Fuzzy Mathematical Modeling Approach for the Nurse Scheduling Problem: A Case Study

Abstract

The nurse scheduling problem (NSP) has received a great amount of attention in recent years. In the NSP, the goal is to assign the shifts to the nurses in order to satisfy the demands of each day during the planning horizon. In this study, we consider the NSP in the largest hospital in Iran, i.e., Milad. A mathematical programming model is proposed to maximize the nurses’ preferences to work in their favorable shifts as well as to minimize the total surplus nurses to cover the demands of each day. The schedule of the nurses on the last days of the previous planning horizon is considered for assigning the shifts to the nurses on the beginning days of the current planning horizon. Moreover, the leave days requested by the nurses are taken into consideration. Considering the uncertainties in the real-world problems has a great effect on providing the higher quality schedules. In this study, the uncertainty is considered in the nurses’ preferences and the number of surplus nurses. To treat the uncertainties in the research problem, four different types of the fuzzy solution approaches are applied. Then, the fuzzy models are formulated based on the proposed fuzzy solution approaches to provide a more flexible solution for policy makers.