Goal Programming Model for Nurse Schedule Problem in the Pandemic Process

Year 2023, Volume: 11 Issue: 2, 391 - 407, 01.06.2023

Müberra Koçak , Gizem Ekren , Rabia Yumuşak , Tamer Eren , Hacı Mehmet Alakaş

https://doi.org/10.36306/konjes.1120463

Abstract

It is observed that nurses working in health institutions during the pandemic process, long working hours negatively affect nurses in psychological and physical terms. As a result of the pandemic process, the increasing workload in hospitals, especially the heavy and exhausting 24-hour shifts and work in the seizure system, and the fact that nurses are exposed to an irregular work schedule, the quality of work and personal life of staff is adversely affected. As a result of this, the quality of service provided to patients also decreases. In order to eliminate the negativity caused by the working conditions of nurses and to increase customer satisfaction, the problem of nurse scheduling was discussed in this study. Two solutions have been proposed for the nurse scheduling problem in the neurology intensive care unit, where 18 nurses work at the state hospital. Firstly, the solution was presented with the 0-1 goal programming method taking into account the current working conditions of the hospital. Secondly, in order to prevent the risks that may arise from a 24-hour shift, a new model was proposed by working on a two-shift system of 8 and 16 hours. In the proposed models, a fair and balanced work program has been established taking into account the rules of the hospital, the specific wishes and experiences of the nurses. This study not only addresses the real-life problem, but also provides a new perspective on the nurse scheduling problem with the analysis of the current situation and the proposal of a new shift system.

Keywords

Nurse Scheduling Problem, 0-1 Goal Programming, Personnel Management, Hospital Management, Pandemic

PANDEMİ SÜRECİNDE HEMŞİRE ÇİZELGELEME PROBLEMİ İÇİN HEDEF PROGRAMLAMA MODELİ

Abstract

Pandemi sürecinde sağlık kuruluşlarında çalışan hemşirelerin, uzun çalışma saatlerinin psikolojik ve fiziksel anlamda hemşireleri olumsuz etkilediği görülmektedir. Pandemi süreciyle hastanelerde artan iş yükü, özellikle 24 saat süren vardiya ve nöbet sistemi içinde çalışmanın ağır ve yorucu olması ve hemşirelerin düzensiz bir iş programına maruz kalması sonucunda personellerin iş ve kişisel yaşam kalitesi olumsuz yönde etkilenmektedir. Bunun sonucu olarak hastalara verilen hizmetin kalitesi de düşmektedir. Hem hemşirelerin çalışma şartlarından kaynaklı olumsuzlukların giderilmesi hem de müşteri memnuniyetinin artırılması amacıyla bu çalışmada hemşire çizelgeleme problemi ele alınmıştır. Bir devlet hastanesinin nöroloji yoğun bakım ünitesinde çalışan 18 hemşirenin çizelgelenmesi problemi için iki çözüm önerisinde bulunulmuştur. İlk olarak hastanenin mevcut çalışma şartları dikkate alınarak 0-1 hedef programlama yöntemi ile çözüm sunulmuştur. İkinci olarak 24 saatlik vardiyadan kaynaklı oluşabilecek risklerin önüne geçebilmek için 8 ve 16 saatlik iki vardiya sistemi üzerinde çalışılarak yeni bir model önerisinde bulunulmuştur. Önerilen modellerde hastanenin kuralları, hemşire özel istekleri ve tecrübeleri dikkate alınarak adil ve dengeli bir çalışma programı oluşturulmuştur. Bu çalışma gerçek hayat problemini ele almakla birlikte mevcut durum analizi ve yeni vardiya sistemi önerisiyle hemşire çizelgeleme problemine yeni bir bakış açısı sunmaktadır.

Keywords

Hemşire çizelgeleme problemi, 0-1 hedef programlama, Personel yönetimi, Hastane yönetimi, Pandemi

