Research Article
BibTex RIS Cite

İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR

Year 2022, Volume: 40 Issue: 2, 368 - 403, 28.06.2022
https://doi.org/10.17065/huniibf.948698

Abstract

Dağıtım ağının birden fazla kademeye bölündüğü çok-aşamalı dağıtım sistemleri, işletmelerin hem ilk kademelerde gerçekleştirdikleri büyük miktarlardaki sevkiyatlardan hem de her kademedeki araç kapasitelerinin etkin kullanımından doğan ölçek ekonomilerinden faydalanmalarını ve yoğun kentsel alanlarda gerçekleştirilen dağıtım faaliyetlerinden kaynaklanan çevresel ve sosyal etkilerin azaltılmasını sağlayabilmektedir. Bu bağlamda, akademik literatürde de çok-kademeli dağıtım sistemlerinin modellenmesine yönelik çalışmalar da artmaktadır. Bu çalışmanın amacı, çok-kademeli dağıtım sistemleri kapsamında yer alan İki-Aşamalı Araç Rotalama Problemine (2A-ARP) kapsamlı bir bakış açısı sunmak ve tek-kademeli dağıtım sistemlerine göre avantajlarını irdelemektir. Bu amaçlar doğrultusunda, literatürde yer alan 2A-ARP uygulamaları çözüm yaklaşımları açısından sınıflandırılarak metodolojik detayları tasnif edilmekte, daha sonra, bir süpermarket zincirinin verisinden hareketle oluşturulan uygulama tasarımı ile 2A-ARP modellemesi klasik Araç Rotalama Problemi (ARP) ile mesafe, yakıt tüketimi, süre ve maliyet gibi dört ayrı amaç fonksiyonu ile kıyaslamaya tabi tutulmaktadır. Kıyaslamalarda, kapasite, talep, araç sayısı ve araç kapasitesi parametrelerindeki değişimin etkisini analiz etmek amacıyla 25 senaryo ile duyarlılık analizi yapılmıştır. Tasarlanan uygulama varsayımları altında elde edilen sonuçlar, 2A-ARP modelinin ARP modeline göre daha maliyetli olmasına rağmen, süre, mesafe ve yakıt tüketimi gibi faktörler açısından daha avantajlı olduğunu göstermektedir.

