ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-Step cycle inequalities: facets for continuous mult
ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-Step cycle inequalities: facets for continuous mult
复制标题
ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}
DOI：
--
复制
发表时间：
2015
影响因子：
2.7
通讯作者：
Kiavash Kianfar
中科院分区：
文献类型：
--
作者：
M. Bansal;Kiavash Kianfar
In this paper, we introduce a generalization of the continuous mixing set, which we refer to as the continuous multi-mixing set. This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. We present a family of valid inequalities for the continuous multi-mixing set and identify conditions under which they are facet-defining. The cycle inequalities, ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-step MIR inequalities, and mixed ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-step MIR inequalities are special cases of these inequalities. We also present an exact separation algorithm for our inequalities. We then use these inequalities to generate valid inequalities for MML with(out) backlogging. Our computational results show that our cuts are very effective in solving the MML instances, resulting in substantial reduction in the integrality gap, number of nodes, and total solution time.
In this paper, we introduce a generalization of the continuous mixing set, which we refer to as the continuous multi-mixing set. This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. We present a family of valid inequalities for the continuous multi-mixing set and identify conditions under which they are facet-defining. The cycle inequalities, ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-step MIR inequalities, and mixed ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document}-step MIR inequalities are special cases of these inequalities. We also present an exact separation algorithm for our inequalities. We then use these inequalities to generate valid inequalities for MML with(out) backlogging. Our computational results show that our cuts are very effective in solving the MML instances, resulting in substantial reduction in the integrality gap, number of nodes, and total solution time.