{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T12:07:14Z","timestamp":1776686834415,"version":"3.51.2"},"reference-count":39,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Operations Research"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.cor.2026.107495","type":"journal-article","created":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T16:46:03Z","timestamp":1775493963000},"page":"107495","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["On the Hierarchical Directed Capacitated Arc Routing Problem"],"prefix":"10.1016","volume":"192","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9923-6309","authenticated-orcid":false,"given":"Minh Ho\u00e0ng","family":"H\u00e0","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2184-191X","authenticated-orcid":false,"given":"Thu Huong","family":"Dang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1980-4274","authenticated-orcid":false,"given":"Ba Luat","family":"Le","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8102-4244","authenticated-orcid":false,"given":"Trung Thanh","family":"Nguyen","sequence":"additional","affiliation":[]},{"given":"Andr\u00e9","family":"Langevin","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.cor.2026.107495_b1","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.orl.2021.01.017","article-title":"The hierarchical Chinese postman problem: the slightest disorder makes it hard, yet disconnectedness is manageable","volume":"49","author":"Afanasev","year":"2021","journal-title":"Oper. Res. Lett."},{"key":"10.1016\/j.cor.2026.107495_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2021.107396","article-title":"Robust optimization for the hierarchical mixed capacitated general routing problem applied to winter road maintenance","volume":"158","author":"Ahabchane","year":"2021","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b3","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1111\/tgis.12495","article-title":"Street-segment-based salt and abrasive prediction for winter maintenance using machine learning and GIS","volume":"23","author":"Ahabchane","year":"2019","journal-title":"Trans. GIS"},{"issue":"2","key":"10.1016\/j.cor.2026.107495_b4","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/03052158808941206","article-title":"Postman routing problem in a hierarchical network","volume":"14","author":"Alfa","year":"1988","journal-title":"Eng. Optim."},{"key":"10.1016\/j.cor.2026.107495_b5","doi-asserted-by":"crossref","DOI":"10.1016\/j.cor.2020.105197","article-title":"Vehicle routing on road networks: how good is Euclidean approximation?","volume":"129","author":"Boyac\u0131","year":"2021","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b6","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1002\/net.22033","article-title":"On matchings, T-joins and arc routing in road networks","volume":"79","author":"Boyac\u0131","year":"2022","journal-title":"Networks"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b7","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1002\/net.22120","article-title":"Fast upper and lower bounds for a large-scale real-world arc routing problem","volume":"81","author":"Boyac\u0131","year":"2023","journal-title":"Networks"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b8","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/S0377-2217(02)00813-5","article-title":"Solving the hierarchical Chinese postman problem as a rural postman problem","volume":"155","author":"Cabral","year":"2004","journal-title":"European J. Oper. Res."},{"issue":"5","key":"10.1016\/j.cor.2026.107495_b9","first-page":"359","article-title":"Operations management for urban snow removal and disposal","volume":"29","author":"Campbell","year":"1995","journal-title":"Transp. Res. Part A: Policy Pract."},{"issue":"6","key":"10.1016\/j.cor.2026.107495_b10","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/0305-0483(73)90089-3","article-title":"The optimum traversal of a graph","volume":"1","author":"Christofides","year":"1973","journal-title":"Omega"},{"key":"10.1016\/j.cor.2026.107495_b11","first-page":"1","article-title":"A time-dependent hierarchical Chinese postman problem","author":"\u00c7odur","year":"2018","journal-title":"Cent. Eur. J. Oper. Res."},{"issue":"2","key":"10.1016\/j.cor.2026.107495_b12","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1287\/trsc.2016.0686","article-title":"The hierarchical mixed rural postman problem","volume":"51","author":"Colombi","year":"2017","journal-title":"Transp. Sci."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ejor.2016.07.026","article-title":"The hierarchical mixed rural postman problem: Polyhedral analysis and a branch-and-cut algorithm","volume":"257","author":"Colombi","year":"2017","journal-title":"European J. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b14","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1002\/net.21965","article-title":"Arc routing problems: A review of the past, present, and future","volume":"77","author":"Corber\u00e1n","year":"2021","journal-title":"Networks"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b15","first-page":"36","article-title":"Lower bounds for hierarchical Chinese postman problem","volume":"15","author":"Damodaran","year":"2008","journal-title":"Int. J. Ind. Eng.: Theory Appl. Pract."},{"issue":"3","key":"10.1016\/j.cor.2026.107495_b16","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1002\/net.3230170304","article-title":"Postman tour on a graph with precedence relation on arcs","volume":"17","author":"Dror","year":"1987","journal-title":"Networks"},{"key":"10.1016\/j.cor.2026.107495_b17","doi-asserted-by":"crossref","first-page":"125","DOI":"10.6028\/jres.069B.013","article-title":"Maximum matching and a polyhedron with 0, 1-vertices","volume":"69","author":"Edmonds","year":"1965","journal-title":"J. Res. Natl. Bur. Stand. B"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b18","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/BF01580113","article-title":"Matching, Euler tours and the Chinese postman","volume":"5","author":"Edmonds","year":"1973","journal-title":"Math. Program."},{"issue":"2","key":"10.1016\/j.cor.2026.107495_b19","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1287\/opre.43.2.231","article-title":"Arc routing problems, part I: The Chinese postman problem","volume":"43","author":"Eiselt","year":"1995","journal-title":"Oper. Res."