{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T19:01:06Z","timestamp":1772305266136,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"19","license":[{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004702","name":"Universit\u00e0 degli Studi di Genova","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004702","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2022,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Nowadays, the need to think about sustainable mobility, both goods and people, is widely recognized. For this reason, many recent papers have moved in this direction. In this context, particular attention is now devoted to urban mobility, mainly from a smart city perspective. The present work focuses on sustainable urban freight distribution and proposes a variant of the VRP, which presents some innovative aspects. The goal is to minimize the routes\u2019 cost components, including traveling and external costs due to environmental issues, depending on the chosen vehicles and the different urban streets to cross. In addition, restrictions on the maximum duration of each route to ensure frequent sanitation of vehicles used for deliveries, as required from the beginning of the COVID-19 pandemic, are imposed. The distribution network is modeled by a weighted digraph for which some properties are proved. To face the problem, we present a mixed-integer linear programming model, a math-heuristic associated with it, and a memetic algorithm approach. The results of the reported computational experimentation with random instances specifically tailored for the problem show the efficiency of the proposed methods. Further, test cases based on data of the distribution network of two B2C companies operating in the city of Genoa, Italy, proved the effective application of the proposed methods in the direction of sustainable urban distribution plans.<\/jats:p>","DOI":"10.1007\/s00500-022-07325-z","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T15:02:54Z","timestamp":1658502174000},"page":"10223-10237","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["VRP in urban areas to optimize costs while mitigating environmental impact"],"prefix":"10.1007","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6243-4512","authenticated-orcid":false,"given":"Carmine","family":"Cerrone","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7934-6992","authenticated-orcid":false,"given":"Anna","family":"Sciomachen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"issue":"4","key":"7325_CR1","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s13675-014-0030-7","volume":"2","author":"C Archetti","year":"2014","unstructured":"Archetti C, Speranza MG (2014) A survey on matheuristics for routing problems. EURO J Comput Optim 2(4):223\u2013246","journal-title":"EURO J Comput Optim"},{"key":"7325_CR2","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.tre.2017.08.011","volume":"106","author":"M Behnke","year":"2017","unstructured":"Behnke M, Kirschstein T (2017) The impact of path selection on ghg emissions in city logistics. Transp Res E Logist Transp Rev 106:320\u2013336","journal-title":"Transp Res E Logist Transp Rev"},{"issue":"8","key":"7325_CR3","doi-asserted-by":"publisher","first-page":"1232","DOI":"10.1016\/j.trb.2011.02.004","volume":"45","author":"T Bekta\u015f","year":"2011","unstructured":"Bekta\u015f T, Laporte G (2011) The pollution-routing problem. Transp Res B Methodol 45(8):1232\u20131250","journal-title":"Transp Res B Methodol"},{"issue":"3","key":"7325_CR4","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1016\/j.ejor.2018.06.001","volume":"274","author":"T Bekta\u015f","year":"2019","unstructured":"Bekta\u015f T, Ehmke JF, Psaraftis HN, Puchinger J (2019) The role of operational research in green freight transportation. Eur J Oper Res 274(3):807\u2013823","journal-title":"Eur J Oper Res"},{"key":"7325_CR5","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/j.tra.2013.09.008","volume":"57","author":"AY Bigazzi","year":"2013","unstructured":"Bigazzi AY, Figliozzi MA (2013) Marginal costs of