Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım

Gülveren Tabansız Göç; Tuğçe Akyüz; Gıyasettin Özcan; Fatih Çavdur

doi:10.17341/gazimmfd.1394465

Araştırma Makalesi

A goal programming-based approach for multi-period security services scheduling

Yıl 2025, Cilt: 40 Sayı: 1, 343 - 354

Gülveren Tabansız Göç Tuğçe Akyüz Gıyasettin Özcan Fatih Çavdur

https://doi.org/10.17341/gazimmfd.1394465

Öz

A shift system implementation is usually required in scheduling security services which also causes important managerial challenges due to the necessity of the 7 days-24 hours continuous nature of the corresponding services. In the construction of a shift schedule, it is also necessary to consider some criteria about the humanitarian issues, such as the equality of not only the number workdays but also the number of shifts for each person as well as the ones imposed by the corresponding labor law legislation usually about the maximum number of workdays and shift transitions. Construction of an ideal schedule for security services under the aforementioned constraints is thus a challenging task, especially for the large-sized real-life problems due to the increases in both the number of people and the length of the planning horizon. An idea to deal with the curse of dimensionality in the shift-scheduling problem is dividing a planning horizon into shorter periods, which might reduce problem size significantly; however, it also requires a flexible approach for relating the solutions of the consecutive periods. Such a flexible approach for relating the corresponding schedules of the consecutive periods is proposed in this study where we propose an integer-goal programming formulation that efficiently handles the issue. We also illustrate its performance on a real-life problem involving the construction of the monthly schedules in a year for a security team of a hundred people. It is noted from the computational experiments that the proposed formulation is able to construct the corresponding monthly schedules in a few minutes, implying its potential for use real-life shift scheduling problems.

Anahtar Kelimeler

Security services, multi-period personnel scheduling, workforce planning, integer programming, goal programming