},{"key":"10.1016\/j.cor.2026.107495_b20","series-title":"Le Probleme Du Postier Chinois Avec Contraintes G\u00e9n\u00e9rales De Pr\u00e9s\u00e9ance. M. Sc. A","author":"G\u00e9linas","year":"1992"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b21","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/S0167-6377(99)00046-2","article-title":"An algorithm for the hierarchical Chinese postman problem","volume":"26","author":"Ghiani","year":"2000","journal-title":"Oper. Res. Lett."},{"key":"10.1016\/j.cor.2026.107495_b22","first-page":"273","article-title":"Graphic programming using odd or even points","volume":"1","author":"Guan","year":"1962","journal-title":"Chin. Math."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b23","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1002\/net.21525","article-title":"Solving the close-enough arc routing problem","volume":"63","author":"Ha","year":"2014","journal-title":"Networks"},{"key":"10.1016\/j.cor.2026.107495_b24","article-title":"Application of routing technologies to rural snow and ice control","volume":"1304","author":"Haslam","year":"1991","journal-title":"Transp. Res. Rec."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b25","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.ejor.2004.06.003","article-title":"On the hierarchical Chinese postman problem with linear ordered classes","volume":"169","author":"Korteweg","year":"2006","journal-title":"European J. Oper. Res."},{"issue":"6","key":"10.1016\/j.cor.2026.107495_b26","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1080\/02630258408970368","article-title":"The snow ploughing problem solved by a graph theory algorithm","volume":"1","author":"Lemieux","year":"1984","journal-title":"Civ. Eng. Syst."},{"key":"10.1016\/j.cor.2026.107495_b27","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.tre.2014.02.002","article-title":"Optimizing road network daily maintenance operations with stochastic service and travel times","volume":"64","author":"Lu","year":"2014","journal-title":"Transp. Res. Part E: Logist. Transp. Rev."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b28","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0278-6125(84)90024-4","article-title":"Pierce point minimization and optimal torch path determination in flame cutting","volume":"3","author":"Manber","year":"1984","journal-title":"J. Manuf. Syst."},{"key":"10.1016\/j.cor.2026.107495_b29","series-title":"Proceedings of International Conference on Information Systems, Logistics and Supply Chain","article-title":"Improving snow removal operations using operations research: A case study","author":"Perrier","year":"2006"},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b30","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1287\/trsc.1070.0195","article-title":"Vehicle routing for urban snow plowing operations","volume":"42","author":"Perrier","year":"2008","journal-title":"Transp. Sci."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b31","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.cor.2004.07.006","article-title":"A survey of models and algorithms for winter road maintenance. Part I: system design for spreading and plowing","volume":"33","author":"Perrier","year":"2006","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b32","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.cor.2004.07.007","article-title":"A survey of models and algorithms for winter road maintenance. Part II: system design for snow disposal","volume":"33","author":"Perrier","year":"2006","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b33","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.cor.2005.05.007","article-title":"A survey of models and algorithms for winter road maintenance. Part III: Vehicle routing and depot location for spreading","volume":"34","author":"Perrier","year":"2007","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2026.107495_b34","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.cor.2005.05.008","article-title":"A survey of models and algorithms for winter road maintenance. Part IV: Vehicle routing and fleet sizing for plowing and snow disposal","volume":"34","author":"Perrier","year":"2007","journal-title":"Comput. Oper. Res."},{"key":"10.1016\/j.cor.2026.107495_b35","doi-asserted-by":"crossref","DOI":"10.1002\/net.21759","article-title":"Solving the large-scale min-max K-rural postman problem for snow plowing","volume":"70","author":"Quirion-Blais","year":"2017","journal-title":"Networks"},{"key":"10.1016\/j.cor.2026.107495_b36","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1179\/1942787514Y.0000000042","article-title":"A case study of snow plow routing using an adaptive large hood search metaheuristic","volume":"7","author":"Quirion-Blais","year":"2015","journal-title":"Transp. Lett."},{"key":"10.1016\/j.cor.2026.107495_b37","series-title":"2015 IEEE International Advance Computing Conference","first-page":"222","article-title":"An algorithm for hierarchical Chinese postman problem using minimum spanning tree approach based on Kruskal\u2019s algorithm","author":"Sayata","year":"2015"},{"key":"10.1016\/j.cor.2026.107495_b38","first-page":"18","article-title":"Development and application of an iterative heuristic for roadway snow and ice control","volume":"127","author":"Sullivan","year":"2019","journal-title":"Transp. Res. Part A: Policy Pract."},{"issue":"6","key":"10.1016\/j.cor.2026.107495_b39","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1061\/(ASCE)0733-947X(1994)120:6(897)","article-title":"Interactive design of service routes","volume":"120","author":"Wang","year":"1994","journal-title":"J. Transp. Eng."}],"container-title":["Computers & Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054826001139?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054826001139?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T11:23:05Z","timestamp":1776684185000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0305054826001139"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":39,"alternative-id":["S0305054826001139"],"URL":"https:\/\/doi.org\/10.1016\/j.cor.2026.107495","relation":{},"ISSN":["0305-0548"],"issn-type":[{"value":"0305-0548","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On the Hierarchical Directed Capacitated Arc Routing Problem","name":"articletitle","label":"Article Title"},{"value":"Computers & Operations Research","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cor.2026.107495","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"107495"}}