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Multi-Agent Reinforcement Learning for Intraday Operating Rooms Scheduling under Uncertainty

Liu, Kailiang, Chen, Ying, Borndörfer, Ralf, Koch, Thorsten

arXiv.org Artificial Intelligence

Intraday surgical scheduling is a multi-objective decision problem under uncertainty-balancing elective throughput, urgent and emergency demand, delays, sequence-dependent setups, and overtime. We formulate the problem as a cooperative Markov game and propose a multi-agent reinforcement learning (MARL) framework in which each operating room (OR) is an agent trained with centralized training and decentralized execution. All agents share a policy trained via Proximal Policy Optimization (PPO), which maps rich system states to actions, while a within-epoch sequential assignment protocol constructs conflict-free joint schedules across ORs. A mixed-integer pre-schedule provides reference starting times for electives; we impose type-specific quadratic delay penalties relative to these references and a terminal overtime penalty, yielding a single reward that captures throughput, timeliness, and staff workload. In simulations reflecting a realistic hospital mix (six ORs, eight surgery types, random urgent and emergency arrivals), the learned policy outperforms six rule-based heuristics across seven metrics and three evaluation subsets, and, relative to an ex post MIP oracle, quantifies optimality gaps. Policy analytics reveal interpretable behavior-prioritizing emergencies, batching similar cases to reduce setups, and deferring lower-value electives. We also derive a suboptimality bound for the sequential decomposition under simplifying assumptions. We discuss limitations-including OR homogeneity and the omission of explicit staffing constraints-and outline extensions. Overall, the approach offers a practical, interpretable, and tunable data-driven complement to optimization for real-time OR scheduling.


A Fair OR-ML Framework for Resource Substitution in Large-Scale Networks

Mohan, Ved, Raqabi, El Mehdi Er, Van Hentenryck, Pascal

arXiv.org Artificial Intelligence

Ensuring that the right resource is available at the right location and time remains a major challenge for organizations operating large-scale logistics networks. The challenge comes from uneven demand patterns and the resulting asymmetric flow of resources across the arcs, which create persistent imbalances at the network nodes. Resource substitution among multiple, potentially composite and interchangeable, resource types is a cost-effective way to mitigate these imbalances. This leads to the resource substitution problem, which aims at determining the minimum number of resource substitutions from an initial assignment to minimize the overall network imbalance. In decentralized settings, achieving globally coordinated solutions becomes even more difficult. When substitution entails costs, effective prescriptions must also incorporate fairness and account for the individual preferences of schedulers. This paper presents a generic framework that combines operations research (OR) and machine learning (ML) to enable fair resource substitution in large networks. The OR component models and solves the resource substitution problem under a fairness lens. The ML component leverages historical data to learn schedulers' preferences, guide intelligent exploration of the decision space, and enhance computational efficiency by dynamically selecting the top-$κ$ resources for each arc in the network. The framework produces a portfolio of high-quality solutions from which schedulers can select satisfactory trade-offs. The proposed framework is applied to the network of one of the largest package delivery companies in the world, which serves as the primary motivation for this research. Computational results demonstrate substantial improvements over state-of-the-art methods, including an 80% reduction in model size and a 90% decrease in execution time while preserving optimality.


An approach of deep reinforcement learning for maximizing the net present value of stochastic projects

Xu, Wei, Yang, Fan, Cui, Qinyuan, Chen, Zhi

arXiv.org Artificial Intelligence

This paper investigates a project with stochastic activity durations and cash flows under discrete scenarios, where activities must satisfy precedence constraints generating cash inflows and outflows. The objective is to maximize expected net present value (NPV) by accelerating inflows and deferring outflows. We formulate the problem as a discrete-time Markov Decision Process (MDP) and propose a Double Deep Q-Network (DDQN) approach. Comparative experiments demonstrate that DDQN outperforms traditional rigid and dynamic strategies, particularly in large-scale or highly uncertain environments, exhibiting superior computational capability, policy reliability, and adaptability. Ablation studies further reveal that the dual-network architecture mitigates overestimation of action values, while the target network substantially improves training convergence and robustness. These results indicate that DDQN not only achieves higher expected NPV in complex project optimization but also provides a reliable framework for stable and effective policy implementation.