References

  • Agardi, A., Kovacs, L., & Banyai, T. (2019). Two-echelon vehicle routing problem with recharge stations. Transport and Telecommunication, 20(4), 305-317. https://doi.org/10.2478/ttj-2019-0025.
  • Anderluh, A., Hemmelmayr, V. C., & Nolz, P. C. (2017). Synchronizing vans and cargo bikes in a city distribution network. Central European Journal of Operations Research, 25(2), 345-376. https://doi.org/10.1007/s10100-016-0441-z.
  • Anderluh, A., Larsen, R., Hemmelmayr, V. C., & Nolz, P. C. (2019). Impact of travel time uncertainties on the solution cost of a two-echelon vehicle routing problem with Synchronization. Flexible Services and Manufacturing Journal, 806-828. https://doi.org/10.1007/s10696-019-09351-w.
  • Anderluh, A., Nolz, P. C., Hemmelmayr, V. C., & Crainic, T. G. (2021). Multi-objective optimization of a two-echelon vehicle routing problem with vehicle synchronization and ‘Grey Zone’ customers arising in urban logistics. European Journal of Operational Research, 940-958. https://doi.org/10.1016/j.ejor.2019.07.049.
  • Angelelli, E., & Speranza, M. G. (2002). The periodic vehicle routing problem with intermediate facilities. European Journal of Operational Research, 137(2), 233-247. https://doi.org/10.1016/S0377-2217(01)00206-5.
  • Babaee Tirkolaee, E., Hadian, S., & Golpira, H. (2019). A Novel multi-objective model for two-Echelon green routing problem of perishable products with intermediate depots. Journal of Industrial Engineering and Management Studies, 6(2), 196-213. https://doi.org/10.22116/JIEMS.2019.94158.
  • Babagolzadeh, M., Shrestha, A., Abbasi, B., Zhang, S., Atefi, R., & Woodhead, A. (2019). Sustainable open vehicle routing with release-time and time-window: A two-echelon distribution system. IFAC-PapersOnLine, 52(13), 571-576. https://doi.org/10.1016/j.ifacol.2019.11.219.
  • Baldacci, R., Battarra, M., & Vigo, D. (2008). Routing a heterogeneous fleet of vehicles in the vehicle routing problem. Latest Advances and New Challenges, Springer, 3-27.
  • Baldacci, R., Mingozzi, A., Roberti, R., & Clavo, R. W. (2013). An Exact algorithm for the two-echelon capacitated vehicle routing roblem. Operations Research, 61(2), 298-314. https://doi.org/10.1287/opre.1120.1153.
  • Bard, J. F., & Nananukul, N. (2009). Heuristics for a multiperiod inventory routing problem with production decisions. Computers & Industrial Engineering, 57(3), 713-723. https://doi.org/10.1016/j.cie.2009.01.020.
  • Behnke, M., Kirschstein, T., & Bierwirth, C. (2021). A Column generation approach for an emission-oriented vehicle routing problem on a multigraph. European Journal of Operational Research, 288(3), 794-809. https://doi.org/10.1016/j.ejor.2020.06.035.
  • Belgin, Ö. (2017). İki aşamalı eş zamanlı topla-dağıt araç rotalama problemi için çözüm yaklaşımları. Doktora Tezi, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara.
  • Belgin, Ö., Karaoglan, I., & Altiparmak, F. (2018). Two-echelon vehicle routing problem with simultaneous pickup and delivery: Mathematical model and heuristic approach. Computers & Industrial Engineering, 115, 1-16. https://doi.org/10.1016/j.cie.2017.10.032.
  • Bent, R., & Van Hentenryck, P. (2004). A Two-stage hybrid local search for the vehicle routing problem with time windows. Transportation Science, 38(4), 515-530. https://doi.org/10.1287/trsc.1030.0049.
  • Bevilaqua, A., Bevilaqua, D., & Yamanaka, K. (2019). Parallel island based memetic algorithm with Lin–Kernighan local search for a real-life two-echelon heterogeneous vehicle routing problem based on Brazilian wholesale companies. Applied Soft Computing Journal, 76, 697-711. https://doi.org/10.1016/j.asoc.2018.12.036.
  • Braekers, K., Ramaekers, K., & Van Nieuwenhuyse, I. (2016). The vehicle routing problem: State of the art classification and review. Computers & Industrial Engineering, 99, 300-313. https://doi.org/10.1016/j.cie.2015.12.007.
  • Breunig, U., Schmid, V., Hartl, R. F., & Vidal, T. (2015). A Fast large neighbourhood based heuristic for the two-echelon vehicle routing problem. Working Paper.
  • Breunig, U., Schmid, V., Hartl, R. F., & Vidal, T. (2016). A Large neighbourhood based heuristic for two-echelon routing problems. Computers & Operations Research, 76, 208-225. https://doi.org/10.1016/j.cor.2016.06.014.
  • Breunig, U., Baldacci, R., Hartl, R. F., & Vidal, T. (2019). The electric two-echelon vehicle routing problem. Computers and Operations Research, 103, 198-210. https://doi.org/10.1016/j.cor.2018.11.005.
  • Cattaruzza, D., Absi, N., Feillet, D., & González-Feliu, J. (2017). Vehicle routing problems for city logistics. EURO Journal on Transportation and Logistics, 6(1), 51-79. https://doi.org/10.1007/s13676-014-0074-0.
  • Christofides, N., Mingozzi, A., & Toth, P. (1981). Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming, 20(1), 255-282. https://doi.org/10.1007/BF01589353.
  • Clarke, G., & Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4), 568-581. https://doi.org/10.1287/opre.12.4.568.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2008). Clustering-based heuristics for the two-echelon vehicle routing problem. Teknik rapor, CIRRELT-2008-46, Montreal, Canada.
  • Crainic, T. G., Perboli, G., Mancini, S., & Tadei, R. (2010). Two-echelon vehicle routing problem: A satellite location analysis. Procedia-Social and Behavioral Sciences, 2(3), 5944-5955. https://doi.org/10.1016/j.sbspro.2010.04.009.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2011). Multi-start heuristics for the two-echelon vehicle routing problem. 11th European Conference on Evolutionary Computation in Combinatorial Optimization, Torino (IT), 27-29 Nisan,179-190. https://doi.org/10.1007/978-3-642-20364-0_16.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2012). Impact of generalized travel costs on satellite location in the two-echelon vehicle routing problem. Procedia Social and Behavioral Sciences, 39, 195-204. https://doi.org/10.1016/j.sbspro.2012.03.101.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2013). GRASP with path relinking for the two-echelon vehicle routing problem. In: Advances in Metaheuristics: Operations Research / Computer Science Interfaces Series, Springer, NewYork, 53, 113-125. https://doi.org/10.1007/978-1-4614-6322-1_7.
  • Cuda, R., Guastaroba, G., & Speranza, M. G. (2015). A Survey on two-echelon routing problems, Computers & Operations Research, 55, 185-199. https://doi.org/10.1016/j.cor.2014.06.008.
  • Çetinkaya, C., Karaoglan, I., & Gökçen, H. (2013). Two-stage vehicle routing problem with arc time windows: a mixed integer programming formulation and a heuristic approach. European Journal of Operational Research, 230(3), 539-550. https://doi.org/10.1016/j.ejor.2013.05.001.
  • Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80-91. https://doi.org/10.1287/mnsc.6.1.80.
  • Dellaert, N., Dashty Saridarq, F., Van Woensel, T., & Crainic, T. G. (2016). Branch & price based algorithms for the two-echelon vehicle routing problem with time windows. Teknik rapor, CIRRELT-2016-45, Montreal, Canada. https://doi.org/10.1287/trsc.2018.0844.
  • Demir, E., Bektaş, T., & Laporte, G. (2012). An Adaptive large neighborhood search heuristic for the pollution-routing problem. European Journal of Operational Research, 223(2), 346-359. https://doi.org/10.1016/j.ejor.2012.06.044.
  • Eitzen, H., Lopez–Pires, F., Baran, B., Sandoya, F., & Chicaiza, J. L. (2017). A Multi-objective two-echelon vehicle routing problem. An Urban Goods Movement Approach for Smart City Logistics. In 2017 XLIII Latin American Computer Conference (CLEI), 4–8 Eylül, 1-10. https://doi.org/10.1109/CLEI.2017.8226454.
  • Enthoven, D. L., Jargalsaikhan, B., Roodbergen, K. J., uit het Broek, M. A., & Schrotenboer, A. H. (2020). The two-echelon vehicle routing problem with covering options: city logistics with cargo bikes and parcel lockers. Computers & Operations Research, 118, 104919. https://doi.org/10.1016/j.cor.2020.104919.
  • Esmaili, M., & Sahraeian, R. (2017). A New bi-objective model for a two-echelon capacitated vehicle routing problem for perishable products with the environmental factor. International Journal of Engineering, 30(4), 523-531. https://doi.org/10.5829/idosi.ije.2017.30.04a.10.
  • Esmaeili, M., & Sahraeian, R. (2019). Comparing two-echelon and single-echelon multi-objective capacitated vehicle routing problems. Journal of Quality Engineering and Production Optimization, 4(1), 1-16. https://doi.org/10.22070/JQEPO.2019.3262.1066.
  • Fukasawa, R., Longo, H., Lysgaard, J., De Aragao, M. P., Reis, M., Uchoa, E., & Werneck, R. F. (2006). Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming, 106(3), 491-511. https://doi.org/10.1007/s10107-005-0644-x.
  • Gonzalez-Feliu, J. (2008). Models and methods for the city logistics: The two-echelon capacitated vehicle routing problem. Doktora Tezi, Politecnico di Torino, Turin, İtalya.
  • Gonzalez-Feliu, J., Perboli, G., Tadei, R., & Vigo, D. (2008). The two-echelon capacitated vehicle routing problem. Teknik Rapor, Politecnico di Torino, İtalya.
  • Grangier, P., Gendreau, M., Lehuédé, F., & Rousseau, L. M. (2016). An Adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization. European Journal of Operational Research, 254(1), 80-91. https://doi.org/10.1016/j.ejor.2016.03.040.
  • He, P., & Li, J. (2019). The two-echelon multi-trip vehicle routing problem with dynamic satellites for crop harvesting and transportation. Applied Soft Computing Journal, 77, 387-398. https://doi.org/10.1016/j.asoc.2019.01.040.
  • Hemmelmayr, V. C., Cordeau, J. F., & Crainic, T. G. (2012). An Adaptive large neighborhood search heuristic for two-echelon vehicle routing problems arising in city logistics. Computers & Operations Research, 39(12), 3215-3228. https://doi.org/10.1016/j.cor.2012.04.007.
  • Jepsen, M., Spoorendonk, S., & Ropke, S. (2013). A Branch-and-cut algorithm for the symmetric two-echelon capacitated vehicle routing problem. Transportation Science, 47(1), 23-37. https://doi.org/10.1287/trsc.1110.0399.
  • Jie, W., Yang, J., Zhang, M., & Huang, Y. (2019). The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology. European Journal of Operational Research, 272(3), 879-904. https://doi.org/10.1016/j.ejor.2018.07.002.
