LABORATUVAR BİRİMİNDEKİ SAĞLIK PERSONELİNİN VARDİYA ÇİZELGELEMESİNDE 0-1 TAMSAYILI HEDEF PROGRAMLAMA UYGULAMASI

Yıl 2024, , 66 - 95, 06.07.2024

Banu Bolayır

https://doi.org/10.11611/yead.1427593

Öz

Nüfustaki artış ile birlikte en yoğun vardiyalı çalışan kurumlar hastanelerdir. Hastanelerde vardiya çizelgelemeleri yapılırken; hastanenin çalışma şartları, hastanın, personelin ve hastanenin memnuniyetleri, personelin izin, tatil vb. tercihleri gibi kısıtların yanı sıra farklı hedeflerin dikkate alınarak her personel için dengeli bir vardiya çizelgesinin yapılması zor olmaktadır. Bu çalışmanın amacı, laboratuvar birimindeki sağlık personelinin vardiya çizelgesinin optimal planlanmasıdır. Çalışmada; Gümüşhane ilindeki bir devlet hastanesinin laboratuvar biriminin Kasım 2022 vardiya çizelgesi kullanılmıştır. Hastanenin çalışma şartlarına ve vardiya çizelgesine göre 0-1 tamsayılı hedef programlama modeli kurulmuştur. Modelin GAMS 42.5.0 programında kodlanarak çözümlenmesi sonucunda optimal vardiya çizelgesi elde edilmiştir.

Anahtar Kelimeler

Laboratuvar Birimi, Sağlık Personeli, Vardiya Çizelgeleme, 0-1 Tamsayılı Hedef Programlama, Optimizasyon

APPLICATION OF 0-1 INTEGER GOAL PROGRAMMING FOR SHIFT SCHEDULING OF MEDICAL STAFF IN LABORATORY DEPARTMENT

Öz

With the increase in population, hospitals are the institutions with the most intensive shift work. When scheduling shifts in hospitals, it is difficult to create a balanced shift schedule for each staff by taking into account constraints such as the working conditions of the hospital, the satisfaction of patients, staff and the hospital, and the wishes of staff in terms of days off, holidays , etc. as well as different objectives. The aim of this study is to optimally plan the shift schedule for medical staff in the laboratory department. The shift schedule of the laboratory department of a government hospital in Gümüşhane in November 2022 was used for the study. According to the working conditions and shift schedule of the hospital, a 0-1 integer goal programming model is established. The optimal shift schedule was obtained as a result of analyzing the model by coding it in the GAMS 42.5.0 program.

Anahtar Kelimeler

Laboratory Department, Medical Staff, Shift Scheduling, 0-1 Integer Goal Programming, Optimization

Etik Beyan

Necessary permissions were obtained from Gümüşhane University Scientific Research and Publication Ethics Board dated 12/27/2022 and numbered 2022/7, and Gümüşhane Provincial Health Directorate dated 01/13/2023 and numbered E-51020271-044-207023258 in the related study.