Kaynakça

1. Morton D. P., Popova E., A Bayesian stochastic programming approach to an employee scheduling problem, Iie Transactions, 36 (2), 155-167, 2004.
2. Burke E. K., Li J., Qu R., 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, 2010.
3. Alsheddy A, Tsang E. P., Empowerment scheduling for a field workforce, Journal of Scheduling, 14, 639-654, 2011.
4. Li J., Burke E. K., Curtois, T., Petrovic, S., Qu, R., The falling tide algorithm: a new multi-objective approach for complex workforce scheduling, Omega, 40 (3), 283-293, 2012.
5. Harper P. R., Powell N. H., Williams J. E., Modelling the size and skill-mix of hospital nursing teams, Journal of the Operational Research Society, 61, 768-779, 2010.
6. Lezaun M., Perez G., Sainz de la Maza E., Staff rostering for the station personnel of a railway company, Journal of the Operational Research Society, 61 (7), 1104-1111, 2010.
7. Brucker P., Burke E. K., Curtois T., Qu R., Vanden Berghe G., A shift sequence based approach for nurse scheduling and a new benchmark dataset, Journal of Heuristics, 16, 559-573, 2010.
8. Stolletz R., Operational workforce planning for check-in counters at airports, Transportation Research Part E: Logistics and Transportation Review, 46 (3), 414-425, 2010.
9. Lu Z., Hao J. K., Adaptive neighborhood search for nurse rostering, European Journal of Operational Research, 218 (3), 865-876, 2012.
10. Avramidis A. N., Chan W., Gendreau M., L’ecuyer P., Pisacane, O., Optimizing daily agent scheduling in a multiskill call center, European Journal of Operational Research, 200 (3), 822-832, 2010.
11. Burke E. K., Curtois T., Qu R., Vanden Berghe G., A scatter search methodology for the nurse rostering problem, Journal of the Operational Research Society, 61 (11), 1667-1679, 2010.
12. Heimerl C., Kolisch R., Scheduling and staffing multiple projects with a multi-skilled workforce, OR spectrum, 32, 343-368, 2010.
13. Hojati M., Near-optimal solution to an employee assignment problem with seniority, Annals of Operations Research, 181, 539-557, 2010.
14. Krishnamoorthy M., Ernst A. T., Baatar D., Algorithms for large scale shift minimisation personnel task scheduling problems, European Journal of Operational Research, 219 (1), 34-48, 2012.
15. Özder E. H., Özcan E., Eren T, Staff task-based shift scheduling solution with an ANP and goal programming method in a natural gas combined cycle power plant, Mathematics, 7 (2), 192, 2019.
16. 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.
17. Gunther M., Nissen V., Particle swarm optimization and an agent-based algorithm for a problem of staff scheduling, In Applications of Evolutionary Computation: EvoApplications 2010: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoMUSART, and EvoTRANSLOG, Istanbul- Turkey, 451-461, 7-9 April, 2010.
18. Nissen V., Gunther M., Automatic generation of optimised working time models in personnel planning, In International Conference on Swarm Intelligence, Brussels- Belgium, 384-391, 8-10 September, 2010.
19. Awadallah M. A., Khader A. T., Al-Betar M. A., Bolaji A. L. A., Nurse rostering using modified harmony search algorithm, In International Conference on Swarm, Evolutionary, Visakhapatnam- Andhra Pradesh- India, 27-37, 19-21 December, 2011.
20. Valouxis C., Gogos C., Goulas G., Alefragis P., Housos E., A systematic two phase approach for the nurse rostering problem, European Journal of Operational Research, 219 (2), 425-433, 2012.
21. Van der Veen E., Veltman B., Rostering from staffing levels: a branch-and-price approach, In International Conference on Operational Research Applied to Health Services (ORAHS), 1-10, University of Leuven, July, 2009.
22. Bai R., Burke E. K., Kendall G., Li J., McCollum B., A hybrid evolutionary approach to the nurse rostering problem, IEEE Transactions on Evolutionary Computation, 14 (4), 580-590, 2010.
23. Ronnberg E., Larsson T., Automating the self-scheduling process of nurses in Swedish healthcare: a pilot study, Health Care Management Science, 13, 35-53, 2010.
24. He F., Qu R., A constraint programming based column generation approach to nurse rostering problems, Computers & Operations Research, 39 (12), 3331-3343, 2012.
25. Aksüt G., Alakaş H. M., Eren T., Model proposal for physically ergonomic risky personnel scheduling problem: An application in textile industry for female employees, Journal of the Faculty of Engineering and Architecture of Gazi University, 38 (1), 245-256, 2023.
26. Lin T. C., Lin B. M., Optimal Fair-Workload Scheduling: A Case Study at Glorytek, Mathematics, 11 (19), 4051, 2023.
27. Wright P. D., Bretthauer K. M., Strategies for addressing the nursing shortage: Coordinated decision making and workforce flexibility, Decision Sciences, 41 (2), 373-401, 2010.
28. Burke E. K., Curtois T., Van Draat L. F., Van Ommeren J. K., Post G., Progress control in iterated local search for nurse rostering, Journal of the Operational Research Society, 62, 360-367, 2011.
29. Mohammadian M., Babaei M., Amin Jarrahi M., Anjomrouz E., Scheduling nurse shifts using goal programming based on nurse preferences: a case study in an emergency department, International Journal of Engineering, 32 (7), 954-963, 2019.
30. Rerkjirattikal P., Huynh V. N., Olapiriyakul S., Supnithi T., A goal programming approach to nurse scheduling with individual preference satisfaction, Mathematical Problems in Engineering, 2020, 1-11, 2020.
31. Knust S., Schumacher E., Shift scheduling for tank trucks, Omega, 39 (5), 513-521, 2011.
32. Shuib A., Kamarudin F.I., Solving shift scheduling problem with days-off preference for power station workers using binary integer goal programming model, Annals of Operations Research, 272 (1-2), 355-372, 2019.
33. Perreault‐Lafleur C., Carvalho M., Desaulniers G., A stochastic integer programming approach to reserve staff scheduling with preferences, International Transactions in Operational Research, 2023.
34. Topaloğlu Ş., A multi-objective programming model for scheduling emergency medicine residents, Computers & Industrial Engineering, 51 (3), 375-388, 2006.
35. Özcan E., Danışan T., Yumuşak R., Gür Ş., Eren T., Goal programming approach for the radiology technician scheduling problem, Sigma Journal of Engineering and Natural Sciences, 37 (4), 1410-1420, 2019.
36. Shirneshan H., Sadegheih A., Hosseini-Nasab H., Lotfi, M. M., A two-stage stochastic programming approach for care providers shift scheduling problems, Journal of Applied Research on Industrial Engineering, 2022.
37. Gençer M. A., Eren T., Alakaş H. M., Train maintenance personnel shift scheduling: case study, Flexible Services and Manufacturing Journal, 1-34, 2023.
38. Kaçmaz Ö., Alakaş H. M., Eren T., Shift scheduling with the goal programming method: a case study in the glass industry, Mathematics, 7 (6), 561, 2019.
39. Nasir D. S. M., Sabri N. D. A., Shafii N. H., Hasan, S. A., Shift Scheduling with the Goal Programming Approach in Fast-Food Restaurant: McDonald’s in Kelantan, Journal of Computing Research and Innovation, 7 (1), 104-112, 2022.
40. Ernst A.T., Jiang H., Krishnamoorthy M., Sier D., Staff scheduling and rostering: a review of applications, methods and models, European Journal of Operational Research, 153 (1), 3-27, 2004.
41. Van den Bergh J., Belien J., De Bruecker P., Demeulemeester E., De Boeck L., Personnel scheduling: A literature review, European Journal of Operational Research, 226 (3), 367-385, 2013.
42. Smet P., Ernst A. T., Berghe G. V., Heuristic decomposition approaches for an integrated task scheduling and personnel rostering problem, Computers & Operations Research, 76, 60-72, 2016.
43. Warner M., Nurse staffing, scheduling, and reallocation in the hospital, Hospital & Health Services Administration, 21 (3), 77–90, 1976.
44. Burke E.K., De Causmaecker P., Petrovic S., Vanden Berghe G., Fitness evaluation for nurse scheduling problems, Proceedings of the Congress on Evolutionary Computation, Seoul- Korea, 1139–1146, May, 2001.
45. Ikegami A., Niwa A., A subproblem-centric model and approach to the nurse scheduling problem, Mathematical Programming, 97, 517–541, 2003.
46. Moz M., Pato M.V., A genetic algorithm approach to a nurse rerostering problem, Computers & Operations Research, 34 (3), 667–691, 2007.
47. Brunner J. O., Bard J. F., Kolisch R., Flexible shift scheduling of physicians, Health care management science, 12, 285-305, 2009.
48. Glass C.A., Knight R.A., The nurse rostering problem: a critical appraisal of the problem structure, European Journal of Operational Research, 202 (2), 379–389, 2010.
49. Zanda S., Zuddas P., Seatzu C., 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, 126, 337-347, 2018.
50. Guo J., Bard J. F., A column generation-based algorithm for midterm nurse scheduling with specialized constraints, preference considerations, and overtime, Computers & Operations Research, 138, 105597, 2022.
51. Smet P., Salassa F., Vanden Berghe G., Local and global constraint consistency in personnel rostering, International Transactions in Operational Research, 24 (5), 1099-1117, 2017.
52. Salassa F., Vanden Berghe G., Kjenstad D., Burke E. K., McCollum B., A stepping horizon view on nurse rostering, In International conference on the practice and theory of automated timetabling, 161-173, August, 2012.

Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım

Yıl 2025, Cilt: 40 Sayı: 1, 343 - 354

Gülveren Tabansız Göç Tuğçe Akyüz Gıyasettin Özcan Fatih Çavdur

https://doi.org/10.17341/gazimmfd.1394465

Öz

7 gün 24 saat kesintisiz hizmet verilme gereksinimi nedeniyle, güvenlik hizmetlerinin çizelgelenmesi genellikle vardiya sisteminin uygulanmasını gerektirmekte ve önemli yönetimsel zorluklar doğurabilmektedir. Vardiya çizelgesi oluşturulurken, çalışanların sadece çalışma günleri sayılarının değil aynı zamanda vardiya sayılarının eşitliği, ardışık olarak çalışılabilecek maksimum gün sayısı ve vardiya geçişleriyle ilgili iş kanununda belirtilen bazı insani unsurların da dikkate alınması gerekmektedir. Söz konusu kısıtlar altında, güvenlik hizmetleri için ideal bir vardiya çizelgesi oluşturmak, özellikle insan sayısının ve planlama döneminin uzunluğundaki artışlarla büyük ölçekli gerçek hayat problemleri için daha da zor bir problem haline gelmektedir. Planlama döneminin daha kısa periyotlara bölünmesiyle problem boyutlarının önemli ölçüde azaltılması söz konusu zorluğun aşılmasında yardımcı olabilir. Ancak bunun yapılması, ardışık dönemlerin çizelgelerini ilişkilendirmek için esnek bir yaklaşım gerekmektedir. Bu çalışmada, ardışık dönemlerin çizelgelerini esnek bir şekilde ilişkilendirmek için bir yaklaşım sunulmakta ve bunu etkin bir şekilde ele alan bir tamsayı-hedef programlama formülasyonu önerilmektedir. Ayrıca, önerilen yaklaşımın performansı, yüz kişilik bir güvenlik ekibinin bir yıl boyunca aylık çizelgelerinin oluşturulmasını içeren gerçekçi bir problem üzerinde gösterilmiştir. Sonuçlar incelendiğinde, aylık vardiya çizelgelerinin birkaç dakika içinde oluşturabildiği gözlemlenmiş ve önerilen yaklaşımın iş mevzuatına uygun, adaletli ve verimli bir şekilde gerçek hayat vardiya çizelgeleme problemlerinde kullanım potansiyeli olabileceği düşünülmektedir.

