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

Hamidur Rahman () and Ashutosh Mahajan ()
Additional contact information
Hamidur Rahman: Indian Institute of Technology Bombay
Ashutosh Mahajan: Indian Institute of Technology Bombay

Mathematical Methods of Operations Research, 2020, vol. 92, issue 3, No 5, 545-575

Abstract: Abstract 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.

Keywords: Mixed-integer programming; Global optimization; Convex hull; Disjunctive cut; Split cut; Split-rank (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00186-020-00723-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:92:y:2020:i:3:d:10.1007_s00186-020-00723-9

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-020-00723-9

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().