Research Article
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Year 2024, Volume: 39 Issue: 1, 593 - 606, 21.08.2023

İlhami Akkuş Ece Arzu Yıldız İsmail Karaoğlan Fulya Altıparmak

https://doi.org/10.17341/gazimmfd.1218090

Abstract

Keywords

Sağlık hizmetleri lojistiği karma tamsayılı doğrusal programlama çok depolu ARP periyodik ARP metasezgisel algoritma

References

  • Rural Health Information Hub. Healthcare Access in Rural Communities. https://www.ruralhealthinfo.org/topics/healthcare-access. Erişim Tarihi: Mart 1, 2021.
  • Soyluoğlu S.B. Çağdaş Sağlık Anlayışı. http://bilheal.bilkent.edu.tr/aykonu/Ay2003/kasim03/cagdassaglik.html. Erişim Tarihi: Şubat 2021.
  • Bollman, B. R. Understanding Rural Canada: Implications for Rural Development Policy and Rural Planning Policy. https://2018.icrps.org/wp-content/uploads/sites/4/2018/06/Reimer-Bollman-2010-Understanding-Rural-Canada.pdf. Erişim Tarihi: Haziran 2020.
  • Wilson, C. R. , Rourke, J., Oandasan, I. F., Bosco, C., Progress made on access to rural healthcare in Canada, Can J Rural Med 25 (1), 14-19, 2020.
  • Lee, C. Tong, A. and Wang M. Chinese Healthcare: The Rural Reality. https://www.coresponsibility.com/chinese-healthcare-the-rural-reality/ . Erişim Tarihi 18 Nisan 2020.
  • Lahooti, H., Rod, K., Kangarlu A., Healthcare Delivery to the rural area in Iran, American Journal of Biomedical Science & Research, 3 (5), 426-430, 2019.
  • Holst, J., Rethinking Medical Training in Germany Towards Rural Health Care. Primary Health Care, 5 (194), 2015.
  • Dantzig G.B., Ramser, J. H., The Truck Dispatching Problem, Management Science, 6 (1), 80-91, 1959.
  • Makan, A., Malamis, D., Assobhei, O., Loizidou, M., Mountadar, M., Solid Waste Management: Case of Collection and Vehicle Routing Problem in The City of Azemmour, Morocco, International Journal of Management Science and Engineering Management, 6 (4), 247-255, 2011.
  • Mancini,S., A Real-Life Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet: Formulation and Adaptive Large Neighborhood Search Based Matheuristic, Transportation Research Part C, 70, 100–112, 2016.
  • Keçeci B., Altıparmak Baykoç F., Kara İ., Heterogeneous vehicle routing problem with simultaneous pickup and delivery: Mathematical formulations and a heuristic algorithm, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (2), 185-195, 2015.
  • Michallet, J., Prins, C., Amodeo, L., Yalaoui, F., Vitry, G., Multi-Start Iterated Local Search for the Periodic Vehicle Routing Problem with Time Windows and Time Spread Constraints on Services, Computers and Operations Research, 41, 196–207, 2014.
  • Montoya-Torres, J. R., Franco, J. L., Isaza, S. N., Jiménez, H. F., & Herazo-Padilla, N., A Literature Review of The Vehicle Routing Problem with Multiple Depots, Computers and Industrial Engineering, 79, 115–129, 2015.
  • Dueck, G., New optimization heuristics: The great deluge algorithm and the record-to-record travel, Journal of Computational physics, 104 (1), 86-92, 1993.
