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A grasp-knapsack hybrid for a nurse-scheduling problem

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Abstract

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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References

  • Abramson, D.: Constructing school timetables using simulated annealing: sequential and parallel algorithms. Manag. Sci. 37, 98–113 (1991)

    Article  Google Scholar 

  • Aickelin, U., Dowsland, K.A.: Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem. J. Sched. 3, 139–153 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Aickelin, U., Dowsland, K.A.: An indirect genetic algorithm for a nurse-scheduling problem. Comput. Oper. Res. 31, 761–778 (2004)

    Article  MATH  Google Scholar 

  • Aickelin, U., Li, J.: An estimation of distribution algorithm for nurse scheduling. Ann. Oper. Res. 155, 289–309 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parall. Comput. 29, 393–430 (2003)

    Article  MathSciNet  Google Scholar 

  • Bellanti, F., Carello, G., Della Croce, F., Tadei, R.: A greedy-based neighbourhood search approach to a nurse rostering problem. Eur. J. Oper. Res. 153, 28–40 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Berrada, I., Ferland, J.A., Michelon, P.: A multi-objective approach to nurse scheduling with both hard and soft constraints. Socio-Econ. Plan. Sci. 30, 183–193 (1996)

    Article  Google Scholar 

  • Binato, S., Hery, W.J., Loewenstern, D.M., Resende, M.G.C.: A GRASP for job shop scheduling. Essays Surv. Metaheuristics 15, 81–100 (2001)

    Google Scholar 

  • Brusco, M.J., Jacobs, L.W.: Cost analysis of alternative formulations for personnel scheduling in continuous operating organizations. Eur. J. Oper. Res. 86, 249–261 (1995)

    Article  MATH  Google Scholar 

  • Burke, E., De Causemaecker, P., Vanden Berghe, G.: A hybrid tabu search algorithm for the nurse rostering problem. In: McKay, B., et al. (eds.) Simulated Evolution and Learning. Lecture Notes in Artificial Intelligence, vol. 1585, pp. 187–194. Springer, Berlin (1999)

    Chapter  Google Scholar 

  • Burke, E., Cowling, P., De Causmaecker, P., Vanden Berghe, G.: A memetic approach to the nurse rostering problem. Appl. Intell. 15(3), 199–214 (2001)

    Article  MATH  Google Scholar 

  • Burke, E., De Causemaecker, P., Petrovic, S., Vanden Berghe, G.: Variable neighbourhood search for nurse rostering problems. In: Resende, M.G.C., de Sousa, J.P. (eds.) METAHEURISTICS: Computer Decision-Making, pp. 153–172. Kluwer Academic, Dordrecht (2003a), Chapter 7

    Google Scholar 

  • Burke, E., Kendall, G., Soubeiga, E.: A tabu-search hyperheuristic for timetabling and rostering. J. Heuristics 9, 451–470 (2003b)

    Article  Google Scholar 

  • Burke, E., De Causemaecker, P., Vanden Burghe, G., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7, 441–499 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Cheang, B., Li, H., Lim, A., Rodrigues, B.: Nurse rostering problems—a bibliographic survey. Eur. J. Oper. Res. 151, 447–460 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Dowsland, K.A.: Nurse scheduling with tabu search and strategic oscillation. Eur. J. Oper. Res. 106, 393–407 (1998)

    Article  MATH  Google Scholar 

  • Dowsland, K.A., Thompson, J.M.: Solving a nurse-scheduling problem with knapsacks, networks and tabu search. J. Oper. Res. Soc. 51, 825–833 (2000)

    Article  MATH  Google Scholar 

  • Drexl, A., Salewski, F.: Distribution requirements and compactness constraints in school timetabling. Eur. J. Oper. Res. 102, 193–214 (1997)

    Article  MATH  Google Scholar 

  • Ernst, T., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: a review of applications, methods and models. Eur. J. Oper. Res. 153, 3–27 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Feo, T.A., Resende, M.G.C., Smith, S.H.: A greedy randomised adaptive search procedure for maximum independent set. Oper. Res. 42, 860–878 (1994)

    Article  MATH  Google Scholar 

  • Fleurent, C., Glover, F.: Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J. Comput. 11, 198–204 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Fuller, E.: Tackling scheduling problems using integer programming. Master Thesis, University of Wales Swansea, United Kingdom (1998)

