EVDE SAĞLIK HİZMETLERİNDE ARAÇ ROTALAMA İLE GÜZERGAHLARIN BELİRLENMESİ: DEVLET HASTANESİNDE BİR UYGULAMA

Öz

Ülke nüfusumuzun giderek yaşlanması ve sağlık alanındaki gelişmelerle birlikte evde sağlık hizmetleri ülkenin her yerinde faaliyet göstermektedir. Evde sağlık bakımı yönlendirme ve zamanlama problemi, aynı coğrafi bölgede yaşayan ve evde tedavi edilmesi gereken hastaların bakımını gerçekleştirmektedir. Personeller ekipler halinde evde bakım hizmeti vermek üzere hastaların adreslerine giderek gerekli bakım ve tedavi hizmetini sunmaktadırlar. Bu çalışmada evde bakım ve tedavi hizmeti yapan araçların rotalaması yapılmıştır. Çalışmada bakım ve tedavi hizmetleri için 155 hastası bulunan bir il ele alınmıştır. Bu ilin 94 hasta bulunan bir bölgesinde 4 araçlı rotalama problemi için matematiksel programlama modeli kurulmuştur. Model sonucunda hizmet için hangi aracın hangi sırayla, hangi hastaları ziyaret edeceği belirlenmiştir. Uygulama sonucunda araçların optimal rotalaması belirlendiği için mevcut duruma göre daha az mesafe kat etmiş ve dolayısıyla maliyet azalmıştır.

Anahtar Kelimeler

• Evde sağlık hizmetleri,Matematiksel programlama modeli,Araç rotalama problemi

DETERMINING ROUTES BY VEHICLE ROTATION AT HOME HEALTHCARE SERVICES: A CASE STUDY IN STATE HOSPITAL

Öz

With the increasing aging of our country's population and improvements in the field of health, the home healthcare service operates all over the country. Home health care orientation and scheduling problem is taking care of patients who live in the same geographical area and need to be treated at home. Personnel provide care and treatment services by going to the addresses of the patients to provide home care services in teams. In this study, the tools of home care and treatment services were routed. In the study, a province with 155 patients for care and treatment services was dealt with. A mathematical programming model for the 4-vehicle locus problem was established in a region with 94 patients in this province. As a result of the model, it was determined which tool to visit and which patients to visit for the service. As a result of the application, the optimal route of the vehicles has been determined, so that it takes less distance than the current situation and therefore the cost is reduced.

Anahtar Kelimeler

• Home health care,mathematical programming model,vehicle locating problem

Kaynakça

1. Akjiratikarl, C., Yenradee, P., & Drake, P. R. (2007). PSO-based algorithm for home care worker scheduling in the UK. Computers & Industrial Engineering, 53(4), 559-583.
2. Allaoua, H., Borne, S., Létocart, L., & Calvo, R. W. (2013). A matheuristic approach for solving a home health care problem. Electronic Notes in Discrete Mathematics, 41, 471-478.
3. Altunay, H.& Eren, T. (2016). Ders Programı Çizelgeleme Problemi için 0-1 Tamsayılı Programlama Modeli ve Bir Örnek Uygulama.Uludağ University Journal of The Faculty of Engineering, 21 (2), 473-488.
4. Al A.& Eren T. (2012). Tamsayılı programlama modeli ile ders çizelgeleme problemi: Bir örnek uygulama”, Kırıkkale Üniversitesi Bilimde Gelişmeler Dergisi, 1 (2), 47-55.
5. Bachouch, R. B., Guinet, A., & Hajri-Gabouj, S. (2011). A Decision-Making Tool for Home Health Care Nurses’ Planning. Paper presented at the Supply Chain Forum: an International Journal.
6. Bard, J. F., Shao, Y., & Jarrah, A. I. (2014). A sequential GRASP for the therapist routing and scheduling problem. Journal of Scheduling, 17(2), 109-133.
7. Bard, J. F., Shao, Y., & Wang, H. (2013). Weekly scheduling models for traveling therapists. Socio-Economic Planning Sciences, 47(3), 191-204.
8. Barrera, D., Velasco, N., & Amaya, C. A. (2012). A network-based approach to the multi-activity combined timetabling and crew scheduling problem: Workforce scheduling for public health policy implementation. Computers & Industrial Engineering, 63(4), 802-812.

