A data-driven hierarchical MILP approach for scheduling clinical pathways: a real-world case study from a German university hospital

Facing economic pressure and case-based compensation systems, hospitals strive for effectively planning patient hospitalization and making efficient use of their resources. To support this endeavor, this paper proposes a flexible hierarchical mixed-integer linear programming (MILP)-based approach for the day-level scheduling of clinical pathways (CP). CP form sequences of ward stays and treatments to be performed during a patient's hospitalization under consideration of all relevant resources such as beds, operating rooms and clinical staff. Since in most hospitals CP-related information needed for planning is not readily available, we propose a data-driven approach in which the structure of the CP to be scheduled including all CP-related constraints is automatically extracted from standardized hospital billing data available in every German hospital. The approach uses a flexible multi-criteria objective function considering several patient- and hospital-related aspects which makes our approach applicable in various scenarios. Furthermore, in contrast to other approaches, it considers several practically relevant aspects ensuring the implementability of the scheduling results such as multiple ward stays per hospitalization and gender-separated room assignments. Regarding the treatment resources such as operation rooms and clinical staff, it considers the eligibility of resources for treatments based on information such as special equipment or qualification and represents complex resources individually to avoid disaggregation problems. To allow solving the resulting complex and large-scale scheduling problem for realistically dimensioned problem instances, we propose a hierarchical two-stage MILP approach involving carefully designed anticipation components in the first-stage model. We evaluate our approach in a case study with real-world data from a German university hospital showing that our approach is able to solve instances with a planning horizon of 1 month exhibiting 1088 treatments and 302 ward stays of 286 patients. In addition to comparing our approach to a monolithic MILP approach, we provide a detailed discussion of the scheduling results for two practically motivated scenarios.