Combinatorial models and algorithms for resource allocation problems in healthcare management and logistics

Scheduling problems represent a fundamental challenge across a wide range of domains, from industrial production to healthcare management. Their complexity arises not only from the intricate nature of the decisions involved, but also from the presence of competing objectives and constraints. In practice, scheduling requires a delicate balance between efficiency and flexibility, short-term constraints and long-term goals, as well as mathematical optimization and qualitative considerations. For this reason, scheduling remains both a rich field for theoretical research and a practical instrument for addressing real-world challenges. In healthcare, the implications are particularly high: scheduling decisions influence not only the utilization of scarce resources but also patient outcomes and the fairness of access to care. Scheduling problems arise in many different forms, and this thesis is unified by a common focus on scheduling as its central theme. Particular attention is devoted to real-world problems and to the practical applicability of the proposed solutions. In this spirit, the first chapter addresses two specific cases: the scheduling of operating rooms and the allocation of healthcare resources across a territory. Both problems are motivated by concrete operational needs and are analyzed with the dual objective of methodological rigor and practical relevance. The second chapter investigates the preemptive Resource-Constrained Project Scheduling Problem, focusing on the balance between reducing project makespan and managing the complexity introduced by preemptions. Allowing an activity to be interrupted and resumed later can lead to shorter project durations, but at the same time it creates additional challenges for coordination, resource allocation, and overall project management. In addition to the theoretical analysis, a real-world case study is presented to illustrate the practical implications of the proposed approach. The third chapter explores scheduling problems in environments where machines are subject to failures presenting two distinct variants of the problem, both analyzed from a theoretical perspective.