9. Begur, S. V., Miller, D. M., & Weaver, J. R. (1997). An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces, 27(4), 35-48.
10. Bennett, A. R., & Erera, A. L. (2011). Dynamic periodic fixed appointment scheduling for home health. IIE Transactions on Healthcare Systems Engineering, 1(1), 6-19.
11. Bertels, S., & 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.
12. Bowers, J., Cheyne, H., Mould, G., & Page, M. (2015). Continuity of care in community midwifery. Health care management science, 18(2), 195-204.
13. Braekers, K., Hartl, R. F., Parragh, S. N., & Tricoire, F. (2016). A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience. European Journal of Operational Research, 248(2), 428-443.
14. Bräysy, O., Dullaert, W., & Nakari, P. (2009). The potential of optimization in communal routing problems: case studies from Finland. Journal of transport geography, 17(6), 484-490.
15. Bredström, D., & Rönnqvist, M. (2008). Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. European Journal of Operational Research, 191(1), 19-31.
16. Cappanera, P., & Scutellà, M. G. (2013). Home Care optimization: impact of pattern generation policies on scheduling and routing decisions. Electronic Notes in Discrete Mathematics, 41, 53-60.
17. Cappanera, P., & Scutellà, M. G. (2014). Joint assignment, scheduling, and routing models to home care optimization: a pattern-based approach. Transportation Science, 49(4), 830-852.
18. De Bruecker, P., Beliën, J., Van den Bergh, J., & Demeulemeester, E. (2018). A three-stage mixed integer programming approach for optimizing the skill mix and training schedules for aircraft maintenance. European Journal of Operational Research, 267(2), 439-452.
19. De Kruijff, J. T., Hurkens, C. A., & de Kok, T. G. (2018). Integer programming models for mid-term production planning for high-tech low-volume supply chains. European Journal of Operational Research, 269(3), 984-997.
20. De Angelis, V. (1998). Planning home assistance for AIDS patients in the city of Rome, Italy. Interfaces, 28(3), 75-83.
21. Dohn, A., Kolind, E., & Clausen, J. (2009). The manpower allocation problem with time windows and job-teaming constraints: A branch-and-price approach. Computers & Operations Research, 36(4), 1145-1157.
22. Duque, P. M., Castro, M., Sörensen, K., & Goos, P. (2015). Home care service planning. The case of Landelijke Thuiszorg. European Journal of Operational Research, 243(1), 292-301.
23. Durmuş, B. (2018). Tamsayılı Programlamada Klasik Ve Greedy Sezgisel Algoritma Sonuçlarının Karşılaştırılması. Muğla Sıtkı Koçman Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi.
24. Eveborn, P., Flisberg, P., & Rönnqvist, M. (2006). Laps Care—an operational system for staff planning of home care. European Journal of Operational Research, 171(3), 962-976.
25. Fernandez, A., Gregory, G., Hindle, A., & Lee, A. (1974). A model for community nursing in a rural county. Operational Research Quarterly, 231-239.
26. Fikar, C., & Hirsch, P. (2015). A matheuristic for routing real-world home service transport systems facilitating walking. Journal of Cleaner Production, 105, 300-310.
27. Hertz, A., & Lahrichi, N. (2009). A patient assignment algorithm for home care services. Journal of the Operational Research Society, 60(4), 481-495.
28. Hewitt, M., Nowak, M., & Nataraj, N. (2016). Planning Strategies for Home Health Care Delivery. Asia-Pacific Journal of Operational Research, 33(05), 1650041.
29. Hiermann, G., Prandtstetter, M., Rendl, A., Puchinger, J., & Raidl, G. R. (2015). Metaheuristics for solving a multimodal home-healthcare scheduling problem. Central European Journal of Operations Research, 23(1), 89-113.
30. Hindle, T., Hindle, A., & Spollen, M. (2000). Resource allocation modelling for home-based health and social care services in areas having differential population density levels: a case study in Northern Ireland. Health services management research, 13(3), 164-169.
