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A Mathematical Programming Model for Scheduling of Nurses’ Labor Shifts

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Abstract

In this study, a mathematical programming model is proposed for scheduling problem of nurses’ labor shifts. The developed mathematical programming model’s aim is to minimize nurses’ total idle waiting time during a week planning horizon. In this model, investigated constraints are as follows: (1) Maximum total working time a week for each nurse must not be exceeded. (2) After a nurse works a shift, the nurse can be assigned to another shift after two shifts at least. This constraints-set ensures resting of the nurse after the nurse works a shift. (3) Total number of nurses worked for each shift must be controlled with maximum and minimum bounds given for number of nurses for each shift. In this manner, total number of nurses worked for each shift is between maximum and minimum limit-values given for each shift. This constraint ensures flexibility to the user to determine number of nurses for each shift. (4) The decision variable that shows nurse-shift assignment pairs is 0 or 1. In this study, maximum total working time a week for a nurse, total number of nurses in a health service, maximum and minimum numbers of nurses worked a shift are user-specified parameters. In this way, this model can be adapted for the studies with different values of these parameters. In this study, the developed model is illustrated using a numerical example and then LINGO8.0 software is used to ensure the global optimum solution of the developed model. Results and also sensitivity analysis carried out for this example are presented in the study.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Arthur, J. L., and Ravindran, A., A multiple objective nurse scheduling model. AIIE Transactions 13:55–60, 1981.

    Article  Google Scholar 

  3. Azaiez, M. N., and Al Sharif, S. S., A 0–1 goal programming model for nurse scheduling. Comput Oper Res 32:491–507, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bell, P. C., Hay, G., and Liang, Y., A visual interactive decision support system for workforce (nurse) scheduling. INFOR 24(2):134–145, 1986.

    Google Scholar 

  5. Brusco, M. J., and Jacobs, L. W., A simulated annealing approach to the cyclic staff-scheduling problem. Nav Res Logist 40:69–84, 1993.

    Article  MATH  Google Scholar 

  6. Chow, K. P., and Hui, C. K., Knowledge-based system for rostering. Expert Syst Appl 6:361–375, 1993.

    Article  Google Scholar 

  7. Dowsland, K. A., Simulated annealing solutions for multi-objective scheduling and timetabling. In: Rayward Smith, V. J., Osman, I. H., Reeves, C. R., and Smith, G. D. (Eds.), Modern Heuristic Search Methods. Wiley, New York, pp. 155–166, 1996.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  9. Gierl, L., Pollwein, B., Heyde, G., and Kurt, H., Knowledge-based scheduling of duty rosters for physicians. Med lnform 18:355–366, 1993.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  11. Knjazew, D., A competent genetic algorithm for solving permutation and scheduling problems. Genetic algorithms and evolutionary computation (Vol. 6). Kluwer Academic Publishers, Boston, 2002. ISBN:0792374606.

    Google Scholar 

  12. Millar, H. H., and Kiragu, M., Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming. Eur J Oper Res 104:582–592, 1998.

    Article  MATH  Google Scholar 

  13. Miller, H. E., Pierskalla, H. P., and Rsth, G. J., Nurse scheduling using mathematical programming. Oper Res 24(5):857–870, 1976.

    Article  MATH  Google Scholar 

  14. Moz, M., and Pato, M. V., A genetic algorithm approach to a nurse rerostering problem. Comput Oper Res 34:667–691, 2007.

    Article  MATH  Google Scholar 

  15. Musa, A. A., and Saxena, U., Scheduling nurses using goal-programming techniques. IIE Transactions 16:216–221, 1984.

    Article  Google Scholar 

  16. Ozkarahan, I., and Bailey, J. E., Goal programming model subsystem of a flexible nurse scheduling support system. IIE Transactions 20(3):306–316, 1988.

    Article  Google Scholar 

  17. Smith, L. D., and Wiggins, A., A computer-based nurse scheduling system. Comput Oper Res 4:195–212, 1977.

    Article  Google Scholar 

  18. Soliman, F., Improving resource utilization through patient dependency systems. J Med Syst 21(5):291–302, 1997.

    Article  Google Scholar 

  19. Thompson, G. M., A simulated annealing heuristic for shift-scheduling using non-continuously available employees. Comput Oper Res 23:275–288, 1996.

    Article  MATH  Google Scholar 

  20. Tsai, C.-C., and Li, S. H. A., A two-stage modeling with genetic algorithms for the nurse scheduling problem. Expert Syst Appl 36:9506–9512, 2009.

    Article  Google Scholar 

  21. Venkataraman, R., and Brusco, M. J., An integrated analysis of nurse staffing and scheduling policies. Omega 24:57–71, 1996.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering and Architecture, Cukurova University, 01330, Adana, Turkey

    Ebru Yilmaz

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  1. Ebru Yilmaz
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Correspondence to Ebru Yilmaz.

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Yilmaz, E. A Mathematical Programming Model for Scheduling of Nurses’ Labor Shifts. J Med Syst 36, 491–496 (2012). https://doi.org/10.1007/s10916-010-9494-z

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  • DOI: https://doi.org/10.1007/s10916-010-9494-z

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