Nurse scheduling problem by considering fuzzy modeling approach to treat uncertainty on nurses’ preferences for working shifts and weekends off

Document Type: Original Manuscript

Authors

Department of Industrial Engineering, Golpayegan University of Technology, Golpayegan, Iran

10.22094/joie.2019.576759.1595

Abstract

Nowadays, the nurse scheduling problem (NSP) has attracted a great amount of attentions. In this problem,the nurses are scheduled to be assigned to the shifts by considering the required nurses for each day during the planning horizon. In the current study, a bi-objective mathematical model is formulated in order to maximize the preferences of the nurses to work on the shifts in addition to be off on the weekends. In real-world problems, higher quality schedules are provided considering the uncertainty. In this point of view, we investigate the uncertainty on the preferences of the nurses for the working shifts and the weekends off. In fact, a compensatory fuzzy approach based on the Werners’ fuzzy and operator is proposed to investigate the effects of the uncertainty on the considered research problem. Then, several sample problems are generated to support the efficiency of the developed fuzzy model. Finally, a sensitivity analysis is implemented to determine the effects of the changes of the parameters on the obtained results.

Graphical Abstract

Nurse scheduling problem by considering fuzzy modeling approach to treat uncertainty on nurses’ preferences for working shifts and weekends off

Highlights

  • The nurse scheduling problem is considered in Milad hospital.
  • A mathematical programming model is proposed.
  • The nurses’ preferences for the working shifts are maximized.
  • A compensatory fuzzy approach is developed based on thefuzzy and operator.
  • A sensitivity analysis is performed on the compensatory coefficient.

Keywords

Main Subjects


Abbasi, F., Allahviranloo, T., & Abbasbandy, S. (2016). A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers. Iranian Journal of Fuzzy Systems, 13(6), 21-39.

Aktunc, E.A., & Tekin, E. (2018). Nurse Scheduling with Shift Preferences in a Surgical Suite Using Goal Programming. Industrial Engineering in the Industry, Springer, Cham, 23-36.

Al-Yakoob, S.M., & Sherali, H.D. (2007). Mixed-integer programming models for an employee scheduling problem with multiple shifts and work locations. Annals of Operations Research, 155(1), 119-142.

Arthur, J.L., & Ravindran, A. (1981) A multiple objective nurse scheduling model. AIIE transactions, 13(1), 55-60.

Bard, J.F., & Purnomo, H.W. (2005). Preference scheduling for nurses using column generation. European Journal of Operational Research, 164(2), 510-534.

Bard, J.F., & Purnomo, H.W. (2007). Cyclic preference scheduling of nurses using a Lagrangian-based heuristic. Journal of Scheduling, 10(1), 5-23.

Beliën, J., & Demeulemeester, E. (2008). A branch-and-price approach for integrating nurse and surgery scheduling. European Journal of Operational Research, 189(3), 652-668.

Demirbilek, M., Branke, J., & Strauss, A. (2018). Dynamically accepting and scheduling patients for home healthcare. Health Care Management Science, 5, 1-6.

Doerner, K.F., & Maniezzo, V. (2018). Metaheuristic search techniques for multi-objective and stochastic problems. Central European Journal of Operations Research, 26(2), 331-356.

El Adoly, A.A., Gheith, M., & Fors, M.N. (2018). A new formulation and solution for the nurse scheduling problem: A case study in Egypt. Alexandria Engineering Journal, 57(4), 2289-2298.

Gutjahr, W.J., & Rauner, M.S. (2007). An ACO algorithm for a dynamic regional nurse-scheduling problem in Austria. Computers & Operations Research, 34(3), 642-666.

Hertz, A., & Kobler, D. (2000). A framework for the description of evolutionary algorithms. European Journal of Operational Research, 126(1), 1-2.

Jafari, H., & Salmasi, N. (2015). Maximizing the nurses’ preferences in nurse scheduling problem: mathematical modeling and a meta-heuristic algorithm. Journal of Industrial Engineering International, 11(3), 439-458.

Jafari, H., Bateni, S., Daneshvar, P., Bateni, S., & Mahdioun, H. (2016). Fuzzy mathematical modeling approach for the nurse scheduling problem: a case study. International Journal of Fuzzy Systems, 18(2), 320-332.

Khorram, E., & Nozari, V. (2012). Multi-objective optimization with preemptive priority subject to fuzzy relation equation constraints. Iranian Journal of Fuzzy Systems, 9(3), 27-45.

Klir, G.J., & Yuan, B. (1996). Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers by Lotfi A. Zadeh. World Scientific Publishing Co., Inc.

Li, J., & Liu, Y. (2017). Property analysis of triple implication method for approximate reasoning on atanassovs Intuitionistic Fuzzy Sets. Iranian Journal of Fuzzy Systems, 25(2), 26-34.

Lin, C.C., Hung, L.P., Liu, W.Y., & Tsai, M.C. (2018). Jointly rostering, routing, and rerostering for home health care services: A harmony search approach with genetic, saturation, inheritance, and immigrant schemes. Computers & Industrial Engineering, 115, 151-166.

Maenhout, B., & Vanhoucke, M. (2013). An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems. Omega, 41(2), 485-499.

Majumdar, J., & Bhunia, A.K. (2007). Elitist genetic algorithm for assignment problem with imprecise goal. European Journal of Operational Research, 177(2), 684-692.

Moghari, S., Zahedi, M.M., & Ameri, R. (2011). New direction in fuzzy tree automata. Iranian Journal of Fuzzy Systems, 8(5), 59-68.

Nezamabadi-Pour, H., Yazdani, S., Farsangi, M.M., & Neyestani, M. (2011). A solution to an economic dispatch problem by a fuzzy adaptive genetic algorithm. Iranian Journal of Fuzzy Systems, 8(3), 1-21.

Osogami, T., & Imai, H. (2000). Classification of various neighborhood operations for the nurse scheduling problem. International Symposium on Algorithms and Computation. Springer, Berlin, Heidelberg.

Topaloglu, S., & Selim, H. (2010). Nurse scheduling using fuzzy modeling approach. Fuzzy Sets and Systems, 161(11), 1543-1563.

Valouxis, C., Gogos, C., Goulas, G., Alefragis, P., & Housos, E. (2012). A systematic two phase approach for the nurse rostering problem. European Journal of Operational Research, 219(2), 425-433.

Werners, B.M. (1988). Aggregation models in mathematical programming. Mathematical models for decision support. Springer, Berlin, Heidelberg.

Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on systems, Man, and Cybernetics, 18(1), 183-190.

Zimmermann, H.J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.

Zimmermann, H.J., & Zysno, P. (1980). Latent connectives in human decision making. Fuzzy sets and systems, 4(1), 37-51.

Zimmermann, H.J., & Zysno, P. (1983). Decisions and evaluations by hierarchical aggregation of information. Fuzzy sets and systems, 10(1-3), 243-260.