On the facet defining inequalities of the mixed-integer bilinear covering set

作     者：Rahman, Hamidur Mahajan, Ashutosh 

作者机构：Indian Inst Technol Ind Engn & Operat Res Mumbai 400076 Maharashtra India 

出 版 物：《MATHEMATICAL METHODS OF OPERATIONS RESEARCH》 (运筹学研究中的数学方法)

年 卷 期：2020年第92卷第3期

页      面：545-575页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

主　　题：Mixed-integer programming Global optimization Convex hull Disjunctive cut Split cut Split-rank 

摘      要：We study the facet defining inequalities of the convex hull of a mixed-integer bilinear covering arising in trim-loss (or cutting stock) problem under the framework of disjunctive cuts. We show that all of them can be derived using a disjunctive procedure. Some of these are split cuts of rank one for a convex mixed-integer relaxation of the covering set, while others have rank at least two. For certain linear objective functions, the rank-one split cuts are shown to be sufficient for finding the optimal value over the convex hull of the covering set. A relaxation of the trim-loss problem has this property, and our computational results show that these rank-one inequalities find the lower bound quickly.