{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T08:39:53Z","timestamp":1772354393586,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T00:00:00Z","timestamp":1747699200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The sharing economy is an inevitable trend in cold chain logistics. Most cold chain logistics enterprises are small and operate independently, with limited collaboration. Joint distribution is key to integrating cold chain logistics and the sharing economy. It aims to share logistics resources, provide collective customer service, and optimize distribution routes. However, existing studies have overlooked uncertainty factors in joint distribution optimization. To address this, we propose the Cold Chain Logistics Joint Distribution Vehicle Routing Problem with Time-Varying Network (CCLJDVRP-TVN). This model integrates traffic congestion uncertainty and constructs a time-varying network to reflect real-world conditions. The solution combines simulated annealing strategies with genetic algorithms. It also uses the entropy mechanism to optimize uncertainties, improving global search performance. The method was applied to optimize vehicle routing for three cold chain logistics companies in Beijing. The results show a reduction in logistics costs by 18.3%, carbon emissions by 15.8%, and fleet size by 12.5%. It also effectively addresses the impact of congestion and uncertainty on distribution. This study offers valuable theoretical support for optimizing joint distribution and managing uncertainties in cold chain logistics.<\/jats:p>","DOI":"10.3390\/e27050540","type":"journal-article","created":{"date-parts":[[2025,5,20]],"date-time":"2025-05-20T06:10:46Z","timestamp":1747721446000},"page":"540","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Research on Cold Chain Logistics Joint Distribution Vehicle Routing Optimization Based on Uncertainty Entropy and Time-Varying Network"],"prefix":"10.3390","volume":"27","author":[{"given":"Huaixia","family":"Shi","sequence":"first","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"},{"name":"Business School, Shanghai DianJi University, Shanghai 201306, China"}]},{"given":"Yu","family":"Hong","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"given":"Qinglei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]},{"given":"Jiyun","family":"Qin","sequence":"additional","affiliation":[{"name":"Logistics Engineering College, Shanghai Maritime University, Shanghai 201306, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.indmarman.2019.08.002","article-title":"Service innovation of cold chain logistics service providers: A multiple-case study in China","volume":"89","author":"Dai","year":"2020","journal-title":"Ind. Mark. Manag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"104585","DOI":"10.1016\/j.resconrec.2019.104585","article-title":"Sharing economy to improve routing for urban logistics distribution using electric vehicles","volume":"153","author":"Li","year":"2020","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104715","DOI":"10.1016\/j.resconrec.2020.104715","article-title":"Vehicle routing problem in cold Chain logistics: A joint distribution model with carbon trading mechanisms","volume":"156","author":"Liu","year":"2020","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Pan, J.S., Zhang, X.Y., Chu, S.C., Wang, R.Y., and Lin, B.S. (2023). An Entropy-Balanced Orthogonal Learning Bamboo Forest Growth Optimization Algorithm with Quasi-Affine Transformation Evolutionary and Its Application in Capacitated Vehicle Routing Problem. Entropy, 25.","DOI":"10.3390\/e25111488"},{"key":"ref_5","first-page":"146","article-title":"Optimization and efficiency of multi-temperature joint distribution of cold chain products: Comparative study based on cold accumulation mode and mechanical refrigeration mode","volume":"33","author":"Wang","year":"2016","journal-title":"J. Highw. Transp. Res. Dev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1016\/j.cor.2004.09.015","article-title":"Vehicle routing and scheduling with dynamic travel times","volume":"33","author":"Potvin","year":"2006","journal-title":"Comput. Oper. Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wang, S., Tao, F., Shi, Y., and Wen, H. (2017). Optimization of vehicle routing problem with time windows for cold chain logistics based on carbon tax. Sustainability, 9.","DOI":"10.3390\/su9050694"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xie, R., Huang, H., Zhang, Y., and Yu, P. (2022). Coupling relationship between cold chain logistics and economic development: A investigation from China. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0264561"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Leng, L., Zhang, J., Zhang, C., Zhao, Y., Wang, W., and Li, G. (2020). A novel bi-objective model of cold chain logistics considering location-routing decision and environmental effects. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0230867"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1186\/s13638-018-1168-4","article-title":"Optimization of cold chain logistics distribution network terminal","volume":"2018","author":"Liu","year":"2018","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.foodcont.2009.08.007","article-title":"Developing an advanced multi-temperature joint distribution system for the food cold chain","volume":"21","author":"Kuo","year":"2010","journal-title":"Food Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.jfoodeng.2006.05.029","article-title":"Vehicle routing problem with time-windows for perishable food delivery","volume":"80","author":"Hsu","year":"2007","journal-title":"J. Food Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.jfoodeng.2007.07.008","article-title":"A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food","volume":"85","author":"Osvald","year":"2008","journal-title":"J. Food Eng."},{"key":"ref_14","first-page":"55","article-title":"The front-end collection transportation optimization of cold chain logistics for fresh fruits and vegetables","volume":"39","author":"Sun","year":"2017","journal-title":"Logist. Eng. