Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması

Özyörük, Bahar; AYDOĞDU, Burak

doi:10.17341/gazimmfd.490179

Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması

Burak AYDOĞDU, (Gazi Üniversitesi, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, Ankara, Türkiye)

Bahar ÖZYÖRÜK (Gazi Üniversitesi, Mühendislik Fakültesi, Endüstri Mühendisliği Bölümü, Ankara, Türkiye)

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

8 2

Yıl: 2020 Cilt: 35 Sayı: 2 Sayfa Aralığı: 563 - 580 Metin Dili: Türkçe DOI: 10.17341/gazimmfd.490179 İndeks Tarihi: 10-01-2021

Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması

Öz:

Firmaların dağıtım ve toplama taleplerini karşılayacak en uygun rotaların bulunması için Araç RotalamaProblemleri (ARP) sıkça kullanılmaktadır. Gerçek hayatta, gün içerisinde gelen yeni toplama taleplerinindolaşımda olan araçlar tarafından karşılanması firmaların taşıma maliyetlerini azaltacaktır. Bu çalışmadamüşterilerden gelen yeni toplama taleplerinin dolaşımda olan araçlar tarafından karşılanabilmesi amacıyla DinamikEş Zamanlı Topla-Dağıt Araç Rotalama Problemi (DETD_ARP) ele alınmış ve problemin çözümü için yeni birmatematiksel model geliştirilmiştir. Geliştirilen matematiksel modelin etkinliğini araştırmak için literatürde yeralan test problemleri kullanılmış ve sonuçlar değerlendirilmiştir. Matematiksel modelde problem boyutu arttıkçaçözüm süresinin üstel olarak arttığı görülmüştür. Bu yüzden DETD_ARP’yi kısa sürede çözebilmek amacıylasezgisel algoritmaların kullanılmasına karar verilmiştir. Çalışma kapsamında Rassal İteratif Yerel Arama DeğişkenKomşu İniş (R-İYA-DKİ) algoritması adında yeni bir algoritma geliştirilmiştir. R-İYA-DKİ’de üst (hyper)sezgiseller kullanılarak komşuluk yapılarının uygulama sırası azalan permütasyon yöntemine göre sürekli olarakdeğiştirilmiştir. Geliştirilen algoritmanın etkinliğini değerlendirmek için çalışma kapsamında matematiksel modelile elde edilen sonuçlar kullanılmıştır. Sonuçlara bakıldığında geliştirilen sezgisel algoritmanın matematiksel modelile elde edilen sonuçlara yakın sonuçlar verdiği görülmüştür. Son olarak orta ve büyük boyutlu problemler önerilenR-İYA-DKİ algoritması ile çözülmüş ve sonuçlar değerlendirilmiştir

Anahtar Kelime:

Mathematical model and heuristic approach for solving dynamic vehicle routing problem with simultaneous pickup and delivery: Random iterative local search variable neighborhood descent search

Öz:

Vehicle Routing Problems (VRP) are used to find the most suitable routes for fulfill the delivery and pickup demands of the companies. In real life, new pickup requests received by routed vehicles will provide a significant reduction in transport costs. As a result, a new mathematical model called as Dynamic Vehicle Routing Problem with Simultaneous Pickup and Delivery (DVRPSPD) has been developed for new pickup requests received by routed vehicles. Small and medium-sized problems were generated and solved for evaluate the effectiveness of the proposed model. The results obtained with the mathematical model were evaluated. The solution time increased exponentially as the problem size increased. In this study, heuristic algorithms were used to solve the problem in a short time. A new algorithm called Random Iterative Local Search Variable Neighborhood Descending (R-ILSVND) algorithm has been developed. Order of the neighborhood structures was changed continuously by decreasing permutation method at R-ILS-VND algorithm. In order to evaluate the effectiveness of the developed algorithm, the results were compared to the mathematical models results. When the results are analyzed, the heuristic algorithm has similar results to the mathematical model. Finally, the medium and large size problems were solved by using the proposed R-ILS-VND algorithm and the results were analyzed.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

