Belirsiz Taleplerle Hemşire Çizelgeleme Problemi için Stokastik Hedef Programlama

Abstract

İşletmelerin verimliliklerine direkt etkili olan vardiya çizelgeleme daima göz önünde bulundurulması gereken bir problemdir. Problemin temelinde kişilerin yetkinliklerine göre vardiyalara atanması, kişilerden beklenen mesailerin birbirinden minimum sapmada olması ve adil bir dağıtım olması amaçlanmaktadır. Bu çalışmada vardiya çizelgeleme probleminin modellenmesi için atama problemi türlerinden sıklıkla kullanılan hemşire çizelgeleme alanı seçilmiştir. Kısıtların belirlenmesinde yasaların belirlediği zorunlu durumlar, hastanenin belirlediği ihtiyaçlar, çalışanların yetkinlik/sorumlulukları ve izin durumları göz önünde bulundurulmuştur. Bunun yanında adil bir çizelgeleme olması için personellerin vardiyalara eşit dağıtımın sağlanması ve izin günlerinin mümkün olduğunda art arda olması hedeflenmiştir. Tüm kısıtların sağlandığı ve birden fazla sayıdaki birbiriyle çelişebilecek hedeflerin minimum sapma ile gerçekleştirebilmesi için hedef programlamadan yararlanılmıştır. Bunların yanında gerçek hayat verileri içeren olasılık temelli farklı senaryolardaki taleplere cevap verilebilmesi için stokastik parametreler de modele eklenmiştir. Seçilen problemin içeriğinde iki farklı birimde çalışan farklı yetkinlikteki yirmi sekiz hemşire için gerekli kısıtları sağlayarak adil dağıtımı sağlayan ve belirsizlik durumlarına uygun cevabı verebilecek bir modelleme yapılmıştır. Kurulan model, GAMS programı ile stokastik karma tamsayılı hedef programlama (MIP) kullanılarak çözüm aranmıştır.

Keywords

• Vardiya çizelgeleme
• hedef programlama
• stokastik modelleme

Stochastic Goal Programming for the Nurse Scheduling Problem with Uncertain Demand

Abstract

Shift scheduling, which has a direct impact on the productivity of enterprises, is a problem that should always be considered. On the basis of the problem, it is aimed to assign people to shifts according to their competencies, to have a fair distribution of overtime expected from each other and to have minimum deviation from each other. In this study, nurse scheduling chose for the assignment problem. In determining the constraints, the mandatory situations determined by the law, the needs determined by the hospital, the competencies/responsibilities of the employees and annual leave situations taken into consideration. Goal programming has been used in order to achieve multiple goals that may conflict with each other, where all the constraints are met, with minimum deviation. In addition, stochastic parameters were added to the model in order to respond to the demands in different scenarios based on probabilistic real-life data. In the content of the selected problem, a modeling that provides fair distribution by providing the necessary constraints for twenty-eight nurses with different competencies working in two different units and can provide the appropriate response to uncertainty situations has been made. The model was solved by using mixed integer programming (MIP) with GAMS program.

Keywords

• Shift scheduling
• goal programming
• stochastic modeling

References

1. [1] Q-K. Pan, P. N. Suganthan, T. J. Chua, and T. X. Cai, “Solving manpower scheduling problem in manufacturing using mixed-integer programming with a two-stage heuristic algorithm,” The International Journal of Advanced Manufacturing Technology, vol. 46, no. 9–12, pp. 1229–1237, Jul. 2009. doi:10.1007/s00170-009-2175-8
2. [2] S. Topaloglu and I. Ozkarahan, “An Implicit Goal Programming Model for the Tour Scheduling Problem Considering the Employee Work Preferences,” Annals of Operations Research, vol. 128, no. 1–4, pp. 135–158, Apr. 2004. doi:10.1023/b:anor.0000019102.68222.df
3. [3] U. Ozcan and B. Toklu, “Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models,” Computers & Operations Research, vol. 36, no. 6, pp. 1955–1965, Jun. 2009. doi:10.1016/j.cor.2008.06.009
4. [4] M. Timor, Yöneylem Araştırması. Turkmen Kitabevi, Istanbul, 2010
5. [5] O. Onalan, Stokastik Süreçler. Nobel Akademik Yayincilik, Ankara, 2022
6. [6] E. H. Ozder, E. Ozcan, and T. Eren, “A Systematic Literature Review for Personnel Scheduling Problems,” International Journal of Information Technology & Decision Making, vol. 19, no. 06, pp. 1695–1735, Oct. 2020. doi:10.1142/s0219622020300050
7. [7] Adel Elomri, S. Elthlatiny, and Zainab Sidi Mohamed, “A Goal Programming Model for Fairly Scheduling Medicine Residents,” International Journal of Supply Chain Management, vol. 4, no. 2, Jun. 2015.
8. [8] H.-T. Lin, Y.-T. Chen, T.-Y. Chou, and Y.-C. Liao, “Crew rostering with multiple goals: An empirical study,” Computers & Industrial Engineering, vol. 63, no. 2, pp. 483–493, Sep. 2012. doi:10.1016/j.cie.2012.04.013

