Dynamic Programming with Approximation Function for Nurse Scheduling

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10122)


Although dynamic programming could ideally solve any combinatorial optimization problem, the curse of dimensionality of the search space seriously limits its application to large optimization problems. For example, only few papers in the literature have reported the application of dynamic programming to workforce scheduling problems. This paper investigates approximate dynamic programming to tackle nurse scheduling problems of size that dynamic programming cannot tackle in practice. Nurse scheduling is one of the problems within workforce scheduling that has been tackled with a considerable number of algorithms particularly meta-heuristics. Experimental results indicate that approximate dynamic programming is a suitable method to solve this problem effectively.


Markov decision process Approximate dynamic programming Nurse scheduling problem 


  1. 1.
    Bellman, R.: Dynamic programming and lagrange multipliers. Proc. Nat. Acad. Sci. 42(10), 767–769 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality, vol. 703. Wiley, Hoboken (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Van den Bergh, J., Beliën, J., De Bruecker, P., Demeulemeester, E., De Boeck, L.: Personnel scheduling: a literature review. Eur. J. Oper. Res. 226(3), 367–385 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Elshafei, M., Alfares, H.K.: A dynamic programming algorithm for days-off scheduling with sequence dependent labor costs. J. Sched. 11(2), 85–93 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cheang, B., Li, H., Lim, A., Rodrigues, B.: Nurse rostering problems–a bibliographic survey. Eur. J. Oper. Res. 151(3), 447–460 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    De Causmaecker, P., Berghe, G.V.: A categorisation of nurse rostering problems. J. Sched. 14(1), 3–16 (2011)CrossRefGoogle Scholar
  7. 7.
    Curtois, T.: Employee shift scheduling benchmark data sets. Technical report, School of Computer Science, The University of Nottingham, Nottingham, UK, September 2014Google Scholar
  8. 8.
    Vanhoucke, M., Maenhout, B.: Characterisation and generation of nurse scheduling problem instances. Technical report, Ghent University, Faculty of Economics and Business Administration (2005)Google Scholar
  9. 9.
    Schuetz, H.-J., Kolisch, R.: Approximate dynamic programming for capacity allocation in the service industry. Eur. J. Oper. Res. 218(1), 239–250 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bertsekas, D.P.: Dynamic Programming and Optimal Control, vol. 1. Athena Scientific, Belmont (1995). (No. 2)zbMATHGoogle Scholar
  11. 11.
    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction, vol. 1. MIT Press, Cambridge (1998). (No. 1)Google Scholar
  12. 12.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2014)zbMATHGoogle Scholar
  13. 13.
    Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)CrossRefGoogle Scholar
  14. 14.
    Koole, G., Pot, A.: Approximate dynamic programming in multi-skill call centers. In: 2005 Proceedings of the Winter Simulation Conference, pp. 576–583. IEEE (2005)Google Scholar
  15. 15.
    Maenhout, B., Vanhoucke, M.: NSPLib - a nurse scheduling problem library: a tool to evaluate (meta-)heuristic procedures. In: OR in Health, pp. 151–165. Elsevier (2005)Google Scholar
  16. 16.
    Maenhout, B., Vanhoucke, M.: New computational results for the nurse scheduling problem: a scatter search algorithm. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2006. LNCS, vol. 3906, pp. 159–170. Springer, Heidelberg (2006). doi: 10.1007/11730095_14 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.School of Computer Science, ASAP Research GroupThe University of NottinghamNottinghamUK

Personalised recommendations