (LSAP). Each group is then allocated a fraction of the total budget proportional to its size. This partitioning effectively decouples the large multi-component MDP into smaller subproblems, which are computationally feasible because the capacity constraint is simplified and the budget constraint can be addressed using existing methods. Subsequently, we use a meta-trained PPO agent to obtain an approximately optimal policy for each group. To validate our approach, we apply it to the problem of scheduling repairs for a large group of industrial robots, constrained by a limited number of repair technicians and a total repair budget. Our results demonstrate that the proposed method outperforms baseline approaches in terms of maximizing the average uptime of the robot swarm, particularly for large swarm sizes.