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s11750-012-0266-4","article-title":"A rich vehicle routing problem dealing with perishable food: A case study","volume":"22","author":"Amorim","year":"2014","journal-title":"Top"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jclepro.2019.05.306","article-title":"Low-carbon cold chain logistics using ribonucleic acid-ant colony optimization algorithm","volume":"233","author":"Zhang","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Qin, G., Tao, F., and Li, L. (2019). A vehicle routing optimization problem for cold chain logistics considering customer satisfaction and carbon emissions. Int. J. Environ. Res. Public health, 16.","DOI":"10.3390\/ijerph16040576"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.physa.2017.02.030","article-title":"Dynamic origin-to-destination routing of wirelessly connected, autonomous vehicles on a congested network","volume":"478","author":"Davis","year":"2017","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.trd.2018.05.005","article-title":"A distributed dynamic route guidance approach based on short-term forecasts in cooperative infrastructure-vehicle systems","volume":"66","author":"Wang","year":"2019","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.trc.2004.07.007","article-title":"Intelligent transportation system based dynamic vehicle routing and scheduling with variable travel times","volume":"12","author":"Taniguchi","year":"2004","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12548","DOI":"10.1016\/j.eswa.2011.04.041","article-title":"An object-oriented evaluation framework for dynamic vehicle routing problems under real-time information","volume":"38","author":"Liao","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1016\/j.swevo.2018.10.015","article-title":"A self-adaptive evolutionary algorithm for dynamic vehicle routing problems with traffic congestion","volume":"44","author":"Sabar","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TITS.2005.848362","article-title":"Optimal vehicle routing with real-time traffic information","volume":"6","author":"Kim","year":"2005","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.cor.2011.04.012","article-title":"Dynamic routing under recurrent and non-recurrent congestion using real-time ITS information","volume":"39","author":"Murat","year":"2012","journal-title":"Comput. Oper. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jclepro.2019.05.344","article-title":"Multi-depot green vehicle routing problem with shared transportation resource: Integration of time-dependent speed and piecewise penalty cost","volume":"232","author":"Wang","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1016\/j.knosys.2018.07.024","article-title":"Collaboration and transportation resource sharing in multiple centers vehicle routing optimization with delivery and pickup","volume":"160","author":"Wang","year":"2018","journal-title":"Knowl.-Based Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"122593","DOI":"10.1016\/j.jclepro.2020.122593","article-title":"Composite multi-objective optimization on a new collaborative vehicle routing problem with shared carriers and depots","volume":"274","author":"Zhang","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ramachandran, V. (2023). Lossy State Communication over Fading Multiple Access Channels. Entropy, 25.","DOI":"10.3390\/e25040588"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.trd.2018.01.026","article-title":"Benefit analysis of shared depot resources for multi-depot vehicle routing problem with fuel consumption","volume":"59","author":"Li","year":"2018","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"15244","DOI":"10.1016\/j.eswa.2011.05.075","article-title":"A simulated annealing heuristic for the truck and trailer routing problem with time windows","volume":"38","author":"Lin","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.jclepro.2018.11.123","article-title":"Promoting low carbon agenda in the urban logistics network distribution system","volume":"211","author":"Wang","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.resconrec.2017.09.021","article-title":"Sustainability implications of connected and autonomous vehicles for the food supply chain","volume":"128","author":"Heard","year":"2018","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1016\/j.procs.2016.08.165","article-title":"The multi-objective optimization for perishable food distribution route considering temporal-spatial distance","volume":"96","author":"Wang","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.resconrec.2019.06.002","article-title":"Digital twins probe into food cooling and biochemical quality changes for reducing losses in refrigerated supply chains","volume":"149","author":"Defraeye","year":"2019","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.resconrec.2018.10.003","article-title":"Evaluating the carbon footprint of WEEE management in the UK","volume":"141","author":"Clarke","year":"2019","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_36","first-page":"473","article-title":"Research on multi-depot green vehicle routing model and its optimization algorithm with time-varying speed","volume":"37","author":"Zhou","year":"2021","journal-title":"Control Decis."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1057\/palgrave.jors.2601163","article-title":"A unified tabu search heuristic for vehicle routing problems with time windows","volume":"52","author":"Cordeau","year":"2001","journal-title":"J. Oper. Res. Soc."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF03343534","article-title":"A cooperative and adaptive variable neighborhood search for the multi depot vehicle routing problem with time windows","volume":"1","author":"Polacek","year":"2008","journal-title":"Bus. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s10732-005-5432-5","article-title":"A variable neighborhood search for the multi depot vehicle routing problem with time windows","volume":"10","author":"Polacek","year":"2004","journal-title":"J. Heuristics"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/5\/540\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:35:40Z","timestamp":1760031340000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/5\/540"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,20]]},"references-count":39,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["e27050540"],"URL":"https:\/\/doi.org\/10.3390\/e27050540","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,20]]}}}