Multi-stage integer linear programming framework for integrated healthcare planning

This paper proposes two approaches for integrated healthcare planning, jointly addressing patient admission scheduling (PAS), nurse-to-room assignment, and surgical case planning (SCP). In particular, we consider the problem introduced in the Integrated Healthcare Timetabling Competition 2024. The first approach is a matheuristic based on Integer Linear Programming, in which a large-scale formulation is decomposed into two stages. However, this formulation remains challenging to solve for medium and large instances. To overcome this limitation, we develop a second, multi-stage approach that incorporates aggregation and disaggregation procedures for PAS and SCP, along with an arc-flow reformulation of the SCP resource constraints inspired by cutting and packing problems. To the best of our knowledge, no previous work integrates these three decisions within a single framework or applies arc-flow techniques to SCP. Computational results show that the multi-stage approach produces highquality solutions with substantially improved scalability. This study therefore fills an important gap by introducing a unified framework that simultaneously addresses these interdependent planning decisions in healthcare systems.