  • Ge, X., Jin, Y., Zhang, L., Genetic-based algorithms for cash-in-transit multi depot vehicle routing problems: economic and environmental optimization, Environment, Development and Sustainability, 25 (1), 557-586, 2023.
  • Golden, B. L., Raghavan, S., Wasil, E. A. The Vehicle Routing Problem: Latest Advances and New Challenges. Springer, 2008.
  • Zhang, H., Ge, H., Yang, J., Review of Vehicle Routing Problems: Models, Classification and Solving Algorithms, Archives of Computational Methods in Engineering, 29, 195–221, 2022.
  • Bae, H., Moon, I. Multi-depot vehicle routing problem with time windows considering delivery and installation vehicles, Appl Math Model, 40 (13-14), 6536-6549, 2016.
  • Wang, J. H., Weng,T. Y., Zhang, Q. F., A Two-Stage Multiobjective Evolutionary Algorithm for Multiobjective Multidepot Vehicle Routing Problem With Time Windows, IEEE Transactions on Cybernetics, 49 (7), 2467-2478, 2019.
  • Li, J., Li, T., Yu, Y., Zhang, Z., Pardalos, P. M., Zhang, Y., Ma, Y., Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery, Appl Soft Comput, 81, 105460, 2019.
  • Wang, Y., Assogba, K., Fan, J. X., Xu, M. Z., Liu, Y., Wang, H. Z., Multi-depot green vehicle routing problem with shared transportation resource: Integration of time-dependent speed and piecewise penalty cost, J Clean Prod, 232, 12-29, 2019.
  • Stodola, P., Hybrid ant colony optimization algorithm applied to the multi-depot vehicle routing problem, Nat Comput, 19 (2), 463-475, 2020.
  • Wang, Y. , Li, Q., Guan, X. Y., Xu, M. Z. Liu, Y., Wang, H. Z., Two-echelon collaborative multi-depot multi-period vehicle routing problem, Expert Syst Appl, 167, 2021.
  • Sadati, M. E. H., Catay, B., Aksen, An efficient variable neighborhood search with tabu shaking for a class of multi-depot vehicle routing problems, Comput Oper Res, 133, 2021.
  • Trautsamwieser, A., Hirsch, P., A Branch-Price-and-Cut Approach for Solving the Medium-Term Home Health Care Planning Problem, Networks, 64 (3), 143-159, 2014.
  • Rodriguez-Martin, I., Salazar-Gonzalez, J. J., Yaman, H., The periodic vehicle routing problem with driver consistency, European Journal of Operational Research, 273 (2), 575-584, 2019.
  • Chen, R. M., Shen, Y. M., Hong, W. Z., Neural-like encoding particle swarm optimization for periodic vehicle routing problems, Expert Syst Appl, 138, 112833, 2019.
  • Wang, Y., Wang, L., Chen, G.C., Cai, Z.Q., Zhou, Y.Q., Xing, L.N., An Improved Ant Colony Optimization algorithm to the Periodic Vehicle Routing Problem with Time Window and Service Choice, Swarm Evol Comput, 55, 100675, 2020.
  • Oztop, H., Kizilay, D., Cil, Z. A., Mathematical models for the periodic vehicle routing problem with time windows and time spread constraints, IJOCTA, 11 (1),10-23, 2021.
  • Cissé, M., Yalçındağ, S., Kergosien, Y., Şahin, E., Lenté, C., Matta, A., OR problems related to Home Health Care: A review of relevant routing and scheduling problems, Operations research for health care, 13, 1-22, 2017.
