Genetic algorithm based on weighted goal programming for doctor rostering problem

Öz

In the healthcare sector, undisrupted service is essential for hospitals. Therefore, shift work plays a vital role in satisfying constraints such as coverage requirements and government regulations. The doctor rostering problem is classified as an NP-hard problem due to its complexity and scale. In addition to the fairness of assignments, including hospital management policies, and government regulations, many related factors must be taken into account during the scheduling process in this scheduling problem. This study aims to generate a rostering system that can satisfy the requirements of the hospital, ensure fairness amongst the doctors, and take preferences into account. A genetic algorithm based on a weighted goal programming model was proposed to solve the doctor rostering problem. The proposed model was applied to the Internal Diseases Department and the Lateral Branches Department of Kütahya Evliya Çelebi Education and Research Hospital. 15 different scenarios were constructed, considering different problem scales and different preference patterns of the doctors that may occur in the the future. It is approved that the proposed algorithm can be applied to different problem scales and conditions. The parameters of the proposed algorithm were calibrated with an experimental design method. In this study, two main contributions were presented. A model with new constraints was introduced for researchers. In addition, a genetic algorithm based on weighted goal programming was proposed to solve the problem and applied to a real-world case study.

Anahtar Kelimeler

• Doctor rostering
• experimental design
• genetic algorithm
• weighted goal programming
• sensitivity analysis

Doktor nöbet cetveli çizelgeleme problemi için ağırlıklı hedef programlama tabanlı genetik algoritma

Öz

Sağlık hizmeti alanında, hastaneler için kesintisiz hizmet esastır. Bu nedenle, vardiyalı çalışma, talep kısıtları ve devlet düzenlemeleri gibi kısıtların karşılanabilmesi açısından oldukça önemli bir rol oynamaktadır. Doktor nöbet cetveli çizelgeleme problemi, problemin karmaşıklığı ve büyüklüğü sebebiyle NP-zor problem grubu içerisinde tanımlanmaktadır. Bu çizelgeleme probleminde, atamaların adilliğine ek olarak, hastane yönetim politikaları ve hükümet düzenlemeleri dâhil olmak üzere ilgili pek çok faktör hesaba katılmalıdır. Bu çalışma, hastane gereksinimlerini, doktorlar arasındaki adilliği karşılayabilen ve doktor tercihlerini göz önünde bulundurabilen bir nöbet cetveli çizelgeleme sistemi oluşturmayı amaçlamıştır. Ele alınan nöbet cetveli çizelgeleme probleminin çözümü için bir ağırlıklı hedef programlama-tabanlı genetik algoritma önerilmiştir. Önerilen model Kütahya Evliya Çelebi Eğitim ve Araştırma Hastanesi Dahiliye Departmanı ve İç Hastalıkları Departmanı’na uygulanmıştır. Gelecekte, oluşabilecek problem boyutları, şartları ve farklı tercih modelleri düşünülerek 15 farklı senaryo oluşturulmuştur. Bu senaryolarla önerilen algoritmanın farklı durumlarda da uygulanabilir olduğu gösterilmiştir. Önerilen algoritmanın parametreleri, bir deneysel tasarım yöntemiyle kalibre edilmiştir. Bu çalışma ile iki ana katkıda bulunulmuştur. Araştırmacılar için yeni kısıtlara sahip bir model önerilmiştir. Ek olarak, problemin çözümü için bir ağırlıklı hedef programlama-tabanlı genetik algoritma önerilerek gerçek-hayat problemine uygulanmıştır.

Anahtar Kelimeler

• Ağırlıklı hedef programlama
• deney tasarımı
• doktor nöbet cetveli çizelgeleme
• genetik algoritma
• duyarlılık analizi