  • Gupta, S.R., Smith, J.S.: Algorithms for single machine total tardiness scheduling with sequence dependent setups. Eur. J. Oper. Res. 175, 722–739 (2006)

    Article  MATH  Google Scholar 

  • Gutjahr, W.J., Rauner, M.S.: An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria. Comput. Oper. Res. 34(3), 642–666 (2007)

    Article  MATH  Google Scholar 

  • Isken, M.: An implicit tour scheduling model with applications in healthcare. Ann. Oper. Res. 128, 91–109 (2004)

    Article  MATH  Google Scholar 

  • Jaumard, B., Semet, F., Vovor, T.: A generalized linear programming model for nurse scheduling. Eur. J. Oper. Res. 107, 1–18 (1998)

    Article  MATH  Google Scholar 

  • Laguna, M., González-Velarde, J.L.: A search heuristic for just-in-time scheduling in parallel machines. J. Intell. Manufact. 2, 253–260 (1991)

    Article  Google Scholar 

  • Laguna, M., Martí, R.: A GRASP for coloring sparse graphs. Comput. Optim. Appl. 19, 165–178 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Lim, A., Rodrigues, B., Zhang, X.: A simulated annealing and hill-climbing algorithm for the travelling tournament problem. Eur. J. Oper. Res. 174, 1459–1478 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Martello, S., Toth, P.: Knapsack Problems Wiley, Chichester (1990)

    MATH  Google Scholar 

  • Meyer auf’m Hofe, H.: Nurse rostering as constraint satisfaction with fuzzy constraints and inferred control strategies, In: DIMACS Workshop on Constraints Programming and Large Scale Discrete Optimisation, pp. 67–100 (2000)

  • Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Berlin (2004)

    MATH  Google Scholar 

  • Moz, M., Pato, M.V.: A genetic algorithm approach to a nurse re-rostering problem. Comput. Oper. Res. 34(3), 667–691 (2007)

    Article  MATH  Google Scholar 

  • Parr, D., Thompson, J.: Solving the multi-objective nurse scheduling problem with a weighted cost function. Ann. Oper. Res. 155, 279–288 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Petrovic, S., Beddoe, G., Vanden Berghe, G.: Storing and adapting repair experiences in personnel rostering. In: Burke, E.K., De Causemaecker, P. (eds.) Practice and Theory of Automated Timetabling, Fourth International Conference, Gent. Lecture Notes in Computer Science, vol. 2740, pp. 149–166. Springer, Berlin (2003)

    Google Scholar 

  • Resende, M.G.C.: Greedy Randomized Adaptive Search Procedures (GRASP). Encyclopedia of Optimisation, vol. 2, pp. 373–382. Kluwer Academic, Dordrecht (2001)

    Google Scholar 

  • Rosenbloom, E.S., Goertzen, N.F.: Cyclic nurse scheduling. Eur. J. Oper. Res. 31, 19–23 (1987)

    Article  Google Scholar 

  • Thompson, J.M., Dowsland, K.A.: Variants of simulated annealing for the examination timetabling problem. Ann. Oper. Res. 63, 637–648 (1996)

    Article  Google Scholar 

  • Wright, M.B.: Scheduling cricket umpires. J. Oper. Res. Soc. 42, 447–452 (1991)

    Article  Google Scholar 

  • Zhu, Y., Lim, A.: Crane scheduling with non-crossing constraint. J. Oper. Res. Soc. 57, 1464–1471 (2006)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, CF24 4AG, UK

    Melissa D. Goodman, Kathryn A. Dowsland & Jonathan M. Thompson

  2. Gower Optimal Algorithms Ltd., 5, Whitestone Lane, Newton, Swansea, UK

    Kathryn A. Dowsland

  3. School of Computer Science and IT, University of Nottingham, Nottingham, UK

    Kathryn A. Dowsland

Authors
  1. Melissa D. Goodman
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  2. Kathryn A. Dowsland
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  3. Jonathan M. Thompson
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Correspondence to Jonathan M. Thompson.

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Goodman, M.D., Dowsland, K.A. & Thompson, J.M. A grasp-knapsack hybrid for a nurse-scheduling problem. J Heuristics 15, 351–379 (2009). https://doi.org/10.1007/s10732-007-9066-7

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  • DOI: https://doi.org/10.1007/s10732-007-9066-7

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