Journal of Heuristics

, Volume 15, Issue 4, pp 351–379

A grasp-knapsack hybrid for a nurse-scheduling problem


  • Melissa D. Goodman
    • School of MathematicsCardiff University
  • Kathryn A. Dowsland
    • School of MathematicsCardiff University
    • Gower Optimal Algorithms Ltd.
    • School of Computer Science and ITUniversity of Nottingham
    • School of MathematicsCardiff University

DOI: 10.1007/s10732-007-9066-7

Cite this article as:
Goodman, M.D., Dowsland, K.A. & Thompson, J.M. J Heuristics (2009) 15: 351. doi:10.1007/s10732-007-9066-7


This paper is concerned with the application of a GRASP approach to a nurse-scheduling problem in which the objective is to optimise a set of preferences subject to a set of binding constraints. The balance between feasibility and optimality is a key issue. This is addressed by using a knapsack model to ensure that the solutions produced by the construction heuristic are easy to repair. Several construction heuristics and neighbourhoods are compared empirically. The best combination is further enhanced by a diversification strategy and a dynamic evaluation criterion. Tests show that it outperforms previously published approaches and finds optimal solutions quickly and consistently.


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© Springer Science+Business Media, LLC 2007