Kaynakça

• Acharya, S., Nanda, S. and Mishra, B. (2011) “Solving Multi-choice Linear Goal Programming Problem with Preemptive Priorities”, Journal of Orissa Mathematical Society, 30, 52-70.
• Agyei, W., Obeng-Denteh, W. and Andaam, E.A. (2015) “Modeling Nurse Scheduling Problem Using 0-1 Goal Programming: A Case Study of Tafo Government Hospital, Kumasi-Ghana”, International Journal of Scientific & Technology Research, 4(3), 5-10. https://www.ijstr.org/final-print/mar2015/Modeling-Nurse-Scheduling-Problem-Using-0-1-Goal-Programming-A-Case-Study-Of-Tafo-Government-Hospital-Kumasi-ghana.pdf
• Ahern, A. and Anandarajah, G. (2007) “Railway Projects Prioritisation for Investment: Application of Goal Programming”, Transport Policy, 14(1): 70-80. https://doi.org/10.1016/j.tranpol.2006.10.003
• Aickelin, U. and White, P. (2004) “Building Better Nurse Scheduling Algorithms”, Annals of Operations Research, 128, 159-177. https://doi.org/10.1023/b:anor.0000019103.31340.a6
• Al-Hinai, N., Al-Yazidy, N., Al-Hooti, A. and Al-Shereiqi, E. (2018) “A Goal Programming Model for Nurse Scheduling at Emergency Department”, In the International Conference on Industrial Engineering and Operations Management (pp. 99-103), March 6-8, Bandung, Indonesia. http://www.ieomsociety.org/ieom2018/papers/42.pdf
• Al-Mudahka, I. and Alhamad, R (2022). “On a Timetabling Problem in the Health Care System”, RAIRO-Operations Research, 56(6), 4347-4362. https://doi.org/10.1051/ro/2022182
• Anderson, M., Bodur, M., Rathwell, S. and Sarhangian, V. (2023) “Optimization Helps Scheduling Nursing Staff at the Long-Term Care Homes of the City of Toronto”, INFORMS Journal on Applied Analytics, 53(2): 133-154. https://doi.org/10.1287/inte.2022.1132
• Ang, B.Y., Lam, S.S.W., Pasupathy, Y. and Ong, M.E.H. (2018) “Nurse Workforce Scheduling in the Emergency Department: A Sequential Decision Support System Considering Multiple Objectives”, Journal of Nursing Management, 26(4): 432-441. https://doi.org/10.1111/jonm.12560
• Arthur, J.L. and Ravindran, A. (1981) “A Multiple Objective Nurse Scheduling Model”, AIIE Transactions, 13(1): 55-60. https://doi.org/10.1080/05695558108974536
• Atmaca, E., Pehlivan, C., Aydoğdu, C.B. and Yakıcı, M. (2012) “Hemşire Çizelgeleme Problemi ve Uygulaması”, Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28(4), 351-358.
• Azadeh, A., Baghersad, M., Farahani, M.H. and Zarrin, M. (2015) “Semi-online Patient Scheduling in Pathology Laboratories”, Artificial Intelligence in Medicine, 64(3): 217-226. https://doi.org/10.1016/j.artmed.2015.05.001
• Azadeh, A., Farahani, M.H., Torabzadeh, S. and Baghersad, M. (2014) “Scheduling Prioritized Patients in Emergency Department Laboratories”, Computer Methods and Programs in Biomedicine, 117(2): 61-70. https://doi.org/10.1016/j.cmpb.2014.08.006
• Azaiez, M.N. and Al Sharif, S.S. (2005) “A 0-1 Goal Programming Model for Nurse Scheduling”, Computers & Operations Research, 32(3): 491-507. https://doi.org/10.1016/S0305-0548(03)00249-1
• Bağ, N., Özdemir, N.M. and Eren, T. (2012) “0-1 Hedef Programlama ve ANP Yöntemi ile Hemşire Çizelgeleme Problemi Çözümü”, International Journal of Engineering Research and Development, 4(1), 2-6.
• Bayraktar, E. and Aytaç Adalı, E. (2022) “Hemşire Çizelgeleme Probleminde Tam Sayılı Hedef Programlama Modeli ve Çocuk Acil Bölümünde Bir Uygulama”, Ömer Halisdemir Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 15(2): 246-260. https://doi.org/10.25287/ohuiibf.855824