1. Dantzig, G. B., and Ramser, J. H., The Truck Dispatching Problem. Management Science, 6 (1), 80- 91,1959.
2. Clarke, G. and Wright, J. Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12, 568–581,1964.
3. Erol, V., Araç rotalama problemleri için popülasyon ve komşuluk tabanlı metasezgisel bir algoritmanın tasarımı ve uygulaması, Yüksek Lisans Tezi, Yıldız Teknik Üniversitesi Fen Bilimleri Enstitüsü, İstanbul, 2006.
4. Irnich, S., Toth, P., and Vigo, D., Chapter 1: The family of vehicle routing problems,Vehicle routing: problems, methods, and applications, Editör: Toth, P., and Vigo, D., Society for Industrial and Applied Mathematics, 2, 2014.
5. Laporte, G., Fifty years of vehicle routing. Transportation Science, 43 (4), 408-416, 2009.
6. Laporte, G., The traveling salesman problem, the vehicle routing problem, and their ımpact on combinatorial optimization, International Journal of Strategic Decision Sciences, 1 (2), 82-92, 2010.
7. Weise T., P. A., Planning and packing problems, solving real-world vehicle routing problems with evolutionary algorithms, Natural Intelligence for Scheduling, Warsaw: Springer, 2010.
8. Göksal, F., Eşzamanlı topla-dağıt araç rotalama problemi için sezgisel yaklaşımlar: genetik algoritma ve kuş sürüsü eniyileme, Yüksek Lisans Tezi, Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Ankara, 2010.
9. Ropke, S., Pisinger., D., A unified heuristic for a large class of vehicle routing problems with backhauls, European Journal of Operational Research, 171 (3), 750- 775, 2006.
10. Berbeglia, G. , Cordeau, J.-F., Gribkovskaia, I., Laporte, G., Static pickup and delivery problems: a classification scheme and survey. TOP Off. J. Span. Soc. Stat. Oper. Res. 15, 1–31, 2007.
11. Parragh, S.N. , Doerner, K.F. , Hartl, R.F., A survey on pickup and delivery prob- lems. part I: transportation between customers and depot. J. Betr. 58, 21–51, 2008a.
12. Parragh, S.N., Doerner, K.F. , Hartl, R.F., A survey on pickup and delivery prob- lems. Part II: transportation between pickup and delivery locations. J. Betr. 58, 81– 117, 2008b.
13. Min, H., The multiple vehicle routing problem with simultaneous delivery and pickup points, Transportation Research A, 23 (5), 377- 386, 1989.
14. Halse, K., Modeling and solving complex vehicle routing problems, Ph.D thesis, Technical University of Denmark, Institute of Mathematical Statistics and Operations Research, 1992.
15. Salhi, S., Nagy, G., A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling, Journal of the Operational Research Society, 50 (10), 1034–1042, 1999.
16. Dethloff, J., Vehicle routing and reverse logistics: The vehicle routing problem with simultaneous delivery and pick-up, OR Spektrum, 23 (1), 79-96, 2001.
17. Tang, F.A., Galvao, R.D., Vehicle routing problem with simultaneous pick-up and delivery service, Journal of the Operational Research Society of India, 39, 19-33, 2002.
18. Nagy, G., Salhi, S., Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries, European Journal of Operational Research, 162 (1), 126–141, 2005.
19. Crispim, J., Brandao, J., “Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls”, Journal of the Operational Research Society, 56, 1296–1302, 2005.
20. Dell’Amico, M., Righini, G., Salani, M., A branch-andprice approach to the vehicle routing problem with simultaneous distribution and collection, Transportation Science, 40 (2), 235–247, 2006.
21. Chen, J. F., Approaches for the vehicle routing problem with simultaneous deliveries and pickups. Journal of the Chinese Institude of Industrial Engineers, 23 (2), 141- 150, 2006.
22. Chen, J. F., Wu., T. H., Vehicle routing problem with simultaneous deliveries and pickups, The journal of the Operational Research Society, 57 (5), 579-587, 2006.
23. Montane, F. A. T., Galvao, R. D., A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service, Computers and Operations Research, 33 (3), 595-619, 2006.
24. Gencer C., Yaşa Ö., Simultaneous Pick-Up And Delivery Decısıon Support Systems Of Transportatıon Command Shuttle Tour’s, Journal of the Faculty of Engineering and Architecture of Gazi University, 22 (3), 437-449, 2007.
25. Wassan, N. A., Wassan, A. H., Nagy, G., A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries, Journal of Combinatorial Optimization, 15 (4), 368–86, 2007.