  • Jin, M., Liu, K., & Eksioglu, B. (2008). A Column generation approach for the split delivery vehicle routing problem. Operations Research Letters, 36(2), 265-270. https://doi.org/10.1016/j.orl.2007.05.012.
  • Kancharla, S. R., & Ramadurai, G. (2019). Multi-Depot Two-Echelon Fuel Minimizing Routing Problem with Heterogeneous Fleets: Model and Heuristic. Networks and Spatial Economics, 19(3), 969-1005. https://doi.org/10.1007/s11067-018-9437-7.
  • Kitjacharoenchai, P., Min, B. C., & Lee, S. (2020). Two echelon vehicle routing problem with drones in last mile delivery. International Journal of Production Economics, 225, 107598. https://doi.org/10.1016/j.ijpe.2019.107598.
  • Kumar, S. N., & Panneerselvam, R. (2012). A Survey on the vehicle routing problem and ıts variants. Intelligent Information Management, 4, 66-74. https://doi.org/10.4236/iim.2012.43010.
  • Laporte, G. (1992). The ehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 59(3), 345-358. https://doi.org/10.1016/0377-2217(92)90192-C.
  • Li, H., Zhang, L., Lv, T., & Chang, X. (2016a). The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems. Transportation Research Part B: Methodological, 94, 169-188. https://doi.org/10.1016/j.trb.2016.09.012.
  • Li, H., Yuan, J., Lv, T., & Chang, X. (2016b). The Two-echelon time-constrained vehicle routing problem in linehaul-delivery systems considering carbon dioxide emissions. Transportation Research Part D: Transport and Environment, 49, 231-245. https://doi.org/10.1016/j.trd.2016.10.002.
  • Li, H., Liu, Y., Jian, X., & Lu, Y. (2018). The two-Echelon Distribution System Considering the Real-Time Transshipment Capacity Varying. Transportation Research Part B: Methodological, 110, 239-260. https://doi.org/10.1016/j.trb.2018.02.015.
  • Li, H., Bai, M., Zhao, Y., & Dai, C. (2019). Vehicle flow formulation for two-echelon time-constrained vehicle routing problem. Journal of Management Science and Engineering, 4(2), 75-90. https://doi.org/10.1016/j.jmse.2019.05.006.
  • Li, H., Liu, Y., Chen, K., & Lin, Q. (2020a). The two-echelon city logistics system with on-street satellites. Computers & Industrial Engineering, 139, 105577. https://doi.org/10.1016/j.cie.2018.12.024.
  • Li, H., Wang, H., Chen, J., & Bai, M. (2020b). Two-echelon vehicle routing problem with time windows and mobile satellites. Transportation Research Part B, 138, 179-201. https://doi.org/10.1016/j.trb.2020.05.010.
  • Liu, R., Tao, Y., Hu, Q., & Xie, X. (2017). Simulation-based optimisation approach for the stochastic two-echelon logistics problem. International Journal of Production Research, 55(1), 187-201. https://doi.org/10.1080/00207543.2016.1201221.
  • Liu, T., Luo, Z., Qin, H., & Lim, A. (2018). A Branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints. European Journal of Operational Research, 266(2), 487-497. https://doi.org/10.1016/j.ejor.2017.10.017.
  • Liu, Y., Gao, B., Liu, H., & Wei, M. (2019). Optimal production, delivery and ınventory policies for perishable products with replenishment lead time in two-echelon distribution network. In 2019 IEEE 6th International Conference on Industrial Engineering and Applications (ICIEA), Nisan, 262-266. https://doi.org/10.1109/IEA.2019.8714984.
  • Liu, Y., Liu, Z., Shi, J., Wu, G., & Pedrycz, W. (2020). Two-echelon routing problem for parcel delivery by cooperated truck and dron. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(12), 7450-7465. https://doi.org/10.1109/TSMC.2020.2968839.
  • Marques, G., Sadykov, R., Deschamps, J. C., & Dupas, R. (2020). An Improved branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. Computers & Operations Research, 114, 104833. https://doi.org/10.1016/j.cor.2019.104833.
  • Martins, L.C., Hirsch, P., & Juan, A. (2021). Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery. International Transactions in Operational Research, 28(1), 201-221 . https://doi.org/10.1111/itor.12796.
  • Meihua, W., Xuhong, T., Shan, C., & Shumin, W. (2011). Hybrid ant colony optimization algorithm for two echelon vehicle routing problem. Procedia Engineering, 15, 3361-3365. https://doi.org/10.1016/j.proeng.2011.08.630.
  • Montoya, A., Guéret, C., Mendoza, J. E., & Villegas, J. G. (2016). A Multi-space sampling heuristic for the green vehicle routing problem. Transportation Research Part C: Emerging Technologies, 70, 113-128. https://doi.org/10.1016/j.trc.2015.09.009.
  • Ombuki, B., Ross, B. J., & Hanshar, F. (2006). Multi-objective genetic algorithms for vehicle routing problem with time windows. Applied Intelligence, 24(1), 17-30. https://doi.org/10.1007/s10489-006-6926-z.
  • Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2013). An Iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 19(2), 201-232. https://doi.org/10.1007/s10732-011-9186-y.
  • Perboli, G., Tadei, R., & Masoero, F. (2009a). Valid ınequalities for the two-echelon capacitated vehicle routing problem. Teknik rapor, CIRRELT-2009-39, Montreal, Canada.
  • Perboli, G., Tadei, R., & Masoero, F. (2009b). Models and cuts for the two-echelon vehicle routing problem. In Proceedings of the International Network Optimization Conference.
  • Perboli, G., Tadei, R., & Masoero, F. (2010). New families of valid inequalities for the two-echelon vehicle routing problem. In Electronic Notes in Discrete Mathematics, 36, 639-646. https://doi.org/10.1016/j.endm.2010.05.081.
  • Perboli, G., Tadei, R., & Vigo, D. (2011). The two-echelon capacitated vehicle routing problem: models and math-based heuristics. Transportation Science, 45(3), 364-380. https://doi.org/10.1287/trsc.1110.0368.
  • Perboli, G., Tadei, R., & Fadda, E. (2018). New valid inequalities for the two-echelon capacitated vehicle routing problem. Electronic Notes in Discrete Mathematics, 64, 75-84. https://doi.org/10.1016/j.endm.2018.01.009.
  • Sahraeian, R., & Esmaeili, M. (2018). A Multi-objective two-echelon capacitated vehicle routing problem for perishable products. Journal of Industrial and Systems Engineering, 11(2), 62-84.
  • Santos, F. A., da Cunha, A. S., & Mateus, G. R. (2013). Branch-and-price algorithms for the two-echelon capacitated vehicle routing problem. Optimization Letters, 7, 1537-1547. https://doi.org/10.1007/s11590-012-0568-3.
  • Savelsbergh, M., & Van Woensel, T. (2016). 50th Anniversary ınvited article-city logistics: challenges and opportunities. Transportation Science, 50(2), 579-590. https://doi.org/10.1287/trsc.2016.0675.
  • Sitek, P., & Wikarek, J. (2014). A Novel integrated approach to the modelling and solving of the two-echelon capacitated vehicle routing problem. Production & Manufacturing Research, 2(1), 326-340. https://doi.org/10.1080/21693277.2014.910716.
  • Soriano, A., Vidal, T., Gansterer, M., & Doerner, K. (2020). The vehicle routing problem with arrival time diversification on a multigraph. European Journal of Operational Research, 286(2), 564-575. https://doi.org/10.1016/j.ejor.2020.03.061.
  • Soysal, M., Bloemhof-Ruwaard, J. M., & Bektaş, T. (2015). The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. International Journal of Production Economics, 164, 366-378. https://doi.org/10.1016/j.ijpe.2014.11.016.
  • Su, B., Zhou, J., Zhou, L., Ji, H., & Lin, G. (2019). Approximate algorithm for two-echelon vehicle routing. In 2019 International Conference on Economic Management and Model Engineering (ICEMME), Aralık, 425-443. https://doi.org/10.1109/ICEMME49371.2019.00092.
  • Tarantilis, C. D., Loannou, G., Kiranoudis, C. T., & Prastacos, G. P. (2005). Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm. Journal of the Operational Research Society, 56(5). 588-596. https://doi.org/10.1057/palgrave.jors.2601848.
  • Toth, P., & Vigo, D. (2014). Vehicle Routing Problems, Methods and Applications, 2. Edition, SIAM.
  • Treitl, S., Nolz, P. C., & Jammernegg, W. (2012). Incorporating environmental aspects in an ınventory routing problem. A Case Study from the Petrochemical Industry. Flexible Services and Manufacturing Journal, 26(1-2), 143-169. https://doi.org/10.1007/s10696-012-9158-z.
  • Vidal, T., Laporte, G., & Matl, P. (2020). A Concise guide to existing and emerging vehicle routing problem variants. European Journal of Operational Research, 286(2), 401-416. https://doi.org/10.1016/j.ejor.2019.10.010.
  • Wang, K., Lan, S., & Zhao, Y. (2017). A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service. Journal of the Operational Research Society, 68(11), 1409-1421. https://doi.org/10.1057/s41274-016-0170-7.
  • Wang, D., Zhou, H., & Feng, R. (2019). A Two-echelon vehicle routing problem ınvolving electric vehicles with time windows. In Journal of Physics: Conference Series, 1324(1), 012071. https://doi.org/10.1088/1742-6596/1324/1/012071.
  • Wang, Y., Yuan, Y., Guan, X., Xu, M., Wang, L., Wang, H., & Liu, Y. (2020). Collaborative two-echelon multicenter vehicle routing optimization based on state–space–time network representation. Journal of Cleaner Production, 258, 120590. https://doi.org/10.1016/j.jclepro.2020.120590.
  • Wang, Z., & Wen, P. (2020). Optimization of a low-carbon two-echelon heterogeneous-fleet vehicle routing for cold chain logistics under mixed time window. Sustainability, 12(5), 1967. https://doi.org/10.3390/su12051967.
  • Wei, M., Guan, H., Liu, Y., Gao, B., & Zhang, C. (2020). Production, replenishment and ınventory policies for perishable products in a two-echelon distribution network. Sustainability, 12, 4735. https://doi.org/10.3390/su12114735.
  • Yan, X., Huang, H., Hao, Z., & Wang, J. (2020). A Graph-based fuzzy evolutionary algorithm for solving two-echelon vehicle routing problems. IEEE Transactions on Evolutionary Computation, 24(1), 129-141. https://doi.org/10.1109/TEVC.2019.2911736.
  • Zeng, Z. Y., Xu, W. S., & Xu, Z. Y. (2013). A Two-phase hybrid heuristic for the two-echelon vehicle routing problem. In 2013 Chinese Automation Congress, Kasım, 625-630. https://doi.org/10.1109/CAC.2013.6775811.
  • Zeng, Z. Y., Xu, W. S., Xu, Z. Y., & Shao, W. H. (2014). A hybrid grasp+ vnd heuristic for the two-echelon vehicle routing problem arising in city logistics. Mathematical Problems in Engineering, 517467. https://doi.org/10.1155/2014/517467.
  • Zhou, L., Baldacci, R., Vigo, D., & Wang, X. (2018). A Multi-depot two-echelon vehicle routing problem with delivery options arising in the last mile distribution. European Journal of Operational Research, 265, 765-778. https://doi.org/10.1016/j.ejor.2017.08.011