freeway traffic congestion with on-road pollution exposure externality. Transp Res A Policy Pract 57:12\u201324","journal-title":"Transp Res A Policy Pract"},{"key":"7325_CR6","doi-asserted-by":"crossref","unstructured":"Capobianco G, Cerrone C, Cerulli R, Felici G (2017) Optimal paths for dual propulsion vehicles on real street network graphs. In: International conference on optimization and decision science. Springer, pp 517\u2013527","DOI":"10.1007\/978-3-319-67308-0_52"},{"key":"7325_CR7","doi-asserted-by":"crossref","unstructured":"Carrabs F, Cerulli R, Sciomachen A (2014) In: Dameri RP, Rosenthal-Sabroux C (eds) Environmental sustainable fleet planning in B2C e-Commerce urban distribution networks. Springer, Cham, pp 183\u2013192","DOI":"10.1007\/978-3-319-06160-3_9"},{"issue":"9","key":"7325_CR8","doi-asserted-by":"publisher","first-page":"2439","DOI":"10.1007\/s00500-016-2406-5","volume":"21","author":"F Carrabs","year":"2017","unstructured":"Carrabs F, Cerulli R, Sciomachen A (2017) An exact approach for the grocery delivery problem in urban areas. Soft Comput 21(9):2439\u20132450","journal-title":"Soft Comput"},{"issue":"2","key":"7325_CR9","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1016\/j.ejor.2018.07.004","volume":"w272","author":"C Cerrone","year":"2019","unstructured":"Cerrone C, Dussault B, Wang X, Golden B, Wasil E (2019) A two-stage solution approach for the directed rural postman problem with turn penalties. Eur J Oper Res w272(2):754\u2013765","journal-title":"Eur J Oper Res"},{"issue":"3","key":"7325_CR10","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1002\/net.22061","volume":"78","author":"C Cerrone","year":"2021","unstructured":"Cerrone C, Cerulli R, Sciomachen A (2021) Grocery distribution plans in urban networks with street crossing penalties. Networks 78(3):248\u2013263","journal-title":"Networks"},{"issue":"2","key":"7325_CR11","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1093\/imaman\/dpw024","volume":"29","author":"R Cerulli","year":"2018","unstructured":"Cerulli R, Dameri RP, Sciomachen A (2018) Operations management in distribution networks within a smart city framework. IMA J Manag Math 29(2):189\u2013205","journal-title":"IMA J Manag Math"},{"key":"7325_CR12","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.tra.2018.02.015","volume":"111","author":"T-H Chang","year":"2018","unstructured":"Chang T-H, Tseng J-S, Hsieh T-H, Hsu Y-T, Lu Y-C (2018) Green transportation implementation through distance-based road pricing. Transp Res A Policy Pract 111:53\u201364","journal-title":"Transp Res A Policy Pract"},{"key":"7325_CR13","first-page":"100233","volume":"8","author":"D Chen","year":"2020","unstructured":"Chen D, Pan S, Chen Q, Liu J (2020) Vehicle routing problem of contactless joint distribution service during covid-19 pandemic. Transp Res Interdiscip Perspect 8:100233","journal-title":"Transp Res Interdiscip Perspect"},{"issue":"3","key":"7325_CR14","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1016\/j.ejor.2011.11.010","volume":"219","author":"R Dekker","year":"2012","unstructured":"Dekker R, Bloemhof J, Mallidis I (2012) Operations research for green logistics-an overview of aspects, issues, contributions and challenges. Eur J Oper Res 219(3):671\u2013679","journal-title":"Eur J Oper Res"},{"issue":"3","key":"7325_CR15","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/j.ejor.2013.08.002","volume":"232","author":"E Demir","year":"2014","unstructured":"Demir E, Bekta\u015f T, Laporte G (2014) The bi-objective pollution-routing problem. Eur J Oper Res 232(3):464\u2013478","journal-title":"Eur J Oper Res"},{"issue":"3","key":"7325_CR16","doi-asserted-by":"publisher","first-page":"1174","DOI":"10.1016\/j.ejor.2006.06.047","volume":"185","author":"AV Donati","year":"2008","unstructured":"Donati AV, Montemanni R, Casagrande N, Rizzoli AE, Gambardella LM (2008) Time dependent vehicle routing problem with a multi ant colony system. Eur J Oper Res 185(3):1174\u20131191","journal-title":"Eur J Oper Res"},{"key":"7325_CR17","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.tre.2018.06.008","volume":"116","author":"JF