26. Bianchessi, N., Righini, G., Heuristic Algorithms for the Vehicle Routing Problem with Simultaneous Pick-Up And Delivery, Computers & Operations Research, 34, 578- 594, 2009.
27. Zachariadis, E. E., Tarantilis, C. D., Kiranoudis, C. T., An adaptive memory methodology optimization for the vehicle routing problem with simultaneous pickups and deliveries, European Journal of Operational Research, 202 (2), 401-411, 2009a.
28. Zachariadis, E. E., Tarantilis, C. D., Kiranoudis, C. T., An adaptive memory methodology optimization for the vehicle routing problem with simultaneous pickups and deliveries. European Journal of Operational Research, 202 (2), 401- 411, 2009b.
29. Ai T., Kachitvichyanukul V., A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery, Computers& Operations Research, 36, 1693-1702, 2009.
30. Gajpal, Y., Abad, P., An ant colony system (ACS) for vehicle routing problem with simultaneous delivery and pickup, Computers & Operations Research, 36 (12), 3215–3223, 2009.
31. Çetin S., Gencer C., Vehicle routing problems with hard time windows and simultaneous pick up and delivery: A mathematical model, Journal of the Faculty of Engineering and Architecture of Gazi University, 25 (3), 579-585, 2010.
32. Subramanian, A., Drummond, L. M. A., Bentes, C., Ochi, L. S., Farias, R., A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery, Computers and Operations Research, 37 (11), 1899-1911,2010.
33. Mingyong, L., and Erbao, C., An improved differential evolution algorithm for vehicle routing problem with simultaneous pickups and deliveries and time Windows, Engineering Applications of Artificial Intelligence, 23, 188-195, 2010.
34. Subramanian, A., Uchoa, E., Pessoa, A. A., Ochi, L. S., Branch-and-cut with lazy separation for the vehicle routing problem with simultaneous pickup and delivery, Operations Research Letters, 39, 338-341, 2011.
35. Zachariadis, E. E., Kiranoudis, C. T., A local search metaheuristic algorithm for the vehicle routing problem with simultaneous pick-ups and deliveries. Expert Systems with Applications, 38, 2717-2726,2011.
36. Tasan, A.S., Gen, M., A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries, Computers & Industrial Engineering, 62 (3), 755–761, 2012.
37. Wang, H.F., Chen Y.Y, A genetic algorithm for the simultaneous delivery and pickup problems with time window, Computers & Industrial Engineering, 62 (1), 84–95, 2012.
38. Cruz, R.C., Silva, T.C.B, Souza M.J.F., Coelho, V.N., Mine M.T., Martins, A.X., GENVNS-TS-CL-PR: A heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery, Electronic Notes in Discrete Mathematics, 39, 217-224, 2012.
39. Zhang, T., Chaovalitwongse, W.A., Zhang Y., Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries, Computers & Operations Research, 39, 2277–2290, 2012.
40. Goksal, F. P., Karaoglan, I, Altiparmak, F., A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery, Computers and Industrial Engineering, 65 (1), 39-53, 2013.
41. Hezer S., Kara Y., Solving vehicle routing problem with simultaneous delivery and pick-up using an algorithm based on bacterial foraging optimization, Journal of the Faculty of Engineering and Architecture of Gazi University, 28 (2), 373-382, 2013.
42. Liu R., Xie, X., Augusto V., Rodriguez C., Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care, European Journal of Operational Research, 230, 475–486, 2013.
43. Avci, M., Topaloğlu, S., An adaptive local search algorithm for vehicle routing problem with simultaneous and mixed pickups and deliveries, Computers & Industrial Engineering, 83, 15–29, 2015.
44. Gschwind, T., A comparison of column generation approaches to the synchronized pickup and delivery problem. European Journal of Operational Research, 247, 60–71,2015.
45. Keçeci B., Altiparmak 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.
46. Wang, C., Mu, D., Zhao, F., Sutherland, J.W., A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup–delivery and time Windows, Computers & Industrial Engineering, 83, 111–122, 2015.
47. Li, J., Pardalos, P.M., Sun, H., Pei, J., Zhang, Y., Iterated local search embedded adaptive neighborhood selection approach for the multi-depot vehicle routing problem with simultaneous deliveries and pickups, Expert Systems with Applications, 42, 3551–3561, 2015.