TWO-ECHELON VEHICLE ROUTING PROBLEM: REVIEW AND COMPARISONS WITH CONVENTIONAL VEHICLE ROUTING PROBLEM

Year 2022, Volume: 40 Issue: 2, 368 - 403, 28.06.2022
https://doi.org/10.17065/huniibf.948698

Abstract

Multi-stage distribution systems, in which the distribution network is divided into more than one level, can enable businesses to benefit from the economies of scale arising from both large quantities of shipments at the first stages and the efficient use of vehicle capacities at all levels, and to reduce environmental and social impacts from distribution activities carried out in dense urban areas. In this context, there is an increasing interest in modeling multi-stage distribution systems in the academic literature. This research aims to provide a comprehensive look at the Two-Echelon Vehicle Routing Problem (2E-VRP) that is within the scope of multi-stage distribution systems and to examine its advantages over single-stage distribution systems. In line with these purposes, we classify 2E-VRP applications in terms of solution approaches and their methodological details, then, we design an application and compare 2E-VRP modeling with the classical Vehicle Routing Problem (VRP) using four different objective functions like distance, fuel consumption, time and cost. A sensitivity analysis is conducted with 25 scenarios to analyze the effect of changes in capacity, demand, number of vehicles, and vehicle capacity parameters. The results reveal that although the 2E-VRP model is costlier than the VRP model, it is more advantageous in terms of factors such as time, distance, and fuel consumption.