Ehmke","year":"2018","unstructured":"Ehmke JF, Campbell AM, Thomas BW (2018) Optimizing for total costs in vehicle routing in urban areas. Transp Res E Logist Transp Rev 116:242\u2013265","journal-title":"Transp Res E Logist Transp Rev"},{"issue":"1","key":"7325_CR18","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.tre.2011.08.001","volume":"48","author":"S Erdo\u011fan","year":"2012","unstructured":"Erdo\u011fan S, Miller-Hooks E (2012) A green vehicle routing problem. Transp Res E Logist Transp Rev 48(1):100\u2013114","journal-title":"Transp Res E Logist Transp Rev"},{"issue":"4","key":"7325_CR19","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.tre.2009.04.005","volume":"46","author":"MA Figliozzi","year":"2010","unstructured":"Figliozzi MA (2010) The impacts of congestion on commercial vehicle tour characteristics and costs. Transp Res E Logist Transp Rev 46(4):496\u2013506","journal-title":"Transp Res E Logist Transp Rev"},{"key":"7325_CR20","doi-asserted-by":"crossref","unstructured":"Hemmelmayr VC, Doerner KF, Hartl RF (2009) A variable neighborhood search heuristic for periodic routing problems. Eur J Oper Res 195(3):791\u2013802","DOI":"10.1016\/j.ejor.2007.08.048"},{"issue":"3","key":"7325_CR21","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s13676-018-0120-4","volume":"8","author":"S Heshmati","year":"2019","unstructured":"Heshmati S, Verstichel J, Esprit E, Berghe GV (2019) Alternative e-commerce delivery policies: a case study concerning the effects on carbon emissions. EURO J Transp Logist 8(3):217\u2013248","journal-title":"EURO J Transp Logist"},{"key":"7325_CR22","volume-title":"Adaptation in nature and artificial systems","author":"J Holland","year":"1975","unstructured":"Holland J (1975) Adaptation in nature and artificial systems. University of Michigan Press, Ann Arbor"},{"key":"7325_CR23","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.trpro.2019.06.016","volume":"39","author":"S Kauf","year":"2019","unstructured":"Kauf S (2019) Smart logistics as a basis for the development of the smart city. Transp Res Procedia 39:143\u2013149","journal-title":"Transp Res Procedia"},{"key":"7325_CR24","doi-asserted-by":"crossref","unstructured":"Kellner F, Otto A, Brab\u00e4nder C (2017) Bringing infrastructure into pricing in road freight transportation-a measuring concept based on navigation service data. Transp Res Procedia 25:794\u2013805","DOI":"10.1016\/j.trpro.2017.05.458"},{"key":"7325_CR25","doi-asserted-by":"crossref","unstructured":"Koyuncu I, Yavuz M (2019) Duplicating nodes or arcs in green vehicle routing: a computational comparison of two formulations. Transp Res E Logist Transp Rev 122:605\u2013623","DOI":"10.1016\/j.tre.2018.11.003"},{"issue":"2","key":"7325_CR26","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/j.ejor.2014.12.009","volume":"243","author":"R Kramer","year":"2015","unstructured":"Kramer R, Subramanian A, Vidal T, Luc\u00eddio\u00a0dos Anjos F.C (2015) A matheuristic approach for the pollution-routing problem. Eur J Oper Res 243(2):523\u2013539","journal-title":"Eur J Oper Res"},{"issue":"1","key":"7325_CR27","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/j.eswa.2011.07.025","volume":"39","author":"X Li","year":"2012","unstructured":"Li X, Leung SC, Tian P (2012) A multistart adaptive memory-based Tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Syst Appl 39(1):365\u2013374","journal-title":"Expert Syst Appl"},{"key":"7325_CR28","doi-asserted-by":"crossref","unstructured":"Minocha B, Tripathi S, Mohan C (2011) Solving vehicle routing and scheduling problems using hybrid genetic algorithm. In: 2011 3rd International Conference on Electronics Computer Technology, vol 2. IEEE, pp 189\u2013193","DOI":"10.1109\/ICECTECH.2011.5941682"},{"key":"7325_CR29","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.trpro.2018.11.043","volume":"34","author":"M Okushima","year":"2018","unstructured":"Okushima M (2018) DIntegrated network transport simulator to evaluate transport policy for reduction of carbon dioxide emission. Transp