9. [9] H. Sulak and Mustafa Bayhan, “A Model Suggestion and an Application for Nurse Scheduling Problem,” Zenodo (CERN European Organization for Nuclear Research), Apr. 2016. doi:10.5281/zenodo.3965502
10. [10] S. Topaloglu, “A shift scheduling model for employees with different seniority levels and an application in healthcare,” European Journal of Operational Research, vol. 198, no. 3, pp. 943–957, Nov. 2009. doi:10.1016/j.ejor.2008.10.032
11. [11] Nurgül Bag, Necati Ozdemir, and T. Eren, “Solving A 0-1 Goal Programming and ANP Methods with Nurse Scheduling Problem,” International Journal of Engineering Research and Development, Jan. 2012.
12. [12] Y. Ozturkoglu and F. Caliskan, “Hemşire Çizelgelemesinde Esnek Vardiya Planlamasi ve Hastane Uygulamasi,” Dokuz Eylül Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, vol. 16, no. 1, p. 115, Apr. 2014, doi:10.16953/deusbed.07850
13. [13] E. Varli and T. Eren, “Vardiya Cizelgeleme Problemi ve Bir Örnek Uygulama,” Bilişim Teknolojileri Dergisi, pp. 185–185, Apr. 2017. doi:10.17671/gazibtd.309302
14. [14] Ediz Atmaca, Ceydanur Pehlivan, C. Begum Aydogdu, and Mehmet Yakici, “Hemşire çizelgeleme problemi ve uygulaması,” Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, vol. 28, no. 4, pp. 351–358, Aug. 2012.
15. [15] C.-C. Lin, J.-R. Kang, D.-J. Chiang, and C.-L. Chen, “Nurse Scheduling with Joint Normalized Shift and Day-Off Preference Satisfaction Using a Genetic Algorithm with Immigrant Scheme,” International Journal of Distributed Sensor Networks, vol. 11, no. 7, p. 595419, Jul. 2015. doi:10.1155/2015/595419
16. [16] A. Legrain, H. Bouarab, and N. Lahrichi, “The Nurse Scheduling Problem in Real-Life,” Journal of Medical Systems, vol. 39, no. 1, Dec. 2014. doi:10.1007/s10916-014-0160-8
17. [17] H. Jafari, S. Bateni, P. Daneshvar, S. Bateni, and H. Mahdioun, “Fuzzy Mathematical Modeling Approach for the Nurse Scheduling Problem: A Case Study,” International Journal of Fuzzy Systems, vol. 18, no. 2, pp. 320–332, Jul. 2015. doi:10.1007/s40815-015-0051-2
18. [18] M. Bagheri, A. Gholinejad Devin, and A. Izanloo, “An application of stochastic programming method for nurse scheduling problem in real word hospital,” Computers & Industrial Engineering, vol. 96, pp. 192–200, Jun. 2016. doi:10.1016/j.cie.2016.02.023
19. [19] E. Varli, B. Ergisi, and T. Eren, “Ozel Kisıtli Hemsire Cizelgeleme Problemi: Hedef Programlama Yaklasimi,” Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 0, no. 49, pp. 189–189, Jun. 2017. doi:10.18070/erciyesiibd.323910
20. [20] M. M. Nasiri and M. Rahvar, “A two-step multi-objective mathematical model for nurse scheduling problem considering nurse preferences and consecutive shifts,” International Journal of Services and Operations Management, vol. 27, no. 1, p. 83, 2017. doi:10.1504/ijsom.2017.083338
21. [21] B. Y. Ang, S. W. S. Lam, Y. Pasupathy, and M. E. H. Ong, “Nurse workforce scheduling in the emergency department: A sequential decision support system considering multiple objectives,” Journal of Nursing Management, vol. 26, no. 4, pp. 432–441, Dec. 2017. doi:10.1111/jonm.12560
