A hybrid integer programming and variable neighborhood search algorithm to solve Nurse Rostering Problems

Erfan Rahimian, Kerem Akartunali, John Levine

Research output: Contribution to journalArticlepeer-review

62 Citations (Scopus)
34 Downloads (Pure)


The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilize the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes.
Original languageEnglish
Pages (from-to)411–423
Number of pages13
JournalEuropean Journal of Operational Research
Issue number2
Early online date22 Sept 2016
Publication statusPublished - 16 Apr 2017


  • timetabling
  • Nurse Rostering
  • hybrid algorithm
  • integer programming
  • variable neighbourhood search


Dive into the research topics of 'A hybrid integer programming and variable neighborhood search algorithm to solve Nurse Rostering Problems'. Together they form a unique fingerprint.

Cite this