A simple OPT+1 algorithm for cutting stock under the modified integer round-up property assumption

Authors:
Klaus Jansen;Roberto Solis-Oba
Affiliations:
Institut für Informatik, Universität zu Kiel, Kiel, Germany;Department of Computer Science, University of Western Ontario, London, Canada
Venue:
Information Processing Letters
Year:
2011

Citing 5
Cited 0

Minkowski's convex body theorem and integer programming

Mathematics of Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Bin packing with fixed number of bins revisited

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
An OPT+1 algorithm for the cutting stock problem with constant number of object lengths

IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Carathéodory bounds for integer cones

Operations Research Letters

Quantified Score

Hi-index	0.89

Visualization

Abstract

We present a simple algorithm for the cutting stock problem with objects of a constant number d of different sizes. Our algorithm produces solutions of value at most OPT+1 in time d^O^(^d^)(log^7n+s^3^.^5), where OPT is the value of an optimum solution, n is the number of objects, and s is the total number of bits needed to encode the object sizes. This algorithm works under the assumption that the modified integer round-up property of Scheithauer and Terno for the cutting stock problem holds.