{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T09:51:31Z","timestamp":1771235491858,"version":"3.50.1"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T00:00:00Z","timestamp":1609718400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T00:00:00Z","timestamp":1609718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Chinese Natural Science Foundation","award":["11631013"],"award-info":[{"award-number":["11631013"]}]},{"name":"Chinese Natural Science Foundation","award":["11331012"],"award-info":[{"award-number":["11331012"]}]},{"name":"National 973 Program of China","award":["2015CB856002"],"award-info":[{"award-number":["2015CB856002"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s10898-020-00967-z","type":"journal-article","created":{"date-parts":[[2021,1,4]],"date-time":"2021-01-04T02:02:48Z","timestamp":1609725768000},"page":"659-689","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron"],"prefix":"10.1007","volume":"81","author":[{"given":"Liang","family":"Chen","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4147-1346","authenticated-orcid":false,"given":"Wei-Kun","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Mu-Ming","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Yu-Hong","family":"Dai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,4]]},"reference":[{"key":"967_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-008-0001-1","volume":"1","author":"T Achterberg","year":"2009","unstructured":"Achterberg, T.: SCIP: solving constraint integer programs. Math. Program. Comput. 1, 1\u201341 (2009)","journal-title":"Math. Program. Comput."},{"key":"967_CR2","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s12532-010-0015-3","volume":"2","author":"T Achterberg","year":"2010","unstructured":"Achterberg, T., Raack, C.: The MCF-separator: detecting and exploiting multi-commodity flow structures in MIPs. Math. Program. Comput. 2, 125\u2013165 (2010)","journal-title":"Math. Program. Comput."},{"key":"967_CR3","unstructured":"Atamturk, A., Gunluk, O.: Multi-commodity multi-facility network design. arXiv preprint arXiv:1707.03810 (2017)"},{"key":"967_CR4","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s101070100284","volume":"92","author":"A Atamt\u00fcrk","year":"2002","unstructured":"Atamt\u00fcrk, A., Rajan, D.: On splittable and unsplittable flow capacitated network design arc-set polyhedra. Math. Program. 92, 315\u2013333 (2002)","journal-title":"Math. Program."},{"key":"967_CR5","doi-asserted-by":"crossref","unstructured":"Avella, P., Boccia, M., Mattia, S.: A branch-and-cut algorithm for the single source capacitated facility location problem. In: 2013 International Conference on Advanced Logistics and Transport, pp. 181\u2013186 (2013)","DOI":"10.1109\/ICAdLT.2013.6568456"},{"key":"967_CR6","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/s10589-008-9183-8","volume":"45","author":"P Avella","year":"2010","unstructured":"Avella, P., Boccia, M., Vasilyev, I.: A computational study of exact knapsack separation for the generalized assignment problem. Comput. Optim. Appl. 45, 543\u2013555 (2010)","journal-title":"Comput. Optim. Appl."},{"issue":"2","key":"967_CR7","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1287\/opre.48.2.318.12378","volume":"48","author":"C Barnhart","year":"2000","unstructured":"Barnhart, C., Hane, C.A., Vance, P.H.: Using branch-and-price-and-cut to solve origin-destination integer multicommodity flow problems. Oper. Res. 48(2), 318\u2013326 (2000)","journal-title":"Oper. Res."},{"key":"967_CR8","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.cor.2015.08.009","volume":"66","author":"A Benhamiche","year":"2016","unstructured":"Benhamiche, A., Mahjoub, A.R., Perrot, N., Uchoa, E.: Unsplittable non-additive capacitated network design using set functions polyhedra. Comput. Oper. Res. 66, 105\u2013115 (2016)","journal-title":"Comput. Oper. Res."