• Bektur, G., Zemzem, M. and Tumkaya, I.S. (2023) “Shift Planning Problem for Cardiology Department in a State Hospital Considering Radiation Exposure of the Physicians”, 2nd International Conference on Engineering, Natural and Social Sciences (pp. 47-50), April 4-6, Konya, Turkey. https://www.icensos.com/
• Bertels, S. and Fahle, T. (2006) “A Hybrid Setup for a Hybrid Scenario: Combining Heuristics for the Home Health Care Problem”, Computers & Operations Research, 33(10): 2866-2890. https://doi.org/10.1016/j.cor.2005.01.015
• Bruni, R. and Detti, P. (2014) “A Flexible Discrete Optimization Approach to the Physician Scheduling Problem”, Operations Research for Health Care, 3(4), 191-199. https://doi.org/10.1016/j.orhc.2014.08.003
• Brunner, J.O., Bard, J.F. and Kolisch, R. (2009) “Flexible Shift Scheduling of Physicians”, Health Care Management Science, 12(3), 285-305. https://doi.org/10.1007/s10729-008-9095-2
• Brunner, J.O. and Edenharter, G.M. (2011) “Long Term Staff Scheduling of Physicians with Different Experience Levels in Hospitals Using Column Generation”, Health Care Management Science, 14(2), 189-202. https://doi.org/10.1007/s10729-011-9155-x
• Burke, E.K., Li, J. and Qu, R. (2010) “A Hybrid Model of Integer Programming and Variable Neighbourhood Search for Highly Constrained Nurse Rostering Problems”, European Journal of Operational Research, 203(2), 484-493. https://doi.org/10.1016/j.ejor.2009.07.036
• Chae, Y.M., Suver, J.D. and Chou, D. (1985) “Goal Programming as a Capital Investment Tool for Teaching Hospitals”, Health Care Management Review, 10(1) 27-35. https://doi.org/10.1097/00004010-198501010-0000
• Charnes, A. and Cooper, W.W. (1961) “Management Models and Industrial Applications of Linear Programming”, New York: John Wiley and Sons.
• Charnes, A. and Cooper, W.W. (1977) “Goal Programming and Multiple Objective Optimizations: Part I”, European Journal of Operational Research, 1(1): 39-54. https://doi.org/10.1016/S0377-2217(77)81007-2
• Charnes, A., Cooper, W.W. and Ferguson, R.O. (1955) “Optimal Estimation of Executive Compensation by Linear Programming”, Management Science, 1(2), 138-151. https://doi.org/10.1287/mnsc.1.2.138
• Chen, J.G. and Yeung, T.W. (1993) “Hybrid Expert-System Approach to Nurse Scheduling”, Computers in Nursing, 11(4): 183-190.
• Chen, P.S., Lin, Y.J. and Peng, N.C. (2016) “A Two-Stage Method to Determine the Allocation and Scheduling of Medical Staff in Uncertain Environments”, Computers & Industrial Engineering, 99, 174-188. https://doi.org/10.1016/j.cie.2016.07.018
• Chiang, A.J., Jeang, A., Chiang, P.C., Chiang, P.S. and Chung, C.P. (2019) “Multi-objective Optimization for Simultaneous Operating Room and Nursing Unit Scheduling”, International Journal of Engineering Business Management, 11: 1-20. https://doi.org/10.1177/1847979019891022
• Dowsland, K.A. and Thompson, J.M. (2000) “Solving a Nurse Scheduling Problem with Knapsacks, Networks and Tabu Search”, Journal of the Operational Research Society, 51(7): 825-833. https://doi.org/10.2307/253963
• Elomri, A., Elthlatiny, S. and Mohamed, Z.S. (2015) “A Goal Programming Model for Fairly Scheduling Medicine Residents”, International Journal of Supply Chain Management, 4(2), 6-10. https://core.ac.uk/reader/230753300
• Franz, L.S., Baker, H.M., Leong, G.K. and Rakes, T.R. (1989) “A Mathematical Model for Scheduling and Staffing Multiclinic Health Regions”, European Journal of Operational Research, 41(3), 277-289. https://doi.org/10.1016/0377-2217(89)90249-X
