A mathematical framework and optimization approach for strategically configuring hospitals to accommodate diverse patient caseloads

In many hospitals, treatment areas are typically dedicated to a single medical or surgical specialty. While shared use by multiple specialties is uncommon, it can be necessary, or even advantageous in certain situations. This article introduces a proof-of-concept mathematical framework for strategically reorganizing treatment-area functions to enhance resilience and operational flexibility. We focus on configuring a hospital so it can robustly treat a selected repertoire of patient caseloads (a.k.a., case mix) should they arise. Using mixed-integer programming and metaheuristic optimization, our solution approach determines which patient types should share each treatment area, maximizing the number of targeted caseloads that can be accommodated. When caseloads vary greatly or are infeasible, the model seeks a best-fit configuration that maximizes fulfilment across all caseload profiles. Because solving the exact model is computationally intractable, we propose and evaluate two matheuristics, one that utilises Simulated Annealing and the other Variable Neighbourhood Search. Numerical testing on a large, real-world instance demonstrates their effectiveness in finding near-optimal, practical solutions, providing strong motivation for further research and validation across diverse healthcare settings.