  • Fikar C., Hirsch, P., Home health care routing and scheduling: A review," Comput Oper Res, 77, 86-95, 2017.
  • An, Y. J., Kim, Y. D., Jeong, B. J., Kim, S. D., Scheduling healthcare services in a home healthcare system, J Oper Res Soc, 63 (11), 1589-1599, 2012.
  • Dengiz A.O., Atalay K.D., 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), 2167-2181, 2021.
  • Erdem M., Koç, Ç., Analysis of electric vehicles in home health care routing problem, J Clean Prod, 234, 1471-1483, 2019.
  • Erdem, M., Koç, Ç., Yucel, E., The electric home health care routing and scheduling problem with time windows and fast chargers, Comput Ind Eng, 172, 2022.
  • Clapper, Y., Berkhout, J., Bekker, R., Moeke, D., A model-based evolutionary algorithm for home health care scheduling, Comput Oper Res, 150, 106081, 2023.
  • Belhor, M., El-Amraoui, A., Jemai, A., Delmotte, F., Multi-objective evolutionary approach based on K-means clustering for home health care routing and scheduling problem, Expert Syst Appl, 213, 119035, 2023.
  • Akkuş, İ., Yıldız, E. A., Karaoğlan, İ., Altıparmak, F., A Mobile Healthcare Service Routing and Scheduling Problem in Rural Areas, in Proceedings of the Fifteenth International Conference on Management Science and Engineering Management, Cham, J., Springer, Editörler: Xu, F. P. García Márquez, M. H. Ali Hassan, G. Duca, A. Hajiyev, and F. Altiparmak, 125-136, 2021.
  • Akkuş, İ., Yıldız, E. A., Karaoğlan, İ., Altıparmak, F., Gezici Sağlık Hizmeti Veren Araçların Rotalanması ve Hekim Çizelgeleme Problemi: Ankara İli Uygulaması, Yöneylem Araştırması ve Endüstri Mühendisliği Kongresi (YA/EM 40), İstanbul, Türkiye, 04 - 07 Temmuz 2021.
  • Resmî Gazete. Yönetmelik: Aile Hekimliği Uygulama Yönetmeliği. Başlık: Gezici ve yerinde sağlık hizmetlerinin yürütülmesi Paragraf 3 Madde 6. https://www.mevzuat.gov.tr/mevzuat?MevzuatNo=17051&MevzuatTur=7&MevzuatTertip=5. Yayın Tarihi: 25.01.2013.
  • Resmî Gazete. Yönetmelik: Aile Hekimliği Ödeme ve Sözleşme Yönetmeliği https://www.mevzuat.gov.tr/MevzuatMetin/3.5.20101237.pdf . Yayın Tarihi: 03.05.2010.
  • Talbi, E.G., Metaheuristics: from design to implementation, John Wiley & Sons, 2009.
  • Li, F., Golden, B. Wasil, E., The open vehicle routing problem: Algorithms, large-scale test problems, and computational results, Comput Oper Res, 34 (10), 2918-2930, 2007.
  • Ramadhan, F., Imran, A., Rizana, A.F., Threshold based algorithms for the multi-product multi-period inventory routing problem, J. Eng. Sci. Technol., 14 (5), 2703-2715, 2019.
  • Hou, Y.E., Dang, L., Dong, W., and Kong, Y., A metaheuristic algorithm for routing school buses with mixed load, IEEE Access, 8, 158293-158305, 2020.
  • TÜİK. Adrese Dayalı Nüfus Kayıt Sistemi Sonuçları 2020. https://data.tuik.gov.tr/Bulten/Index?p=Adrese-Dayali-Nufus-Kayit-Sistemi-Sonuclari-2020-37210#:~:text=T%C3%BCrkiye%20n%C3%BCfusu%2083%20milyon%20614%20bin%20362%20ki%C5%9Fi%20oldu&text=Di%C4%9Fer%20bir%20ifadeyle%20toplam%20n%C3%BCfusun,333%20bin%20410%20ki%C5%9Fi%20oldu. Erişim Tarihi: Eylül 2021.

Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması

Year 2024, Volume: 39 Issue: 1, 593 - 606, 21.08.2023

İlhami Akkuş Ece Arzu Yıldız İsmail Karaoğlan Fulya Altıparmak

https://doi.org/10.17341/gazimmfd.1218090

Abstract

Küreselleşme ve teknolojik gelişmelerle birlikte 21. Yüzyılın ikinci yarısında toplumların sağlık ihtiyaçları değişmiş ve sağlık hizmeti sunumunda değişiklikler yapılması zorunlu hale gelmiştir. Nüfusun seyrek olduğu yerleşim yerlerinde kapsamlı sağlık tesisleri kurmanın ekonomik olarak sürdürülebilir olmaması, devletlerin vatandaşlarının sağlık hizmetlerine eşit erişimini sağlamakla yükümlü olması sağlık hizmeti sunumunda farklı arayışlara neden olmuştur. Türkiye Cumhuriyeti Sağlık Bakanlığı halka eşit şartlarda sağlık hizmeti sunabilmek için 3400 sağlık kuruluşu ve yaklaşık 7500 doktorla kırsal bölgelere gezici sağlık hizmeti (GSH) sunumu uygulamasını başlatmıştır. GSH sunan doktorlar günde 8 saat çalışarak her ay yaklaşık 9 milyon kişiye GSH vermektedir. Türkiye genelinde uygulanan kapsamlı bir hizmet olması nedeniyle hizmet sunumu planlaması için kırsal yerleşim bölgelerine sağlık merkezi ve doktor atama, rotalama, çizelgeleme ihtiyacı doğmuştur. Bu çalışmada, kırsal alanlarda GSH rotalama ve çizelgeleme problemi (GSH-RÇP) ele alınmıştır. GSH-RÇP’de amaç, çalışma saati, rota süresi, ziyaret başına minimum hizmet süresi, köylere her ay aynı doktorların hizmet sunması gibi kısıtlar altında, toplam katedilen mesafeyi enazlayacak şekilde aylık periyotlarda doktorların günlük rotalarını belirlemektir. Problemin çözümü için öncelikle karma tamsayılı matematiksel model geliştirilmiştir. GSH-RÇP, çok depolu zaman kısıtlı periyodik araç rotalama problemine eşdeğer olduğu için NP-zor problemler sınıfında yer almaktadır. Bu nedenle, orta ve büyük boyutlu problemlere makul sürelerde çözüm bulabilmek amacıyla bir karma sezgisel algoritma geliştirilmiştir. Açgözlü çözüm kurucu (Greedy Constructive) sezgiseli ve Kayıttan Kayıta Gezinti (Record to Record Travel) metasezgiseline dayalı olan bu karma sezgisel algoritma “AGS-KKG” olarak adlandırılmıştır. Matematiksel model ve AGS-KKG algoritmasının performansı Ankara iline ait verilere dayalı olarak mevcut planlar ile karşılaştırmalı incelenmiştir. Karşılaştırma sonucunda mevcut planlara göre toplam katedilen mesafede matematiksel model ile %15,6, AGS-KKG ile %22,3 iyileşme sağlanmıştır.

Keywords

Sağlık hizmetleri lojistiği karma tamsayılı doğrusal programlama çok depolu ARP periyodik ARP metasezgisel algoritma