Kaynakça

1. 1. Ernst, A. T., Jiang, H., Krishnamoorthy, M., Owens, B., & Sier, D., An annotated bibliography of personnel scheduling and rostering, Ann. Oper. Res., 127 (1–4), 21–144, 2004.
2. 2. Ernst, A. T., Jiang, H., Krishnamoorthy, M., & Sier, D., Staff scheduling and rostering: A review of applications, methods and models, Eur. J. Oper. Res., 153 (1), 3–27, 2004.
3. 3. Glover, F., & McMillan, C., The general employee scheduling problem: An integration of MS and AI, Computers and Operations Research, 13 (5), 563–773, 1986.
4. 4. Puente, J., Gomez, A., Fernandez, I., & Priore P., Medical doctor rostering problem in a hospital emergency department by means of genetic algorithms, Comput. Ind. Eng., 56, 1232-1242, 2009.
5. 5. OECD, Health at a Glance 2017: OECD Indicators, Ed: Marlène Mohier, Kate Lancaster and Andrew Esson, OECD Publishing, Paris, 2017.
6. 6. Chen, Z., De Causmaecker, P., & Dou, Y., A combined mixed integer programming and deep neural network–assisted heuristics algorithm for the nurse rostering problem, Appl. Soft Comput., 919-957, 2023.
7. 7. Chawasemerwa, T., Taifa, I. W., & Hartmann, D., Development of a doctor scheduling system: a constraint satisfaction and penalty minimisation scheduling model, International Journal of Research in Industrial Engineering, 7, 396-422, 2018.
8. 8. M’Hallah, R., & Alkhabbaz, A., Scheduling of nurses: A case study of a Kuwaiti health care unit, Oper. Res. Health Care, 2, 1-19, 2013.