Evaluating the stability of model explanations in instance-dependent cost-sensitive credit scoring

Ballegeer, Matteo, Bogaert, Matthias, Benoit, Dries F.

arXiv.org Artificial Intelligence

Instance-dependent cost-sensitive (IDCS) classifiers offer a promising approach to improving cost-efficiency in credit scoring by tailoring loss functions to instance-specific costs. However, the impact of such loss functions on the stability of model explanations remains unexplored in literature, despite increasing regulatory demands for transparency. This study addresses this gap by evaluating the stability of Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP) when applied to IDCS models. Using four publicly available credit scoring datasets, we first assess the discriminatory power and cost-efficiency of IDCS classifiers, introducing a novel metric to enhance cross-dataset comparability. We then investigate the stability of SHAP and LIME feature importance rankings under varying degrees of class imbalance through controlled resampling. Our results reveal that while IDCS classifiers improve cost-efficiency, they produce significantly less stable explanations compared to traditional models, particularly as class imbalance increases, highlighting a critical trade-off between cost optimization and interpretability in credit scoring. Amid increasing regulatory scrutiny on explainability, this research underscores the pressing need to address stability issues in IDCS classifiers to ensure that their cost advantages are not undermined by unstable or untrustworthy explanations.


An experimental approach: The graph of graphs

Szádoczki, Zsombor, Bozóki, Sándor, Sipos, László, Galambosi, Zsófia

arXiv.org Artificial Intelligence

One of the essential issues in decision problems and preference modeling is the number of comparisons and their pattern to ask from the decision maker. We focus on the optimal patterns of pairwise comparisons and the sequence including the most (close to) optimal cases based on the results of a color selection experiment. In the test, six colors (red, green, blue, magenta, turquoise, yellow) were evaluated with pairwise comparisons as well as in a direct manner, on color-calibrated tablets in ISO standardized sensory test booths of a sensory laboratory. All the possible patterns of comparisons resulting in a connected representing graph were evaluated against the complete data based on 301 individual's pairwise comparison matrices (PCMs) using the logarithmic least squares weight calculation technique. It is shown that the empirical results, i.e., the empirical distributions of the elements of PCMs, are quite similar to the former simulated outcomes from the literature. The obtained empirically optimal patterns of comparisons were the best or the second best in the former simulations as well, while the sequence of comparisons that contains the most (close to) optimal patterns is exactly the same. In order to enhance the applicability of the results, besides the presentation of graph of graphs, and the representing graphs of the patterns that describe the proposed sequence of comparisons themselves, the recommendations are also detailed in a table format as well as in a Java application.


Minimizing the Weighted Number of Tardy Jobs: Data-Driven Heuristic for Single-Machine Scheduling

Antonov, Nikolai, Šůcha, Prěmysl, Janota, Mikoláš, Hůla, Jan

arXiv.org Machine Learning

Existing research on single-machine scheduling is largely focused on exact algorithms, which perform well on typical instances but can significantly deteriorate on certain regions of the problem space. In contrast, data-driven approaches provide strong and scalable performance when tailored to the structure of specific datasets. Leveraging this idea, we focus on a single-machine scheduling problem where each job is defined by its weight, duration, due date, and deadline, aiming to minimize the total weight of tardy jobs. We introduce a novel data-driven scheduling heuristic that combines machine learning with problem-specific characteristics, ensuring feasible solutions, which is a common challenge for ML-based algorithms. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art in terms of optimality gap, number of optimal solutions, and adaptability across varied data scenarios, highlighting its flexibility for practical applications. In addition, we conduct a systematic exploration of ML models, addressing a common gap in similar studies by offering a detailed model selection process and providing insights into why the chosen model is the best fit.