References

  • Rural Health Information Hub. Healthcare Access in Rural Communities. https://www.ruralhealthinfo.org/topics/healthcare-access. Erişim Tarihi: Mart 1, 2021.
  • Soyluoğlu S.B. Çağdaş Sağlık Anlayışı. http://bilheal.bilkent.edu.tr/aykonu/Ay2003/kasim03/cagdassaglik.html. Erişim Tarihi: Şubat 2021.
  • Bollman, B. R. Understanding Rural Canada: Implications for Rural Development Policy and Rural Planning Policy. https://2018.icrps.org/wp-content/uploads/sites/4/2018/06/Reimer-Bollman-2010-Understanding-Rural-Canada.pdf. Erişim Tarihi: Haziran 2020.
  • Wilson, C. R. , Rourke, J., Oandasan, I. F., Bosco, C., Progress made on access to rural healthcare in Canada, Can J Rural Med 25 (1), 14-19, 2020.
  • Lee, C. Tong, A. and Wang M. Chinese Healthcare: The Rural Reality. https://www.coresponsibility.com/chinese-healthcare-the-rural-reality/ . Erişim Tarihi 18 Nisan 2020.
  • Lahooti, H., Rod, K., Kangarlu A., Healthcare Delivery to the rural area in Iran, American Journal of Biomedical Science & Research, 3 (5), 426-430, 2019.
  • Holst, J., Rethinking Medical Training in Germany Towards Rural Health Care. Primary Health Care, 5 (194), 2015.
  • Dantzig G.B., Ramser, J. H., The Truck Dispatching Problem, Management Science, 6 (1), 80-91, 1959.
  • Makan, A., Malamis, D., Assobhei, O., Loizidou, M., Mountadar, M., Solid Waste Management: Case of Collection and Vehicle Routing Problem in The City of Azemmour, Morocco, International Journal of Management Science and Engineering Management, 6 (4), 247-255, 2011.
  • Mancini,S., A Real-Life Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet: Formulation and Adaptive Large Neighborhood Search Based Matheuristic, Transportation Research Part C, 70, 100–112, 2016.
  • Keçeci B., Altıparmak Baykoç F., Kara İ., Heterogeneous vehicle routing problem with simultaneous pickup and delivery: Mathematical formulations and a heuristic algorithm, Journal of the Faculty of Engineering and Architecture of Gazi University, 30 (2), 185-195, 2015.
  • Michallet, J., Prins, C., Amodeo, L., Yalaoui, F., Vitry, G., Multi-Start Iterated Local Search for the Periodic Vehicle Routing Problem with Time Windows and Time Spread Constraints on Services, Computers and Operations Research, 41, 196–207, 2014.
  • Montoya-Torres, J. R., Franco, J. L., Isaza, S. N., Jiménez, H. F., & Herazo-Padilla, N., A Literature Review of The Vehicle Routing Problem with Multiple Depots, Computers and Industrial Engineering, 79, 115–129, 2015.
  • Dueck, G., New optimization heuristics: The great deluge algorithm and the record-to-record travel, Journal of Computational physics, 104 (1), 86-92, 1993.
  • Ge, X., Jin, Y., Zhang, L., Genetic-based algorithms for cash-in-transit multi depot vehicle routing problems: economic and environmental optimization, Environment, Development and Sustainability, 25 (1), 557-586, 2023.
  • Golden, B. L., Raghavan, S., Wasil, E. A. The Vehicle Routing Problem: Latest Advances and New Challenges. Springer, 2008.
  • Zhang, H., Ge, H., Yang, J., Review of Vehicle Routing Problems: Models, Classification and Solving Algorithms, Archives of Computational Methods in Engineering, 29, 195–221, 2022.
  • Bae, H., Moon, I. Multi-depot vehicle routing problem with time windows considering delivery and installation vehicles, Appl Math Model, 40 (13-14), 6536-6549, 2016.
  • Wang, J. H., Weng,T. Y., Zhang, Q. F., A Two-Stage Multiobjective Evolutionary Algorithm for Multiobjective Multidepot Vehicle Routing Problem With Time Windows, IEEE Transactions on Cybernetics, 49 (7), 2467-2478, 2019.
  • Li, J., Li, T., Yu, Y., Zhang, Z., Pardalos, P. M., Zhang, Y., Ma, Y., Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery, Appl Soft Comput, 81, 105460, 2019.
  • Wang, Y., Assogba, K., Fan, J. X., Xu, M. Z., Liu, Y., Wang, H. Z., Multi-depot green vehicle routing problem with shared transportation resource: Integration of time-dependent speed and piecewise penalty cost, J Clean Prod, 232, 12-29, 2019.
  • Stodola, P., Hybrid ant colony optimization algorithm applied to the multi-depot vehicle routing problem, Nat Comput, 19 (2), 463-475, 2020.
  • Wang, Y. , Li, Q., Guan, X. Y., Xu, M. Z. Liu, Y., Wang, H. Z., Two-echelon collaborative multi-depot multi-period vehicle routing problem, Expert Syst Appl, 167, 2021.