31. Ikegami, A., & Uno, A. (2007). Bounds For Staff Size In Home Help Staff Scheduling (< Special Issue> the 50th Anniversary of the Operations Research Society of Japan). Journal of the Operations Research Society of Japan, 50(4), 563-575.
32. Issaoui, B., Zidi, I., Marcon, E., & Ghedira, K. (2015). New multi-objective approach for the home care service problem based on scheduling algorithms and variable neighborhood descent. Electronic Notes in Discrete Mathematics, 47, 181-188.
33. Koeleman, P. M., Bhulai, S., & van Meersbergen, M. (2012). Optimal patient and personnel scheduling policies for care-at-home service facilities. European Journal of Operational Research, 219(3), 557-563.
34. Lara, C. L., Mallapragada, D. S., Papageorgiou, D. J., Venkatesh, A., & Grossmann, I. E. (2018). Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm. European Journal of Operational Research, 271(3), 1037-1054.
35. Liu, R., Yuan, B., & Jiang, Z. (2017). Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements. International Journal of Production Research, 55(2), 558-575.
36. Milburn, A. B., & Spicer, J. (2013). Multi-objective home health nurse routing with remote monitoring devices. International Journal of Planning and Scheduling, 1(4), 242-263.
37. Mısır, M., Smet, P., & Berghe, G. V. (2015). An analysis of generalised heuristics for vehicle routing and personnel rostering problems. Journal of the Operational Research Society, 66(5), 858-870.
38. Mutingi, M., & Mbohwa, C. (2014). Multi-objective homecare worker scheduling: A fuzzy simulated evolution algorithm approach. IIE Transactions on Healthcare Systems Engineering, 4(4), 209-216.
39. Nickel, S., Schröder, M., & Steeg, J. (2012). Mid-term and short-term planning support for home health care services. European Journal of Operational Research, 219(3), 574-587.
40. Özer, Ö., & Şantaş, F. (2012). Kamunun sunduğu evde bakım hizmetleri ve finansmanı.Acıbadem Üniversitesi Sağlık Bilimleri Dergisi, 3(2), 96-103.
41. Patir, S. (2009). Tam Sayılı Programlama Ve Malatya Maksan Transformatör İşletmesinde Bir Uygulama. Ataturk University Journal of Economics & Administrative Sciences, 23(1), 193-206.
42. Pour, S. M., Drake, J. H., Ejlertsen, L. S., Rasmussen, K. M., & Burke, E. K. (2018). A hybrid Constraint Programming/Mixed Integer Programming framework for the preventive signaling maintenance crew scheduling problem. European Journal of Operational Research, 269(1), 341-352.
43. Rasmussen, M. S., Justesen, T., Dohn, A., & Larsen, J. (2012). The home care crew scheduling problem: Preference-based visit clustering and temporal dependencies. European Journal of Operational Research, 219(3), 598-610.
44. Redjem, R., & Marcon, E. (2016). Operations management in the home care services: a heuristic for the caregivers’ routing problem. Flexible Services and Manufacturing Journal, 28(1-2), 280-303.
45. Rendl, A., Prandtstetter, M., Hiermann, G., Puchinger, J., & Raidl, G. R. (2012). Hybrid Heuristics for Multimodal Homecare Scheduling. Paper presented at the CPAIOR.
46. Rest, K.-D., & Hirsch, P. (2016). Daily scheduling of home health care services using time-dependent public transport. Flexible Services and Manufacturing Journal, 28(3), 495-525.
47. Rodriguez, C., Garaix, T., Xie, X., & Augusto, V. (2015). Staff dimensioning in homecare services with uncertain demands. International Journal of Production Research, 53(24), 7396-7410.
48. Akjiratikarl, C., Yenradee, P., & Drake, P. R. (2007). PSO-based algorithm for home care worker scheduling in the UK. Computers & Industrial Engineering, 53(4), 559-583.
49. Allaoua, H., Borne, S., Létocart, L., & Calvo, R. W. (2013). A matheuristic approach for solving a home health care problem. Electronic Notes in Discrete Mathematics, 41, 471-478.
