{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,8]],"date-time":"2026-08-08T09:25:06Z","timestamp":1786181106145,"version":"3.56.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["444657906"],"award-info":[{"award-number":["444657906"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["OR Spectrum"],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An increasing number of local shops offer same-day delivery in order to compete with the online giants. However, the distribution of parcels from individual shops to customers reduces the rare consolidation opportunities in the last mile even further. Thus, shops start collaborating on urban same-day delivery by using shared vehicles and micro-depots for consolidated transportation of parcels. At this, many stakeholders (storekeepers, drivers, and customers) need to be coordinated. Consistent routes between micro-hubs simplify the distribution process and increase reliability for all stakeholders involved. The shared vehicles thus conduct consistent daily routes between micro-hubs in the city, serving as transshipment and consolidation centres. This allows stores to bring orders to the next micro-hub, where the parcel is picked up by a vehicle and delivered to the micro-hub closest to its destination\u2014if it is feasible with respect to the vehicle\u2019s consistent daily schedule. Creating effective schedules is therefore very important. The difficulty of finding an effective consistent route is amplified by the daily uncertainty in order placements. We model the problem as a two-stage stochastic program. While the first stage determines the vehicle schedules, the second stage optimises the flow of realised orders. The goal is to satisfy as many orders per day as possible with the shared vehicles. We propose a time-expanded network formulation of the problem which is solved to optimality using commercial MIP-software. We assess our model against a non-consistent upper bound and a practically-inspired heuristic to evaluate the cost of consistency and the consolidation of goods. We analyse the performance of our method for a variety of instance settings. We observe that collaborative delivery via micro-hubs is worthwhile for delivery time promises of two hours or more. Noticeably, for these service promises, the costs of consistency are surprisingly low.<\/jats:p>","DOI":"10.1007\/s00291-023-00735-x","type":"journal-article","created":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T15:02:31Z","timestamp":1702652551000},"page":"375-409","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Consistent routing for local same-day delivery via micro-hubs"],"prefix":"10.1007","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3484-5656","authenticated-orcid":false,"given":"Charlotte","family":"Ackva","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marlin W.","family":"Ulmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"735_CR1","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1016\/j.cor.2016.12.025","volume":"81","author":"E Angelelli","year":"2017","unstructured":"Angelelli E, Archetti C, Filippi C, Vindigni M (2017) The probabilistic orienteering problem. Comput Oper Res 81:269\u2013281","journal-title":"Comput Oper Res"},{"key":"735_CR2","doi-asserted-by":"crossref","unstructured":"Bernardo M, Pannek J (2018) Robust solution approach for the dynamic and stochastic vehicle routing problem. J Adv Transp 2018:1\u201311","DOI":"10.1155\/2018\/9848104"},{"issue":"6","key":"735_CR3","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1287\/opre.38.6.1019","volume":"38","author":"DJ Bertsimas","year":"1990","unstructured":"Bertsimas DJ, Jaillet P, Odoni AR (1990) A priori optimization. Oper Res 38(6):1019\u20131033","journal-title":"Oper Res"},{"key":"735_CR4","unstructured":"Bundesverband Paket und Expresslogistik e.V. (BIEK) (2021) KE-CONSULT Kurte & Esser GbR: M\u00f6glichmacher in bewegten Zeiten, KEP-Studie 2021\u2014Analyse des Marktes in Deutschland. https:\/\/www.biek.de\/publikationen\/studien.html. Accessed 25 Feb 2022"},{"key":"735_CR5","unstructured":"Burns T, Davis A, Harris T, Kuzmanovic A (2022) Beyond the distribution center. https:\/\/www.mckinsey.com\/industries\/retail\/our-insights\/beyond-the-distribution-center. Accessed 24 June 2022"},{"key":"735_CR6","unstructured":"Cameron I (2022) Metapack integrates with Homerr to offer sustainable deliveries