Bi-Objective Receding-Horizon Scheduling of Nurses and Hospital Service Robots

Abstract

This paper studies the joint scheduling of nurses and hospital service robots as a bi-objective mixed-integer linear programming problem. The formulation represents heterogeneous nursing skills, alternative skill-coverage modes, nurse availability and temporal rules, workload balance, robot task capability, charging and battery dynamics, and human supervision. Robot workload relief is credited only when an eligible service is actually executed, and explicit supervision-load variables deduct the corresponding nurse capacity from clinical coverage. The receding-horizon formulation also includes a cross-window night--morning constraint and a terminal battery reserve. The computational study is presented as numerical verification on synthetic hospital-like instances rather than clinical validation. Under the proposed formulation, the eight-nurse reference case gives $Z_1=0.78$ and $Z_2=3.164$. A common-budget comparison on B20 seed~1 yields total shortage $53.70$ for the integrated model, compared with $58.03$ for sequential nurse--robot scheduling and $59.46$ for the nurse-only baseline. Additional experiments examine multiple epsilon budgets on a larger B30 instance, sensitivity to robot-relief/supervision parameters and objective weights, and one-day versus two-day rolling horizons against a static full-horizon reference. The battery and routing representations remain aggregate planning approximations, and the scalability evidence is interpreted accordingly. No patient records or real hospital staff data are used, so the results establish model behavior and comparative numerical evidence rather than practical clinical effectiveness.