Abstract
In this paper, we present a novel meta-heuristic technique for the nurse scheduling problem (NSP). This well-known scheduling problem assigns nurses to shifts per day maximizing the overall quality of the roster while taking various constraints into account. The problem is known to be NP-hard.
Due to its complexity and relevance, many algorithms have been developed to solve practical and often case-specific models of the NSP. The huge variety of constraints and the several objective function possibilities have led to exact and meta-heuristic procedures in various guises, and hence comparison and state-of-the-art reporting of standard results seem to be a utopian idea.
We present a meta-heuristic procedure for the NSP based on the framework proposed by Birbil and Fang (J. Glob. Opt. 25, 263–282, 2003). The Electromagnetic (EM) approach is based on the theory of physics, and simulates attraction and repulsion of sample points in order to move towards a promising solution. Moreover, we present computational experiments on a standard benchmark dataset, and solve problem instances under different assumptions. We show that the proposed procedure performs consistently well under many different circumstances, and hence, can be considered as robust against case-specific constraints.
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Ahuja, R., Ergun, Ö., Orlin, J., Punnen, A.: A survey of very large-scale neighborhood search techniques. Discret. Appl. Math. 123, 75–102 (2002)
Aickelin, U.: Genetic algorithms for multiple-choice optimisation problems. PhD thesis, European Business Management School, University of Swansea, 1999
Aickelin, U., Dowsland, K.: Exploiting problem structure in a genetic algorithm approach to a nurse rostering problem. J. Sched. 3, 139–153 (2000)
Aickelin, U., Dowsland, K.: An indirect genetic algorithm for a nurse scheduling problem. Comput. Oper. Res. 31, 761–778 (2004)
Aickelin, U., White, P.: Building better nurse scheduling algorithms. Ann. Oper. Res. 128, 159–177 (2004)
Arthur, J., Ravindran, A.: A multiple objective nurse scheduling model. AIIE Trans. 1, 55–60 (1981)
Bard, J., Purnomo, H.: Preference scheduling for nurses using column generation. Eur. J. Oper. Res. 164, 510–534 (2005a)
Bard, J., Purnomo, H.: Hospital-wide reactive scheduling of nurses with preference considerations. IIE Trans. 37, 589–608 (2005b)
Beasley, J., Chu, P.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94, 392–404 (1996)
Berrada, I., Ferland, J., Michelon, P.: A multi-objective approach to nurse scheduling with both hard and soft constraints. Socio-Econ. Plan. Sci. 30, 183–193 (1996)
Birbil, I., Fang, S.C.: An electro-magnetism-like mechanism for global optimization. J. Glob. Optim. 25, 263–282 (2003)
Birbil, I., Fang, S.C., Sheu, R.: On the convergence of a population based global optimization algorithm. J. Glob. Optim. 30, 301–318 (2004)
Blau, R., Sear, A.: Nurse scheduling with a micro-computer. J. Ambul. Care Manag. 6, 1–13 (1983)
Burke, E.K., Cowling, P., De Causmacker, P., Vanden Berghe, G.: A memetic approach to the nurse rostering problem. Appl. Intell. 3, 199–214 (2001a)
Burke, E.K., Cowling, P., De Causmacker, P., Vanden Berghe, G.: Fitness evaluation for nurse scheduling problems. In: Proceedings of Congress on Evolutionary Computation, CEC2001, pp. 1139–1146. IEEE Press, Seoul (2001b)
Burke, E.K., De Causmacker, P., Petrovic, S., Vanden Berghe, G.: A multi criteria metaheuristic approach to nurse rostering. In: Proceedings of Congress on Evolutionary Computation, CEC2002, pp. 1197–2002. IEEE Press, Honolulu (2002)
