Hastanelere Aşı Dağıtımı İçin Uygun Rotaların Belirlenmesi: Ankara İli Örneği

Year 2021, Volume , Issue , 1 - 1, 31.12.2021

Beste DESTİCİOĞLU Kemal Gürol KURTAY Aygün ALTUNDAŞ Hakan Ayhan DAĞISTANLI

https://doi.org/10.2339/politeknik.1014921

Abstract

Çin’in Wuhan kentinde başlayıp tüm dünyaya yayılan COVID-19 salgını ile birlikte geleneksel uygulamalarda değişiklikler yaşanmaya başlamış ve bu gelişmelerle paralel olarak yeni problemler ortaya çıkmaya başlamıştır. COVID-19 salgınıyla ortaya çıkan bu problemler, araştırmacıların ilgisini çeken konular arasında yer almaktadır. Hem ülkemizin hem de dünyanın bu salgınla başa çıkabilmesi için tüm nüfusun aşılanarak toplum bağışıklığının sağlanması önem kazanmaktadır. Aşılanacak kişi sayısındaki artışla beraber, hastanelerin aşı kapasitelerinin belirlenmesi, aşı uygulaması yapılacak hastanelerin seçilmesi, hastanelere aşı dağıtım rotalarının belirlenmesi gibi yeni problemler karşımıza çıkmaktadır. Araç rotalama problemi ilk olarak 1950’li yıllarda literatürde yerini almaya başlamış ve günümüzde farklı varsayımlar altında yeni problem için uyarlanabilen, gelişmeye açık bir problem alanı olarak görülmektedir. Bu çalışmada, aşıların bir dağıtım merkezinden uygulama yapılacağı hastanelere en kısa sürede, minimum maliyet altında taşınmasının sağlanması amacıyla bir matematiksel model önerisinde bulunulmuştur. Bu problem için, literatürde yer alan araç rotalama problemi modelleri kullanılarak yeni bir matematiksel model önerisi yapılmıştır. Geliştirilen modelin etkinliğini analiz etmek için Ankara ili için bir uygulama yapılmış ve oluşturulan problem GAMS 24.1.3 programında kodlanarak çözülmüştür. Problemin çözümünde elde edilen sonuçlar değerlendirilerek, hastaneleri ziyaret edecek araçların minimum maliyetli rotaları belirlenmiştir.

Keywords

COVID-19, dağıtım problemi, matematiksel model, araç rotalama problemi

Determining Suitable Routes for Vaccine Distribution to Hospitals: Application of Ankara Province

Abstract

With the COVID-19 epidemic, which started in Wuhan, China in 2019 and spread all over the world, changes in traditional practices began to occur and new problems emerged in parallel with these developments. These problems, which emerged with the COVID-19 pandemic, have become a subject that attracts the attention of researchers. In order for the world to cope with this epidemic more quickly, it is important to ensure community immunity by vaccinating the population both in our country and in the world. With the increase in the supply of vaccines, new problems arise such as determining the capacities of hospitals where vaccines will be administered, choosing hospitals where vaccines can be administered, and determining routes to distribute vaccines to hospitals. Vehicle routing problem first started to take its place in the literature in the 1950s, and today it is seen as an open problem area that can be adapted for the new problem under different assumptions. In this study, a mathematical model has been proposed in order to ensure that vaccines are transported from a distribution center to the hospitals where they will be administered, as soon as possible and at minimum cost. For this problem, a new mathematical model has been proposed by using the vehicle routing problem models in the literature. In order to test the effectiveness of the developed model, an application example was made for the province of Ankara and the problem was solved in the GAMS 24.3.1 program. By evaluating the results obtained in the solution of the problem, the minimum cost routes of the vehicles to visit the hospitals were determined.