• Geçici, E. and Güler, M.G. (2020) “Hemşire Çizelgeleme Problemi için Bir Karar Destek Sistemi Uygulaması”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 26(4): 749-757. https://doi.org/10.5505/pajes.2019.86402
• Girginer, N. and Kaygısız, Z. (2009) “İstatistiksel Yazılım Seçiminde Analitik Hiyerarşi Süreci ve 0-1 Hedef Programlama Yöntemlerinin Birlikte Kullanımı”, Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi, 10(1), 211-233.
• Güler, M.G., İdi, K. and Güler, E.Y. (2013) “A Goal Programming Model for Scheduling Residents in an Anesthesia and Reanimation Department”, Expert Systems with Applications, 40(6): 2117-2126. https://doi.org/10.1016/j.eswa.2012.10.030
• Güngör, İ. (2002) “Hemşire Görevlendirme ve Çizelgeleme Sorununa Bir Model Önerisi”, Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 7(2): 77-94.
• Gür, Ş., Pınarbaşı, M., Alakaş, H.M. and Eren, T. (2022) “Operating Room Scheduling with Surgical Team: A New Approach with Constraint Programming and Goal Programming”, Central European Journal of Operations Research, 1–25. https://doi.org/10.1007/s10100-022-00835-z
• Hakim, L., Bakhtiar, T. and Jaharuddin (2017) “The Nurse Scheduling Problem: A Goal Programming and Nonlinear Optimization Approaches”, In IOP Conference Series: Materials Science and Engineering, 166, IOP Publishing. https://doi.org/10.1088/1757-899X/166/1/012024
• Hidri, L. and Labidi, M. (2016) “Optimal Physicians Schedule in an Intensive Care Unit”, In IOP Conference Series: Materials Science and Engineering, 131, IOP Publishing. https://doi.org/10.1088/1757-899X/131/1/012001
• Horvat, A.M., Dudic, B., Radovanov, B., Melovic, B., Sedlak, O. and Davidekova, M. (2020) “Binary Programming Model for Rostering Ambulance Crew-Relevance for the Management and Business”, Mathematics, 9(1): 64, 1-13. https://doi.org/10.3390/math9010064
• Huarng, F. (1999) “A Primary Shift Rotation Nurse Scheduling Using Zero-One Linear Goal Programming”, Computers in Nursing, 17(3): 135-144.
• Ignizio, J.P. (1985) “Introduction to Linear Goal Programming”, Beverly Hills, California, USA: Sage Publications.
• Ismail, W.R. and Jenal, R. (2013) “Master Plan Nurse Duty Roster Using the 0-1 Goal Programming Technique”, In AIP Conference Proceedings (pp. 1394-1400), 1522, AIP Publishing. https://doi.org/10.1063/1.4801292
• Jaumard, B., Semet, F. and Vovor, T. (1998) “A Generalized Linear Programming Model for Nurse Scheduling”, European Journal of Operational Research, 107(1): 1-18. https://doi.org/10.1016/s0377-2217(97)00330-5
• Jenal, R., Ismail, W.R., Yeun, L.C. and Oughalime, A. (2011) “A Cyclical Nurse Schedule Using Goal Programming”, ITB Journal of Science, 43A(3), 151-164. https://doi.org/10.5614/itbj.sci.2011.43.3.1
• Karaatlı, M. and Güngör, İ. (2010) “Hemşire Çizelgeleme Sorununa Bir Çözüm Önerisi ve Bir Uygulama”, Uluslararası Alanya İşletme Fakültesi Dergisi, 2(1), 22-52.
• Karayel, S.D. and Atmaca, E. (2017) “Özel Bir Hastane Için Hemşire Çizelgeleme Problemi”, Çukurova Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 21(2), 111-132.
• Keskin, M.E., Kılıç Delice, E. and Akkaya, G. (2020) “Çoklu Bölüm için Adil Hemşire Çizelgeleme”, Atatürk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 24(4), 1705-1720.
• Kumar, B.S., Nagalakshmi, G. and Kumaraguru, S. (2014) “A Shift Sequence for Nurse Scheduling Using Linear Programming Problem”, IOSR Journal of Nursing and Health Science, 3(6): 24-28. https://www.iosrjournals.org/iosr-jnhs/papers/vol3-issue6/Version-1/E03612428.pdf