},{"key":"967_CR9","doi-asserted-by":"crossref","unstructured":"Boccia, M., Hanafi, S., Vasilyev, I.: New computational results with an exact knapsack separation procedure for structured binary integer programming problems. In: 2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), pp. 1\u20135 (2013)","DOI":"10.1109\/ICMSAO.2013.6552688"},{"issue":"4","key":"967_CR10","doi-asserted-by":"publisher","first-page":"734","DOI":"10.1137\/0803038","volume":"3","author":"EA Boyd","year":"1993","unstructured":"Boyd, E.A.: Generating Fenchel cutting planes for knapsack polyhedra. SIAM J. Optim. 3(4), 734\u2013750 (1993)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"967_CR11","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1287\/opre.42.1.53","volume":"42","author":"EA Boyd","year":"1994","unstructured":"Boyd, E.A.: Fenchel cutting planes for integer programs. Oper. Res. 42(1), 53\u201364 (1994)","journal-title":"Oper. Res."},{"issue":"2","key":"967_CR12","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1137\/0805021","volume":"5","author":"EA Boyd","year":"1995","unstructured":"Boyd, E.A.: On the convergence of fenchel cutting planes in mixed-integer programming. SIAM J. Optim. 5(2), 421\u2013435 (1995)","journal-title":"SIAM J. Optim."},{"key":"967_CR13","unstructured":"Brockm\u00fcller, B., G\u00fcnl\u00fcck, O., Wolsey, L.A.: Designing private line networks - Polyhedral analysis and computation. CORE Discussion Papers 1996047, Universit\u00e9 catholique de Louvain (1996)"},{"issue":"1\u20132","key":"967_CR14","first-page":"7","volume":"16","author":"B Brockm\u00fcller","year":"2004","unstructured":"Brockm\u00fcller, B., G\u00fcnl\u00fcck, O., Wolsey, L.A.: Designing private line networks. Trans. Oper. Res. 16(1\u20132), 7\u201324 (2004)","journal-title":"Trans. Oper. Res."},{"issue":"3","key":"967_CR15","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/S0166-218X(98)00024-9","volume":"85","author":"S Chopra","year":"1998","unstructured":"Chopra, S., Gilboa, I., Sastry, S.: Source sink flows with capacity installation in batches. Discr. Appl. Math. 85(3), 165\u2013192 (1998)","journal-title":"Discr. Appl. Math."},{"key":"967_CR16","unstructured":"CPLEX: https:\/\/www.ibm.com\/analytics\/cplex-optimizer"},{"key":"967_CR17","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan, E.D., Mor\u00e9, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201\u2013213 (2002)","journal-title":"Math. Program."},{"issue":"1","key":"967_CR18","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1287\/opre.2013.1231","volume":"62","author":"M Fischetti","year":"2014","unstructured":"Fischetti, M., Monaci, M.: Exploiting erraticism in search. Oper. Res. 62(1), 114\u2013122 (2014)","journal-title":"Oper. Res."},{"issue":"3","key":"967_CR19","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1287\/ijoc.2.3.236","volume":"2","author":"B Gavish","year":"1990","unstructured":"Gavish, B., Altinkemer, K.: Backbone network design tools with economic tradeoffs. ORSA J. Comput. 2(3), 236\u2013252 (1990)","journal-title":"ORSA J. Comput."},{"key":"967_CR20","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10107-010-0359-5","volume":"124","author":"K Kaparis","year":"2010","unstructured":"Kaparis, K., Letchford, A.N.: Separation algorithms for 0\u20131 knapsack polytopes. Math. Program. 124, 69\u201391 (2010)","journal-title":"Math. Program."