References

• [1] S.D. Karayel ve E. Atmaca, “Özel bir hastane için hemşire çizelgeleme problemi”. Çukurova Üniversitesi İİBF Dergisi, Vol. 21, No. 2, pp. 111-132, 2017.
• [2] M.S. Aktürk, E. Varlı and T. Eren, “Tam gün vardiyalı ve özel izin istekli hemşire çizelgeleme probleminin hedef programlama ile çözümü”. Kırıkkale Üniversitesi Sosyal Bilimler Dergisi, Vol 7, No. 2, pp. 1-16, 2017.
• [3] E. Geçici ve M.G. Güler, “Hemşire çizelgeleme problemi için bir karar destek sistemi uygulaması”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, Vol. 26, No. 4, pp. 749-757, 2020.
• [4] M. Tohidi, M. Kazemi Zanjani, and I. Contreras, “Integrated physician and clinic scheduling in ambulatory polyclinics.” Journal of the Operational Research Society, Vol. 70, No. 2, pp. 177-191, 2018.
• [5] P. Damcı-Kurt, M. Zhang, B. Marentay, and N. Govind, “Improving physician schedules by leveraging equalization: Cases from hospitals in US,” Omega, Vol. 85, June, pp. 182-193, 2018.
• [6] G. Leeftink, and E. W. Hans. “Case mix classification and a benchmark set for surgery scheduling”. Journal of scheduling, Vol. 21, No. 1, pp. 17-33, 2018.
• [7] A. Al-Refaie, T. Chen, and M. Judeh.”Optimal operating room scheduling for normal and unexpected events in a smart hospital”. Operational Research, vol. 18, No. 3, pp.579-602, 2018.
• [8] H. Liu, T. Zhang, S. Luo, and D. Xu, “Operating room scheduling and surgeon assignment problem under surgery durations uncertainty”. Technology and Health Care, Vol. 26 No. 2, pp.297-304, 2018.
• [9] Ş. Gür and T. Eren, “Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview” Journal of Healthcare Engineering, Volume 2018, pp. 1-15, 2018.
• [10] W. Y. Wang, D. Gupta, and S. Potthoff, “On evaluating the impact of flexibility enhancing strategies on the performance of nurse schedules”. Health policy, Vol. 93 No.2-3, pp. 188-200, 2009.
• [11] F. C. Coelli, R. B. Ferreira, R. M. V. Almeida, and W. C. A. Pereira, “Computer simulation and discrete-event models in the analysis of a mammography clinic patient flow.” Computer methods and programs in biomedicine, Vol. 87, No.3, pp. 201-207, 2007.
• [12] N. Al-Hinai, N. Al-Yazidy, A. Al-Hooti, and E. Al-Shereiqi, (2018, January). “A goal programming model for nurse scheduling at emergency department.” In 8th International Conference on Industrial Engineering and Operations Management, IEOM Society, pp. 99-103, 2018.
• [13] E. A. Aktunc and E. Tekin, “Nurse Scheduling with Shift Preferences in a Surgical Suite Using Goal Programming.” In Industrial Engineering in the Industry 4.0 Era Springer, Cham., pp. 23-36, 2018.
• [14] J. Kim, W. Jeon, Y. W. Ko, S. Uhmn and D. H. Kim, “Genetic Local Search for Nurse Scheduling Problem” Advanced Science Letters, Vol.24 No.1, pp. 608-612, 2018.
• [15] M. Moz, and M. V. Pato, “Solving the problem of rerostering nurse schedules with hard constraints: new multicommodity flow models.” Annals of Operations Research, Vol. 128 No.1-4, pp. 179-197, 2004.
• [16] E. K. Burke, P. De Causmaecker, G. V. Berghe and H. Van Landeghem, “The state of the art of nurse rostering.” Journal of Scheduling, Vol. 7 No.6, pp. 441-499, 2004.
• [17] M.N. Azaiez and S.S. Al Sharif, “A 0-1 goal programming model for nurse scheduling”. Computers & Operations Research, Vol. 32, No. 3, pp. 491-507, 2005.
• [18] L. Trilling, A. Guinet and D. LeMagny, “Nurse scheduling using ınteger linear programming and constraint programming”. IFAC Proceedings Volumes, Vol. 39, No. 3, pp. 671-676, 2006.
• [19] C. C. Tsai and C. J. Lee, “Optimization of nurse scheduling problem with a two-stage mathematical programming model.” Asia Pacific Management Review, 15(4), 503-516, 2010.
• [20] E.K. Burke, J., Li, and R. Qu, “A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems”. European Journal of Operational Research, Vol. 203, No. 2, pp. 484-493, 2010.
• [21] S. Topaloğlu, and H. Selim,”Nurse scheduling using fuzzy modeling approach.” Fuzzy sets and systems, Vol.161 No.11, pp. 1543-1563, 2010.
• [22] W. K. Zen-El-Din, M. S. Kamel and Mohamed, A. S., “A binary integer programming for nurse scheduling.” In Biomedical Engineering Conference (CIBEC), Cairo International pp. 122-125, IEEE December 2012.
• [23] N. Bağ, N. M. Özdemir ve T. Eren, “0-1 Hedef programlama ve ANP yöntemi ile hemşire çizelgeleme problemi çözümü.” International Journal of Engineering Research and Development, Vol. 4 No.1, pp. 2-6, 2012.
• [24] E. Varlı ve T. Eren, “Hemşire çizelgeleme problemi ve hastanede bir uygulama” Akademik Platform Mühendislik ve Fen Bilimleri Dergisi, Vol. 5, No. 1, pp. 34-40, 2017.