• Li, Y. and Kozan, E. (2009) “Rostering Ambulance Services”, Gen, M. & Oyabi, T. (eds.), Proceedings of Asia Pacific Industrial Engineering & Management Systems Conference 2009 (pp. 795-801). APIEMS, Kitakyushu, Japan. https://eprints.qut.edu.au/29823/
• Lim, G.J., Mobasher, A. and Côté, M.J. (2012) “Multi-objective Nurse Scheduling Models with Patient Workload and Nurse Preferences”, Management, 2(5), 149-160. https://doi.org/10.5923/j.mm.20120205.03
• Liu, Z., Liu, Z., Zhu, Z., Shen, Y. and Dong, J. (2018) “Simulated Annealing for a Multi-level Nurse Rostering Problem in Hemodialysis Service”, Applied Soft Computing, 64: 148-160. https://doi.org/10.1016/j.asoc.2017.12.005
• Moz, M. and Pato, M.V. (2004) “Solving the Problem of Rerostering Nurse Schedules with Hard Constraints: New Multicommodity Flow Models”, Annals of Operations Research, 128, 179-197. https://doi.org/10.1023/B:ANOR.0000019104.39239.ed
• Musa, A.A. and Saxena, U. (1984) “Scheduling Nurses Using Goal-Programming Techniques”, IIE Transactions, 16(3): 216-221. https://doi.org/10.1080/07408178408974687
• Narlı, M. and Oğulata, S.N. (2008) “Hemşirelerin Çalışma Vardiyalarının Değerlendirilmesi ve Çizelgelenmesi”, Çukurova Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 19(1): 31-40.
• Nasir, D.S.M., Bahrom, N.H.C., Shafii, N.H. and Nor, N.A.M (2021) “Cyclical Nurse Scheduling in Shah Alam Hospital Using Goal Programming”, Journal of Computing Research and Innovation, 6(1): 1-10. https://doi.org/10.24191/jcrinn.v6i1.175
• Ogulata, S.N., Koyuncu, M. and Karakas, E. (2008) “Personnel and Patient Scheduling in the High Demanded Hospital Services: A Case Study in the Physiotherapy Service”, Journal of Medical Systems, 32, 221-228. https://doi.org/10.1007/s10916-007-9126-4
• Ozkarahan, I. (1991) “A Disaggregation Model of a Flexible Nurse Scheduling Support System”, Socio-Economic Planning Sciences, 25(1), 9-26. https://doi.org/10.1016/0038-0121(91)90025-m
• Ozkarahan, I. and Bailey, J.E. (1988) “Goal Programming Model Subsystem of a Flexible Nurse Scheduling Support System”, IIE Transactions, 20(3): 306-316. https://doi.org/10.1080/07408178808966185
• Özcan, E., Danışan, T., Yumuşak, R., Gür, Ş. and Eren, T. (2019) “Goal Programming Approach for the Radiology Technician Scheduling Problem”, Sigma Journal of Engineering and Natural Sciences, 37(4): 1411-1420.
• Öztürkoğlu, Y. and Çalışkan, F. (2014) “Hemşire Çizelgelemesinde Esnek Vardiya Planlaması ve Hastane Uygulaması”, Dokuz Eylül Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 16(1), 115-133. https://doi.org/10.16953/deusbed.07850
• Rerkjirattikal, P., Huynh, V.N., Olapiriyakul, S. and Supnithi, T. (2020) “A Goal Programming Approach to Nurse Scheduling with Individual Preference Satisfaction”, Mathematical Problems in Engineering, 1-11. https://doi.org/10.1155/2020/2379091
• Rifai, A.K. (1996) “A Note on the Structure of the Goal‐Programming Model: Assessment and Evaluation”, International Journal of Operations & Production Management, 16(1): 40-49. https://doi.org/10.1108/01443579610106355
• Seçkiner, S. and Kurt, M. (2005) “Bütünleşik Tur-Rotasyon Çizelgeleme Yaklaşımı ile Işyükü Minimizasyonu”, Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 20(2): 161-169.
• Smalley, H.K., Keskinocak, P. and Vats, A. (2015) “Physician Scheduling for Continuity: An Application in Pediatric Intensive Care”, Interfaces, 45(2), 133-148. https://doi.org/10.1287/inte.2014.0774
