{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T05:09:30Z","timestamp":1778908170846,"version":"3.51.4"},"reference-count":55,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T00:00:00Z","timestamp":1777507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>With the rapid development of e-commerce and the increasing complexity of urban logistics, traditional delivery methods face significant challenges due to regional traffic restrictions and congestion. This paper presents a two-stage optimization approach for urban delivery routing, integrating the Split Delivery Vehicle Routing Problem (SDVRP) and truck-drone collaboration to address these challenges. In the first stage, a transportation route optimization model based on SDVRP is proposed, which accounts for regional constraints and vehicle capacity limitations. The model allows for demand splitting, reducing the number of vehicles required and minimizing transportation costs. In the second stage, a truck-drone collaborative delivery model is introduced to handle the \u201clast mile\u201d distribution, where drones complement trucks by delivering to areas with restricted vehicle access. The optimization model aims to minimize overall delivery costs while ensuring timely service. An enhanced genetic algorithm is further developed to solve this complex, multi-constrained model. Experimental results show that the proposed collaborative strategy reduces delivery costs by over 10% compared to truck-only delivery, and the improved algorithm achieves a 4.77% average cost reduction over traditional approaches. This study provides valuable insights for optimizing urban logistics systems under regional constraints, offering both theoretical and practical contributions to smart logistics development.<\/jats:p>","DOI":"10.3390\/systems14050491","type":"journal-article","created":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T14:35:53Z","timestamp":1777559753000},"page":"491","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimization of Transportation and Delivery Routes Under Regional Constraints: A Two-Stage Solution Model Based on SDVRP and Truck-Drone Collaboration"],"prefix":"10.3390","volume":"14","author":[{"given":"Weiquan","family":"Kong","sequence":"first","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6138-5130","authenticated-orcid":false,"given":"Senlai","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gaoming","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1287\/mnsc.6.1.80","article-title":"The Truck Dispatching Problem","volume":"6","author":"Dantzig","year":"1959","journal-title":"Manag. Sci."},{"key":"ref_2","first-page":"2466105","article-title":"Optimisation of multi-type vehicle routing considering soft capacity constraint and carbon emissions","volume":"12","author":"Shan","year":"2025","journal-title":"Int. J. Syst. Sci. Oper. Logist."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.endm.2010.05.081","article-title":"New Families of Valid Inequalities for the Two-Echelon Vehicle Routing Problem","volume":"36","author":"Perboli","year":"2010","journal-title":"Electron. Notes Discret. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.trc.2019.11.003","article-title":"The multiple flying sidekicks traveling salesman problem: Parcel delivery with multiple drones","volume":"110","author":"Murray","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_5","first-page":"223","article-title":"Dynamic vehicle routing problems","volume":"Volume 16","author":"Psaraftis","year":"1988","journal-title":"Vehicle Routing: Methods and Studies"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1287\/trsc.29.2.156","article-title":"Algorithms for the vehicle routing problem with time windows","volume":"29","author":"Solomon","year":"1995","journal-title":"Transp. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1287\/trsc.23.2.141","article-title":"Savings by split delivery routing","volume":"23","author":"Dror","year":"1989","journal-title":"Transp. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1002\/nav.3800370304","article-title":"Split delivery routing","volume":"37","author":"Dror","year":"1990","journal-title":"Nav. Res. Logist."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/07408179908969843","article-title":"Fleet management models and algorithms for an oil-tanker routing and scheduling problem","volume":"31","author":"Sherali","year":"1999","journal-title":"IIE Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1023\/A:1018900705946","article-title":"Routing helicopters for crew exchanges on off-shore locations","volume":"76","author":"Sierksma","year":"1998","journal-title":"Ann. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1057\/palgrave.jors.2600338","article-title":"Split-Delivery Routeing Heuristics in Livestock Feed Distribution","volume":"48","author":"Mullaseril","year":"1997","journal-title":"J. Oper. Res. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.tre.2006.05.004","article-title":"Ant colony optimization for disaster relief operations","volume":"43","author":"Wei","year":"2007","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0166-218X(92)00172-I","article-title":"Vehicle routing with split deliveries","volume":"50","author":"Dror","year":"1994","journal-title":"Discret. Appl. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.trb.2004.11.004","article-title":"A shortest path approach to the multiple-vehicle routing problem with split pick-ups","volume":"40","author":"Lee","year":"2004","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.orl.2010.04.008","article-title":"Improved lower bounds for the Split Delivery Vehicle Routing Problem","volume":"38","author":"Moreno","year":"2010","journal-title":"Oper. Res. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/net.20467","article-title":"A column generation approach for the split delivery vehicle routing problem","volume":"58","author":"Archetti","year":"2011","journal-title":"Networks"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1504\/IJMHEUR.2010.033123","article-title":"A tabu search with vocabulary building approach for the vehicle routing problem with split demands","volume":"1","author":"Aleman","year":"2010","journal-title":"Int. J. Metaheuristics"},{"key":"ref_18","first-page":"207","article-title":"A genetic algorithm for the split delivery vehicle routing problem","volume":"2","author":"Wilck","year":"2012","journal-title":"Am. J. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s10479-012-1282-3","article-title":"A Randomized Granular Tabu Search heuristic for the split delivery vehicle routing problem","volume":"222","author":"Berbotto","year":"2014","journal-title":"Ann. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4173","DOI":"10.1109\/TCYB.2019.2950626","article-title":"An evolutionary multiobjective route grouping-based heuristic algorithm for large-scale capacitated vehicle routing problems","volume":"51","author":"Zheng","year":"2021","journal-title":"IEEE Trans. Cybern."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/0305-0548(84)90007-8","article-title":"The fleet size and mix vehicle routing problem","volume":"11","author":"Golden","year":"1984","journal-title":"Comput. Oper. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3215","DOI":"10.1016\/j.cor.2012.04.007","article-title":"An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics","volume":"39","author":"Hemmelmayr","year":"2012","journal-title":"Comput. Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"104919","DOI":"10.1016\/j.cor.2020.104919","article-title":"The two-echelon vehicle routing problem with covering options: City logistics with cargo bikes and parcel lockers","volume":"118","author":"Enthoven","year":"2020","journal-title":"Comput. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1287\/trsc.2018.0844","article-title":"Branch-and-Price\u2013Based Algorithms for the Two-Echelon Vehicle Routing Problem with Time Windows","volume":"53","author":"Dellaert","year":"2019","journal-title":"Transp. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1016\/j.ejor.2017.10.017","article-title":"A branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints","volume":"266","author":"Liu","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1007\/s10878-016-0028-6","article-title":"A lower bound for the adaptive two-echelon capacitated vehicle routing problem","volume":"33","author":"Song","year":"2017","journal-title":"J. Comb. Optim."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sitek, P., Wikarek, J., and Grzybowska, K. (2014, January 4\u20136). A multi-agent approach to the multi-echelon capacitated vehicle routing problem. Proceedings of the Highlights of Practical Applications of Heterogeneous Multi-Agent Systems, Salamanca, Spain.","DOI":"10.1007\/978-3-319-07767-3_12"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Raidl, G.R., Baumhauer, T., and Hu, B. (2014). Speeding up logic-based benders\u2019 decomposition by a metaheuristic for a bi-level capacitated vehicle routing problem. Proceedings of the International Workshop on Hybrid Metaheuristics, Hamburg, Germany, 11\u201313 June 2014, Springer.","DOI":"10.1007\/978-3-319-07644-7_14"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1287\/trsc.2013.0500","article-title":"A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem","volume":"49","author":"Santos","year":"2015","journal-title":"Transp. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Akbay, M.A., Kalayci, C.B., Blum, C., and Polat, O. (2022). Variable Neighborhood Search for the Two-Echelon Electric Vehicle Routing Problem with Time Windows. Appl. Sci., 12, Correction in Appl. Sci. 2022, 12, 10737. https:\/\/doi.org\/10.3390\/app122110737.","DOI":"10.3390\/app122110737"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Akbay, M.A., and Blum, C. (2024). Mathematical formulations and results regarding two echelon electric vehicle routing problems. arXiv.","DOI":"10.1016\/j.dib.2025.111470"},{"key":"ref_32","unstructured":"Moradi, B., Faulin, J., and Juan, A.A. (2024). Two-echelon electric vehicle routing problem in parcel delivery: A literature review. arXiv."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1016\/j.ejor.2021.02.022","article-title":"Ground-vehicle and unmanned-aerial-vehicle routing problems from two-echelon scheme perspective: A review","volume":"294","author":"Li","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.trb.2023.01.002","article-title":"An exact algorithm for the two-echelon vehicle routing problem with drones","volume":"168","author":"Zhou","year":"2023","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1016\/j.ejor.2022.02.022","article-title":"Two-echelon vehicle routing problems: A literature review","volume":"304","author":"Sluijk","year":"2023","journal-title":"Eur. J. Oper. Res."