The consideration of two scalarization methods for the multi-objective nurse-to-patient assignment problem

IIn this research, the application of two scalarization methods, namely the conic scalarization method and the $\varepsilon$-constraint method, is investigated within the context of a multi-objective optimization problem. These methods are used to address the challenge of assigning nurses to patients on a hospital unit during a shift. The two objective functions of this assignment problem are based on patient workload metrics and unit-related travel distance measures. The proposed solution approach demonstrates the ability to generate solutions that eluded the previous mathematical programming techniques that relied on simplistic weightings of conflicting objective functions. In addition, it is found that the $\varepsilon$-constraint method outperforms the conic scalarization method in terms of solution time. This work contributes to enhancing our understanding of effective strategies for addressing complex workload distribution challenges within healthcare settings.