Worst-case bounds for bin-packing heuristics with applications to the duality gap of the one-dimensional cutting stock problem

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/15329 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/15329 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/15329 archive 4031 disk0/00/00/02/66 2011-10-06 12:24:23 2019-01-23 09:51:49 2011-10-06 12:24:23 thesis show 0 Tuenter Hans J. H. Cuninghame-Green R. A. ftp://ubira.bham.ac.uk/eTheses/266_Tuenter/ University of Birmingham Worst-case bounds for bin-packing heuristics with applications to the duality gap of the one-dimensional cutting stock problem unpub QA T1 40fac_sci The thesis considers the one-dimensional cutting stock problem, the bin-packing problem, and their relationship. The duality gap of the former is investigated and a characterisation of a class of cutting stock problems with the next round-up property is given. It is shown that worst-case bounds for bin-packing heuristics can be and are best expressed in terms of the linear programming relaxation of the corresponding cutting stock problem. The concept of recurrency is introduced for a bin-packing heuristic, which allows a more natural derivation of a measure for the worst-case behaviour. The ideas are tested on some well known bin-packing heuristics and (slightly) tighter bounds for these are derived. These new bounds (in terms of the linear programming relaxation) are then used to make inferences about the duality gap of the cutting stock problem. In particular; these bounds allow à priori, problem-specific bounds. The thesis ends with conclusions and a number of suggestions to extend the analysis to higher dimensional problems. 1997 1996-12 graduation 1462376 eng blscanned This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public 284 University of Birmingham School of Mathematics and Statistics, Research group of Management Mathematics d_ph na 1997 graduation