},{"key":"ref_36","first-page":"318","article-title":"A multifidelity-based ant colony optimization algorithm for capacitated electric vehicle routing problems","volume":"27","author":"Wang","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"16854","DOI":"10.1109\/TITS.2025.3581316","article-title":"A surrogate-assisted bi-level evolutionary algorithm for multi-depot vehicle routing problems with uncertain demand","volume":"26","author":"Jiang","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10846-017-0548-z","article-title":"Drone-Aided Healthcare Services for Patients with Chronic Diseases in Rural Areas","volume":"88","author":"Kim","year":"2017","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wen, T., Zhongnan, Z., and Wong, K.K.L. (2016). Multi-Objective Algorithm for Blood Supply via Unmanned Aerial Vehicles to the Wounded in an Emergency Situation. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0155176"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"105443","DOI":"10.1016\/j.cor.2021.105443","article-title":"Logistics for a fleet of drones for medical item delivery: A case study for Louisville, KY","volume":"135","author":"Ghelichi","year":"2021","journal-title":"Comput. Oper. Res."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.trc.2015.03.005","article-title":"The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery","volume":"54","author":"Murray","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"102813","DOI":"10.1016\/j.trc.2020.102813","article-title":"The multiple flying sidekicks traveling salesman problem with variable drone speeds","volume":"120","author":"Raj","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"102813","DOI":"10.1016\/j.trc.2020.102913","article-title":"A column-and-row generation approach for the flying sidekick travelling salesman problem","volume":"124","author":"Boccia","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.trc.2019.02.018","article-title":"An adaptive large neighborhood search metaheuristic for the vehicle routing problem with drones","volume":"102","author":"Sacramento","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.cie.2019.01.020","article-title":"Multiple traveling salesman problem with drones: Mathematical model and heuristic approach","volume":"129","author":"Kitjacharoenchai","year":"2019","journal-title":"Comput. Ind. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1287\/ijoc.2018.0879","article-title":"The mothership and drone routing problem","volume":"32","author":"Poikonen","year":"2020","journal-title":"Inf. J. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1287\/trsc.2017.0791","article-title":"Optimization approaches for the traveling salesman problem with drone","volume":"52","author":"Agatz","year":"2018","journal-title":"Transp. Sci."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.trc.2018.04.009","article-title":"A decomposition-based iterative optimization algorithm for traveling salesman problem with drone","volume":"91","author":"Yurek","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1287\/trsc.2020.1017","article-title":"Exact methods for the traveling salesman problem with drone","volume":"55","author":"Roberti","year":"2021","journal-title":"Transp. Sci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"100025","DOI":"10.1016\/j.jatrs.2024.100025","article-title":"Coordinated last-mile deliveries with trucks and drones: A comparative study of operational modes","volume":"3","author":"Ding","year":"2024","journal-title":"J. Air Transp. Res. Soc."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"102970","DOI":"10.1016\/j.trb.2024.102970","article-title":"Hybrid truck\u2013drone delivery under aerial traffic congestion","volume":"185","author":"She","year":"2024","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"ElSayed, M., and Mohamed, M. (2020). The Uncertainty of Autonomous Unmanned Aerial Vehicles\u2019 Energy consumption. Proceedings of the IEEE Transportation Electrification Conference & Expo (ITEC), IEEE.","DOI":"10.1109\/ITEC48692.2020.9161517"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Kunarak, S. (2025). Energy Management Revolution in Unmanned Aerial Vehicles Using Deep Learning Approach. Appl. Sci., 16.","DOI":"10.3390\/app16010503"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Kierzkowski, A., Dziewonski, B., Kaliszuk, K., and Kucharski, M. (2025). Evaluation of Light Electric Flying-Wing Unmanned Aerial System Energy Consumption During Holding Maneuver. Energies, 18.","DOI":"10.3390\/en18051300"},{"key":"ref_55","first-page":"9235","article-title":"A data-driven evolutionary algorithm for dynamic vehicle routing problems with time windows under limited computational time","volume":"24","author":"Liu","year":"2023","journal-title":"IEEE Trans. Intell. Transp. Syst."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/491\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T04:25:36Z","timestamp":1778905536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/5\/491"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,30]]},"references-count":55,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["systems14050491"],"URL":"https:\/\/doi.org\/10.3390\/systems14050491","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,30]]}}}