A note on the integrality gap of cutting and skiving stock instances

John Martinovic ()
Additional contact information
John Martinovic: Technische Universität Dresden

4OR, 2022, vol. 20, issue 1, No 4, 85-104

Abstract: Abstract In this paper, we consider the (additive integrality) gap of the cutting stock problem (CSP) and the skiving stock problem (SSP). Formally, the gap is defined as the difference between the optimal values of the ILP and its LP relaxation. For both, the CSP and the SSP, this gap is known to be bounded by 2 if, for a given instance, the bin size is an integer multiple of any item size, hereinafter referred to as the divisible case. In recent years, some improvements of this upper bound have been proposed. More precisely, the constants 3/2 and 7/5 have been obtained for the SSP and the CSP, respectively, the latter of which has never been published in English language. In this article, we introduce two reduction strategies to significantly restrict the number of representative instances which have to be dealt with. Based on these observations, we derive the new and improved upper bound 4/3 for both problems under consideration.

Keywords: Cutting and packing; Cutting stock problem; Skiving stock problem; Additive integrality gap; Divisible case; 90C10; 90C27 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10288-020-00469-4 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:aqjoor:v:20:y:2022:i:1:d:10.1007_s10288-020-00469-4

Ordering information: This journal article can be ordered from
https://www.springer ... ch/journal/10288/PSE

DOI: 10.1007/s10288-020-00469-4

Access Statistics for this article

4OR is currently edited by Yves Crama, Michel Grabisch and Silvano Martello

More articles in 4OR from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().