9. 9. Wirnitzer, J., Heckmann, I., Meyer, A., & Nickel, S., Patient-based nurse rostering in home care, Oper. Res. Health Care, 8, 91-102, 2016.
10. 10. Wright, P. D., & Mahar, S., Centralized nurse scheduling to simultaneously improve schedule cost and nurse satisfaction, Omega, 41, 1042-1052, 2013.
11. 11. Böðvarsdottir, E. B., Smet, P., & Berghe, G. V., Behind-the-scenes weight tuning for applied nurse rostering, Oper. Res. Health Care, 26, 265-278, 2020.
12. 12. Samah, A. A., Yusoff, S. N. M., Zainudin, Z., & Abd Majid, H., A study on rostering on-call doctor using genetic algorithm with enhanced genetic operator, 2012 Third International Conference on Intelligent Systems Modelling and Simulation, Kota Kinabalu-Sabah Malaysia, 126-130, 8-10 February, 2012.
13. 13. Majid, H. A., Yusuf, L. M., Samah, A. A., Othman, M. S., & Ren, A. N. W. Application of genetic algorithm for doctor rostering at primary care clinics in Malaysia, 2017 6th ICT International Student Project Conference, Johor-Malaysia, 1-4, 2017, 23-24 May.
14. 14. Alharbi, A., & AlQahtani, K., An evolutionary ıntelligent algorithm approach for the doctor scheduling problem, International Journal on Advances in Software, 10, 180-190, 2017.
15. 15. Samah, A. A., Zainudin, Z., Majid, H. A., & Yusoff, S. N. M., A framework using an evolutionary algorithm for on-call doctor scheduling, Journal of Computer Science & Computational Mathematics, 2 (3), 9-16, 2012.
16. 16. Wu, T. H., Yeh, J. Y., & Lee, Y. M., A particle swarm optimization approach with refinement procedure for nurse rostering problem, Comput. Oper. Res., 54, 52-63, 2015.
17. 17. Hadwan, M., Ayob, M., Sabar, N. R., & Qu, R., A harmony search algorithm for nurse rostering problems, Inf. Sci., 233, 126-140, 2013.
18. 18. Awadallah, M. A., Khader, A. T., Al-Betar, M. A., & Bolaji, A. L., Global best harmony search with a new pitch adjustment designed for nurse rostering, Computer and Information Sciences, 25, 142-162, 2013.
19. 19. Tassopoulos, I. X., Solos, I. P., & Beligiannis, G. N., Α two-phase adaptive variable neighborhood approach for nurse rostering, Comput. Oper. Res., 60, 150-169, 2015.
20. 20. Zheng, Z., Liu, X., & Gong, X., A simple randomized variable neighbourhood search for nurse rostering, Comput. Ind. Eng., 110, 165-174, 2017.
21. 21. Cürebal A., Eren T., Competency-based security personnel scheduling during the covid-19 pandemic, Journal of the Faculty of Engineering and Architecture of Gazi University, 36 (3), 1483-1498, 2021.
22. 22. Akkuş İ., Yıldız E.A., Karaoğlan İ., Altıparmak, F., Mobile healthcare service planning in rural areas: A hybrid record to record travel algorithm, Journal of the Faculty of Engineering and Architecture of Gazi University, 39 (1), 593-606, 2024.
23. 23. Dengiz A.Ö., Atalay K., Altıparmak F., A goal programming approach for multi objective, multi-trips and time window routing problem in home health care service, Journal of the Faculty of Engineering and Architecture of Gazi University, 36 (4), 2167-2182, 2021.
24. 24. Otay İ., Intuitionistic fuzzy multi-expert & multi-criteria decision making methodology: An application in healthcare industry, Journal of the Faculty of Engineering and Architecture of Gazi University, 37 (2), 1047-1062, 2022.
25. 25. Saad, G., Harb, H., Abouaissa, A., Idoumghar, L., & Charara, N., A sensing-based patient classification framework for efficient patient-nurse scheduling. Sustainable Comput. Inf. Syst., 38, 100855, 2023.
26. 26. Yin, P. Y., Chao, C. C., & Chiang, Y. T., Multiobjective optimization for nurse scheduling, Advances in Swarm Intelligence: Second International Conference, International Conference on Swarm Intelligence, Chongqing-China, 66-73, 12-15 June, 2011.
27. 27. Maenhout, B., & Vanhoucke, M., An evolutionary approach for the nurse rerostering problem, Comput. Oper. Res., 38, 1400-1411, 2011.
28. 28. He, F., & Qu, R., A constraint programming based column generation approach to nurse rostering problems, Comput. Oper. Res., 39, 3331-3343, 2012.
29. 29. Lü, Z., & Hao, J. K., Adaptive neighborhood search for nurse rostering, Cent. Eur. Oper. Res. Central, 218, 865-876, 2012.
30. 30. Valouxis, C., Gogos, C., Goulas, G., Alefragis, P., & Housos, E., A systematic two phase approach for the nurse rostering problem, Eur. J. Oper. Res., 219, 425-433, 2012.