48. Zachariadis E.E., Tarantilis C.D. and Kiranoudis, C.T., The vehicle routing problem with simultaneous pick-ups and deliveries and two-dimensional loading constraints. European Journal of Operational Research, 251 (2), 369–386, 2016.
49. Kalayci, C.B. and Kaya, C., An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert Systems with Applications, 66, 163–175, 2016.
50. Iassinovskaia, G., Limbourg, S. and Riane, F., The inventory-routing problem of returnable transport items with time windows and simultaneous pickup and delivery in closed-loop supply chains. International Journal Production Economics, 183, 570–582, 2017.
51. Bayrak, A. ve Özyörük, B., Comparative mathematical models for split delivery simultaneous pickup and delivery vehicle routing problem. Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (2), 469-479, 2017.
52. Zhu, L., Sheu, J-B., Failure-specific cooperative recourse strategy for simultaneous pickup and delivery problem with stochastic demands, European Journal of Operational Research, 271, 3, 896-912, 2018.
53. Belgin, O., Karaoglan, I., Altiparmak, F., Two-echelon vehicle routing problem with simultaneous pickup and delivery: Mathematical model and heuristic approach, Computers & Industrial Engineering, 115, 1-16, 2018.
54. Zhang, Z., Cheang, B., Li, C., Lim, A., Multicommodity demand fulfillment via simultaneous pickup and delivery for a fast fashion retailer, Computers & Operations Research, 103, 81-96, 2019.
55. Psaraftis, H.N., Vehicle routing: methods and studies, Elsevier Science Publishers, Amsterdam, 1988.
56. Pillac, V., Gendreau, M., Guéret, C., Medaglia, A.L., A review of dynamic vehicle routing problems, European Journal of Operational Research, 225 (1), 1–11, 2013.
57. Taillard, E.D., Gambardella, L.M., Gendreau, M., Potvin, J.-Y., Adaptive memory programming: a unified view of metaheuristics, European Journal of Operational Research, 135 (1), 1–16, 2001.
58. Lund K., Madsen O., Rygaard J., Vehicle routing problems with varying degrees of dynamism, Technical report, IMM. Department of Mathematical Modeling, Technical University of Denmark, Kogens, Lyngby, Denmark, 1996.
59. Bent, R.W., Hentenryck, P.V., Scenario-Based Planning for Partially Dynamic Vehicle Routing with Stochastic Customers, 52 (6), 977–987, 2004.
60. Du, T.C., Li, E.,Y., Chou, D., Dynamic vehicle routing for online B2C delivery, Omega, 33, 33 – 45, 2005.
61. Montemannı, R., Gambardella, L.M., Rizzoli, A.E., Donati, A.V., Ant Colony System for a Dynamic Vehicle Routing Problem, Journal of Combinatorial Optimization, 10, 327–343, 2005.
62. Haghani, A., Jung, S., A dynamic vehicle routing problem with time-dependent travel times, Computers & Operations Research, 32, 2959–2986, 2005.
63. Hanshar, F.T., Ombuki-Berman, B.M., Dynamic vehicle routing using genetic algorithms, Applied Intelligence, 27, 89–99, 2007.
64. Cheunga, B.K-S, Choyb, K.L., Lic, C-L., Shid, W., Tange, J., Dynamic routing model and solution methods for fleet management with mobile technologies, International Journal of Production Economics, 113, 694–705, 2008.
65. Liao, T.S., Hu, T-Y., An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information, Expert Systems with Applications, 38, 12548–12558, 2011.
66. Pillac, V., Guéret, C., Medaglia, A.L., An event-driven optimization framework for dynamic vehicle routing, Decision Support Systems, 54, 414–423, 2012.
67. Azi, N., Gendreau, M., Potvin, J-W, A dynamic vehicle routing problem with multiple delivery routes, Annals of Operation Research, 199, 103–112, 2012.
68. Ferrucci, F., Bock, S., Gendreau, M., A pro-active realtime control approach for dynamic vehicle routing problems dealing with the delivery of urgent goods, European Journal of Operational Research, 225,130– 141, 2013.
69. Xu, Y., Wang, L., and Yang, Y., Dynamic Vehicle Routing Using an Improved Variable Neighborhood Search Algorithm, Hindawi Publishing Corporation Journal of Applied Mathematics 2013 (2013), 12, 2013.
70. Ghannadpoura, S.F., Nooria, S., TavakkoliMoghaddam, R., Ghoseiri, K., A multi-objective dynamic vehicle routing problem with fuzzy timewindows: Model, solution and application, Applied Soft Computing, 14, 504–527, 2014.
71. Mavrovouniotis, M., Yang, S., Ant algorithms with immigrants schemes for the dynamic vehicle routing problem, Information Sciences, 294, 456–477, 2015.