A Comparative Study of SMT and MILP for the Nurse Rostering Problem

Combrink, Alvin, Do, Stephie, Bengtsson, Kristofer, Roselli, Sabino Francesco, Fabian, Martin

arXiv.org Artificial Intelligence

The effects of personnel scheduling on the quality of care and working conditions for healthcare personnel have been thoroughly documented. However, the ever-present demand and large variation of constraints make healthcare scheduling particularly challenging. This problem has been studied for decades, with limited research aimed at applying Satisfiability Modulo Theories (SMT). SMT has gained momentum within the formal verification community in the last decades, leading to the advancement of SMT solvers that have been shown to outperform standard mathematical programming techniques. In this work, we propose generic constraint formulations that can model a wide range of real-world scheduling constraints. Then, the generic constraints are formulated as SMT and MILP problems and used to compare the respective state-of-the-art solvers, Z3 and Gurobi, on academic and real-world inspired rostering problems. Experimental results show how each solver excels for certain types of problems; the MILP solver generally performs better when the problem is highly constrained or infeasible, while the SMT solver performs better otherwise. On real-world inspired problems containing a more varied set of shifts and personnel, the SMT solver excels. Additionally, it was noted during experimentation that the SMT solver was more sensitive to the way the generic constraints were formulated, requiring careful consideration and experimentation to achieve better performance. We conclude that SMT-based methods present a promising avenue for future research within the domain of personnel scheduling.


Integrating Response Time and Attention Duration in Bayesian Preference Learning for Multiple Criteria Decision Aiding

Jiang, Jiaxuan, Liu, Jiapeng, Kadziński, Miłosz, Liao, Xiuwu, Dong, Jingyu

arXiv.org Artificial Intelligence

We introduce a multiple criteria Bayesian preference learning framework incorporating behavioral cues for decision aiding. The framework integrates pairwise comparisons, response time, and attention duration to deepen insights into decision-making processes. The approach employs an additive value function model and utilizes a Bayesian framework to derive the posterior distribution of potential ranking models by defining the likelihood of observed preference data and specifying a prior on the preference structure. This distribution highlights each model's ability to reconstruct Decision-Makers' holistic pairwise comparisons. By leveraging both response time as a proxy for cognitive effort and alternative discriminability as well as attention duration as an indicator of criterion importance, the proposed model surpasses traditional methods by uncovering richer behavioral patterns. We report the results of a laboratory experiment on mobile phone contract selection involving 30 real subjects using a dedicated application with time-, eye-, and mouse-tracking components. We validate the novel method's ability to reconstruct complete preferences. The detailed ablation studies reveal time- and attention-related behavioral patterns, confirming that integrating comprehensive data leads to developing models that better align with the DM's actual preferences.


A Beam Search Based Parallel Algorithm for the Two-Dimensional Strip Packing Problem

Wen, Yajie, Zhang, Defu

arXiv.org Artificial Intelligence

This paper introduces BSPA, a parallel algorithm that leverages beam search to address the two-dimensional strip packing problem. The study begins with a comprehensive review of existing approaches and methodologies, followed by a detailed presentation of the BSPA algorithm. Experimental results demonstrate the effectiveness of the proposed method. To facilitate further research, both the code and datasets are publicly available.


Evaluating utility in synthetic banking microdata applications

Caceres, Hugo E., Moews, Ben

arXiv.org Artificial Intelligence

Financial regulators such as central banks collect vast amounts of data, but access to the resulting fine-grained banking microdata is severely restricted by banking secrecy laws. Recent developments have resulted in mechanisms that generate faithful synthetic data, but current evaluation frameworks lack a focus on the specific challenges of banking institutions and microdata. We develop a framework that considers the utility and privacy requirements of regulators, and apply this to financial usage indices, term deposit yield curves, and credit card transition matrices. Using the Central Bank of Paraguay's data, we provide the first implementation of synthetic banking microdata using a central bank's collected information, with the resulting synthetic datasets for all three domain applications being publicly available and featuring information not yet released in statistical disclosure. We find that applications less susceptible to post-processing information loss, which are based on frequency tables, are particularly suited for this approach, and that marginal-based inference mechanisms to outperform generative adversarial network models for these applications. Our results demonstrate that synthetic data generation is a promising privacy-enhancing technology for financial regulators seeking to complement their statistical disclosure, while highlighting the crucial role of evaluating such endeavors in terms of utility and privacy requirements.