},{"key":"967_CR21","unstructured":"Koberstein, A.: The dual simplex method, techniques for a fast and stable implementation. Ph.D. thesis, Universit\u00e4t Paderborn (2005)"},{"key":"967_CR22","doi-asserted-by":"crossref","unstructured":"Lodi, A., Tramontani, A.: Performance variability in mixed-integer programming. In: Topaloglu, H. (ed.) Tutorials in Operations Research: Theory Driven by Influential Applications, pp. 1\u201312. Catonsville, INFORMS (2013)","DOI":"10.1287\/educ.2013.0112"},{"key":"967_CR23","unstructured":"Luo, H., Kianfar, K.: n-step cutset inequalities: facets for multi-module capacitated network design problem (2019). http:\/\/www.optimization-online.org\/DB_HTML\/2018\/11\/6904.html"},{"issue":"1","key":"967_CR24","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1287\/opre.43.1.142","volume":"43","author":"TL Magnanti","year":"1995","unstructured":"Magnanti, T.L., Mirchandani, P., Vachani, R.: Modeling and solving the two-facility capacitated network loading problem. Oper. Res. 43(1), 142\u2013157 (1995)","journal-title":"Oper. Res."},{"key":"967_CR25","volume-title":"Geometrie der Zahlen","author":"HH Minkowski","year":"1896","unstructured":"Minkowski, H.H.: Geometrie der Zahlen. Teubner, Stuttgart (1896)"},{"issue":"3","key":"967_CR26","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1002\/net.20371","volume":"55","author":"S Orlowski","year":"2010","unstructured":"Orlowski, S., Wess\u00e4ly, R., Pi\u00f3ro, M., Tomaszewski, A.: SNDlib 1.0\u2013Survivable Network Design Library. Networks 55(3), 276\u2013286 (2010)","journal-title":"Networks"},{"issue":"1","key":"967_CR27","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1287\/ijoc.12.1.75.11898","volume":"12","author":"D Pisinger","year":"2000","unstructured":"Pisinger, D.: A minimal algorithm for the bounded knapsack problem. INFORMS J. Comput. 12(1), 75\u201382 (2000)","journal-title":"INFORMS J. Comput."},{"issue":"2","key":"967_CR28","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1002\/net.20395","volume":"57","author":"C Raack","year":"2011","unstructured":"Raack, C., Koster, A.M., Orlowski, S., Wess\u00e4ly, R.: On cut-based inequalities for capacitated network design polyhedra. Networks 57(2), 141\u2013156 (2011)","journal-title":"Networks"},{"issue":"2","key":"967_CR29","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1287\/ijoc.1070.0237","volume":"20","author":"F Salman","year":"2008","unstructured":"Salman, F., Ravi, R., Hooker, J.: Solving the capacitated local access network design problem. INFORMS J. Comput. 20(2), 243\u2013254 (2008)","journal-title":"INFORMS J. Comput."},{"key":"967_CR30","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s101070200292","volume":"92","author":"SP Van Hoesel","year":"2002","unstructured":"Van Hoesel, S.P., Koster, A.M., van de Leensel, R.L., Savelsbergh, M.W.: Polyhedral results for the edge capacity polytope. Math. Program. 92, 335\u2013358 (2002)","journal-title":"Math. Program."},{"key":"967_CR31","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/s10898-015-0294-3","volume":"66","author":"I Vasilyev","year":"2016","unstructured":"Vasilyev, I., Boccia, M., Hanafi, S.: An implementation of exact knapsack separation. J. Global Optim. 66, 127\u2013150 (2016)","journal-title":"J. Global Optim."},{"key":"967_CR32","first-page":"3","volume-title":"Contributions to the Theory of Games","author":"H Weyl","year":"1952","unstructured":"Weyl, H.: The elementary of convex polyhedra. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, pp. 3\u201318. Princeton, Princeton University Press (1952)"},{"key":"967_CR33","unstructured":"Wolter, K.: Implementation of cutting plane separators for mixed integer programs. Dipolma thesis, Technische Universit\u00e4t Berlin (2006)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00967-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-020-00967-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-020-00967-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T18:56:09Z","timestamp":1697482569000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-020-00967-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,4]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["967"],"URL":"https:\/\/doi.org\/10.1007\/s10898-020-00967-z","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,4]]},"assertion":[{"value":"1 January 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}