72. Euchi, J., Yassine, A., Chabchoub, H., The dynamic vehicle routing problem: Solution with hybrid metaheuristic approach, Swarm and Evolutionary Computation, 21, 41-53, 2015.
73. Schyns, M., An ant colony system for responsive dynamic vehicle routing. European Journal of Operational Research, 245, 704–718, 2015.
74. Barkaoui, M., Berger, J. and Boukhtouta, A., Customer satisfaction in dynamic vehicle routing problem with time windows. Applied Soft Computing, 35, 423–432, 2015.
75. Kuo, R.J., Wibowo, B.S. and Zulvia, F.E., Application of a fuzzy ant colony system to solve the dynamic vehicle routing problem with uncertain service time. Applied Mathematical Modelling, 40, 9990–10001, 2016.
76. AbdAllah, A.M.F.M., Essam, D.L. and Sarker R.A., On solving periodic re-optimization dynamic vehicle routing problems. Applied Soft Computing, 55, 1–12, 2017.
77. Chen, S., Chen, R., Wang, G., Gao, J., Sangaiah, A.R., An adaptive large neighborhood search heuristic for dynamic vehicle routing problems, Computers & Electrical Engineering, 67, 596-607, 2018.
78. Ulmer, M.W.,Soeffker, N., Mattfeld, D.C., Value function approximation for dynamic multi-period vehicle routing, European Journal of Operational Research, 269 (3), 883-899, 2018.
79. Sabar, N.R., Bhaskar, A., Chung, E., Turky, A., Song, A., A self-adaptive evolutionary algorithm for dynamic vehicle routing problems with traffic congestion, Swarm and Evolutionary Computation, 44, 1018-1027, 2019.
80. Okulewicz, M., Mańdziuk, J., A metaheuristic approach to solve Dynamic Vehicle Routing Problem in continuous search space, Swarm and Evolutionary Computation, 48, 44-61, 2019.
81. Bektaş, T., Repoussis, P. P., Tarantilis, C. D., Chapter 11: Dynamic vehicle routing problems. In Vehicle Routing: Problems, Methods, and Applications, Second Edition, Society for Industrial and Applied Mathematics, 299-347, 2014.
82. Karaoğlan, İ., Dağıtım Ağları Tasarımında Yer Seçimi Ve Eşzamanlı Topla-Dağıt Araç Rotalama Problemleri, Doktor Tezi, Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Ankara, 2009.
83. Keçeci, B., Heterojen Eş-Zamanlı Topla-Dağıt Araç Rotalama Problemi İçin Matematiksel Modeller Ve Sezgisel Yaklaşımlar, Doktor Tezi, Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Ankara, 2014.
84. Ekizler, H., Araç Rotalama Probleminin Çözümünde Karınca Kolonisi Optimizasyonu Algoritmasının Kullanılması. Yüksek Lisans Tezi, İstanbul Üniversitesi, Fen Bilimleri Enstitüsü, İstanbul, 24, 2011.
85. Subramanian, A., Ochi, L. S., and Cabral, L.A.F., An efficient ILS heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery, Instituto de Computaçao – UFF, Technical Report – RT 07/08, 2012.
86. Penna, P. H. V., Subramanian, A., and Ochi, L. S., An iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 19, 201– 232, 2013.
87. Potvin, J-Y., and Rousseau, J-M., An exchange heuristic for routing problems with time windows. The Journal of the Operational Research Society, 46 (12), 1433-1446, 1995.
88. Nagy, G., Salhi, S., Heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries. European Journal of Operational Research, 162 (1), 126–141, 2005.
89. Osman, I.H., and Christofides, N., Simulated annealing and descent algorithms for capacitated clustering problem, Research Report, Imperial College, University of London, 1989.
90. Subramanian, A., Drummond, L. M. A., Bentes, C., Ochi, L. S., and Farias, R., A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. Computers and Operations Research, 37 (11), 1899-1911, 2010.
91. Tan, K.C., Lee, L.H., Zhu, Q.L., and Ou, K., Heuristic methods for vehicle routing problem with time Windows. Artificial Intelligence in Engineering, 15, 281-295, 2001.
92. Subramanian, A., Penna, P. H. V., Uchoa, E., Ochi, L. S., A hybrid algorithm for the Heterogeneous Fleet Routing Problem. European Journal of Operational Research, 221 (2), 285-295, 2012.
93. Taillard, E., Badeau, P., Gendreau, M., Guertin, F., Potvin, J-Y., A tabu search heuristic for the vehicle routing problem with soft time windows. Transportation Science, 31, 170-186, 1997.
94. Angelelli, E., Mansini, R., Quantitative Approaches to Distribution Logistics and Supply Chain Management, Editörler: Klose, A., Speranza, M. G., Van Wassenhove, L. N., Springer-Verlag, Berlin, 249-267, 2002.

