An OPT+1 algorithm for the cutting stock problem with constant number of object lengths

Authors:
Klaus Jansen;Roberto Solis-Oba
Affiliations:
Institut für Informatik, Universität zu Kiel, Kiel, Germany;Department of Computer Science, The University of Western Ontario, London, Canada
Venue:
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Year:
2010

Citing 9
Cited 3

Theory of linear and integer programming

Theory of linear and integer programming
Combinatorial optimization: algorithms and complexity

Combinatorial optimization: algorithms and complexity
Minkowski's convex body theorem and integer programming

Mathematics of Operations Research
Approximation algorithms for bin packing: a survey

Approximation algorithms for NP-hard problems
A Polynomial Algorithm for Multiprocessor Scheduling with Two Job Lengths

Mathematics of Operations Research
On the complexity of computing determinants

Computational Complexity
An asymptotically exact algorithm for the high-multiplicity bin packing problem

Mathematical Programming: Series A and B
An efficient approximation scheme for the one-dimensional bin-packing problem

SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Carathéodory bounds for integer cones

Operations Research Letters

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

Information Processing Letters
Bin packing via discrepancy of permutations

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bin Packing via Discrepancy of Permutations

ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the cutting stock problem we are given a set T of object types, where objects of type Ti∈T have integer length pi0. Given a set O of n objects containing ni objects of type Ti, for each i=1, ..., d, the problem is to pack O into the minimum number of bins of capacity β. In this paper we consider the version of the problem in which the number d of different object types is constant and we present an algorithm that computes a solution using at most OPT+1 bins, where OPT is the value of an optimum solution.