Mathematical programming algorithms for bin packing problems with item fragmentation

In this paper we consider a class of bin packing problems from the literature having the following distinctive feature: items may be fragmented at a price. Problems of this kind arise in diverse application fields like logistics and telecommunications, and have already been extensively tackled from...

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Published in:	Computers & operations research Vol. 46; pp. 1 - 11
Main Authors:	Casazza, Marco, Ceselli, Alberto
Format:	Journal Article
Language:	English
Published:	Kidlington Elsevier Ltd 01.06.2014 Elsevier Pergamon Press Inc
Subjects:	Algorithms Applied sciences Approximation Bin packing Branch-and-price Exact sciences and technology Flows in networks. Combinatorial problems Fragmentation Heuristic Item fragmentation Logistics Mathematical analysis Mathematical models Mathematical programming Operational research and scientific management Operational research. Management science Optimization Optimization algorithms Packing problem Studies Bin packing Branch-and-price Item fragmentation Mathematical programming Branch and bound method Bin packing problem Telecommunication Combinatorial optimization Modeling Fragmentation Column generation Heuristic method Logistics
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	In this paper we consider a class of bin packing problems from the literature having the following distinctive feature: items may be fragmented at a price. Problems of this kind arise in diverse application fields like logistics and telecommunications, and have already been extensively tackled from an approximation point of view. We focus on the case in which splitting produces no overhead, a fixed number of bins is given and the number of fragments or fragmentations needs to be minimized. We first investigate the theoretical properties of the problem. Then we elaborate on them to devise mathematical programming models and algorithms, yielding both exact optimization algorithms and effective heuristics. An extensive experimental campaign proves that our approach is very effective, and highlights which features make an instance computationally harder to solve.
AbstractList	In this paper we consider a class of bin packing problems from the literature having the following distinctive feature: items may be fragmented at a price. Problems of this kind arise in diverse application fields like logistics and telecommunications, and have already been extensively tackled from an approximation point of view. We focus on the case in which splitting produces no overhead, a fixed number of bins is given and the number of fragments or fragmentations needs to be minimized. We first investigate the theoretical properties of the problem. Then we elaborate on them to devise mathematical programming models and algorithms, yielding both exact optimization algorithms and effective heuristics. An extensive experimental campaign proves that our approach is very effective, and highlights which features make an instance computationally harder to solve. In this paper we consider a class of bin packing problems from the literature having the following distinctive feature: items may be fragmented at a price. Problems of this kind arise in diverse application fields like logistics and telecommunications, and have already been extensively tackled from an approximation point of view. We focus on the case in which splitting produces no overhead, a fixed number of bins is given and the number of fragments or fragmentations needs to be minimized. We first investigate the theoretical properties of the problem. Then we elaborate on them to devise mathematical programming models and algorithms, yielding both exact optimization algorithms and effective heuristics. An extensive experimental campaign proves that our approach is very effective, and highlights which features make an instance computationally harder to solve. [PUBLICATION ABSTRACT]
Author	Casazza, Marco Ceselli, Alberto
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Keywords	Bin packing Branch-and-price Item fragmentation Mathematical programming Branch and bound method Bin packing problem Telecommunication Combinatorial optimization Modeling Fragmentation Column generation Heuristic method Logistics
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SubjectTerms	Algorithms Applied sciences Approximation Bin packing Branch-and-price Exact sciences and technology Flows in networks. Combinatorial problems Fragmentation Heuristic Item fragmentation Logistics Mathematical analysis Mathematical models Mathematical programming Operational research and scientific management Operational research. Management science Optimization Optimization algorithms Packing problem Studies
Title	Mathematical programming algorithms for bin packing problems with item fragmentation
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