JOURNAL OF INDUSTRIAL AND doi:10.3934/jimo.2020058 MANAGEMENT OPTIMIZATION A HYBRID VARIABLE NEIGHBOURHOOD SEARCH AND DYNAMIC PROGRAMMING APPROACH FOR THE NURSE ROSTERING PROBLEM Mohammed Abdelghany * and Amr B. Eltawil Industrial Engineering and Systems Management Egypt-Japan University of Science and Technology New Borg Elarab City, Alexandria 21934, Egypt Zakaria Yahia Mechanical Engineering Department Faculty of Engineering, Fayoum University Fayoum, Egypt Kazuhide Nakata Industrial Engineering and Economics School of Engineering, Tokyo Institute of Technology Tokyo, Japan (Communicated by Mutsunori Yagiura) Abstract. Nurse Rostering is the activity of assigning nurses to daily shifts in order to satisfy the cover requirements, taking into account the operational requirements and nurses’ preferences. The problem is usually modeled as sets of hard and soft constraints with an objective function to minimize violations of soft constraints. The nurse rostering problem is known to be NP-hard. Many metaheuristics were used to tackle this problem. One of the frequently used heuristics is the Variable Neighbourhood Search (VNS). The VNS is usually used as a standalone method or in integration with another exact or heuristic method. In this paper, a new hybrid VNS and Dynamic Programming based heuristic approach is proposed to handle the nurse rostering problem. In the proposed approach, two perturbation mechanisms are adopted simultaneously. The proposed approach is tested on two different benchmark data sets. A com- parison with state-of-the-art methods from literature revealed the competitive performance of the proposed approach. 1. Introduction. Hospitals have to be staffed 24 hours a day, seven days a week. Nurses are one of the most crucial resources in hospitals. Therefore, proper nurses’ schedules have to be prepared frequently (daily/weekly/monthly) to maintain the quality of healthcare services. The Nurse Rostering Problem (NRP) deals with the assignment of nurses to daily shifts in order to satisfy cover requirements while considering the legal regulations, nurses’ preferences and some other requirements. Switching from the manual nurse rostering process to an automated one is resulting 2010 Mathematics Subject Classification. Primary: 90B35; Secondary: 90C59, 90C39. Key words and phrases. Variable neighbourhood search, heuristics, dynamic programming, nurse rostering, timetabling. * Corresponding author: Mohammed Abdelghany. 1