Anahtar Kelimeler

Güvenlik hizmetleri, çok dönemli personel çizelgeleme, işgücü planlaması, tamsayılı programlama, hedef programlama

Kaynakça

1. Morton D. P., Popova E., A Bayesian stochastic programming approach to an employee scheduling problem, Iie Transactions, 36 (2), 155-167, 2004.
2. Burke E. K., Li J., Qu R., 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, 2010.
3. Alsheddy A, Tsang E. P., Empowerment scheduling for a field workforce, Journal of Scheduling, 14, 639-654, 2011.
4. Li J., Burke E. K., Curtois, T., Petrovic, S., Qu, R., The falling tide algorithm: a new multi-objective approach for complex workforce scheduling, Omega, 40 (3), 283-293, 2012.
5. Harper P. R., Powell N. H., Williams J. E., Modelling the size and skill-mix of hospital nursing teams, Journal of the Operational Research Society, 61, 768-779, 2010.
6. Lezaun M., Perez G., Sainz de la Maza E., Staff rostering for the station personnel of a railway company, Journal of the Operational Research Society, 61 (7), 1104-1111, 2010.
7. Brucker P., Burke E. K., Curtois T., Qu R., Vanden Berghe G., A shift sequence based approach for nurse scheduling and a new benchmark dataset, Journal of Heuristics, 16, 559-573, 2010.
8. Stolletz R., Operational workforce planning for check-in counters at airports, Transportation Research Part E: Logistics and Transportation Review, 46 (3), 414-425, 2010.
9. Lu Z., Hao J. K., Adaptive neighborhood search for nurse rostering, European Journal of Operational Research, 218 (3), 865-876, 2012.
10. Avramidis A. N., Chan W., Gendreau M., L’ecuyer P., Pisacane, O., Optimizing daily agent scheduling in a multiskill call center, European Journal of Operational Research, 200 (3), 822-832, 2010.
11. Burke E. K., Curtois T., Qu R., Vanden Berghe G., A scatter search methodology for the nurse rostering problem, Journal of the Operational Research Society, 61 (11), 1667-1679, 2010.
12. Heimerl C., Kolisch R., Scheduling and staffing multiple projects with a multi-skilled workforce, OR spectrum, 32, 343-368, 2010.
13. Hojati M., Near-optimal solution to an employee assignment problem with seniority, Annals of Operations Research, 181, 539-557, 2010.
14. Krishnamoorthy M., Ernst A. T., Baatar D., Algorithms for large scale shift minimisation personnel task scheduling problems, European Journal of Operational Research, 219 (1), 34-48, 2012.
15. Özder E. H., Özcan E., Eren T, Staff task-based shift scheduling solution with an ANP and goal programming method in a natural gas combined cycle power plant, Mathematics, 7 (2), 192, 2019.
16. 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.
17. Gunther M., Nissen V., Particle swarm optimization and an agent-based algorithm for a problem of staff scheduling, In Applications of Evolutionary Computation: EvoApplications 2010: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoMUSART, and EvoTRANSLOG, Istanbul- Turkey, 451-461, 7-9 April, 2010.
18. Nissen V., Gunther M., Automatic generation of optimised working time models in personnel planning, In International Conference on Swarm Intelligence, Brussels- Belgium, 384-391, 8-10 September, 2010.
19. Awadallah M. A., Khader A. T., Al-Betar M. A., Bolaji A. L. A., Nurse rostering using modified harmony search algorithm, In International Conference on Swarm, Evolutionary, Visakhapatnam- Andhra Pradesh- India, 27-37, 19-21 December, 2011.
20. Valouxis C., Gogos C., Goulas G., Alefragis P., Housos E., A systematic two phase approach for the nurse rostering problem, European Journal of Operational Research, 219 (2), 425-433, 2012.
21. Van der Veen E., Veltman B., Rostering from staffing levels: a branch-and-price approach, In International Conference on Operational Research Applied to Health Services (ORAHS), 1-10, University of Leuven, July, 2009.
22. Bai R., Burke E. K., Kendall G., Li J., McCollum B., A hybrid evolutionary approach to the nurse rostering problem, IEEE Transactions on Evolutionary Computation, 14 (4), 580-590, 2010.
23. Ronnberg E., Larsson T., Automating the self-scheduling process of nurses in Swedish healthcare: a pilot study, Health Care Management Science, 13, 35-53, 2010.
24. He F., Qu R., A constraint programming based column generation approach to nurse rostering problems, Computers & Operations Research, 39 (12), 3331-3343, 2012.
25. Aksüt G., Alakaş H. M., Eren T., Model proposal for physically ergonomic risky personnel scheduling problem: An application in textile industry for female employees, Journal of the Faculty of Engineering and Architecture of Gazi University, 38 (1), 245-256, 2023.
26. Lin T. C., Lin B. M., Optimal Fair-Workload Scheduling: A Case Study at Glorytek, Mathematics, 11 (19), 4051, 2023.