50. Altunay, H.& Eren, T. (2016). Ders Programı Çizelgeleme Problemi için 0-1 Tamsayılı Programlama Modeli ve Bir Örnek Uygulama.Uludağ University Journal of The Faculty of Engineering, 21 (2), 473-488.
51. Al A.& Eren T. (2012). Tamsayılı programlama modeli ile ders çizelgeleme problemi: Bir örnek uygulama”, Kırıkkale Üniversitesi Bilimde Gelişmeler Dergisi, 1 (2), 47-55.
52. Bachouch, R. B., Guinet, A., & Hajri-Gabouj, S. (2011). A Decision-Making Tool for Home Health Care Nurses’ Planning. Paper presented at the Supply Chain Forum: an International Journal. Bard, J. F., Shao, Y., & Jarrah, A. I. (2014). A sequential GRASP for the therapist routing and scheduling problem. Journal of Scheduling, 17(2), 109-133.
53. Bard, J. F., Shao, Y., & Wang, H. (2013). Weekly scheduling models for traveling therapists. Socio-Economic Planning Sciences, 47(3), 191-204.
54. Barrera, D., Velasco, N., & Amaya, C. A. (2012). A network-based approach to the multi-activity combined timetabling and crew scheduling problem: Workforce scheduling for public health policy implementation. Computers & Industrial Engineering, 63(4), 802-812.
55. Begur, S. V., Miller, D. M., & Weaver, J. R. (1997). An integrated spatial DSS for scheduling and routing home-health-care nurses. Interfaces, 27(4), 35-48.
56. Bennett, A. R., & Erera, A. L. (2011). Dynamic periodic fixed appointment scheduling for home health. IIE Transactions on Healthcare Systems Engineering, 1(1), 6-19.
57. Bertels, S., & 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.
58. Bowers, J., Cheyne, H., Mould, G., & Page, M. (2015). Continuity of care in community midwifery. Health care management science, 18(2), 195-204.
59. Braekers, K., Hartl, R. F., Parragh, S. N., & Tricoire, F. (2016). A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience. European Journal of Operational Research, 248(2), 428-443.
60. Bräysy, O., Dullaert, W., & Nakari, P. (2009). The potential of optimization in communal routing problems: case studies from Finland. Journal of transport geography, 17(6), 484-490.
61. Bredström, D., & Rönnqvist, M. (2008). Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. European Journal of Operational Research, 191(1), 19-31.
62. Cappanera, P., & Scutellà, M. G. (2013). Home Care optimization: impact of pattern generation policies on scheduling and routing decisions. Electronic Notes in Discrete Mathematics, 41, 53-60.
63. Cappanera, P., & Scutellà, M. G. (2014). Joint assignment, scheduling, and routing models to home care optimization: a pattern-based approach. Transportation Science, 49(4), 830-852.
64. De Bruecker, P., Beliën, J., Van den Bergh, J., & Demeulemeester, E. (2018). A three-stage mixed integer programming approach for optimizing the skill mix and training schedules for aircraft maintenance. European Journal of Operational Research, 267(2), 439-452.
65. De Kruijff, J. T., Hurkens, C. A., & de Kok, T. G. (2018). Integer programming models for mid-term production planning for high-tech low-volume supply chains. European Journal of Operational Research, 269(3), 984-997.
66. De Angelis, V. (1998). Planning home assistance for AIDS patients in the city of Rome, Italy. Interfaces, 28(3), 75-83.
67. Dohn, A., Kolind, E., & Clausen, J. (2009). The manpower allocation problem with time windows and job-teaming constraints: A branch-and-price approach. Computers & Operations Research, 36(4), 1145-1157. Duque, P. M., Castro, M., Sörensen, K., & Goos, P. (2015). Home care service planning. The case of Landelijke Thuiszorg. European Journal of Operational Research, 243(1), 292-301.
68. Durmuş, B. (2018). Tamsayılı Programlamada Klasik Ve Greedy Sezgisel Algoritma Sonuçlarının Karşılaştırılması. Muğla Sıtkı Koçman Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi.