APA	AYDOĞDU B, Özyörük B (2020). Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması. , 563 - 580. 10.17341/gazimmfd.490179
Chicago	AYDOĞDU Burak,Özyörük Bahar Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması. (2020): 563 - 580. 10.17341/gazimmfd.490179
MLA	AYDOĞDU Burak,Özyörük Bahar Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması. , 2020, ss.563 - 580. 10.17341/gazimmfd.490179
AMA	AYDOĞDU B,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. . 2020; 563 - 580. 10.17341/gazimmfd.490179
Vancouver	AYDOĞDU B,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. . 2020; 563 - 580. 10.17341/gazimmfd.490179
IEEE	AYDOĞDU B,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." , ss.563 - 580, 2020. 10.17341/gazimmfd.490179
ISNAD	AYDOĞDU, Burak - Özyörük, Bahar. "Dinamik eş zamanlı topla dağıt araç rotalama probleminin çözümü için matematiksel model ve sezgisel yaklaşım: Rassal iteratif yerel arama değişken komşu iniş algoritması". (2020), 563-580. https://doi.org/10.17341/gazimmfd.490179

APA	AYDOĞDU B, Özyörük B (2020). 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. 10.17341/gazimmfd.490179
Chicago	AYDOĞDU Burak,Özyörük Bahar 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, no.2 (2020): 563 - 580. 10.17341/gazimmfd.490179
MLA	AYDOĞDU Burak,Özyörük Bahar 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, vol.35, no.2, 2020, ss.563 - 580. 10.17341/gazimmfd.490179
AMA	AYDOĞDU B,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. 2020; 35(2): 563 - 580. 10.17341/gazimmfd.490179
Vancouver	AYDOĞDU B,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. 2020; 35(2): 563 - 580. 10.17341/gazimmfd.490179
IEEE	AYDOĞDU B,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, ss.563 - 580, 2020. 10.17341/gazimmfd.490179
ISNAD	AYDOĞDU, Burak - Özyörük, Bahar. "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 (2020), 563-580. https://doi.org/10.17341/gazimmfd.490179