for retailers. https:\/\/www.chargedretail.co.uk\/2022\/05\/27\/metapack-integrates-with-homerr-to-offer-sustainable-deliveries-for-retailers\/. Accessed 24 June 2022"},{"key":"735_CR7","doi-asserted-by":"crossref","unstructured":"Campbell AM, Thomas BW (2008) Challenges and advances in a priori routing. In: The vehicle routing problem: latest advances and new challenges. Springer, pp\u00a0123\u2013142","DOI":"10.1007\/978-0-387-77778-8_6"},{"issue":"2","key":"735_CR8","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1287\/trsc.2015.0606","volume":"50","author":"TG Crainic","year":"2016","unstructured":"Crainic TG, Errico F, Rei W, Ricciardi N (2016) Modeling demand uncertainty in two-tier city logistics tactical planning. Transp Sci 50(2):559\u2013578","journal-title":"Transp Sci"},{"key":"735_CR9","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.cor.2014.06.008","volume":"55","author":"R Cuda","year":"2015","unstructured":"Cuda R, Guastaroba G, Speranza MG (2015) A survey on two-echelon routing problems. Comput Oper Res 55:185\u2013199","journal-title":"Comput Oper Res"},{"issue":"2","key":"735_CR10","first-page":"495","volume":"33","author":"K Dalmeijer","year":"2021","unstructured":"Dalmeijer K, Desaulniers G (2021) Addressing orientation symmetry in the time window assignment vehicle routing problem. INFORMS J Comput 33(2):495\u2013510","journal-title":"INFORMS J Comput"},{"key":"735_CR11","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.cor.2017.08.015","volume":"89","author":"K Dalmeijer","year":"2018","unstructured":"Dalmeijer K, Spliet R (2018) A branch-and-cut algorithm for the time window assignment vehicle routing problem. Comput Oper Res 89:140\u2013152","journal-title":"Comput Oper Res"},{"key":"735_CR12","unstructured":"Datex (2021) 2021 update: e-commerce, last mile delivery and 3PLs. https:\/\/www.datexcorp.com\/2021-update-e-commerce-last-mile-delivery-and-3pls\/. Accessed 29 June 2022"},{"issue":"8","key":"735_CR13","doi-asserted-by":"publisher","first-page":"1937","DOI":"10.1111\/poms.13200","volume":"29","author":"M Emadikhiav","year":"2020","unstructured":"Emadikhiav M, Bergman D, Day R (2020) Consistent routing and scheduling with simultaneous pickups and deliveries. Prod Oper Manag 29(8):1937\u20131955","journal-title":"Prod Oper Manag"},{"issue":"5","key":"735_CR14","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1287\/trsc.2022.1129","volume":"56","author":"AM Florio","year":"2022","unstructured":"Florio AM, Feillet D, Poggi M, Vidal T (2022) Vehicle routing with stochastic demands and partial reoptimization. Transp Sci 56(5):1393\u20131408","journal-title":"Transp Sci"},{"issue":"4","key":"735_CR15","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1287\/msom.1080.0243","volume":"11","author":"C Gro\u00ebr","year":"2009","unstructured":"Gro\u00ebr C, Golden B, Wasil E (2009) The consistent vehicle routing problem. Manuf Serv Oper Manag 11(4):630\u2013643","journal-title":"Manuf Serv Oper Manag"},{"key":"735_CR16","unstructured":"Gurobi Optimization LLC (2021) Gurobi optimizer reference manual. http:\/\/www.gurobi.com"},{"issue":"4","key":"735_CR17","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1287\/trsc.1060.0166","volume":"40","author":"LM Hvattum","year":"2006","unstructured":"Hvattum LM, L\u00f8kketangen A, Laporte G (2006) Solving a dynamic and stochastic vehicle routing problem with a sample scenario hedging heuristic. Transp Sci 40(4):421\u2013438","journal-title":"Transp Sci"},{"issue":"4","key":"735_CR18","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1080\/00207543.2020.1721589","volume":"59","author":"D Jiang","year":"2021","unstructured":"Jiang D, Li X (2021) Order fulfilment problem with time windows and synchronisation arising in the online retailing. Int J Prod Res 59(4):1187\u20131215","journal-title":"Int J Prod Res"},{"key":"735_CR19","unstructured":"Kiezbote (2021) Berliner Kiezbote liefert Pakete zur Wunschzeit: Aus Forschungsprojekt wird ein Start-up. https:\/\/www.htw-berlin.de\/einrichtungen\/zentrale-referate\/kommunikation\/pressemitteilungen\/berliner-kiezbote-liefert-pakete-zur-wunschzeit-aus-forschungsprojekt-wird-ein-start-up\/. Accessed 04 Nov 2022"},{"key":"735_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2020.104987","volume":"122","author":"\u00c7 Ko\u00e7","year":"2020","unstructured":"Ko\u00e7 \u00c7, Laporte G, T\u00fckenmez \u0130 (2020) A review of vehicle routing with simultaneous pickup and delivery. Comput Oper Res 122:104987","journal-title":"Comput Oper Res"},{"key":"735_CR21","doi-asserted-by":"crossref","unstructured":"Kovacs AA, Golden BL, Hartl RF, Parragh SN (2014a) Vehicle routing problems in which consistency considerations are important: a survey. Networks 64(3):192\u2013213","DOI":"10.1002\/net.21565"},{"key":"735_CR22","doi-asserted-by":"crossref","unstructured":"Kovacs AA, Parragh SN, Hartl RF (2014b) A template-based adaptive large neighborhood search for the consistent vehicle routing problem. Networks 63(1):60\u201381","DOI":"10.1002\/net.21522"},{"key":"735_CR23","unstructured":"Lagos F, Klapp MA, Toriello A (2019) Branch-and-price for routing with probabilistic customers. Research Report. Working Paper"},{"key":"735_CR24","unstructured":"Lian K (2017) Service consistency in vehicle routing. PhD thesis. University of Arkansas"},{"issue":"3","key":"735_CR25","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1016\/j.ejor.2020.12.064","volume":"293","author":"S Mancini","year":"2021","unstructured":"Mancini S, Gansterer M, Hartl RF (2021) The collaborative consistent vehicle routing problem with workload balance. Eur J Oper Res 293(3):955\u2013965","journal-title":"Eur J Oper Res"},{"key":"735_CR26","unstructured":"Metapack (2022) Ecommerce delivery benchmark report 2022. https:\/\/info.metapack.com\/ecommerce-delivery-benchmark-report-2022.html?utm_source=press &utm_medium=referral &utm_campaign=delivery+benchmark+2022. Accessed 29 June 2022"},{"key":"735_CR27","unstructured":"Nahata K (2022) Why retailers must simplify complex last-mile delivery. https:\/\/www.retailtouchpoints.com\/topics\/fulfillment-last-mile\/why-retailers-must-simplify-complex-last-mile-delivery. Accessed 04 Nov 2022"},{"key":"735_CR28","doi-asserted-by":"crossref","unstructured":"Neumann-Saavedra BA, Crainic TG, Gendron B, Mattfeld DC, R\u00f6mer M (2016) Service network design of bike sharing systems with resource constraints. In: Computational logistics: 7th international conference, ICCL 2016, Lisbon, Portugal, September 7\u20139, 2016, Proceedings 7 Springer (event), pp\u00a0352\u2013366","DOI":"10.1007\/978-3-319-44896-1_23"},{"key":"735_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.tre.2022.102716","volume":"161","author":"I Orenstein","year":"2022","unstructured":"Orenstein I, Raviv T (2022) Parcel delivery using the hyperconnected service network. Transp Res Part E Logist Transp Rev 161:102716","journal-title":"Transp Res Part E Logist Transp Rev"},{"issue":"1","key":"735_CR30","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.ejor.2018.07.039","volume":"273","author":"M Salavati-Khoshghalb","year":"2019","unstructured":"Salavati-Khoshghalb M, Gendreau M, Jabali O, Rei W (2019) An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy. Eur J Oper Res 273(1):175\u2013189","journal-title":"Eur J Oper Res"},{"key":"735_CR31","unstructured":"Sampaio A, Kinable J, Veelenturf LP, Van Woensel T (2019) A scenario-based approach for the vehicle routing problem with roaming delivery locations under stochastic travel times. In: Optimization online, pp\u00a01\u201329"},{"key":"735_CR32","doi-asserted-by":"crossref","unstructured":"Sluijk N, Florio AM, Kinable J, Dellaert N, Van Woensel T (2022) Two-echelon vehicle routing problems: a literature review. Eur J Oper Res 304(3):865\u2013886","DOI":"10.1016\/j.ejor.2022.02.022"},{"issue":"2","key":"735_CR33","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1287\/trsc.1120.0407","volume":"47","author":"K Smilowitz","year":"2013","unstructured":"Smilowitz K, Nowak M, Jiang T (2013) Workforce management in periodic delivery operations. Transp Sci 47(2):214\u2013230","journal-title":"Transp Sci"},{"issue":"3","key":"735_CR34","doi-asserted-by":"publisher","first-page":"823","DOI":"10.1287\/trsc.2019.0927","volume":"54","author":"Y Song","year":"2020","unstructured":"Song Y, Ulmer MW, Thomas BW, Wallace SW (2020) Building trust in home services-stochastic team-orienteering with consistency constraints. Transp Sci 54(3):823\u2013838","journal-title":"Transp Sci"},{"issue":"2","key":"735_CR35","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1287\/trsc.2016.0705","volume":"52","author":"R Spliet","year":"2018","unstructured":"Spliet R, Dabia S, Van Woensel T (2018) The time window assignment vehicle routing problem