{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T07:03:21Z","timestamp":1773299001219,"version":"3.50.1"},"reference-count":48,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[2002,11,1]],"date-time":"2002-11-01T00:00:00Z","timestamp":1036108800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3911,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Applied Mathematics"],"published-print":{"date-parts":[[2002,11]]},"DOI":"10.1016\/s0166-218x(01)00351-1","type":"journal-article","created":{"date-parts":[[2002,10,14]],"date-time":"2002-10-14T15:12:20Z","timestamp":1034608340000},"page":"487-512","source":"Crossref","is-referenced-by-count":273,"title":["Models, relaxations and exact approaches for the capacitated vehicle routing problem"],"prefix":"10.1016","volume":"123","author":[{"given":"Paolo","family":"Toth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniele","family":"Vigo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0166-218X(01)00351-1_BIB1","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1002\/net.3230190702","article-title":"A set-partitioning-based exact algorithm for the vehicle routing problem","volume":"19","author":"Agarwal","year":"1989","journal-title":"Networks"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB2","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1287\/opre.12.2.300","article-title":"On an integer program for a delivery problem","volume":"12","author":"Balinski","year":"1964","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB3","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1287\/opre.19.2.278","article-title":"Pathology of travelling salesman subtour-elimination algorithms","volume":"19","author":"Bellmore","year":"1971","journal-title":"Oper. Res."},{"issue":"2","key":"10.1016\/S0166-218X(01)00351-1_BIB4","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/0305-0548(83)90030-8","article-title":"Routing and scheduling of vehicles and crews, the state of the art","volume":"10","author":"Bodin","year":"1983","journal-title":"Comput. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB5","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1287\/opre.45.2.295","article-title":"On the effectiveness of the set partitioning formulation for the vehicle routing problem","volume":"45","author":"Bramel","year":"1997","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB6","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1287\/mnsc.26.7.736","article-title":"Some new branching and bounding criteria for the asymmetric traveling salesman problem","volume":"26","author":"P. Toth","year":"1980","journal-title":"Manage. Sci."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB7","series-title":"The Traveling Salesman Problem","first-page":"431","article-title":"Vehicle routing","author":"Christofides","year":"1985"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB8","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1057\/jors.1969.75","article-title":"An algorithm for the vehicle dispatching problem","volume":"20","author":"Christofides","year":"1969","journal-title":"Oper. Res. Quart."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB9","series-title":"Logistics: Where Ends Have to Meet","first-page":"30","article-title":"Vehicle routing: practical and algorithmic aspects","author":"Christofides","year":"1989"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB10","series-title":"Combinatorial Optimization","first-page":"315","article-title":"The vehicle routing problem","author":"Christofides","year":"1979"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB11","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF01589353","article-title":"Exact algorithms for the vehicle routing problem based on the spanning tree and shortest path relaxations","volume":"20","author":"Christofides","year":"1981","journal-title":"Math. Programming"},{"issue":"1","key":"10.1016\/S0166-218X(01)00351-1_BIB12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF01580599","article-title":"Polyhedral study of the capacitated vehicle routing problem","volume":"60","author":"Cornu\u00e9jols","year":"1993","journal-title":"Math. Programming"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0167-6377(91)90083-2","article-title":"Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints","volume":"10","author":"Desrochers","year":"1991","journal-title":"Oper. Res. Lett."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB14","doi-asserted-by":"crossref","unstructured":"J. Desrosiers, Y. Dumas, M.M. Solomon, F. Soumis, Time constrained routing and scheduling, in: M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, (Eds.), Network Routing, Handbooks in Operations Research and Management Science, North-Holland, Amsterdam, 1995, pp. 35\u2013139.","DOI":"10.1016\/S0927-0507(05)80106-9"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB15","unstructured":"J.J. Dongarra, Performance of various computers using standard linear equations software, Technical Report CS-89-85, University of Tennessee, Knoxville, 1996."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB16","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1287\/opre.37.2.319","article-title":"An additive bounding procedure for combinatorial optimization problems","volume":"37","author":"Fischetti","year":"1989","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB17","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/BF01585701","article-title":"An additive bounding procedure for the asymmetric travelling salesman problem","volume":"53","author":"Fischetti","year":"1992","journal-title":"Math. Programming"},{"issue":"5","key":"10.1016\/S0166-218X(01)00351-1_BIB18","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1287\/opre.42.5.846","article-title":"A branch-and-bound algorithm for the capacitated vehicle routing problem on directed graphs","volume":"42","author":"Fischetti","year":"1994","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB19","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1287\/inte.15.2.10","article-title":"An application oriented guide to Lagrangian relaxation","volume":"15","author":"Fisher","year":"1985","journal-title":"Interfaces"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB20","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1287\/opre.42.4.626","article-title":"Optimal solution of vehicle routing problems using minimum k-trees","volume":"42","author":"Fisher","year":"1994","journal-title":"Oper. Res."},{"issue":"4","key":"10.1016\/S0166-218X(01)00351-1_BIB21","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1287\/opre.42.4.775","article-title":"A polynomial algorithm for the degree constrained k-tree problem","volume":"42","author":"Fisher","year":"1994","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB22","doi-asserted-by":"crossref","unstructured":"M.L. Fisher, Vehicle routing, in: M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser (Eds.), Network Routing, Handbooks in Operations Research and Management Science, North-Holland, Amsterdam, 1995, pp. 1\u201333.","DOI":"10.1016\/S0927-0507(05)80105-7"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB23","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/0196-6774(84)90042-7","article-title":"Efficient algorithms for a family of matroid intersection problems","volume":"5","author":"Gabow","year":"1984","journal-title":"J. Algorithms"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB24","series-title":"Vehicle Routing: Methods and Studies","author":"Golden","year":"1988"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB25","series-title":"Fleet Management and Logistic","first-page":"33","article-title":"The impact of metaheuristics on solving the vehicle routing problem: algorithms, problem sets, and computational results","author":"Golden","year":"1998"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB26","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02098280","article-title":"A new exact algorithm for the vehicle routing problem based on q-Paths and k-Shortest paths relaxations","volume":"61","author":"Hadjiconstantinou","year":"1995","journal-title":"Ann. