A Satisfaction-Based Multi-Objective Mixed-Integer Programming Model for the Nurse Rostering Problem

Abstract

A well-balanced working schedule for nurses also means a better patient service quality. Yet, the nurse scheduling problem—also known as a nurse rostering problem—is one of challenging optimization problems, as we need to assign groups of nurses to work functions under a wide variety set of practical constraints. To this end, a nurse may be able to perform limited work functions. Furthermore, the number of assignments must not exceed that allowed by the law—despite the fact that each work function must have at least a predefined number of nurses to perform services. We aim to address this problem, with an overall goal to maximize nurse’s quality of life, which is achieved by a multi-objective mixed-integer programming modeling approach. Four different objectives, under different objective orders, are herein considered and the resulting model is solved by means of the epsilon constraint method. With this solution methodology, we are able to determine a group of well-balanced solutions that helps enhance nurse’s satisfaction in a long run.