  • Sadati, M. E. H., Catay, B., Aksen, An efficient variable neighborhood search with tabu shaking for a class of multi-depot vehicle routing problems, Comput Oper Res, 133, 2021.
  • Trautsamwieser, A., Hirsch, P., A Branch-Price-and-Cut Approach for Solving the Medium-Term Home Health Care Planning Problem, Networks, 64 (3), 143-159, 2014.
  • Rodriguez-Martin, I., Salazar-Gonzalez, J. J., Yaman, H., The periodic vehicle routing problem with driver consistency, European Journal of Operational Research, 273 (2), 575-584, 2019.
  • Chen, R. M., Shen, Y. M., Hong, W. Z., Neural-like encoding particle swarm optimization for periodic vehicle routing problems, Expert Syst Appl, 138, 112833, 2019.
  • Wang, Y., Wang, L., Chen, G.C., Cai, Z.Q., Zhou, Y.Q., Xing, L.N., An Improved Ant Colony Optimization algorithm to the Periodic Vehicle Routing Problem with Time Window and Service Choice, Swarm Evol Comput, 55, 100675, 2020.
  • Oztop, H., Kizilay, D., Cil, Z. A., Mathematical models for the periodic vehicle routing problem with time windows and time spread constraints, IJOCTA, 11 (1),10-23, 2021.
  • Cissé, M., Yalçındağ, S., Kergosien, Y., Şahin, E., Lenté, C., Matta, A., OR problems related to Home Health Care: A review of relevant routing and scheduling problems, Operations research for health care, 13, 1-22, 2017.
  • Fikar C., Hirsch, P., Home health care routing and scheduling: A review," Comput Oper Res, 77, 86-95, 2017.
  • An, Y. J., Kim, Y. D., Jeong, B. J., Kim, S. D., Scheduling healthcare services in a home healthcare system, J Oper Res Soc, 63 (11), 1589-1599, 2012.
  • Dengiz A.O., Atalay K.D., 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), 2167-2181, 2021.
  • Erdem M., Koç, Ç., Analysis of electric vehicles in home health care routing problem, J Clean Prod, 234, 1471-1483, 2019.
  • Erdem, M., Koç, Ç., Yucel, E., The electric home health care routing and scheduling problem with time windows and fast chargers, Comput Ind Eng, 172, 2022.
  • Clapper, Y., Berkhout, J., Bekker, R., Moeke, D., A model-based evolutionary algorithm for home health care scheduling, Comput Oper Res, 150, 106081, 2023.
  • Belhor, M., El-Amraoui, A., Jemai, A., Delmotte, F., Multi-objective evolutionary approach based on K-means clustering for home health care routing and scheduling problem, Expert Syst Appl, 213, 119035, 2023.
  • Akkuş, İ., Yıldız, E. A., Karaoğlan, İ., Altıparmak, F., A Mobile Healthcare Service Routing and Scheduling Problem in Rural Areas, in Proceedings of the Fifteenth International Conference on Management Science and Engineering Management, Cham, J., Springer, Editörler: Xu, F. P. García Márquez, M. H. Ali Hassan, G. Duca, A. Hajiyev, and F. Altiparmak, 125-136, 2021.
  • Akkuş, İ., Yıldız, E. A., Karaoğlan, İ., Altıparmak, F., Gezici Sağlık Hizmeti Veren Araçların Rotalanması ve Hekim Çizelgeleme Problemi: Ankara İli Uygulaması, Yöneylem Araştırması ve Endüstri Mühendisliği Kongresi (YA/EM 40), İstanbul, Türkiye, 04 - 07 Temmuz 2021.
  • Resmî Gazete. Yönetmelik: Aile Hekimliği Uygulama Yönetmeliği. Başlık: Gezici ve yerinde sağlık hizmetlerinin yürütülmesi Paragraf 3 Madde 6. https://www.mevzuat.gov.tr/mevzuat?MevzuatNo=17051&MevzuatTur=7&MevzuatTertip=5. Yayın Tarihi: 25.01.2013.
  • Resmî Gazete. Yönetmelik: Aile Hekimliği Ödeme ve Sözleşme Yönetmeliği https://www.mevzuat.gov.tr/MevzuatMetin/3.5.20101237.pdf . Yayın Tarihi: 03.05.2010.
  • Talbi, E.G., Metaheuristics: from design to implementation, John Wiley & Sons, 2009.
  • Li, F., Golden, B. Wasil, E., The open vehicle routing problem: Algorithms, large-scale test problems, and computational results, Comput Oper Res, 34 (10), 2918-2930, 2007.
  • Ramadhan, F., Imran, A., Rizana, A.F., Threshold based algorithms for the multi-product multi-period inventory routing problem, J. Eng. Sci. Technol., 14 (5), 2703-2715, 2019.
  • Hou, Y.E., Dang, L., Dong, W., and Kong, Y., A metaheuristic algorithm for routing school buses with mixed load, IEEE Access, 8, 158293-158305, 2020.
  • TÜİK. Adrese Dayalı Nüfus Kayıt Sistemi Sonuçları 2020. https://data.tuik.gov.tr/Bulten/Index?p=Adrese-Dayali-Nufus-Kayit-Sistemi-Sonuclari-2020-37210#:~:text=T%C3%BCrkiye%20n%C3%BCfusu%2083%20milyon%20614%20bin%20362%20ki%C5%9Fi%20oldu&text=Di%C4%9Fer%20bir%20ifadeyle%20toplam%20n%C3%BCfusun,333%20bin%20410%20ki%C5%9Fi%20oldu. Erişim Tarihi: Eylül 2021.
There are 46 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