with time-dependent travel times. Transp Sci 52(2):261\u2013276","journal-title":"Transp Sci"},{"issue":"2","key":"735_CR36","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.ejor.2015.01.020","volume":"244","author":"R Spliet","year":"2015","unstructured":"Spliet R, Desaulniers G (2015) The discrete time window assignment vehicle routing problem. Eur J Oper Res 244(2):379\u2013391","journal-title":"Eur J Oper Res"},{"issue":"4","key":"735_CR37","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1287\/trsc.2013.0510","volume":"49","author":"R Spliet","year":"2015","unstructured":"Spliet R, Gabor AF (2015) The time window assignment vehicle routing problem. Transp Sci 49(4):721\u2013731","journal-title":"Transp Sci"},{"issue":"2","key":"735_CR38","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1287\/trsc.2017.0741","volume":"52","author":"A Subramanyam","year":"2018","unstructured":"Subramanyam A, Gounaris CE (2018) A decomposition algorithm for the consistent traveling salesman problem with vehicle idling. Transp Sci 52(2):386\u2013401","journal-title":"Transp Sci"},{"key":"735_CR39","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.trb.2018.09.008","volume":"117","author":"A Subramanyam","year":"2018","unstructured":"Subramanyam A, Wang A, Gounaris CE (2018) A scenario decomposition algorithm for strategic time window assignment vehicle routing problems. Transp Res Part B Methodol 117:296\u2013317","journal-title":"Transp Res Part B Methodol"},{"issue":"2","key":"735_CR40","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1287\/trsc.1090.0303","volume":"44","author":"I Sungur","year":"2010","unstructured":"Sungur I, Ren Y, Ord\u00f3\u00f1ez F, Dessouky M, Zhong H (2010) A model and algorithm for the courier delivery problem with uncertainty. Transp Sci 44(2):193\u2013205","journal-title":"Transp Sci"},{"issue":"4","key":"735_CR41","doi-asserted-by":"publisher","first-page":"4233","DOI":"10.1016\/j.eswa.2011.09.111","volume":"39","author":"CD Tarantilis","year":"2012","unstructured":"Tarantilis CD, Stavropoulou F, Repoussis PP (2012) A template-based tabu search algorithm for the consistent vehicle routing problem. Expert Syst Appl 39(4):4233\u20134239","journal-title":"Expert Syst Appl"},{"key":"735_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cor.2019.03.017","volume":"108","author":"MW Ulmer","year":"2019","unstructured":"Ulmer MW, Streng S (2019) Same-day delivery with pickup stations and autonomous vehicles. Comput Oper Res 108:1\u201319","journal-title":"Comput Oper Res"},{"key":"735_CR43","unstructured":"velove (2022) https:\/\/www.velove.se\/. Accessed 05 May 2022"},{"key":"735_CR44","unstructured":"Visser T, Savelsbergh M (2019) Strategic time slot management: a priori routing for online grocery retailing. Research Report. Working Paper"},{"issue":"1","key":"735_CR45","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1287\/trsc.2021.1072","volume":"56","author":"K Wang","year":"2021","unstructured":"Wang K, Zhen L, Xia J, Baldacci R, Wang S (2021) Routing optimization with generalized consistency requirements. Transp Sci 56(1):223\u2013244","journal-title":"Transp Sci"},{"issue":"5","key":"735_CR46","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1080\/01605682.2019.1590134","volume":"71","author":"L Zhen","year":"2020","unstructured":"Zhen L, Lv W, Wang K, Ma C, Xu Z (2020) Consistent vehicle routing problem with simultaneous distribution and collection. J Oper Res Soc 71(5):813\u2013830","journal-title":"J Oper Res Soc"}],"container-title":["OR Spectrum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-023-00735-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00291-023-00735-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-023-00735-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T16:02:14Z","timestamp":1717257734000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00291-023-00735-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,15]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["735"],"URL":"https:\/\/doi.org\/10.1007\/s00291-023-00735-x","relation":{},"ISSN":["0171-6468","1436-6304"],"issn-type":[{"value":"0171-6468","type":"print"},{"value":"1436-6304","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,15]]},"assertion":[{"value":"1 July 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 September 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}