Approximate Dynamic Programming with Combined Policy Functions for Solving Multi-stage Nurse Rostering Problem

  • Peng ShiEmail author
  • Dario Landa-Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10710)


An approximate dynamic programming that incorporates a combined policy, value function approximation and lookahead policy, is proposed. The algorithm is validated by applying it to solve a set of instances of the nurse rostering problem tackled as a multi-stage problem. In each stage of the problem, a weekly roster is constructed taking into consideration historical information about the nurse rosters in the previous week and assuming the future demand for the following weeks as unknown. The proposed method consists of three phases. First, a pre-process phase generates a set of valid shift patterns. Next, a local phase solves the weekly optimization problem using value function approximation policy. Finally, the global phase uses lookahead policy to evaluate the weekly rosters within a lookahead period. Experiments are conducted using instances from the Second International Nurse Rostering Competition and results indicate that the method is able to solve large instances of the problem which was not possible with a previous version of approximate dynamic programming.


Dynamic programming Approximation function Policy function Nurse scheduling problem 


  1. 1.
    Puterman, M.L.: Markov decision processes: discrete stochastic dynamic programming. Wiley, New York (2014)zbMATHGoogle Scholar
  2. 2.
    Powell, W.B.: Approximate Dynamic Programming: Solving the curses of dimensionality, vol. 703. Wiley, Hoboken (2007)Google Scholar
  3. 3.
    Burke, E.K., de Causmaecker, P., Berghe, G.V., van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7(6), 441–499 (2004)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Ceschia, S., Dang, N.T.T., de Causmaecker, P., Haspeslagh, S., Schaerf, A.: Second international nurse rostering competition (INRC-II)—problem description and rules—. arXiv preprint arXiv:1501.04177 (2015)
  5. 5.
    Tesauro, G.: Practical issues in temporal difference learning. In: Sutton, R.S. (ed.) Reinforcement Learning. The Springer International Series in Engineering and Computer Science (Knowledge Representation, Learning and Expert Systems), vol. 173, pp. 33–53. Springer, Boston (1992). Scholar
  6. 6.
    Shi, P., Landa-Silva, D.: Dynamic programming with approximation function for nurse scheduling. In: Pardalos, P.M., Conca, P., Giuffrida, G., Nicosia, G. (eds.) MOD 2016. LNCS, vol. 10122, pp. 269–280. Springer, Cham (2016). Scholar
  7. 7.
    Dang, N.T.T., Ceschia, S., Schaerf, A., de Causmaecker, P., Haspeslagh, S.: Solving the multi-stage nurse rostering problem. In: Proceedings of the 11th International Conference of the Practice and Theory of Automated Timetabling, pp. 473–475 (2016)Google Scholar
  8. 8.
    INRC-II the second nurse rostering competition. Accessed 23 May 2016

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.ASAP Research Group, School of Computer ScienceThe University of NottinghamNottinghamUK

Personalised recommendations