Keywords

COVID-19, distribution problem, mathematical model, vehicle routing problem

References

• [1] Desticioğlu, B. ve Özyörük, B. “Stokastik Talepli Araç Rotalama Problemi İçin Literatür Taraması.” Savunma Bilimleri Dergisi, 18(36), 181-222. (2019).
• [2] Dantzig, G.B. and Ramser, J.H. “The Truck Dispatching Problem”, Management Science, 6(1), 80-91, (1959).
• [3] Toth, P. and Vigo, D. “Branch and Bound Algorithms for the Capacitated VRP”, In P., The Vehicle Routing Problem, SIAM, Philadelphia, USA, (2002).
• [4] Aydoğdu, B. and Özyörük, B.. “Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması.” Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 35(2), 563-580. (2020).
• [5] Erdoğan, S. “Tam sayılı doğrusal programlama ile araç rotalama problemi çözümü ve bir servis ağında uygulaması”, Yüksek Lisans Tezi, Sakarya Üniversitesi, Fen Bilimleri Enstitüsü (2019).
• [6] Almoustafa, S. “Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)”, Doctoral dissertation, Brunel University, School of Information Systems, Computing and Mathematics, (2013).
• [7] Rabbani, M., Heidari, R., Farrokhi-Asl, H. and Rahimi, N. “Using metaheuristic algorithms to solve a multi-objective industrial hazardous waste locationrouting problem considering incompatible waste types”, Journal of Cleaner Production, 170: 227-241, (2018).
• [8] Florio, A. M., Hartl, R. F., and Minner, S. “Optimal a priori tour and restocking policy for the single-vehicle routing problem with stochastic demands.” European Journal of Operational Research, 285(1), 172-182, (2020).
• [9] Poonthalir, G. and Nadarajan, R. “A Fuel Efficient Green Vehicle Routing Problem with varying speed constraint (F-GVRP)”, Expert Systems with Applications, 100, 131–144, (2018).
• [10] Calvet, L.,Wang, D., Juan, A. and Bove, L. “Solving the multidepot vehicle routing problem with limited depot capacity and stochastic demands”, International Transactions in Operational Research, 26(2019), 459-484, (2019).
• [11] Rojas-Cuevas, I.D., Caballero-Morales, S.O., Martinez-Flores, J.L., and Mendoza-Vazquez, J.R. “Capacitated vehicle routing problem model for carriers”, Journal of Transport and Supply Chain Management, 12(1), 1-9, (2018).
• [12] Arakaki, R.K. and Usberti, F.L. “An Efficiency-Based Path-Scanning Heuristic for the Capacitated arc Routing Problem”, Computers & Operations Research, 103: 288-295, (2019).
• [13] Benrahou, F. and Tairi, A. “Capacitated Vehicle Routing Problem for Collection Waste Lube Oil in Algiers”, Fresenius Environ. Bull, 28, 4500-4505, (2019).
• [14] Mulloorakam, A.T. and Nidhiry, N.M. “Combined objective optimization for vehicle routing using genetic algorithm”, Materials Today: Proceedings, 11, 891-902, (2019).
• [15] Almouhanna, A., Quintero-Araujo, C.L., Panadero, J., Juan, A.A., Khosravi, B. and Ouelhadj, D. “The location routing problem using electric vehicles with constrained distance”, Computers & Operations Research, 115, 104864, (2020).
• [16] Abdallah, K.S. and Adel, Y. “Electric Vehicles Routing Problem With Variable Speed And Time Windows” International Conference on Industry, Engineering & Management Systems, Belgium, 55-65, (2020).
• [17] Granada-Echeverri, M., Cubides, L. and Bustamante, J. “The electric vehicle routing problem with backhauls”, International Journal of Industrial Engineering Computations, 11(1), 131–152, (2020).
• [18] Lysgaard, J., Lopez-Sanchez, A.D. and Hernandez-Diaz, A.G. “A matheuristic for the minmax capacitated open vehicle routing problem”, International Transactions In Operational Research, 394-417, (2020).
• [19] Corberán, Á., Plana, I., Reula, M. and Sanchis, J.M. “On the distance-constrained close enough arc routing problem”, European Journal of Operational Research, 291(1), 32-51, (2021).
• [20] Basso, R., Kulcs´ ar, B. and Sanchez-Diaz, I. “Electric vehicle routing problem with machine learning for energy prediction”, Transportation Research Part B: Methodological, 145, 24-55. (2021).
• [21] Ceselli, A., Felipe, A., ´ Ortuno, ˜ M. T., Righini, G. and Tirado, G. “A branch-and-cutand-price algorithm for the electric vehicle routing problem with multiple Technologies”, Operations Research Forum, 2(1), 1-33, (2021).
• [22] Ghobadi, A., Tavakkoli-Moghaddam, R., Fallah, M. and Kazemipoor, H. “Multidepot electric vehicle routing problem with fuzzy time windows and pickup/delivery constraints”, Journal of Applied Research on Industry, 8(1): 1-18, (2021).
• [23] Dalbah, L.M., Al-Betar, M.A., Awadallah, M.A. and Zitar, R.A. “A modified coronavirus herd immunity optimizer for capacitated vehicle routing problem”, Journal of King Saud University- Computer and Information Sciences, (In Press, 2021).
• [23] Kucukoglu, I., Dewil, R. And Cattrysse, D. “The electric vehicle routing problem and its variations: A literature review”, Computers & Industrial Engineering, 107650. (2021).
• [24] Oropeza, A., Cruz-Chávez, M., Cruz-Rosal Martín H. es, P. Bernal and J .C.Abarca , “Unsupervised Clustering Method for the Capacited Vehicle Routing Problem,Ninth Electronics”, Robotics and Automotive Mechanics Conference, Mexico, 211-216, (2012).
• [25] Solomon, M.M. “Algorithms for the vehicle routing and scheduling problems with time window constraints”, Operations research, 35(2), 254-265, (1987).
• [26] Sağlık Bakanlığı (2021), 19 Ağustos 2021 tarihinde https://covid19asi.saglik.gov.tr/TR-77809/turkiyenin-asi-soguk-zincir-ve-lojistik-kapasitesi.html adresinden alınmıştır.