Abstract
Due to the complexity of nurse rostering problems (NRPs), Constraint Programming (CP) approaches on their own have shown to be ineffective in solving these highly constrained problems. We investigate a two-stage hybrid CP approach on real world benchmark NRPs. In the first stage, a constraint satisfaction model is used to generate weekly rosters consist of high quality shift sequences satisfying a subset of constraints. An iterative forward search is then adapted to extend them to build complete feasible solutions. Variable and value selection heuristics are employed to improve the efficiency. In the second stage, a simple Variable Neighborhood Search is used to quickly improve the solution obtained. The basic idea of the hybrid approach is based on the observations that high quality nurse rosters consist of high quality shift sequences. By decomposing the problems into solvable sub-problems for CP, the search space of the original problems are significantly reduced. The results on benchmark problems demonstrate the efficiency of this hybrid CP approach when compared to the state-of-the-art approaches in the literature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Aickelin and K. Dowsland. Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem, Journal of Scheduling, 3(3): 139–153, 2000
U. Aickelin and K. Dowsland. An indirect genetic algorithm for a nurse scheduling problem, Journal of Operations Research Society, 31(5): 761–778, 2003
E. K. Burke, P. De Causmaecker and G. Vanden Berghe. A hybrid tabu search algorithm for the nurse rostering problem. Lecture Notes in Artificial Intelligence, vol. 1585, 187–194, 1998
E. K. Burke, P. Cowling, P. De Causmaecker and G. Vanden Berghe. A memetic approach to the nurse rostering problem, Applied Intelligence, 15, 119–214, 2001
E. K. Burke, P. De Causmaecker, S. Petrovic and G. Vanden Berghe. Variable neighborhood search for nurse rostering problems. In: M.G.C. Resende and J.P. de Sousa (eds.), Metaheuristics: Computer Decision-Making (Combinatorial Optimization Book Series), Kluwer, 153–172, 2003
E. K. Burke, P. De Causmaecker, G. Vanden Berghe and H. Van Landeghem. The state of the art of nurse rostering, Journal of Scheduling, 7, 441–499, 2004
E. K. Burke, T. E. Curtois, G. Post, R. Qu and B. Veltman. A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem, European Journal of Operational Research, 2, 330–341, 2008.
P. Brucker, R. Qu, E. K. Burke and G. Post. A decomposition, construction and post-processing approach for a specific nurse rostering problem, MISTA’05, 397–406. New York, USA, Jul 2005
P. Brucker, E.K. Burke, T. Curtois, R. Qu and G. Vanden Berghe. Adaptive construction of nurse schedules: A shift sequence based approach. Under review at European Journal of Operational Research. Technical Report NOTTCS-TR-2007-1, School of Computer Science, University of Nottingham
B. Cheang, H. Li, A. Lim and B. Rodrigues. Nurse rostering problems — a bibliographic survey, European Journal of Operational Research, 151, 447–460, 2003
B. M. W. Cheng, J. H. M. Lee, and J. A. C. K. Wu. A nurse rostering system using constraint programming and redundant modelling, IEEE Transactions on information technology in biomedicine, vol. 1(1), 44–54, 1997
K. Dowsland. Nurse scheduling with tabu search and strategic oscillation, European Journal of Operational Research, 106, 393–407, 1998
A.T. Ernst, H. Jiang, M. Krishnamoorthy and D. Sier. Staff scheduling and rostering: A review of applications, methods and models, European Journal of Operational Research, 153, 3–27, 2004
P. Hansen, N. Mladenovic, Variable Neighborhood Search: Principles and Applications, European Journal of Operational Research, 130, 449–467, 2001
J. Hooke, Integrated Methods for Optimization, Springer, 2006
R. M. Karp. Reducibility among combinatorial problems, In: R.E. Miller and J.W. Thatcher (eds.), Complexity of Computer Computations, Plenum Press, New York, 85–103, 1972
H. Meyer auf’m Hofe. Solving rostering tasks as constraint optimisation. In: Burke E.K. and W. Erben (eds.) Lecture Notes in Computer Science, vol. 2079, 280–297, 2000, Springer, Berlin
T. Muller, R. Bartak and H. Rudova. Iterative forward search algorithm: combining local search with maintaining arc consistency and a conflict-based statistics. Lecture Notes in Computer Science, Vol 3258, 802–817, 2004, Springer, Berlin
G. Pesant. A filtering algorithm for the stretch constraint. In: Principles and Practice of Constraint Programming-CP01: The Proceedings of the Seventh International Conference, Lecture Notes in Computer Science, Vol. 2239, 183–195, 2001, Springer, Berlin
G. Post and B. Veltman. Harmonious personnel scheduling. In: E. Burke and M. Trick (eds.), Proceedings of the 5th International Conference on Practice and Automated Timetabling (PATAT’04), 557–559, 2004
C. G. Quimper, A. Lopez-Ortiz, P. van Beek, and A. Golynski. Improved algorithms for the global cardinality constraint. In: M. Wallace (editor), Principles and Practice of Constraint Programming (CP 2004), Lecture Notes in Computer Science, Vol 3258, 542–556, 2004, Springer, Berlin
J. C. Regin. Generalized arc consistency for global cardinality constraint. National Conference on Artificial Intelligence (AAAI 1996), AAAI Press, 209–215, 1996
J. C. Regin and J. F. Puget. A filtering algorithm for global sequencing constraint, in: Principles and Practice of Constraint Programming-CP97: The Proceedings of the Third International Conference, Lecture Notes in Computer Science, Vol. 1330, 32–46, 1997, Springer, Berlin
L. M. Rousseau, M. Gendreau and G. Pesant. A general approach to the physician rostering problems, Annals of Operations Research, 115, 193–205, 2002
M. Sellmann. Crew assignment via constraint programming: integrating column generation and heuristic tree search, Annals of Operations Research, 115, 207–225, 2002
G.Y.C. Wonga and A.H.W. Chun. Constraint-based rostering using meta-level reasoning and probability-based ordering, Engineering Applications of Artificial Intelligence, 17, 599–610, 2004
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag London Limited
About this paper
Cite this paper
Qu, R., He, F. (2009). A Hybrid Constraint Programming Approach for Nurse Rostering Problems. In: Allen, T., Ellis, R., Petridis, M. (eds) Applications and Innovations in Intelligent Systems XVI. SGAI 2008. Springer, London. https://doi.org/10.1007/978-1-84882-215-3_16
Download citation
DOI: https://doi.org/10.1007/978-1-84882-215-3_16
Publisher Name: Springer, London
Print ISBN: 978-1-84882-214-6
Online ISBN: 978-1-84882-215-3
eBook Packages: Computer ScienceComputer Science (R0)