• Stolletz, R. and Brunner, J.O. (2012) “Fair Optimization of Fortnightly Physician Schedules with Flexible Shifts”, European Journal of Operational Research, 219(3): 622-629. https://doi.org/10.1016/j.ejor.2011.10.038
• Sulak, H. and Bayhan, M. (2016) “A Model Suggestion and an Application for Nurse Scheduling Problem”, Journal of Research in Business, Economics and Management, 5(5), 755-760. https://core.ac.uk/download/pdf/267832923.pdf
• Sundari, V.E. and Mardiyati, S. (2017) “Solving Cyclical Nurse Scheduling Problem Using Preemptive Goal Programming”, In AIP Conference Proceedings, 1862, AIP Publishing. https://doi.org/10.1063/1.4991236
• Tan, M., Gan, J. and Ren, Q. (2019) “Scheduling Emergency Physicians Based on a Multiobjective Programming Approach: A Case Study of West China Hospital of Sichuan University”, Journal of Healthcare Engineering, 1-9. https://doi.org/10.1155/2019/5647078
• Taylor, A.M. (1940) “A Staff Nurse Program”, The American Journal of Nursing, 40(2): 137-145. https://doi.org/10.2307/3414625
• Topaloglu, S. (2006) “A Multi-objective Programming Model for Scheduling Emergency Medicine Residents”, Computers & Industrial Engineering, 51(3): 375-388. https://doi.org/10.1016/j.cie.2006.08.003
• Topaloğlu, S. (2009) “A Shift Scheduling Model for Employees with Different Seniority Levels and an Application in Healthcare”, European Journal of Operational Research, 198(3): 943-957. https://doi.org/10.1016/j.ejor.2008.10.032
• Topaloğlu, S. and Selim, H. (2010) “Nurse Scheduling Using Fuzzy Modeling Approach”, Fuzzy Sets and Systems, 161(11), 1543-1563. https://doi.org/10.1016/j.fss.2009.10.003
• Trilling, L., Guinet, A. and Le Magny, D. (2006) “Nurse Scheduling Using Integer Linear Programming and Constraint Programming”, IFAC Proceedings Volumes, 39(3): 671-676. https://doi.org/10.3182/20060517-3-FR-2903.00340
• Trivedi, V.M. (1981) “A Mixed-Integer Goal Programming Model for Nursing Service Budgeting”, Operations Research, 29(5), 1019-1034. https://doi.org/10.1287/opre.29.5.1019
• Varlı, E. and Eren, T. (2017) “Hemşire Çizelgeleme Problemi ve Hastanede Bir Uygulama”, Academic Platform-Journal of Engineering and Science, 5(1): 34-40. https://doi.org/10.21541/apjes.73975
• Wang, S.P., Hsieh, Y.K., Zhuang, Z.Y. and Ou, N.C. (2014) “Solving an Outpatient Nurse Scheduling Problem by Binary Goal Programming”, Journal of Industrial and Production Engineering, 31(1): 41-50. https://doi.org/10.1080/21681015.2014.881425
• Warner, D.M. (1976) “Scheduling Nursing Personnel According to Nursing Preference: A Mathematical Programming Approach”, Operations Research, 24(5): 842-856. https://doi.org/10.1287/opre.24.5.842
• Warner, D.M. and Prawda, J. (1972) “A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital”, Management Science, 19(4-part-1): 411-422. https://doi.org/10.1287/mnsc.19.4.411
• Wolfe, H. and Young, J.P. (1965) “Staffing the Nursing Unit: Part I. Controlled Variable Staffing”, Nursing Research, 14(3): 236-243. https://doi.org/10.1097/00006199-196501430-00011
• Wolfe, H. and Young, J.P. (1965) “Staffing the Nursing Unit: Part II. The Multiple Assignment Technique”, Nursing Research, 14(4): 299-303. https://doi.org/10.1097/00006199-196501440-00004
• Woodall, J.C., Gosselin, T., Boswell, A., Murr, M. and Denton, B.T. (2013) “Improving Patient Access to Chemotherapy Treatment at Duke Cancer Institute”, Interfaces, 43(5), 449-461. https://doi.org/10.1287/inte.2013.0695