{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T14:12:29Z","timestamp":1697983949049},"reference-count":22,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7223,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1987,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A lower plane for the network design problem is a linear lower approximation of the objective function and is used to obtain a lower bound in the branch and bound algorithm. In this article, we derive two new lower planes for the network design problems through combinatorial arguments. The first lower plane is of complexity <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>4<\/jats:sup>) and produces a lower bound which is sharper than those of existing lower planes. The second lower plane is of complexity <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic><jats:sup>3<\/jats:sup>) and produces a reasonably good lower bound. Computational results are presented comparing the bounds obtained by the new lower planes with those of the existing lower planes.<\/jats:p>","DOI":"10.1002\/net.3230170202","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T22:18:08Z","timestamp":1178921888000},"page":"113-127","source":"Crossref","is-referenced-by-count":3,"title":["New lower planes for the network design problem"],"prefix":"10.1002","volume":"17","author":[{"given":"R. K.","family":"Ahuja","sequence":"first","affiliation":[]},{"given":"V. V. S.","family":"Murty","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Exact and heuristic algorithms for optimum communication spanning tree","author":"Ahuja R. K.","journal-title":"Trans. Sci."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1068\/a050519"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0191-2615(79)90007-9"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0191-2615(79)90003-1"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230090104"},{"key":"e_1_2_1_7_2","first-page":"121","article-title":"The engine scheduling problem on a railway network","volume":"14","author":"Florian M.","year":"1976","journal-title":"INFOR J."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/367766.368168"},{"key":"e_1_2_1_9_2","unstructured":"G.Gallo A new branch and bound algorithm for the network design problem. Report L 81\u20131 Instituto Di Elaborazione Dell' Informazione Pisa Italy 1981."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130309"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.20.5.822"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.19.5.488"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/TAC.1982.1102873","article-title":"Topological optimization of networks: a nonlinear mixed integer model employing generalized Benders decomposition","volume":"27","author":"Hoang H. H.","year":"1983","journal-title":"IEEE Trans. Automatic Control"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0203015"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230080402"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.9.3.183"},{"key":"e_1_2_1_17_2","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0191-2615(82)90030-3","article-title":"Combinatorial programming, statistical optimization and the optimal transportation network problem","volume":"16","author":"Los M.","year":"1980","journal-title":"Trans. Res."},{"key":"e_1_2_1_18_2","unstructured":"T. L.Magnanti P.Mireault andR. T.Wong Tailoring Benders decomposition for network design. Working paper OR 125\u201383 Operations Research Center Massachusetts Institute of Technology 1983."},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.29.3.464"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.18.1.1"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1145\/355616.364037"},{"key":"e_1_2_1_22_2","doi-asserted-by":"publisher","DOI":"10.1287\/trsc.10.1.52"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0041-1647(69)90152-X"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230170202","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230170202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T16:25:00Z","timestamp":1697905500000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230170202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,1]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1987,1]]}},"alternative-id":["10.1002\/net.3230170202"],"URL":"https:\/\/doi.org\/10.1002\/net.3230170202","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,1]]}}}