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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We study two-stage stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader's problem. Both bounding problems are equivalent to explicit mixed-integer linear programs that are amenable to efficient numerical solution. The method is illustrated through a facility location problem involving sellers and customers with conflicting preferences.<\/jats:p>","DOI":"10.1137\/16m1098486","type":"journal-article","created":{"date-parts":[[2018,1,30]],"date-time":"2018-01-30T12:03:05Z","timestamp":1517313785000},"page":"198-222","source":"Crossref","is-referenced-by-count":22,"title":["Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs"],"prefix":"10.1137","volume":"28","author":[{"given":"\u0130hsan","family":"Yan\u0131ko\u011flu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Kuhn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2013.10.002"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-006-6159-x"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. Ben-Tal, L. El Ghaoui, and A. Nemirovski,\n                      Robust Optimization\n                      , Princeton University Press, Princeton, NJ, 2009.","DOI":"10.1515\/9781400831050"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0454-y"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1287\/opre.21.1.37"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0457"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s001580100115"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.rpm.5170046"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/02331939208843831"},{"key":"atypb10","unstructured":"S. Dempe,\n                      Foundations of Bilevel Programming\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002."},{"key":"atypb11","first-page":"3","author":"Dempe S.","year":"2006","journal-title":"New York"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-011-0508-5"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-005-0597-0"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOTA.0000026131.04418.b7"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-006-9100-6"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-007-9066-4"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-014-0789-6"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1090.0795"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-015-0958-2"},{"key":"atypb20","unstructured":"C. Henkel,\n                      An Algorithm for the Global Resolution of Linear Stochastic Bilevel Programs\n                      , Ph.D. thesis, Universita\u0308t Duisburg-Essen, Duisburg and Essen, Germany, 2014."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0431"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1021\/ie970383i"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-009-0331-4"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/130931011"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/CACSD.2004.1393890"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/BF01099649"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-007-9260-z"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2008.0007"},{"key":"atypb29","unstructured":"M. Patriksson and L. Wynter,\n                      Stochastic Nonlinear Bilevel Programming\n                      , Technical report, Citeseer, 1997."},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00052-8"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2003.09.021"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2006.09.019"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-005-7566-x"},{"key":"atypb34","first-page":"111","author":"Shapiro A.","year":"2005","journal-title":"New York"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1080\/02331930801954177"},{"key":"atypb36","unstructured":"J. Tirole and D. 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