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB27","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/BF01584070","article-title":"The traveling salesman problem and minimum spanning tress: Part II","volume":"1","author":"Held","year":"1971","journal-title":"Math. Programming"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB28","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/0377-2217(85)90284-X","article-title":"Integer programming formulations of vehicle routing problems","volume":"20","author":"Kulkarni","year":"1985","journal-title":"European J. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB29","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0377-2217(92)90192-C","article-title":"The vehicle routing problem: An overview of exact and approximate algorithms","volume":"59","author":"Laporte","year":"1992","journal-title":"European J. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB30","series-title":"Annotated Bibliographies in Combinatorial Optimization","article-title":"Vehicle routing","author":"Laporte","year":"1997"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB31","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/net.3230160104","article-title":"An exact algorithm for the asymmetrical capacitated vehicle routing problem","volume":"16","author":"Laporte","year":"1986","journal-title":"Networks"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB32","first-page":"147","article-title":"Exact algorithms for the vehicle routing problem","volume":"31","author":"Laporte","year":"1987","journal-title":"Ann. Discrete Math."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB33","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1287\/opre.33.5.1050","article-title":"Optimal routing under capacity and distance restrictions","volume":"33","author":"Laporte","year":"1985","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB34","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF02098290","article-title":"Routing problems: a bibliography","volume":"61","author":"Laporte","year":"1995","journal-title":"Ann. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB35","doi-asserted-by":"crossref","first-page":"717","DOI":"10.1057\/jors.1975.151","article-title":"Some simple applications of the traveling salesman problem","volume":"26","author":"Lenstra","year":"1975","journal-title":"Oper. Res. Quart."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB36","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1287\/opre.21.2.498","article-title":"An effective heuristic algorithm for the travelling salesman problem","volume":"21","author":"Lin","year":"1973","journal-title":"Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB37","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/net.3230110209","article-title":"Combinatorial optimization and vehicle fleet planning: Perspectives and prospects","volume":"11","author":"Magnanti","year":"1981","journal-title":"Networks"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB38","series-title":"Knapsack Problems: Algorithms and Computer Implementations","author":"Martello","year":"1990"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB39","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1145\/321043.321046","article-title":"Integer programming formulations and traveling salesman problems","volume":"7","author":"Miller","year":"1960","journal-title":"ACM"},{"issue":"1","key":"10.1016\/S0166-218X(01)00351-1_BIB40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1287\/ijoc.7.1.1","article-title":"A matching based exact algorithm for capacitated vehicle routing problems","volume":"7","author":"Miller","year":"1995","journal-title":"ORSA J. Comput."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB41","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1287\/ijoc.7.3.298","article-title":"A staged primal-dual algorithm for perfect b-matching with edge capacities","volume":"7","author":"Miller","year":"1995","journal-title":"ORSA J. Comput."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB42","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1287\/ijoc.6.1.68","article-title":"A staged primal-dual algorithm for finding a minimum cost perfect two-matching in an undirected graph","volume":"6","author":"Pekny","year":"1994","journal-title":"ORSA J. Comput."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB43","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF02098285","article-title":"An exact algorithm for the capacitated shortest spanning arborescence","volume":"61","author":"Toth","year":"1995","journal-title":"Ann. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB44","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1287\/trsc.31.4.372","article-title":"An exact algorithm for the vehicle routing problem with backhauls","volume":"31","author":"Toth","year":"1997","journal-title":"Transport. Sci."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB45","series-title":"Fleet Management and Logistic","first-page":"1","article-title":"Exact solution of the vehicle routing problem","author":"Toth","year":"1998"},{"key":"10.1016\/S0166-218X(01)00351-1_BIB46","unstructured":"P. Toth, D. Vigo, The granular tabu search (and its application to the vehicle routing problem). Technical Report OR\/98\/9, D.E.I.S. - Universit\u00e0 di Bologna, 1998."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB47","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/0377-2217(96)00223-8","article-title":"A heuristic algorithm for the asymmetric capacitated vehicle routing problem","volume":"89","author":"Vigo","year":"1996","journal-title":"European J. Oper. Res."},{"key":"10.1016\/S0166-218X(01)00351-1_BIB48","unstructured":"D. Vigo, VRPLIB: a vehicle routing problem library, Technical Report OR\/99\/9, D.E.I.S., Universit\u00e1 di Bologna, 1999."}],"container-title":["Discrete Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X01003511?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0166218X01003511?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T05:50:47Z","timestamp":1680760247000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0166218X01003511"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,11]]},"references-count":48,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2002,11]]}},"alternative-id":["S0166218X01003511"],"URL":"https:\/\/doi.org\/10.1016\/s0166-218x(01)00351-1","relation":{},"ISSN":["0166-218X"],"issn-type":[{"value":"0166-218X","type":"print"}],"subject":[],"published":{"date-parts":[[2002,11]]}}}