  Assigning patients to rooms and nurses to patients are critical tasks within
hospitals that directly affect patient and staff satisfaction, quality of care,
and hospital efficiency. Both patient-to-room assignments and nurse-to-patient
assignments are typically agreed upon at the ward level, and they interact in
several ways such as jointly determining the walking distances nurses must
cover between different patient rooms. This motivates to consider both problems
jointly in an integrated fashion.
  This paper presents the first optimization models and algorithms for the
integrated patient-to-room and nurse-to-patient assignment problem. We provide
a mixed integer programming formulation of the integrated problem that
considers the typical objectives from the single problems as well as additional
objectives that can only be properly evaluated when integrating both problems.
Moreover, motivated by the inherent complexity that results from integrating
these two NP-hard and already computationally challenging problems, we devise
an efficient heuristic for the integrated patient-to-room and nurse-to-patient
assignment problem. To evaluate the running time and quality of the solution
obtained with the heuristic, we conduct extensive computational experiments on
both artificial and real-world instances. The artificial instances are
generated by a parameterized instance generator for the integrated problem that
is made freely available.