22. [22] Nasr Al-Hinai, Noor Al-Yazidy, Anfal Al-Hooti, and Ekhlas Al-Shereiqi, “A goal programming model for nurse scheduling at emergency department,” International Conference on Industrial Engineering and Operations Management, pp. 99–103, Jan. 2018.
23. [23] S. Zanda, P. Zuddas, and C. Seatzu, “Long term nurse scheduling via a decision support system based on linear integer programming: A case study at the University Hospital in Cagliari,” Computers & Industrial Engineering, vol. 126, pp. 337–347, Dec. 2018. doi:10.1016/j.cie.2018.09.027
24. [24] S. Batun and E. Karpuz, “Belirsizlik Varken Hemsire Cizelgeleme Problemi,” Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 38, no. 1, pp. 75–95, Mar. 2020. doi:10.17065/huniibf.483986
25. [25] M. Arslan and B. Ozcan, “Hemsire Cizelgeleme Problemi ve Bir Saglik Kurulusunda Uygulama,” Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Nov. 2021. doi:10.25092/baunfbed.947636
26. [26] E. Bayraktar and E. A. Adali, “Hemsire Cizelgeleme Probleminde Tam Sayili Hedef Programlama Modeli ve Cocuk Acil Bolumunde Bir Uygulama,” Ömer Halisdemir Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 15, no. 2, pp. 246–260, Apr. 2022. doi:10.25287/ohuiibf.855824
27. [27] H. Li, A. Lim, and B. Rodrigues, “A hybrid AI approach for nurse rostering problem,” Mar. 2003. doi:10.1145/952532.952675
28. [28] L.H. Tein, R. Ramli, “Recent advancements of nurse scheduling models and a potential path,” in Proceedings of the 6thIMT-GT Conference on Mathematics, Statistics and its Applications (ICMSA2010), Citeseer, 2009, pp. 395-409.
29. [29] C. Chang, H. Jen, and W. Su, “Trends in artificial intelligence in nursing: Impacts on nursing management,” Journal of Nursing Management, vol. 30, no. 8, Aug. 2022. doi:10.1111/jonm.13770
30. [30] U. Aickelin and K. A. Dowsland, “An indirect Genetic Algorithm for a nurse-scheduling problem,” Computers & Operations Research, vol. 31, no. 5, pp. 761–778, Apr. 2004. doi:10.1016/s0305-0548(03)00034-0
31. [31] A. Amindoust, M. Asadpour, and S. Shirmohammadi, “A Hybrid Genetic Algorithm for Nurse Scheduling Problem considering the Fatigue Factor,” Journal of Healthcare Engineering, vol. 2021, pp. 1–11, Mar. 2021. doi:10.1155/2021/5563651
32. [32] J. Schrack, R. Ortega, K. Dabu, D. Truong, M. Aibin, and A. Aibin, “Combining Tabu Search and Genetic Algorithm to Determine Optimal Nurse Schedules,” IEEE Xplore, Sep. 01, 2021. https://ieeexplore.ieee.org/document/9569111 [accessed Jan. 27, 2023].
33. [33] R. Ramli, S. N. I. Ahmad, S. Abdul-Rahman, and A. Wibowo, “A tabu search approach with embedded nurse preferences for solving nurse rostering problem,” International Journal for Simulation and Multidisciplinary Design Optimization, vol. 11, p. 10, 2020. doi:10.1051/smdo/2020002
34. [34] A. A. Abayomi-Alli, F. O. Uzedu, S. Misra, O. O. Abayomi-Alli, and O. T. Arogundade, “Hybrid model of genetic algorithms and Tabu search memory for Nurse Scheduling Systems,” International Journal of Service Science, Management, Engineering, and Technology, vol. 13, no. 1, pp. 1–20, 2022. doi:10.4018/ijssmet.297494