31. 31. Martin, S., Quelhadj, D., Smet, P., Berghe, G. V., & Özcan, E., Cooperative search for fair nurse rosters. Expert Syst. Appl., 40, 6674-6683, 2013.
32. 32. Maenhout, B., & Vanhoucke, M., An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems, Omega, 41, 485-499, 2013.
33. 33. Maenhout, B., & Vanhoucke, M., Reconstructing nurse schedules: Computational insights in the problem size parameters, Omega, 41, 903-918, 2013.
34. 34. Burke, E. K., & Curtois, T., New approaches to nurse rostering benchmark instances, Eur. J. Oper. Res., 237, 71-81, 2014.
35. 35. Wong, T. C., Xu, M., & Chin, K. S., A two-stage heuristic approach for nurse scheduling problem: A case study in an emergency department, Comput. Oper. Res., 51, 99-110, 2014.
36. 36. Baeklund, J., Nurse rostering at a Danish ward, Ann Oper. Res., 222, 107-123, 2014.
37. 37. Awadallah, M. A., Bolaji, A. L., & Al-Betar, M. A., A hybrid artificial bee colony for a nurse rostering problem, Appl. Soft Comput., 35, 726-739, 2015.
38. 38. Rahimian, E., Akartunalı, K., & Levine, J., A hybrid integer programming and variable neighbourhood search algorithm to solve nurse rostering problems, Eur. J. Oper. Res., 258, 411-423, 2016.
39. 39. Asta, S., Özcan, E., & Curtois, T., A tensor based hyper-heuristic for nurse rostering, Knowledge-Based Syst., 98, 185-199, 2016.
40. 40. Lin, W. D., & Chia, L., Combined forecasting of patient arrivals and doctor rostering simulation modelling for hospital emergency department, 2017 IEEE International conference on industrial engineering and engineering management, Singapore, 2391-2395, December, 2017.
41. 41. Lavygina, A., Welsh, K., & Crispin, A., Doctor rostering in compliance with the new UK junior doctor contract, The 11th Annual International Conference on Combinatorial Optimization and Applications, Shanghai-China, 394-408, 16-18 December, 2017.
42. 42. Rahimian, E., Akartunalı, K., & Levine, J., A hybrid integer and constraint programming approach to solve nurse rostering problems, Computers and Operations Research, 82, 83-94, 2017.
43. 43. Liu, Z., Liu, Z., Zhu, Z., Shen, Y., & Dong, J., Simulated annealing for a multi-level nurse rostering problem in hemodialysis service, Appl. Soft Comput., 64, 148-160, 2017.
44. 44. Gomes, R. A. M., Toffoloa, T. A. M., & Santos, H. G., Variable neighborhood search accelerated column generation for the nurse rostering problem, Electron. Notes Discrete Math., 58, 31-38, 2017.
45. 45. Landtsheer, R. D., Delannay, G., & Ponsard, C., Dealing with perceived fairness when planning doctor shifts in hospitals, Proceedings of the 7th International Conference on Operations Research and Enterprise Systems, Madeira-Portugal, 320-326, 24-26 January, 2018.
46. 46. Fügener, A., Pahr, A., & Brunner, J. O., Mid-term nurse rostering considering cross-training effects, Int. J. Prod. Econ., 196, 176-187, 2018.
47. 47. Aktunc, E. A., & Tekin, E., Nurse scheduling with shift preferences in a surgical suite using goal programming, Global Joint Conference on Industrial Engineering and Its Application (GJCIE 2018) Areas, Nevsehir-Turkey, 23-36, 21-22 July, 2018.
48. 48. Jaradat, G. M., Al-Badareen, A., Ayob, M., Al-Smadi, M., Al-Marashdeh, I., Ash-Shuqran, M., & Al-Odat, E., Hybrid elitist-ant system for nurse-rostering problem, J. King Saud Univ. Comput. Inf. Sci., 31, 378-384, 2019.
49. 49. Wickert, T. I., Smet, P., & Berghe, G. V., The nurse rerostering problem: Strategies for reconstructing disrupted schedules, Computers and Operations Research, 104, 319-337, 2019.
50. 50. Hadwan, M., Ayob, M., Al-Hagery, M., & Al-Tamimi, B. N., Climbing harmony search algorithm for nurse rostering problems, Recent Trends in Data Science and Soft Computing: 3rd International Conference of Reliable Information and Communication Technology, Kuala Lumpur-Malaysia, 74-83, 23-24 July, 2019.
51. 51. Turhan, A. M., & Bilgen, B., A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem, Comput. Ind. Eng., 145, 531-542, 2020.
52. 52. Böðvarsdottir, E. B., Smet, P., Berghe, G. V., & Stidsen, T. J. R., Achieving compromise solutions in nurse rostering by using automatically estimated acceptance thresholds, Eur. J. Oper. Res., 292, 980-995, 2020.
53. 53. Chen, P. S., & Zeng, Z. Y., Developing two heuristic algorithms with metaheuristic algorithms to improve solutions of optimization problems with soft and hard constraints: An application to nurse rostering problems, Appl. Soft Comput., 93, 336-358, 2020.