References

  • Agardi, A., Kovacs, L., & Banyai, T. (2019). Two-echelon vehicle routing problem with recharge stations. Transport and Telecommunication, 20(4), 305-317. https://doi.org/10.2478/ttj-2019-0025.
  • Anderluh, A., Hemmelmayr, V. C., & Nolz, P. C. (2017). Synchronizing vans and cargo bikes in a city distribution network. Central European Journal of Operations Research, 25(2), 345-376. https://doi.org/10.1007/s10100-016-0441-z.
  • Anderluh, A., Larsen, R., Hemmelmayr, V. C., & Nolz, P. C. (2019). Impact of travel time uncertainties on the solution cost of a two-echelon vehicle routing problem with Synchronization. Flexible Services and Manufacturing Journal, 806-828. https://doi.org/10.1007/s10696-019-09351-w.
  • Anderluh, A., Nolz, P. C., Hemmelmayr, V. C., & Crainic, T. G. (2021). Multi-objective optimization of a two-echelon vehicle routing problem with vehicle synchronization and ‘Grey Zone’ customers arising in urban logistics. European Journal of Operational Research, 940-958. https://doi.org/10.1016/j.ejor.2019.07.049.
  • Angelelli, E., & Speranza, M. G. (2002). The periodic vehicle routing problem with intermediate facilities. European Journal of Operational Research, 137(2), 233-247. https://doi.org/10.1016/S0377-2217(01)00206-5.
  • Babaee Tirkolaee, E., Hadian, S., & Golpira, H. (2019). A Novel multi-objective model for two-Echelon green routing problem of perishable products with intermediate depots. Journal of Industrial Engineering and Management Studies, 6(2), 196-213. https://doi.org/10.22116/JIEMS.2019.94158.
  • Babagolzadeh, M., Shrestha, A., Abbasi, B., Zhang, S., Atefi, R., & Woodhead, A. (2019). Sustainable open vehicle routing with release-time and time-window: A two-echelon distribution system. IFAC-PapersOnLine, 52(13), 571-576. https://doi.org/10.1016/j.ifacol.2019.11.219.
  • Baldacci, R., Battarra, M., & Vigo, D. (2008). Routing a heterogeneous fleet of vehicles in the vehicle routing problem. Latest Advances and New Challenges, Springer, 3-27.
  • Baldacci, R., Mingozzi, A., Roberti, R., & Clavo, R. W. (2013). An Exact algorithm for the two-echelon capacitated vehicle routing roblem. Operations Research, 61(2), 298-314. https://doi.org/10.1287/opre.1120.1153.
  • Bard, J. F., & Nananukul, N. (2009). Heuristics for a multiperiod inventory routing problem with production decisions. Computers & Industrial Engineering, 57(3), 713-723. https://doi.org/10.1016/j.cie.2009.01.020.
  • Behnke, M., Kirschstein, T., & Bierwirth, C. (2021). A Column generation approach for an emission-oriented vehicle routing problem on a multigraph. European Journal of Operational Research, 288(3), 794-809. https://doi.org/10.1016/j.ejor.2020.06.035.
  • Belgin, Ö. (2017). İki aşamalı eş zamanlı topla-dağıt araç rotalama problemi için çözüm yaklaşımları. Doktora Tezi, Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara.
  • Belgin, Ö., Karaoglan, I., & Altiparmak, F. (2018). Two-echelon vehicle routing problem with simultaneous pickup and delivery: Mathematical model and heuristic approach. Computers & Industrial Engineering, 115, 1-16. https://doi.org/10.1016/j.cie.2017.10.032.
  • Bent, R., & Van Hentenryck, P. (2004). A Two-stage hybrid local search for the vehicle routing problem with time windows. Transportation Science, 38(4), 515-530. https://doi.org/10.1287/trsc.1030.0049.
  • Bevilaqua, A., Bevilaqua, D., & Yamanaka, K. (2019). Parallel island based memetic algorithm with Lin–Kernighan local search for a real-life two-echelon heterogeneous vehicle routing problem based on Brazilian wholesale companies. Applied Soft Computing Journal, 76, 697-711. https://doi.org/10.1016/j.asoc.2018.12.036.
  • Braekers, K., Ramaekers, K., & Van Nieuwenhuyse, I. (2016). The vehicle routing problem: State of the art classification and review. Computers & Industrial Engineering, 99, 300-313. https://doi.org/10.1016/j.cie.2015.12.007.
  • Breunig, U., Schmid, V., Hartl, R. F., & Vidal, T. (2015). A Fast large neighbourhood based heuristic for the two-echelon vehicle routing problem. Working Paper.
  • Breunig, U., Schmid, V., Hartl, R. F., & Vidal, T. (2016). A Large neighbourhood based heuristic for two-echelon routing problems. Computers & Operations Research, 76, 208-225. https://doi.org/10.1016/j.cor.2016.06.014.
  • Breunig, U., Baldacci, R., Hartl, R. F., & Vidal, T. (2019). The electric two-echelon vehicle routing problem. Computers and Operations Research, 103, 198-210. https://doi.org/10.1016/j.cor.2018.11.005.
  • Cattaruzza, D., Absi, N., Feillet, D., & González-Feliu, J. (2017). Vehicle routing problems for city logistics. EURO Journal on Transportation and Logistics, 6(1), 51-79. https://doi.org/10.1007/s13676-014-0074-0.
  • Christofides, N., Mingozzi, A., & Toth, P. (1981). Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming, 20(1), 255-282. https://doi.org/10.1007/BF01589353.
  • Clarke, G., & Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4), 568-581. https://doi.org/10.1287/opre.12.4.568.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2008). Clustering-based heuristics for the two-echelon vehicle routing problem. Teknik rapor, CIRRELT-2008-46, Montreal, Canada.
  • Crainic, T. G., Perboli, G., Mancini, S., & Tadei, R. (2010). Two-echelon vehicle routing problem: A satellite location analysis. Procedia-Social and Behavioral Sciences, 2(3), 5944-5955. https://doi.org/10.1016/j.sbspro.2010.04.009.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2011). Multi-start heuristics for the two-echelon vehicle routing problem. 11th European Conference on Evolutionary Computation in Combinatorial Optimization, Torino (IT), 27-29 Nisan,179-190. https://doi.org/10.1007/978-3-642-20364-0_16.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2012). Impact of generalized travel costs on satellite location in the two-echelon vehicle routing problem. Procedia Social and Behavioral Sciences, 39, 195-204. https://doi.org/10.1016/j.sbspro.2012.03.101.
  • Crainic, T. G., Mancini, S., Perboli, G., & Tadei, R. (2013). GRASP with path relinking for the two-echelon vehicle routing problem. In: Advances in Metaheuristics: Operations Research / Computer Science Interfaces Series, Springer, NewYork, 53, 113-125. https://doi.org/10.1007/978-1-4614-6322-1_7.
  • Cuda, R., Guastaroba, G., & Speranza, M. G. (2015). A Survey on two-echelon routing problems, Computers & Operations Research, 55, 185-199. https://doi.org/10.1016/j.cor.2014.06.008.
  • Çetinkaya, C., Karaoglan, I., & Gökçen, H. (2013). Two-stage vehicle routing problem with arc time windows: a mixed integer programming formulation and a heuristic approach. European Journal of Operational Research, 230(3), 539-550. https://doi.org/10.1016/j.ejor.2013.05.001.
  • Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80-91. https://doi.org/10.1287/mnsc.6.1.80.
  • Dellaert, N., Dashty Saridarq, F., Van Woensel, T., & Crainic, T. G. (2016). Branch & price based algorithms for the two-echelon vehicle routing problem with time windows. Teknik rapor, CIRRELT-2016-45, Montreal, Canada. https://doi.org/10.1287/trsc.2018.0844.