İlhami Akkuş 0000-0002-1154-2046

Ece Arzu Yıldız 0000-0001-6000-7472

İsmail Karaoğlan 0000-0002-6023-6918

Fulya Altıparmak 0000-0003-1730-4214

Early Pub Date August 21, 2023
Publication Date August 21, 2023
Submission Date December 13, 2022
Acceptance Date March 19, 2023
Published in Issue Year 2024 Volume: 39 Issue: 1

Cite

APA Akkuş, İ., Yıldız, E. A., Karaoğlan, İ., Altıparmak, F. (2023). Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(1), 593-606. https://doi.org/10.17341/gazimmfd.1218090
AMA Akkuş İ, Yıldız EA, Karaoğlan İ, Altıparmak F. Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması. GUMMFD. August 2023;39(1):593-606. doi:10.17341/gazimmfd.1218090
Chicago Akkuş, İlhami, Ece Arzu Yıldız, İsmail Karaoğlan, and Fulya Altıparmak. “Kırsal Alanlarda Gezici sağlık Hizmeti planlaması: Karma kayıttan kayıta Gezinti Algoritması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39, no. 1 (August 2023): 593-606. https://doi.org/10.17341/gazimmfd.1218090.
EndNote Akkuş İ, Yıldız EA, Karaoğlan İ, Altıparmak F (August 1, 2023) Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39 1 593–606.
IEEE İ. Akkuş, E. A. Yıldız, İ. Karaoğlan, and F. Altıparmak, “Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması”, GUMMFD, vol. 39, no. 1, pp. 593–606, 2023, doi: 10.17341/gazimmfd.1218090.
ISNAD Akkuş, İlhami et al. “Kırsal Alanlarda Gezici sağlık Hizmeti planlaması: Karma kayıttan kayıta Gezinti Algoritması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 39/1 (August 2023), 593-606. https://doi.org/10.17341/gazimmfd.1218090.
JAMA Akkuş İ, Yıldız EA, Karaoğlan İ, Altıparmak F. Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması. GUMMFD. 2023;39:593–606.
MLA Akkuş, İlhami et al. “Kırsal Alanlarda Gezici sağlık Hizmeti planlaması: Karma kayıttan kayıta Gezinti Algoritması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, vol. 39, no. 1, 2023, pp. 593-06, doi:10.17341/gazimmfd.1218090.
Vancouver Akkuş İ, Yıldız EA, Karaoğlan İ, Altıparmak F. Kırsal alanlarda gezici sağlık hizmeti planlaması: Karma kayıttan kayıta gezinti algoritması. GUMMFD. 2023;39(1):593-606.