54. 54. Strandmark, P., Qu, Y., & Curtois, T., First-order linear programming in a column generation-based heuristic approach to the nurse rostering problem, Computers and Operations Research, 120, 945-959, 2020.
55. 55. Kheiri, A., Gretsista, A., Keedwell, E., Lulli, G., Epitropakis, M. G., & Burke, E. K., A hyper-heuristic approach based upon a hidden Markov model for the multi-stage nurse rostering problem, Computers and Operations Research, 130, 221-234, 2021.
56. 56. Hassani, M. R., & Behnamian, J., A scenario-based robust optimization with a pessimistic approach for nurse rostering problem, J. Comb. Optim., 41, 143-169, 2021.
57. 57. Guo, J., & Bard, J. F., A column generation-based algorithm for midterm nurse scheduling with specialized constraints, preference considerations, and overtime. Comput. Oper. Res., 138, 597-623, 2022.
58. 58. Turhan, A. M., & Bilgen, B., A mat-heuristic based solution approach for an extended nurse rostering problem with skills and units, Socio-Economic Planning Sciences, 82, 300-311, 2022.
59. 59. Otero-Caicedo, R., Casas, C. E. M., Jaimes, C. B., Garzón, C. F. G., Vergel, E. A. Y., & Valdés, J. C. Z. A preventive–reactive approach for nurse scheduling considering absenteeism and nurses’ preferences, Oper. Res. Health Care, 38, 100389, 2023.
60. 60. Alharbi, A., & AlQuahtani, K., A Genetic algorithm solution for the doctor scheduling problem, The Tenth International Conference on Advanced Engineering Computing and Applications in Sciences, Venice-Italy, 91-98, 9-13 October, 2016.
61. 61. Zhang, Z., Hao, Z., & Huang, H., Hybrid swarm-based optimization algorithm of ga & vns for nurse scheduling problem, Information Computing and Applications: Second International Conference, Qinhuangdao-China, 375-382, 2011, 28-31 October.
62. 62. Burke, E. K., Li, J., & Qu, R., A Pareto-based search methodology for multi-objective nurse scheduling, Ann Oper. Res., 196, 91-109, 2012.
63. 63. Fan, N., Mujahid, S., Zhang, J., Georgiev, P., Papajorgji, P., Steponavice, I., Neugard, B., & Pardalos, P. M., Nurse scheduling problem: an integer programming model with a practical application, Systems Analysis Tools For Better Health Care Delivery, Pardalos, P., Georgiev, P., Papajorgji, P., Neugaard, B. (Eds), Springer. New York, NY, 74, 65-98, 2013.
64. 64. Rasip, M. N., Basari, A. S. H., Ibrahim, N. K., & Hussin, B., Enhancement of nurse scheduling steps using particle swarm optimization, Advanced Computer and Communication Engineering Technology: Proceedings of the 1st International Conference on Communication and Computer Engineering, Kanyakumari-India, 459-469, 2-3 November, 2015.
65. 65. Legraina, A., Omer, J., & Rosat, S., A rotation-based branch-and-price approach for the nurse scheduling problem, Math. Program. Comput., 12, 417-450, 2020.
66. 66. Legraina, A., Omer, J., & Rosat, S., An online stochastic algorithm for a dynamic nurse scheduling problem, Eur. J. Oper. Res., 285, 196-210, 2020.
67. 67. Sarkar, P., Chaki, R., & Cortesi, A., A patient-centric nurse scheduling algorithm. SN Comput. Sci., 3, 1-16, 2022.
68. 68. Chen, Z., Dou, Y., & De Causmaecker, P., Neural networked-assisted method for the nurse rostering problem, Comput. Ind. Eng., 171, 430-444, 2022.
69. 69. Michael, C., Jeffery, C., & David, C., Nurse preference rostering using agents and iterated local search, Annals of Operational Research, 226, 443-461, 2015.
70. 70. Shukla, M., Li, X., & Sun, Y., Time-interval based coverage constraint for nurse scheduling problems, 2015 Industrial and Systems Engineering Research Conference, Nashville-Tennessee, 1234-1242, 30 May – 2 June, 2015.
71. 71. Kumar, M., Husian, M., Upreti, N., & Gupta, D., Genetic algorithm: review and application, International Journal of Information Technology and Knowledge Management, 2, 451-454, 2010.
72. 72. Min, L., & Cheng, W., A genetic algorithm for minimizing the makespan in the case of scheduling identical paralel machines, Artificial Intelligence in Engineering, 13, 399-403, 1999.
73. 73. Huanga, M., Ma, Y., Wan, J. & Chen, X., A sensor-software based on a genetic algorithm-based neural fuzzy system for modeling and simulating a wastewater treatment process, Appl. Soft Comput., 27, 1-10, 2015.