Burke, E.K., De Causmacker, P., Petrovic, S., Vanden Berghe, G.: Variable neighbourhood search for nurse rostering problems. In: Metaheuristics: Computer Decision-Making, pp. 153–172. Kluwer, Norwell (2004a)
Burke, E.K., De Causmacker, P., Vanden Berghe, G., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7, 441–499 (2004b)
Caron, G., Hansen, P., Jaumard, B.: The assignment problem with seniority and job priority constraints. Oper. Res. 3, 449–453 (1999)
Cheang, B., Li, H., Lim, A., Rodrigues, B.: Nurse rostering problems—a bibliographic survey. Eur. J. Oper. Res. 151, 447–460 (2003)
Debels, D., De Reyck, B., Leus, R., Vanhoucke, M.: A hybrid scatter search/electromagnetism meta-heuristic for project scheduling. Eur. J. Oper. Res. 169, 638–653 (2006)
Debels, D., Vanhoucke, M.: An electromagnetism meta-heuristic for the resource-constrained project scheduling problem. In: Lecture Notes in Computer Science, vol. 3871, pp. 259–270. Springer, New York (2006)
De Causmaecker, P., Vanden Berghe, G.: Relaxation of coverage constraints in hospital personnel rostering. In: Lecture Notes in Computer Science, vol. 2740, pp. 129–147. Springer, New York (2003)
Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)
Dowsland, K.: Nurse scheduling with Tabu search and strategic oscillation. Eur. J. Oper. Res. 106, pp. 393–407 (1998)
Dowsland, K., Thompson, J.: Solving a nurse scheduling problem with knapsacks, networks and tabu search. J. Oper. Res. Soc. 51, 825–833 (2000)
Eppstein, D.: Finding the k shortest paths. SIAM J. Comput. 28, 652–673 (1998)
Gutjahr, W., Rauner, M.: An ACO algorithm for a dynamic nurse scheduling problem in Austria. Comput. Oper. Res. 34, 642–666 (2007)
Hansen, P., Mladenović, N.: Variable neighbourhood search: Principles and applications. Eur. J. Oper. Res. 130, 449–467 (2001)
Jaszkiewicz, A.: A metaheuristic approach to multiple objective nurse scheduling. Found. Comput. Decis. Sci. 22, 169–184 (1997)
Kolisch, R., Hartmann, S.: Experimental investigation of heuristics for resource-constrained project scheduling: An update. Eur. J. Oper. Res. 174, 23–37 (2006)
Kuhn, H.: The Hungarian method for the assignment problem. Nav. Res. Logist. 2, 83–97 (1955)
Li, J., Aickelin, U.: A bayesian optimization algorithm for the nurse scheduling problem. In: Proceedings of 2003 Congress on Evolutionary Computation (CEC2003), pp. 2149–2156. (2003)
Martins, E., Pascoal, M.: A new implementation of Yen’s ranking loopless paths algorithm. Q. J. Belg. Fr. Italian Oper. Res. Soc. 1, 121–134 (2003)
Millar, H., Kiragu, M.: Cyclic and non-cyclic scheduling of 12h shift nurses by network programming. Eur. J. Oper. Res. 104, 582–592 (1998)
Miller, H., Pierskalla, W., Rath, G.: Nurse scheduling using mathematical programming. Oper. Res. 24, 857–870 (1976)
Osogami, T., Imai, H.: Classification of various neighbourhood operations for the nurse scheduling problem. In: Lecture Notes in Computer Science, vol. 1969, pp. 72–83. Springer, New York (2000),
Schrage, L.: LINDO: Optimization Software for Linear Programming. LINDO Systems, Chicago (1995)
Vanhoucke, M., Maenhout, B.: Characterisation and generation of nurse scheduling problem instances. Characterisation and generation of nurse scheduling problem instances. Working paper 05/339, Ghent University (2005)
Warner, M.: Scheduling nursing personnel according to nursing preference: A mathematical approach. Oper. Res. 24, 842–856 (1976)
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Maenhout, B., Vanhoucke, M. An electromagnetic meta-heuristic for the nurse scheduling problem. J Heuristics 13, 359–385 (2007). https://doi.org/10.1007/s10732-007-9013-7
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DOI: https://doi.org/10.1007/s10732-007-9013-7