• [25] E. Varlı, B. Ergişi ve T. Eren, “Özel kısıtlı hemşire çizelgeleme problemi: hedef programlama yaklaşımı”. Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, Vol. 49, pp. 189-206, 2017.
• [26] A. J. Mason and M. C. Smith, “A nested column generator for solving rostering problems with integer programming.” In International conference on optimisation: techniques and applications. Curtin University of Technology Perth, Australia, pp. 827-834, July 1998.
• [27] B. Maenhout, and M. Vanhoucke, “Branching strategies in a branch-and-price approach for a multiple objective nurse scheduling problem.” Journal of scheduling, Vol.13 No.1, pp. 77-93, 2010.
• [28] A. Legrain, H. Bouarab and N. Lahrichi, “The nurse scheduling problem in real-life.” Journal of medical systems, Vol. 39 No.1, pp. 1-11, 2015.
• [29] D. Santos, P. Fernandes, H. L. Cardoso, and E. Oliveira, “A weighted constraint optimization approach to the nurse scheduling problem.” In 2015 IEEE 18th International Conference on Computational Science and Engineering pp. 233-239, October 2015.
• [30] S. Ceschia, N. Dang, P. De Causmaecker, S. Haspeslagh, and A. Schaerf, “The second international nurse rostering competition.” Annals of Operations Research, Vol.274 No.1, pp.171-186, 2019.
• [31] J. Inafune, S. Watanabe and M. Okudera, New approach combining branch and price with metaheuristics to solve nurse scheduling problem. Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol. 21 No.7, 1251-1261, 2017.
• [32] E. K. Burke, and T. Curtois, “New approaches to nurse rostering benchmark instances.” European Journal of Operational Research, Vol. 237 No. 1, pp. 71-81, 2014.
• [33] X. Zhong, J. Zhang, and X. Zhang, “A two-stage heuristic algorithm for the nurse scheduling problem with fairness objective on weekend workload under different shift designs.” IISE transactions on healthcare systems engineering, Vol.7 No. 4, pp. 224-235, 2017.
• [34] E. Özcan, T. Danışan, R. Yumuşak, Ş. Gür and T. Eren, “Goal programming approach for the radiology technician scheduling problem”. Sigma Journal of Engineering and Natural Sciences. Vol. 37, No. 4, pp. 1410-1420, 2019.
• [35] J. F. Bard and H. W. Purnomo, “A column generation-based approach to solve the preference scheduling problem for nurses with downgrading.” Socio-Economic Planning Sciences, Vol.39 No.3, pp. 193-213, 2005.
• [36] P. Eveborn and M. Rönnqvist, “Scheduler–a system for staff planning.” Annals of Operations Research, Vol.128 No.1, pp. 21-45, 2004.
• [37] F. He and R. Qu, A constraint programming based column generation approach to nurse rostering problems. Computers & Operations Research, Vol. 39 No. 12, pp. 3331-3343, 2012.
• [38] K. Leksakul and S. Phetsawat, “Nurse scheduling using genetic algorithm.” Mathematical Problems in Engineering, Vol.2014, pp. 1-16, 2014.
• [39] G. J. Lim, A. Mobasher, J. F. Bard, and A. Najjarbashi, Nurse scheduling with lunch break assignments in operating suites. Operations Research for Health Care, Vol.10, pp. 35-48, 2016.
• [40] B. Jaumard, F. Semet and T. Vovor, “A generalized linear programming model for nurse scheduling.” European journal of operational research, Vol.107 No. 1, 1-18, 1998.
• [41] G. Lim and A. Mobasher, “Nurse scheduling problem in an operating suite.” In IIE Annual Conference. Proceedings (p. 1). Institute of Industrial and Systems Engineers (IISE), 2011.
• [42] J. Guo and J. F. Bard, “A column generation-based algorithm for midterm nurse scheduling with specialized constraints, preference considerations, and overtime.” Computers & Operations Research, Vol. 138, pp. 105597, 2022.
• [43] H. W. Purnomo and J. F. Bard, “Cyclic preference scheduling for nurses using branch and price.” Naval Research Logistics (NRL), Vol.54 No.2, pp. 200-220 2007.
• [44] E. Rahimian, K. Akartunalı, and J. Levine, “A hybrid integer and constraint programming approach to solve nurse rostering problems.” Computers & Operations Research, Vol.82, pp. 83-94, 2017.
• [45] E. Rahimian, K. Akartunalı and J. Levine, “A hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems.” European Journal of Operational Research, Vol.258 No. 2, pp. 411-423, 2017.
• [46] P. Strandmark, Y. Qu and T. Curtois, “First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem.” Computers & Operations Research, Vol. 120, pp. 104945, 2020.
• [47] B. Sinha and N. Sen, “Goal programming approach to tea industry of Barak Valley of Assam.” Applied Mathematical Sciences, Vol. 5 No.29, pp. 1409-1419, 2011.