{"id":356,"date":"2019-11-08T12:27:24","date_gmt":"2019-11-08T03:27:24","guid":{"rendered":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/?p=356"},"modified":"2019-11-08T12:27:25","modified_gmt":"2019-11-08T03:27:25","slug":"%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-11-13","status":"publish","type":"post","link":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/2019\/11\/08\/%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-11-13\/","title":{"rendered":"\u300c\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0\u300d\u30bb\u30df\u30ca\u30fc\u6848\u5185 (11\/13)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u65e5\u6642\uff1a\u30002019\u5e7411\u670813\u65e5(\u6c34) 16:00\uff5e17:00<br>\u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e 534\u53f7\u5ba4<br><a href=\"https:\/\/www.u-tokyo.ac.jp\/campusmap\/cam01_04_15_j.html\" rel=\"noreferrer noopener\" target=\"_blank\">https:\/\/www.u-tokyo.ac.jp\/campusmap\/cam01_04_15_j.html<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8b1b\u6f14\u8005\uff1a\u3000S. Thomas McCormick (UBC)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8b1b\u6f14\u984c\u76ee\uff1a Separation of Series Constraints for One-Machine Scheduling with Precedence<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5171\u540c\u7814\u7a76\u8005\uff1a\u3000A. Ridha Mahjoub, Y. Kobayashi<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8b1b\u6f14\u6982\u8981\uff1a<br>A 1991 paper by Queyranne and Wang proposed three classes of valid<br>constraints for the convex hull of feasible completion times for<br>schedules on a single machine subject to precedence constraints. These<br>classes are called the parallel constraints, serial constraints, and Z<br>constraints. These constraints have been very useful in many contexts.<br>Queyranne and Wang showed how to separate the parallel constraints, but<br>the complexity of separating the serial and Z constraints has remained<br>open. Here we show that it is NP Hard to separate even a very special<br>subclass of serial constraints.&nbsp; We also develop a fast, parametric way<br>to find an earliest feasible deadline for a subset of jobs, and use it<br>to show that separation is polynomial when the precedence constraints<br>are series-parallel.&nbsp; We also note that there is a compact extended<br>formulation of the problem by Wolsey, and in this context separation of<br>both series and parallel constraints becomes trivial.&nbsp; It is surprising<br>that an NP Hard separation problem can &#8220;hide&#8221; within an extended<br>formulation where separation is much easier.&nbsp; We further consider the<br>case of two-dimensional precedence constraints, whose underlying problem<br>is solvable in polynomial time.&nbsp; We show how to separate the serial<br>constraints in this case as well.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65e5\u6642\uff1a\u30002019\u5e7411\u670813\u65e5(\u6c34) 16:00\uff5e17:00\u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-356","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/356","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/comments?post=356"}],"version-history":[{"count":1,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/356\/revisions"}],"predecessor-version":[{"id":357,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/356\/revisions\/357"}],"wp:attachment":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/media?parent=356"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/categories?post=356"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/tags?post=356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}