Res Procedia 34:283\u2013290","journal-title":"Transp Res Procedia"},{"key":"7325_CR30","unstructured":"OpenStreetMap contributors: planet dump retrieved from https:\/\/planet.osm.org. https:\/\/www.openstreetmap.org (2017)"},{"key":"7325_CR31","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1016\/j.trpro.2019.07.162","volume":"40","author":"F Petro","year":"2019","unstructured":"Petro F, Kone\u010dn\u1ef3 V (2019) Calculation of external costs from production of direct and indirect emissions from traffic operation. Transp Res Procedia 40:1162\u20131167","journal-title":"Transp Res Procedia"},{"key":"7325_CR32","unstructured":"Ricardo A (2014) Final report for the European Commission. Report ED57769. European Commission\u2014Mobility and Transport DG, Brussels, p 28-0361049"},{"key":"7325_CR33","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1016\/j.tra.2019.10.002","volume":"130","author":"M Strale","year":"2019","unstructured":"Strale M (2019) Sustainable urban logistics: What are we talking about? Transp Res A Policy Pract 130:745\u2013751","journal-title":"Transp Res A Policy Pract"},{"key":"7325_CR34","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1016\/j.trpro.2019.06.054","volume":"39","author":"K Szymczyk","year":"2019","unstructured":"Szymczyk K, Kad\u0142ubek M (2019) Challenges in general cargo distribution strategy in urban logistics-comparative analysis of the biggest logistics operators in EU. Transp Res Procedia 39:525\u2013533","journal-title":"Transp Res Procedia"},{"key":"7325_CR35","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.sbspro.2012.03.087","volume":"39","author":"E Taniguchi","year":"2012","unstructured":"Taniguchi E, Thompson RG, Yamada T (2012) Emerging techniques for enhancing the practical application of city logistics models. Procedia Soc Behav Sci 39:3\u201318","journal-title":"Procedia Soc Behav Sci"},{"issue":"1","key":"7325_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2013.02.053","volume":"231","author":"T Vidal","year":"2013","unstructured":"Vidal T, Crainic TG, Gendreau M, Prins C (2013) Heuristics for multi-attribute vehicle routing problems: a survey and synthesis. Eur J Oper Res 231(1):1\u201321","journal-title":"Eur J Oper Res"},{"key":"7325_CR37","first-page":"66","volume":"6","author":"T Vidal","year":"2019","unstructured":"Vidal T, Laporte G, Matl P (2019) A concise guide to existing and emerging vehicle routing problem variants. Eur J Oper Res 6:66","journal-title":"Eur J Oper Res"},{"key":"7325_CR38","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/j.trd.2019.09.001","volume":"75","author":"X Xu","year":"2019","unstructured":"Xu X, Aziz HA, Guensler R (2019) A modal-based approach for estimating electric vehicle energy consumption in transportation networks. Transp Res D Transp Environ 75:249\u2013264","journal-title":"Transp Res D Transp Environ"},{"key":"7325_CR39","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.trb.2019.03.009","volume":"122","author":"Y Yu","year":"2019","unstructured":"Yu Y, Wang S, Wang J, Huang M (2019) A branch-and-price algorithm for the heterogeneous fleet green vehicle routing problem with time windows. Transp Res B Methodol 122:511\u2013527","journal-title":"Transp Res B Methodol"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07325-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-022-07325-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-022-07325-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T15:17:22Z","timestamp":1662995842000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-022-07325-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,22]]},"references-count":39,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["7325"],"URL":"https:\/\/doi.org\/10.1007\/s00500-022-07325-z","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,22]]},"assertion":[{"value":"19 April 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"Code developed for the model will be made available from the corresponding author on reasonable request.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}]}}