  • Demir, E., Bektaş, T., & Laporte, G. (2012). An Adaptive large neighborhood search heuristic for the pollution-routing problem. European Journal of Operational Research, 223(2), 346-359. https://doi.org/10.1016/j.ejor.2012.06.044.
  • Eitzen, H., Lopez–Pires, F., Baran, B., Sandoya, F., & Chicaiza, J. L. (2017). A Multi-objective two-echelon vehicle routing problem. An Urban Goods Movement Approach for Smart City Logistics. In 2017 XLIII Latin American Computer Conference (CLEI), 4–8 Eylül, 1-10. https://doi.org/10.1109/CLEI.2017.8226454.
  • Enthoven, D. L., Jargalsaikhan, B., Roodbergen, K. J., uit het Broek, M. A., & Schrotenboer, A. H. (2020). The two-echelon vehicle routing problem with covering options: city logistics with cargo bikes and parcel lockers. Computers & Operations Research, 118, 104919. https://doi.org/10.1016/j.cor.2020.104919.
  • Esmaili, M., & Sahraeian, R. (2017). A New bi-objective model for a two-echelon capacitated vehicle routing problem for perishable products with the environmental factor. International Journal of Engineering, 30(4), 523-531. https://doi.org/10.5829/idosi.ije.2017.30.04a.10.
  • Esmaeili, M., & Sahraeian, R. (2019). Comparing two-echelon and single-echelon multi-objective capacitated vehicle routing problems. Journal of Quality Engineering and Production Optimization, 4(1), 1-16. https://doi.org/10.22070/JQEPO.2019.3262.1066.
  • Fukasawa, R., Longo, H., Lysgaard, J., De Aragao, M. P., Reis, M., Uchoa, E., & Werneck, R. F. (2006). Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming, 106(3), 491-511. https://doi.org/10.1007/s10107-005-0644-x.
  • Gonzalez-Feliu, J. (2008). Models and methods for the city logistics: The two-echelon capacitated vehicle routing problem. Doktora Tezi, Politecnico di Torino, Turin, İtalya.
  • Gonzalez-Feliu, J., Perboli, G., Tadei, R., & Vigo, D. (2008). The two-echelon capacitated vehicle routing problem. Teknik Rapor, Politecnico di Torino, İtalya.
  • Grangier, P., Gendreau, M., Lehuédé, F., & Rousseau, L. M. (2016). An Adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization. European Journal of Operational Research, 254(1), 80-91. https://doi.org/10.1016/j.ejor.2016.03.040.
  • He, P., & Li, J. (2019). The two-echelon multi-trip vehicle routing problem with dynamic satellites for crop harvesting and transportation. Applied Soft Computing Journal, 77, 387-398. https://doi.org/10.1016/j.asoc.2019.01.040.
  • Hemmelmayr, V. C., Cordeau, J. F., & Crainic, T. G. (2012). An Adaptive large neighborhood search heuristic for two-echelon vehicle routing problems arising in city logistics. Computers & Operations Research, 39(12), 3215-3228. https://doi.org/10.1016/j.cor.2012.04.007.
  • Jepsen, M., Spoorendonk, S., & Ropke, S. (2013). A Branch-and-cut algorithm for the symmetric two-echelon capacitated vehicle routing problem. Transportation Science, 47(1), 23-37. https://doi.org/10.1287/trsc.1110.0399.
  • Jie, W., Yang, J., Zhang, M., & Huang, Y. (2019). The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology. European Journal of Operational Research, 272(3), 879-904. https://doi.org/10.1016/j.ejor.2018.07.002.
  • Jin, M., Liu, K., & Eksioglu, B. (2008). A Column generation approach for the split delivery vehicle routing problem. Operations Research Letters, 36(2), 265-270. https://doi.org/10.1016/j.orl.2007.05.012.
  • Kancharla, S. R., & Ramadurai, G. (2019). Multi-Depot Two-Echelon Fuel Minimizing Routing Problem with Heterogeneous Fleets: Model and Heuristic. Networks and Spatial Economics, 19(3), 969-1005. https://doi.org/10.1007/s11067-018-9437-7.
  • Kitjacharoenchai, P., Min, B. C., & Lee, S. (2020). Two echelon vehicle routing problem with drones in last mile delivery. International Journal of Production Economics, 225, 107598. https://doi.org/10.1016/j.ijpe.2019.107598.
  • Kumar, S. N., & Panneerselvam, R. (2012). A Survey on the vehicle routing problem and ıts variants. Intelligent Information Management, 4, 66-74. https://doi.org/10.4236/iim.2012.43010.
  • Laporte, G. (1992). The ehicle routing problem: An overview of exact and approximate algorithms. European Journal of Operational Research, 59(3), 345-358. https://doi.org/10.1016/0377-2217(92)90192-C.
  • Li, H., Zhang, L., Lv, T., & Chang, X. (2016a). The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems. Transportation Research Part B: Methodological, 94, 169-188. https://doi.org/10.1016/j.trb.2016.09.012.
  • Li, H., Yuan, J., Lv, T., & Chang, X. (2016b). The Two-echelon time-constrained vehicle routing problem in linehaul-delivery systems considering carbon dioxide emissions. Transportation Research Part D: Transport and Environment, 49, 231-245. https://doi.org/10.1016/j.trd.2016.10.002.
  • Li, H., Liu, Y., Jian, X., & Lu, Y. (2018). The two-Echelon Distribution System Considering the Real-Time Transshipment Capacity Varying. Transportation Research Part B: Methodological, 110, 239-260. https://doi.org/10.1016/j.trb.2018.02.015.
  • Li, H., Bai, M., Zhao, Y., & Dai, C. (2019). Vehicle flow formulation for two-echelon time-constrained vehicle routing problem. Journal of Management Science and Engineering, 4(2), 75-90. https://doi.org/10.1016/j.jmse.2019.05.006.
  • Li, H., Liu, Y., Chen, K., & Lin, Q. (2020a). The two-echelon city logistics system with on-street satellites. Computers & Industrial Engineering, 139, 105577. https://doi.org/10.1016/j.cie.2018.12.024.
  • Li, H., Wang, H., Chen, J., & Bai, M. (2020b). Two-echelon vehicle routing problem with time windows and mobile satellites. Transportation Research Part B, 138, 179-201. https://doi.org/10.1016/j.trb.2020.05.010.
  • Liu, R., Tao, Y., Hu, Q., & Xie, X. (2017). Simulation-based optimisation approach for the stochastic two-echelon logistics problem. International Journal of Production Research, 55(1), 187-201. https://doi.org/10.1080/00207543.2016.1201221.
  • Liu, T., Luo, Z., Qin, H., & Lim, A. (2018). A Branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints. European Journal of Operational Research, 266(2), 487-497. https://doi.org/10.1016/j.ejor.2017.10.017.
  • Liu, Y., Gao, B., Liu, H., & Wei, M. (2019). Optimal production, delivery and ınventory policies for perishable products with replenishment lead time in two-echelon distribution network. In 2019 IEEE 6th International Conference on Industrial Engineering and Applications (ICIEA), Nisan, 262-266. https://doi.org/10.1109/IEA.2019.8714984.
  • Liu, Y., Liu, Z., Shi, J., Wu, G., & Pedrycz, W. (2020). Two-echelon routing problem for parcel delivery by cooperated truck and dron. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(12), 7450-7465. https://doi.org/10.1109/TSMC.2020.2968839.
  • Marques, G., Sadykov, R., Deschamps, J. C., & Dupas, R. (2020). An Improved branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. Computers & Operations Research, 114, 104833. https://doi.org/10.1016/j.cor.2019.104833.
