Ralf Borndörfer

Kailiang Liu, Ying Chen, Ralf Borndörfer et al.

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.

Ricardo Euler, Pedro Maristany de las Casas, Ralf Borndörfer

The logic-constrained shortest path problem (LCSPP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authorities are enforcing a set of traffic flow restrictions (TFRs) on aircraft routes in order to increase safety and throughput. We propose a new branch and bound-based algorithm for the LCSPP. The resulting algorithm has three main degrees of freedom: the node selection rule, the branching rule and the conflict. While node selection and branching rules have been long studied in the MIP and SAT communities, most of them cannot be applied out of the box for the LCSPP. We review the existing literature and develop tailored variants of the most prominent rules. The conflict, the set of variables to which the branching rule is applied, is unique to the LCSPP. We analyze its theoretical impact on the B&B algorithm. In the second part of the paper, we show how to model the flight planning problem with TFRs as an LCSPP and solve it using the branch and bound algorithm. We demonstrate the algorithm's efficiency on a dataset consisting of a global flight graph and a set of around 20000 real TFRs obtained from our industry partner Lufthansa Systems GmbH. We make this dataset publicly available. Finally, we conduct an empirical in-depth analysis of dynamic shortest path algorithms, node selection rules, branching rules and conflicts. Carefully choosing an appropriate combination yields an improvement of an order of magnitude compared to an uninformed choice.