A dynamic programming-based heuristic for the variable sized two-dimensional bin packing problem

This paper addresses a variable sized two-dimensional bin packing problem. We propose two heuristics, H1 and H2, stemming from the dynamic programming idea by aggregating states to avoid the explosion in the number of states. These algorithms are elaborated for different purposes: H1 builds a genera...

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Bibliographic Details
Published in:International journal of production research Vol. 49; no. 13; pp. 3815 - 3831
Main Authors: Liu, Ya, Chu, Chengbin, Wang, Kanliang
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis Group 01.07.2011
Taylor & Francis
Taylor & Francis LLC
Subjects:
Algorithms
Applied sciences
Bins
Construction
Dynamic programming
Dynamische Optimierung
Exact sciences and technology
Flows in networks. Combinatorial problems
Heuristic
Heuristik
Lower bounds
Mathematical models
Mathematical programming
operational research
Operational research and scientific management
Operational research. Management science
optimisation
Optimization
Optimization algorithms
Packing problem
Packproblem
Studies
Two dimensional
Lower bound
Multiple solution
Variable geometry
optimisation
Supply demand balance
Heuristic method
operational research
Bin packing problem
Dynamic programming
Rotation
Bounded solution
ISSN:0020-7543, 1366-588X
Online Access:Get full text
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Summary:This paper addresses a variable sized two-dimensional bin packing problem. We propose two heuristics, H1 and H2, stemming from the dynamic programming idea by aggregating states to avoid the explosion in the number of states. These algorithms are elaborated for different purposes: H1 builds a general packing plan for items, while H2 can provide solutions by considering a variety of customer demands, such as guillotine cutting style and rotation of items. The performance of both algorithms is evaluated based on randomly generated instances reported in the literature by comparing them with the lower bounds and optimal solutions for identical bins. Computational results show that the average gaps are 8.97% and 13.41%, respectively, for H1 and H2 compared with lower bounds, and 5.26% and 6.26% compared with optimal solutions for identical bins. We also found that we can save 6.67% of space, on average, by considering variable sized bins instead of a bin packing problem with identical bins.
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ISSN:0020-7543
1366-588X
DOI:10.1080/00207543.2010.501549