  • Martins, L.C., Hirsch, P., & Juan, A. (2021). Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery. International Transactions in Operational Research, 28(1), 201-221 . https://doi.org/10.1111/itor.12796.
  • Meihua, W., Xuhong, T., Shan, C., & Shumin, W. (2011). Hybrid ant colony optimization algorithm for two echelon vehicle routing problem. Procedia Engineering, 15, 3361-3365. https://doi.org/10.1016/j.proeng.2011.08.630.
  • Montoya, A., Guéret, C., Mendoza, J. E., & Villegas, J. G. (2016). A Multi-space sampling heuristic for the green vehicle routing problem. Transportation Research Part C: Emerging Technologies, 70, 113-128. https://doi.org/10.1016/j.trc.2015.09.009.
  • Ombuki, B., Ross, B. J., & Hanshar, F. (2006). Multi-objective genetic algorithms for vehicle routing problem with time windows. Applied Intelligence, 24(1), 17-30. https://doi.org/10.1007/s10489-006-6926-z.
  • Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2013). An Iterated local search heuristic for the heterogeneous fleet vehicle routing problem. Journal of Heuristics, 19(2), 201-232. https://doi.org/10.1007/s10732-011-9186-y.
  • Perboli, G., Tadei, R., & Masoero, F. (2009a). Valid ınequalities for the two-echelon capacitated vehicle routing problem. Teknik rapor, CIRRELT-2009-39, Montreal, Canada.
  • Perboli, G., Tadei, R., & Masoero, F. (2009b). Models and cuts for the two-echelon vehicle routing problem. In Proceedings of the International Network Optimization Conference.
  • Perboli, G., Tadei, R., & Masoero, F. (2010). New families of valid inequalities for the two-echelon vehicle routing problem. In Electronic Notes in Discrete Mathematics, 36, 639-646. https://doi.org/10.1016/j.endm.2010.05.081.
  • Perboli, G., Tadei, R., & Vigo, D. (2011). The two-echelon capacitated vehicle routing problem: models and math-based heuristics. Transportation Science, 45(3), 364-380. https://doi.org/10.1287/trsc.1110.0368.
  • Perboli, G., Tadei, R., & Fadda, E. (2018). New valid inequalities for the two-echelon capacitated vehicle routing problem. Electronic Notes in Discrete Mathematics, 64, 75-84. https://doi.org/10.1016/j.endm.2018.01.009.
  • Sahraeian, R., & Esmaeili, M. (2018). A Multi-objective two-echelon capacitated vehicle routing problem for perishable products. Journal of Industrial and Systems Engineering, 11(2), 62-84.
  • Santos, F. A., da Cunha, A. S., & Mateus, G. R. (2013). Branch-and-price algorithms for the two-echelon capacitated vehicle routing problem. Optimization Letters, 7, 1537-1547. https://doi.org/10.1007/s11590-012-0568-3.
  • Savelsbergh, M., & Van Woensel, T. (2016). 50th Anniversary ınvited article-city logistics: challenges and opportunities. Transportation Science, 50(2), 579-590. https://doi.org/10.1287/trsc.2016.0675.
  • Sitek, P., & Wikarek, J. (2014). A Novel integrated approach to the modelling and solving of the two-echelon capacitated vehicle routing problem. Production & Manufacturing Research, 2(1), 326-340. https://doi.org/10.1080/21693277.2014.910716.
  • Soriano, A., Vidal, T., Gansterer, M., & Doerner, K. (2020). The vehicle routing problem with arrival time diversification on a multigraph. European Journal of Operational Research, 286(2), 564-575. https://doi.org/10.1016/j.ejor.2020.03.061.
  • Soysal, M., Bloemhof-Ruwaard, J. M., & Bektaş, T. (2015). The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. International Journal of Production Economics, 164, 366-378. https://doi.org/10.1016/j.ijpe.2014.11.016.
  • Su, B., Zhou, J., Zhou, L., Ji, H., & Lin, G. (2019). Approximate algorithm for two-echelon vehicle routing. In 2019 International Conference on Economic Management and Model Engineering (ICEMME), Aralık, 425-443. https://doi.org/10.1109/ICEMME49371.2019.00092.
  • Tarantilis, C. D., Loannou, G., Kiranoudis, C. T., & Prastacos, G. P. (2005). Solving the open vehicle routeing problem via a single parameter metaheuristic algorithm. Journal of the Operational Research Society, 56(5). 588-596. https://doi.org/10.1057/palgrave.jors.2601848.
  • Toth, P., & Vigo, D. (2014). Vehicle Routing Problems, Methods and Applications, 2. Edition, SIAM.
  • Treitl, S., Nolz, P. C., & Jammernegg, W. (2012). Incorporating environmental aspects in an ınventory routing problem. A Case Study from the Petrochemical Industry. Flexible Services and Manufacturing Journal, 26(1-2), 143-169. https://doi.org/10.1007/s10696-012-9158-z.
  • Vidal, T., Laporte, G., & Matl, P. (2020). A Concise guide to existing and emerging vehicle routing problem variants. European Journal of Operational Research, 286(2), 401-416. https://doi.org/10.1016/j.ejor.2019.10.010.
  • Wang, K., Lan, S., & Zhao, Y. (2017). A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service. Journal of the Operational Research Society, 68(11), 1409-1421. https://doi.org/10.1057/s41274-016-0170-7.
  • Wang, D., Zhou, H., & Feng, R. (2019). A Two-echelon vehicle routing problem ınvolving electric vehicles with time windows. In Journal of Physics: Conference Series, 1324(1), 012071. https://doi.org/10.1088/1742-6596/1324/1/012071.
  • Wang, Y., Yuan, Y., Guan, X., Xu, M., Wang, L., Wang, H., & Liu, Y. (2020). Collaborative two-echelon multicenter vehicle routing optimization based on state–space–time network representation. Journal of Cleaner Production, 258, 120590. https://doi.org/10.1016/j.jclepro.2020.120590.
  • Wang, Z., & Wen, P. (2020). Optimization of a low-carbon two-echelon heterogeneous-fleet vehicle routing for cold chain logistics under mixed time window. Sustainability, 12(5), 1967. https://doi.org/10.3390/su12051967.
  • Wei, M., Guan, H., Liu, Y., Gao, B., & Zhang, C. (2020). Production, replenishment and ınventory policies for perishable products in a two-echelon distribution network. Sustainability, 12, 4735. https://doi.org/10.3390/su12114735.
  • Yan, X., Huang, H., Hao, Z., & Wang, J. (2020). A Graph-based fuzzy evolutionary algorithm for solving two-echelon vehicle routing problems. IEEE Transactions on Evolutionary Computation, 24(1), 129-141. https://doi.org/10.1109/TEVC.2019.2911736.
  • Zeng, Z. Y., Xu, W. S., & Xu, Z. Y. (2013). A Two-phase hybrid heuristic for the two-echelon vehicle routing problem. In 2013 Chinese Automation Congress, Kasım, 625-630. https://doi.org/10.1109/CAC.2013.6775811.
  • Zeng, Z. Y., Xu, W. S., Xu, Z. Y., & Shao, W. H. (2014). A hybrid grasp+ vnd heuristic for the two-echelon vehicle routing problem arising in city logistics. Mathematical Problems in Engineering, 517467. https://doi.org/10.1155/2014/517467.
  • Zhou, L., Baldacci, R., Vigo, D., & Wang, X. (2018). A Multi-depot two-echelon vehicle routing problem with delivery options arising in the last mile distribution. European Journal of Operational Research, 265, 765-778. https://doi.org/10.1016/j.ejor.2017.08.011
There are 90 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Ergül Kısa 0000-0002-7755-5173

