Skip to main content

A heuristic algorithm based on multi-assignment procedures for nurse scheduling


This paper tackles a Nurse Scheduling Problem which consists of generating work schedules for a set of nurses while considering their shift preferences and other requirements. The objective is to maximize the satisfaction of nurses’ preferences and minimize the violation of soft constraints. This paper presents a new deterministic heuristic algorithm, called MAPA (multi-assignment problem-based algorithm), which is based on successive resolutions of the assignment problem. The algorithm has two phases: a constructive phase and an improvement phase. The constructive phase builds a full schedule by solving successive assignment problems, one for each day in the planning period. The improvement phase uses a couple of procedures that re-solve assignment problems to produce a better schedule. Given the deterministic nature of this algorithm, the same schedule is obtained each time that the algorithm is applied to the same problem instance. The performance of MAPA is benchmarked against published results for almost 250,000 instances from the NSPLib dataset. In most cases, particularly on large instances of the problem, the results produced by MAPA are better when compared to best-known solutions from the literature. The experiments reported here also show that the MAPA algorithm finds more feasible solutions compared with other algorithms in the literature, which suggest that this proposed approach is effective and robust.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. 1.

    We excluded 33 cases involving 30 nurses and 5 cases involving 60 nurses for which NSPLib reports infeasible solutions.


  1. Bilgin, B., De Causmaecker, P., Rossie, B., & Vanden Berghe, G. (2008). Local search neighbourhoods to deal with a novel nurse rostering model. In Proceedings of the 7th international conference on practice and theory of automated timetabling, Montreal (pp. WA3-2/6–WA3-2/24).

  2. Burke, E. K., Curtois, T., Post, G., Qu, R., & Veltman, B. (2008). A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem. European Journal of Operational Research, 188, 330–341.

    Article  Google Scholar 

  3. Burke, E. K., De Causmaecker, P., Vanden Berghe, G., & Van Landeghem, H. (2004). The state of the art of nurse rostering. Journal of Scheduling, 7, 441–499.

    Article  Google Scholar 

  4. Burke, E. K., Li, J., & Qu, R. (2012). A Pareto-based search methodology for multi-objective nurse scheduling. Annals of Operations Research, 196(1), 91–109.

    Article  Google Scholar 

  5. Carpaneto, G., & Toth, P. (1987). Primal-dual algorithms for the assignment problem. Discrete Applied Mathematics, 18, 137–153.

    Article  Google Scholar 

  6. Cheang, B., Li, H., Lim, A., & Rodrigues, B. (2003). Nurse rostering problems—a bibliographic survey. European Journal of Operational Research, 151, 447–460.

    Article  Google Scholar 

  7. Cordeau, J. F., Gendreau, M., Laporte, G., Potvin, J. Y., & Semet, F. (2002). A guide to vehicle routing heuristics. Journal of the Operational Research Society, 53, 512–522.

    Article  Google Scholar 

  8. De Causmaecker, P., & Vanden Berghe, G. (2011). A categorisation of nurse rostering problems. Journal of Scheduling, 14(1), 3–16.

    Article  Google Scholar 

  9. Haspeslagh, S., De Causmaecker, P., Schaerf, A., & Stølevik, M. (2012). The first international nurse rostering competition 2010. Annals of Operations Research.

  10. Maenhout, B., & Vanhoucke, M. (2005). NSPLib—a Nurse Scheduling Problem Library: a tool to evaluate (meta-)heuristic procedures. In O.R. in health (pp. 151–165). 31st meeting of the EURO working group on OR applied to health services. Amsterdam: Elsevier.

    Google Scholar 

  11. Maenhout, B., & Vanhoucke, M. (2006). Lecture notes in computer science: Vol. 3906. New computational results for the nurse scheduling problem: a scatter search algorithm (pp. 159–170).

    Google Scholar 

  12. Maenhout, B., & Vanhoucke, M. (2007). An electromagnetic meta-heuristic for the nurse scheduling problem. Journal of Heuristics, 13, 359–385.

    Article  Google Scholar 

  13. Maenhout, B., & Vanhoucke, M. (2008). Comparison and hybridization of crossover operators for the nurse scheduling problem. Annals of Operations Research, 159, 333–353.

    Article  Google Scholar 

  14. Osogami, T., & Imai, H. (2000). Lecture notes in computer science: Vol. 1969. Classification of various neighborhood operations for the nurse scheduling problem (pp. 72–83).

    Google Scholar 

  15. Petrovic, S., & Vanden Berghe, G. (2012). A comparison of two approaches to nurse rostering problems. Annals of Operations Research, 194(1), 365–384.

    Article  Google Scholar 

Download references


The authors thank the referees very much for their valuable input during the review process which helped a lot in improving earlier versions of this paper. Also, thanks to the CNPq (National Council for Scientific and Technological Development) and CAPES (Brazil’s Ministry of Education) for partial financial support to develop this work.

Author information



Corresponding author

Correspondence to Ademir Aparecido Constantino.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Constantino, A.A., Landa-Silva, D., de Melo, E.L. et al. A heuristic algorithm based on multi-assignment procedures for nurse scheduling. Ann Oper Res 218, 165–183 (2014).

Download citation


  • Nurse scheduling problem
  • Assignment problem
  • Heuristic algorithms
  • Combinatorial optimization