Robust Operating Room Planning and Optimization under Resource Constraints and Uncertainty

Operating rooms represent one of the most critical and resource-intensive units within hospitals, accounting for up to 40% of hospital expenses and generating up to 70% of revenues. Effective management of operating room scheduling faces significant challenges due to multiple objectives and inherent uncertainties in surgery durations, recovery times, and resource availability.
These uncertainties, coupled with the interconnected nature of downstream resources (post-anesthesia care units, intensive care units), create a complex optimization challenge that significantly impacts healthcare delivery efficiency and patient outcomes. This operating room planning problem considering downstream resources is particularly challenging, being a special case of the hybrid flow shop problem, which is proven to be NP-hard.
While traditional deterministic approaches to operating room scheduling fail to capture the stochastic nature of healthcare operations, and purely stochastic methods often become computationally intractable for real-world instances, Adaptive robust optimization offers a promising framework by combining the tractability of robust optimization with the flexibility of recourse decisions. Operating room managers often struggle with accurate predictions of key metrics like length of stay and emergency cases, which can have multiple peaks in their distributions.
This thesis aims to develop novel approaches for large-scale adaptive robust optimization problems, combining tactical and operational decision levels of operating room planning (Master Surgical Schedule, allocation scheduling, and advance scheduling) with downstream resource management. The doctoral candidate will conduct extensive analyses and comparisons of ambiguity sets and uncertainty sets for operating room problems.
The candidate will develop practical solutions for hospital operations, implement new decomposition methods for two-stage or multi-stage adaptive robust optimization problems, evaluate solution quality through algorithmic analysis, and incorporate machine learning techniques to improve optimization time. They will implement decomposition algorithms such as Benders decomposition variants, column-and-constraint generation methods, and propose hybrid algorithms combining exact and heuristic approaches.
The ideal candidate should hold a Master's degree or Engineering degree in Operations Research, Applied Mathematics, or Computer Science, with a strong focus on mathematical optimization and modeling techniques. Skills in mathematical programming, duality theory, decomposition methods, robust optimization, stochastic programming, and computer programming (Julia/Python/C++) are essential.
The PhD will be conducted within the LIST3N laboratory (OPTI team) at the Université de Technologie de Troyes, benefiting from solid expertise in optimization and operations research, access to high-performance computing facilities, and collaborations with healthcare partners providing real-world case studies and validation opportunities. This doctoral project offers a unique opportunity to contribute to the improvement of healthcare systems through the development of innovative optimization methods.

Research Unit: Laboratoire Informatique et Société Numérique (LIST3N)

Website LIST3N : http://recherche.utt.fr/list3n

The ideal candidate for this doctoral project must hold a Master's degree or Engineering degree in Operations Research, Applied Mathematics, or Computer Science, with a strong focus on mathematical optimization and modeling. Advanced proficiency in English is imperative, both written and oral, as the candidate will be required to publish research in international journals, present at scientific conferences, and collaborate with international partners. The doctoral student must possess excellent programming skills, particularly in Julia, Python or C++, enabling them not only to develop and implement complex algorithms efficiently but also to conduct extensive numerical experiments. Practical experience with optimization libraries and commercial solvers (CPLEX, Gurobi, Hexaly) is strongly appreciated, as well as the ability to manipulate and analyze large volumes of data. Proficiency with modern development tools will be considered an important asset. The candidate should demonstrate the ability to transform complex problems into mathematical models and efficient algorithmic solutions, while maintaining a rigorous and methodical approach in their research work.