74. 74. Kechagias, J.D., Aslani, K. E., Fountas, N. A., Vaxevanidis, N. M., & Manolakos, D. E., A comparative investigation of Taguchi and full factorial design for machinability prediction in turning of a titanium alloy, Measurement, 151, 1-11, 2020.
75. 75. Basheer, P. A. M., Montgomery, F. R., & Long, A. E., Factorial experimental design for concrete durability research, Proc. Inst. Civ. Eng. Struct. Build., 104, 449 – 462, 1994.
76. 76. Antony, J., "Some key things industrial engineers should know about experimental design", Logist. Inf. Manage., 11, 386 – 392, 1995.
77. 77. Eşme, U., Application of Taguchi method for the optimization of resistance spot welding process, Arabian J. Sci. Eng., 34, 519-528, 2009.
78. 78. Hosny, M., & Al Turiki, N., A genetic-based nurse rostering tool: A Riyadh hospital case, International Conference on Genetic and Evolutionary Methods (GEM), Las Vegas-Nevada, 1-7, 22-25 July,2013.
79. 79. Rae, C. S. W. E., A study of evolutionary perturbative hyper-heuristics for the nurse rostering problem, Doctoral Thesis, University of Kwazulu-Natal, Master of Science, Kwazulu-Natal, 2017.
80. 80. Lin, C. C., Kang, J. R., Chiang, D. J., & Chen, C. L., Nurse scheduling with joint normalized shift and day-off preference satisfaction using a genetic algorithm with immigrant scheme. Int. J. of Distrib. Sens. Netw., 11, 1-10, 2015.
81. 81. Andriansyah, Alfadilla, N., Sentia, P. D., & Asmadi, D., Optimization of nurse scheduling problem using genetic algorithm: a case study, IOP Conference Series: Materials Science and Engineering, 536, International Conference on Science and Innovated Engineering, Aceh-Indonesia, 131-137, 28 May – 2 June, 2019.
82. 82. Abadi, M. Q. H., Rahmati, S., Sharifi, A., & Ahmadi, M., HSSAGA: Designation and scheduling of nurses for taking care of COVID-19 patients using novel method of hybrid salp swarm algorithm and genetic algorithm, Appl, Soft Comput., 108, 449-459, 2021.
83. 83. Rurifandho, A., Renaldi, F., & Santikarama, I., Doctors dynamic scheduling for outpatient, inpatient, and surgery using genetic algorithm, International Conference on Science and Technology, Batam-Indonesia, 1-8, 3-4 February, 2022.
84. 84. Kim, T. K., Understanding one-way ANOVA using conceptual figures, Korean Journal of Anesthesiology, 70 (1), 22-26, 2017.
85. 85. Cramer, A. O. J., van Ravenzwaaij, D., Matzke, D., Steingroever, H., Wetzels, R., Grasman, R. P., Waldorp, L. J., & Wagenmakers, E. J., Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies, Psychonomic Bulletin & Review, 23, 640-647, 2016.
86. 86. Perazzi, A., Gomiero, C., Corain, L., Iacopetti, I., Grisan, E., Lombardo, M., Lombardo, G., Salvalaio, G., Contin, R., Patruno, M., Martinello, T., & Peruffo, A., An assay system to evaluate riboflavin/UV-A corneal phototherapy efficacy in a porcine corneal organ culture model, Animals, 10 (4), 730-746, 2020.
87. 87. Millman, J., & Glass, J. V., Rules of thumb for writing the ANOVA table, Journal of Educational Measurement, 4 (2), 41-51, 1967.
88. 88. Lee, J. Y., A genetic algorithm for a two-machine flowshop with a limited waiting time constraint and sequence-dependent setup times, Math. Probl. Eng., 2020, 1-13, 2020.
89. 89. Gerostathopoulos, I., Prehofer, C., & Bures, T., Adapting a system with noisy outputs with statistical guarantees, Proceedings of the 13th International Conference on Software Engineering for Adaptive and Self-Managing Systems, Gothenburg-Sweden, 58-68, 28-29 May, 2018.
90. 90. Banerjee, S., Poria, S., Sutradhar, G., & Sahoo, P., Wear performance of Mg-WC metal matrix nanocomposites using taguchi methodology, Mater. Today Proc., 19, 177-18, 2019.
91. 91. Trucano, T. G., Swiler, L. P., Igusa, T., Oberkampf, W. L., & Pilch, M., Calibration, validation, and sensitivity analysis: What's what, Reliab. Eng. Syst. Saf., 91, 1331-1357, 2006.
92. 92. Chitnis, N., Hyman, J. M., & Cushing, J. M., Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70, 1272-1296, 2008.
93. 93. Sutanto, E. M., Sampson, J. S., & Mulyono, F., Organizational Justice work environment and motivation, International Journal of Business and Society, 19, 313-322, 2018.
94. 94. Yalçın, A. Doktor nöbet çizelgeleme problemi için ağırlıklı hedef programlama tabanlı genetik algoritma, Yüksek Lisans Tezi, Kütahya Dumlupınar Üniversitesi, Fen Bilimleri Enstitüsü, Kütahya, 2023.