69. Eveborn, P., Flisberg, P., & Rönnqvist, M. (2006). Laps Care—an operational system for staff planning of home care. European Journal of Operational Research, 171(3), 962-976.
70. Fernandez, A., Gregory, G., Hindle, A., & Lee, A. (1974). A model for community nursing in a rural county. Operational Research Quarterly, 231-239.
71. Fikar, C., & Hirsch, P. (2015). A matheuristic for routing real-world home service transport systems facilitating walking. Journal of Cleaner Production, 105, 300-310.
72. Hertz, A., & Lahrichi, N. (2009). A patient assignment algorithm for home care services. Journal of the Operational Research Society, 60(4), 481-495.
73. Hewitt, M., Nowak, M., & Nataraj, N. (2016). Planning Strategies for Home Health Care Delivery. Asia-Pacific Journal of Operational Research, 33(05), 1650041.
74. Hiermann, G., Prandtstetter, M., Rendl, A., Puchinger, J., & Raidl, G. R. (2015). Metaheuristics for solving a multimodal home-healthcare scheduling problem. Central European Journal of Operations Research, 23(1), 89-113. Hindle, T., Hindle, A., & Spollen, M. (2000). Resource allocation modelling for home-based health and social care services in areas having differential population density levels: a case study in Northern Ireland. Health services management research, 13(3), 164-169.
75. Ikegami, A., & Uno, A. (2007). Bounds For Staff Size In Home Help Staff Scheduling (< Special Issue> the 50th Anniversary of the Operations Research Society of Japan). Journal of the Operations Research Society of Japan, 50(4), 563-575.
76. Issaoui, B., Zidi, I., Marcon, E., & Ghedira, K. (2015). New multi-objective approach for the home care service problem based on scheduling algorithms and variable neighborhood descent. Electronic Notes in Discrete Mathematics, 47, 181-188.
77. Koeleman, P. M., Bhulai, S., & van Meersbergen, M. (2012). Optimal patient and personnel scheduling policies for care-at-home service facilities. European Journal of Operational Research, 219(3), 557-563.
78. Lara, C. L., Mallapragada, D. S., Papageorgiou, D. J., Venkatesh, A., & Grossmann, I. E. (2018). Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algorithm. European Journal of Operational Research, 271(3), 1037-1054.
79. Liu, R., Yuan, B., & Jiang, Z. (2017). Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements. International Journal of Production Research, 55(2), 558-575.
80. Milburn, A. B., & Spicer, J. (2013). Multi-objective home health nurse routing with remote monitoring devices. International Journal of Planning and Scheduling, 1(4), 242-263.
81. Mısır, M., Smet, P., & Berghe, G. V. (2015). An analysis of generalised heuristics for vehicle routing and personnel rostering problems. Journal of the Operational Research Society, 66(5), 858-870.
82. Mutingi, M., & Mbohwa, C. (2014). Multi-objective homecare worker scheduling: A fuzzy simulated evolution algorithm approach. IIE Transactions on Healthcare Systems Engineering, 4(4), 209-216.
83. Nickel, S., Schröder, M., & Steeg, J. (2012). Mid-term and short-term planning support for home health care services. European Journal of Operational Research, 219(3), 574-587.
84. Özer, Ö., & Şantaş, F. (2012). Kamunun sunduğu evde bakım hizmetleri ve finansmanı.Acıbadem Üniversitesi Sağlık Bilimleri Dergisi, 3(2), 96-103.
85. Patir, S. (2009). Tam Sayılı Programlama Ve Malatya Maksan Transformatör İşletmesinde Bir Uygulama. Ataturk University Journal of Economics & Administrative Sciences, 23(1), 193-206.
86. Pour, S. M., Drake, J. H., Ejlertsen, L. S., Rasmussen, K. M., & Burke, E. K. (2018). A hybrid Constraint Programming/Mixed Integer Programming framework for the preventive signaling maintenance crew scheduling problem. European Journal of Operational Research, 269(1), 341-352.
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