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Nurse Scheduling Problem using Fuzzy Goal Programming with MINMAX Approach

Shely Nur Fitriani1, *, Bambang Irawanto1, Abdul Aziz1

Corresponding Author:

Shely Nur Fitriani


1. Department of Mathematics, Faculty of Science and Mathematics, Diponegoro University, Semarang, Indonesia
*Corresponding Author, Email: [email protected]


Nurse scheduling is a complex issue since each nurse has its own work day and day off which needs to be managed. The non-singular hospital objectives, as well as the uncertainty of the objective value add to the complexity of this problem. In this article, nurse scheduling problems will be solved using Fuzzy Goal Programming with the MINMAX approach. The hospital’s objectives of optimizing the number of days off for nurses, the number of working days, evening shifts, and isolated work days can be achieved. The resulting solution from the computation process meets the specified deviation tolerance limits. Problem constraints regarding requests for nurse leave, the minimum number of nurses on duty per shift, restrictions on sequential working days, and other managerial rules can also be met. With the MINMAX approach, the imbalance between positive and negative deviation values can be overcome. In addition, sensitivity analysis is also easier to be done. This article contributes to the future by revealing that the use of fuzzy set theory with unbalanced positive and negative deviations can be effectively used in nurse scheduling problems. Thus, a satisfactory schedule which can meet nurse preferences and hospital policies can be made properly.


Fuzzy logic, Goal Programming, MINMAX Goal Programming, nurses scheduling, paid leave

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Cite This Paper:

Shely Nur Fitriani, Bambang Irawanto, Abdul Aziz (2020). Nurse Scheduling Problem using Fuzzy Goal Programming with MINMAX Approach . Journal of the Institute of Electronics and Computer, 2, 151-161.


[1] R. Narasimhan, “GOAL PROGRAMMING IN A FUZZY ENVIRONMENT,” Decis. Sci., vol. 11, no. 2, pp. 325–336, Apr. 1980.
[2] R. N. Tiwari, S. Dharmar, and J. R. Rao, “Fuzzy goal programming - An additive model,” Fuzzy Sets Syst., vol. 24, no. 1, pp. 27–34, 1987.
[3] Y. Kara, T. Paksoy, and C. Ter Chang, “Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing,” Eur. J. Oper. Res., vol. 195, no. 2, pp. 335–347, Jun. 2009.
[4] M. A. Yaghoobi and M. Tamiz, “A method for solving fuzzy goal programming problems based on MINMAX approach,” vol. 177, pp. 1580–1590, 2007.
[5] R. Flavell, “A new goal programming formulation,” Omega, vol. 4, no. 6, pp. 731–732, 1976.
[6] B. S. Kumar, M. G. Nagalakshmi, and S. Kumaraguru, “A Shift Sequence for Nurse Scheduling Using Linear Programming Problem,” vol. 3, no. 6, pp. 24–28, 2014.
[7] P. Smet, F. Salassa, and G. Vanden Berghe, “Local and global constraint consistency in personnel rostering,” Int. Trans. Oper. Res., vol. 24, no. 5, pp. 1099–1117, Sep. 2017.
[8] N. Fan et al., “Nurse scheduling problem: An integer programming model with a practical application,” Springer Optim. Its Appl., vol. 74, pp. 65–98, 2013.
[9] L. Trilling, A. Guinet, and D. Le Magny, “NURSE SCHEDULING USING INTEGER LINEAR PROGRAMMING AND CONSTRAINT PROGRAMMING,” IFAC Proc. Vol., vol. 39, no. 3, pp. 671–676, Jan. 2006.
[10] H. H. Millar and M. Kiragu, “Cyclic and non-cyclic scheduling of 12 h shift nurses by network programming,” Eur. J. Oper. Res., vol. 104, no. 3, pp. 582–592, Feb. 1998.
[11] H. W. Purnomo and J. F. Bard, “Cyclic preference scheduling for nurses using branch and price,” Nav. Res. Logist., vol. 54, no. 2, pp. 200–220, Mar. 2007.
[12] M. Moz and M. V. Pato, “Solving the problem of rerostering nurse schedules with hard constraints: New multicommodity flow models,” Ann. Oper. Res., vol. 128, no. 1–4, pp. 179–197, Apr. 2004.
[13] S. Topaloglu and H. Selim, “Nurse scheduling using fuzzy modeling approach,” Fuzzy Sets Syst., vol. 161, no. 11, pp. 1543–1563, Jun. 2010.
[14] R. E. Bellman and L. A. Zadeh, “Decision-Making in a Fuzzy Environment,” Manage. Sci., vol. 17, no. 4, p. B-141-B-164, Dec. 1970.
[15] B. M. Werners, “Aggregation Models in Mathematical Programming,” in Mathematical Models for Decision Support, Springer Berlin Heidelberg, 1988, pp. 295–305.
[16] R.J.Li, “Multiple objective decision making in a fuzzy environment,” Kansas State University, 1990.
[17] E. Çetin and A. Sarucan, “Nurse scheduling using binary fuzzy goal programming,” 6th Int. Conf. Model. Simulation, Appl. Optim. ICMSAO 2015 - Dedic. to Mem. Late Ibrahim El-Sadek, no. May 2015, 2015.
[18] C. Ter Chang, “Binary fuzzy goal programming,” Eur. J. Oper. Res., vol. 180, no. 1, pp. 29–37, Jul. 2007.
[19] M. Bagheri, A. Gholinejad Devin, and A. Izanloo, “An application of stochastic programming method for nurse scheduling problem in real word hospital,” Comput. Ind. Eng., vol. 96, pp. 192–200, 2016.