Kazım Barış Atıcı 0000-0003-0786-9641

Aydın Ulucan 0000-0002-0439-2211

Publication Date June 28, 2022
Submission Date June 6, 2021
Published in Issue Year 2022 Volume: 40 Issue: 2

Cite

APA Kısa, E., Atıcı, K. B., & Ulucan, A. (2022). İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR. Hacettepe Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, 40(2), 368-403. https://doi.org/10.17065/huniibf.948698
AMA Kısa E, Atıcı KB, Ulucan A. İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR. Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi. June 2022;40(2):368-403. doi:10.17065/huniibf.948698
Chicago Kısa, Ergül, Kazım Barış Atıcı, and Aydın Ulucan. “İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR”. Hacettepe Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi 40, no. 2 (June 2022): 368-403. https://doi.org/10.17065/huniibf.948698.
EndNote Kısa E, Atıcı KB, Ulucan A (June 1, 2022) İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR. Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 40 2 368–403.
IEEE E. Kısa, K. B. Atıcı, and A. Ulucan, “İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR”, Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, vol. 40, no. 2, pp. 368–403, 2022, doi: 10.17065/huniibf.948698.
ISNAD Kısa, Ergül et al. “İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR”. Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 40/2 (June 2022), 368-403. https://doi.org/10.17065/huniibf.948698.
JAMA Kısa E, Atıcı KB, Ulucan A. İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR. Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi. 2022;40:368–403.
MLA Kısa, Ergül et al. “İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR”. Hacettepe Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, vol. 40, no. 2, 2022, pp. 368-03, doi:10.17065/huniibf.948698.
Vancouver Kısa E, Atıcı KB, Ulucan A. İKI-AŞAMALI ARAÇ ROTALAMA PROBLEMİ: TEMEL YAKLAŞIMLAR VE KONVANSİYONEL ARAÇ ROTALAMA PROBLEMİ İLE KARŞILAŞTIRMALAR. Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi. 2022;40(2):368-403.

Manuscripts must conform to the requirements indicated on the last page of the Journal - Guide for Authors- and in the web page.


Privacy Statement

Names and e-mail addresses in this Journal Web page will only be used for the specified purposes of the Journal; they will not be opened for any other purpose or use by any other person.