Bi-Objective Receding-Horizon Scheduling of Nurses and Hospital Service Robots
Keywords:
nurse scheduling, hospital service robots, bi-objective optimization, mixed-integer linear programming, model predictive controlAbstract
This paper studies the joint scheduling of nurses and hospital service robots as a bi-objective mixed-integer linear programming problem. The model accounts for heterogeneous nursing skills, alternative skill-coverage modes, nurse availability, rest and night-shift restrictions, workload balance, overtime, robot task capability, charging, battery dynamics, energy use, and human supervision. The first objective penalizes shortages in clinical coverage and robot services, while the second captures workload imbalance, overtime, night assignments, preference penalties, robot energy consumption, and charging. Alternative skill mixes are represented through a selected-mode formulation, and robot location is separated from robot task execution so that service capacity is not overstated. The static scheduling problem is embedded in a receding-horizon model predictive control structure in which battery, cumulative nurse workload, night-duty history, availability, and demand information are updated between decision windows. The reference eight-nurse case is reproduced with $Z_1=0$ and $Z_2=3.15$. The computational study then considers 20 synthetic hospital-like instances with up to 60 nurses, 6 wards, and 8 robots. Imposing the bound $Z_1\le0.60Z_1^{op}$ guarantees a reduction of at least 40\% relative to the operational-reference shortage, while the mean increase in $Z_2$ ranges from 2.18\% to 3.80\% across the four size classes. A separate lexicographically refined epsilon-constraint study on the B20 seed-1 instance produces a nondominated set of trade-off points after explicit tie-breaking in both objectives. A seven-day rolling-horizon experiment further illustrates the response to demand changes, short-notice nurse absences, and a robot battery disruption. The larger instances are synthetic and are used to examine model behavior rather than to represent clinical staffing standards.
