On a cardinality-constrained transportation problem with market choice

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• 作者：Matthias Walter^a ; ^{matthias.walter@ovgu.de" class="auth_mail" title="E-mail the corresponding author} ; Pelin Damcı-Kurt^b ; ^{damci-kurt.1@osu.edu" class="auth_mail" title="E-mail the corresponding author} ; Santanu S. Dey^c ; ^{santanu.dey@isye.gatech.edu" class="auth_mail" title="E-mail the corresponding author} ; Simge Kü ; ç ; ü ; kyavuz^b ; ^{kucukyavuz.2@osu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Transportation problem with market choice ; Cardinality constraint ; Integral polytope
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：44
• 期：2
• 页码：170-173
• 全文大小：366 K

文摘

It is well-known that the intersection of the matching polytope with a cardinality constraint is integral (Schrijver, 2003) [8]. In this note, we prove a similar result for the polytope corresponding to the transportation problem with market choice (TPMC) (introduced in Damcı-Kurt et al. (2015)) when the demands are in the set class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167637715001601&_mathId=si1.gif&_user=111111111&_pii=S0167637715001601&_rdoc=1&_issn=01676377&md5=b9b14accfaf5b5672ab2dea98aac04c7" title="Click to view the MathML source">{1,2}class="mathContainer hidden">class="mathCode">$\{1,2\}$. This result generalizes the result regarding the matching polytope. The result in this note implies that some special classes of minimum weight perfect matching problem with a cardinality constraint on a subset of edges can be solved in polynomial time.