27. Wright P. D., Bretthauer K. M., Strategies for addressing the nursing shortage: Coordinated decision making and workforce flexibility, Decision Sciences, 41 (2), 373-401, 2010.
28. Burke E. K., Curtois T., Van Draat L. F., Van Ommeren J. K., Post G., Progress control in iterated local search for nurse rostering, Journal of the Operational Research Society, 62, 360-367, 2011.
29. Mohammadian M., Babaei M., Amin Jarrahi M., Anjomrouz E., Scheduling nurse shifts using goal programming based on nurse preferences: a case study in an emergency department, International Journal of Engineering, 32 (7), 954-963, 2019.
30. Rerkjirattikal P., Huynh V. N., Olapiriyakul S., Supnithi T., A goal programming approach to nurse scheduling with individual preference satisfaction, Mathematical Problems in Engineering, 2020, 1-11, 2020.
31. Knust S., Schumacher E., Shift scheduling for tank trucks, Omega, 39 (5), 513-521, 2011.
32. Shuib A., Kamarudin F.I., Solving shift scheduling problem with days-off preference for power station workers using binary integer goal programming model, Annals of Operations Research, 272 (1-2), 355-372, 2019.
33. Perreault‐Lafleur C., Carvalho M., Desaulniers G., A stochastic integer programming approach to reserve staff scheduling with preferences, International Transactions in Operational Research, 2023.
34. Topaloğlu Ş., A multi-objective programming model for scheduling emergency medicine residents, Computers & Industrial Engineering, 51 (3), 375-388, 2006.
35. Özcan E., Danışan T., Yumuşak R., Gür Ş., Eren T., Goal programming approach for the radiology technician scheduling problem, Sigma Journal of Engineering and Natural Sciences, 37 (4), 1410-1420, 2019.
36. Shirneshan H., Sadegheih A., Hosseini-Nasab H., Lotfi, M. M., A two-stage stochastic programming approach for care providers shift scheduling problems, Journal of Applied Research on Industrial Engineering, 2022.
37. Gençer M. A., Eren T., Alakaş H. M., Train maintenance personnel shift scheduling: case study, Flexible Services and Manufacturing Journal, 1-34, 2023.
38. Kaçmaz Ö., Alakaş H. M., Eren T., Shift scheduling with the goal programming method: a case study in the glass industry, Mathematics, 7 (6), 561, 2019.
39. Nasir D. S. M., Sabri N. D. A., Shafii N. H., Hasan, S. A., Shift Scheduling with the Goal Programming Approach in Fast-Food Restaurant: McDonald’s in Kelantan, Journal of Computing Research and Innovation, 7 (1), 104-112, 2022.
40. Ernst A.T., Jiang H., Krishnamoorthy M., Sier D., Staff scheduling and rostering: a review of applications, methods and models, European Journal of Operational Research, 153 (1), 3-27, 2004.
41. Van den Bergh J., Belien J., De Bruecker P., Demeulemeester E., De Boeck L., Personnel scheduling: A literature review, European Journal of Operational Research, 226 (3), 367-385, 2013.
42. Smet P., Ernst A. T., Berghe G. V., Heuristic decomposition approaches for an integrated task scheduling and personnel rostering problem, Computers & Operations Research, 76, 60-72, 2016.
43. Warner M., Nurse staffing, scheduling, and reallocation in the hospital, Hospital & Health Services Administration, 21 (3), 77–90, 1976.
44. Burke E.K., De Causmaecker P., Petrovic S., Vanden Berghe G., Fitness evaluation for nurse scheduling problems, Proceedings of the Congress on Evolutionary Computation, Seoul- Korea, 1139–1146, May, 2001.
45. Ikegami A., Niwa A., A subproblem-centric model and approach to the nurse scheduling problem, Mathematical Programming, 97, 517–541, 2003.
46. Moz M., Pato M.V., A genetic algorithm approach to a nurse rerostering problem, Computers & Operations Research, 34 (3), 667–691, 2007.
47. Brunner J. O., Bard J. F., Kolisch R., Flexible shift scheduling of physicians, Health care management science, 12, 285-305, 2009.
48. Glass C.A., Knight R.A., The nurse rostering problem: a critical appraisal of the problem structure, European Journal of Operational Research, 202 (2), 379–389, 2010.
49. Zanda S., Zuddas P., Seatzu C., 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, 126, 337-347, 2018.
50. Guo J., Bard J. F., A column generation-based algorithm for midterm nurse scheduling with specialized constraints, preference considerations, and overtime, Computers & Operations Research, 138, 105597, 2022.
51. Smet P., Salassa F., Vanden Berghe G., Local and global constraint consistency in personnel rostering, International Transactions in Operational Research, 24 (5), 1099-1117, 2017.
52. Salassa F., Vanden Berghe G., Kjenstad D., Burke E. K., McCollum B., A stepping horizon view on nurse rostering, In International conference on the practice and theory of automated timetabling, 161-173, August, 2012.

