{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T21:53:38Z","timestamp":1784584418203,"version":"3.55.0"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,1,28]],"date-time":"2016-01-28T00:00:00Z","timestamp":1453939200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-05623"],"award-info":[{"award-number":["RGPIN-05623"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2016,5]]},"DOI":"10.1007\/s10107-016-0979-5","type":"journal-article","created":{"date-parts":[[2016,1,28]],"date-time":"2016-01-28T09:04:41Z","timestamp":1453971881000},"page":"191-217","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["On the mixing set with a knapsack constraint"],"prefix":"10.1007","volume":"157","author":[{"given":"Ahmad","family":"Abdi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ricardo","family":"Fukasawa","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,1,28]]},"reference":[{"key":"979_CR1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s101070000154.","volume":"89","author":"A Atamt\u00fcrk","year":"2000","unstructured":"Atamt\u00fcrk, A., Nemhauser, G.L., Savelsbergh, M.W.P.: The mixed vertex packing problem. Math. Program. 89, 35\u201353 (2000)","journal-title":"Math. Program."},{"key":"979_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0166-218X(98)00096-1","volume":"89","author":"E Balas","year":"1998","unstructured":"Balas, E.: Disjunctive programming: properties of the convex hull of feasible points. Discrete Appl. Math. 89, 1\u201344 (1998)","journal-title":"Discrete Appl. Math."},{"key":"979_CR3","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/0606047","volume":"6","author":"E Balas","year":"1985","unstructured":"Balas, E.: Disjunctive programming and a hierarchy of relaxations for discrete optimization problems. SIAM J. Algebr. Discrete Methods 6, 466\u2013486 (1985)","journal-title":"SIAM J. Algebr. Discrete Methods"},{"key":"979_CR4","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1007\/BF01580440","volume":"8","author":"E Balas","year":"1975","unstructured":"Balas, E.: Facets of the knapsack polytope. Math. Program. 8, 146\u2013164 (1975)","journal-title":"Math. Program."},{"key":"979_CR5","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1137\/0134010","volume":"34","author":"E Balas","year":"1978","unstructured":"Balas, E., Zemel, E.: Facets of the knapsack polytope from minimal covers. SIAM J. Appl. Math. 34, 119\u2013148 (1978)","journal-title":"SIAM J. Appl. Math."},{"key":"979_CR6","unstructured":"Barrera, J., Homem-de-Mello, T., Moreno, E., Pagnoncelli, B.K., Canessa, G.: Chance-constrained problems and rare events: an importance sampling approach. http:\/\/www.optimization-online.org\/DB_HTML\/2014\/02\/4250.html"},{"key":"979_CR7","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1080\/1055678021000033937","volume":"17","author":"P Beraldi","year":"2002","unstructured":"Beraldi, P., Ruszczy\u0144ski, A.: A branch and bound method for stochastic integer programs under probabilistic constraints. Optim. Methods Softw. 17, 359\u2013382 (2002)","journal-title":"Optim. Methods Softw."},{"key":"979_CR8","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.orl.2007.09.003","volume":"36","author":"D Bienstock","year":"2008","unstructured":"Bienstock, D.: Approximate formulations for 0\u20131 knapsack sets. Oper. Res. Lett. 36, 317\u2013320 (2008)","journal-title":"Oper. Res. Lett."},{"key":"979_CR9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.disopt.2006.10.003","volume":"4","author":"Y Guan","year":"2007","unstructured":"Guan, Y., Ahmed, S., Nemhauser, G.L.: Sequential pairing of mixed integer inequalities. Discrete Optim. 4, 21\u201339 (2007)","journal-title":"Discrete Optim."},{"key":"979_CR10","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/PL00011430","volume":"90","author":"O G\u00fcnl\u00fck","year":"2001","unstructured":"G\u00fcnl\u00fck, O., Pochet, Y.: Mixing mixed-integer inequalities. Math. Program. 90, 429\u2013457 (2001)","journal-title":"Math. Program."},{"key":"979_CR11","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/BF01580442","volume":"8","author":"PL Hammer","year":"1975","unstructured":"Hammer, P.L., Johnson, E.L., Peled, U.N.: Facets of regular 0\u20131 polytopes. Math. Program. 8, 179\u2013206 (1975)","journal-title":"Math. Program."},{"issue":"1","key":"979_CR12","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10107-010-0385-3","volume":"132","author":"S K\u00fc\u00e7\u00fckyavuz","year":"2012","unstructured":"K\u00fc\u00e7\u00fckyavuz, S.: On mixing sets arising in chance-constrained programming. Math. Program. 132(1), 31\u201356 (2012)","journal-title":"Math. Program."},{"key":"979_CR13","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10107-013-0684-6","volume":"146","author":"J Luedtke","year":"2014","unstructured":"Luedtke, J.: A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Math. Program. 146, 219\u2013244 (2014)","journal-title":"Math. Program."},{"issue":"2","key":"979_CR14","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10107-008-0247-4","volume":"122","author":"J Luedtke","year":"2010","unstructured":"Luedtke, J., Ahmed, S., Nemhauser, G.: An integer programming approach for linear programs with probabilistic constraints. Math. Program. 122(2), 247\u2013272 (2010)","journal-title":"Math. Program."},{"key":"979_CR15","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10107-002-0337-7","volume":"93","author":"A Ruszczy\u0144ski","year":"2002","unstructured":"Ruszczy\u0144ski, A.: Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Math. Program. 93, 195\u2013215 (2002)","journal-title":"Math. Program."},{"key":"979_CR16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0167-6377(92)90037-4","volume":"11","author":"S Sen","year":"1992","unstructured":"Sen, S.: Relaxations for probabilistically constrained programs with discrete random variables. Oper. Res. Lett. 11, 81\u201386 (1992)","journal-title":"Oper. Res. Lett."},{"key":"979_CR17","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/BF01580441","volume":"8","author":"LA Wolsey","year":"1975","unstructured":"Wolsey, L.A.: Faces for linear inequality in 0\u20131 variables. Math. Program. 8, 165\u2013178 (1975)","journal-title":"Math. Program."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-0979-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-016-0979-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-0979-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T06:00:09Z","timestamp":1559109609000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-016-0979-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,28]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["979"],"URL":"https:\/\/doi.org\/10.1007\/s10107-016-0979-5","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,28]]}}}