Toplam 52 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	Türkçe
Konular	Endüstri Mühendisliği
Bölüm	Makaleler
Yazarlar	Gülveren Tabansız Göç 0000-0003-4204-1364 Tuğçe Akyüz 0009-0001-1674-3349 Gıyasettin Özcan 0000-0002-1166-5919 Fatih Çavdur 0000-0001-8054-5606
Erken Görünüm Tarihi	20 Mayıs 2024
Yayımlanma Tarihi
Gönderilme Tarihi	22 Kasım 2023
Kabul Tarihi	6 Nisan 2024
Yayımlandığı Sayı	Yıl 2025 Cilt: 40 Sayı: 1

Kaynak Göster

APA	Tabansız Göç, G., Akyüz, T., Özcan, G., Çavdur, F. (2024). Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 40(1), 343-354. https://doi.org/10.17341/gazimmfd.1394465
AMA	Tabansız Göç G, Akyüz T, Özcan G, Çavdur F. Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım. GUMMFD. Mayıs 2024;40(1):343-354. doi:10.17341/gazimmfd.1394465
Chicago	Tabansız Göç, Gülveren, Tuğçe Akyüz, Gıyasettin Özcan, ve Fatih Çavdur. “Çok dönemli güvenlik Hizmetleri çizelgelemesi için Hedef Programlama Tabanlı Bir yaklaşım”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40, sy. 1 (Mayıs 2024): 343-54. https://doi.org/10.17341/gazimmfd.1394465.
EndNote	Tabansız Göç G, Akyüz T, Özcan G, Çavdur F (01 Mayıs 2024) Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40 1 343–354.
IEEE	G. Tabansız Göç, T. Akyüz, G. Özcan, ve F. Çavdur, “Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım”, GUMMFD, c. 40, sy. 1, ss. 343–354, 2024, doi: 10.17341/gazimmfd.1394465.
ISNAD	Tabansız Göç, Gülveren vd. “Çok dönemli güvenlik Hizmetleri çizelgelemesi için Hedef Programlama Tabanlı Bir yaklaşım”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 40/1 (Mayıs 2024), 343-354. https://doi.org/10.17341/gazimmfd.1394465.
JAMA	Tabansız Göç G, Akyüz T, Özcan G, Çavdur F. Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım. GUMMFD. 2024;40:343–354.
MLA	Tabansız Göç, Gülveren vd. “Çok dönemli güvenlik Hizmetleri çizelgelemesi için Hedef Programlama Tabanlı Bir yaklaşım”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 40, sy. 1, 2024, ss. 343-54, doi:10.17341/gazimmfd.1394465.
Vancouver	Tabansız Göç G, Akyüz T, Özcan G, Çavdur F. Çok dönemli güvenlik hizmetleri çizelgelemesi için hedef programlama tabanlı bir yaklaşım. GUMMFD. 2024;40(1):343-54.

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