Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing

Issue		RAIRO Oper. Res. Volume 39, Number 3, July-September 2005


Page(s)		163 - 183
DOI		10.1051/ro:2006001
Published online		25 January 2006

RAIRO Oper. Res. 39 (2005) 163-183
DOI: 10.1051/ro:2006001

Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing

Luke Finlay¹ and Prabhu Manyem²

¹ Centre for Industrial and Applied Mathematics (CIAM), University of South Australia, Mawson Lakes, SA 5095, Australia; luke.finlay@unisa.edu.au
² Centre for Informatics and Applied Optimisation (CIAO), University of Ballarat, Mount Helen, VIC 3350, Australia; p.manyem@ballarat.edu.au

(Received January 25, 2004. Accepted September 7, 2005 / Published online: 25 January 2006)

Abstract
We consider the NP Hard problems of online Bin Covering and Packing while requiring that larger (or longer, in the one dimensional case) items be placed at the bottom of the bins, below smaller (or shorter) items - we call such a version, the LIB version of problems. Bin sizes can be uniform or variable. We look at computational studies for both the Best Fit and Harmonic Fit algorithms for uniform sized bin covering. The Best Fit heuristic for this version of the problem is introduced here. The approximation ratios obtained were well within the theoretical upper bounds. For variable sized bin covering, a more thorough analysis revealed definite trends in the maximum and average approximation ratios. Finally, we prove that for online LIB bin packing with uniform size bins, no heuristic can guarantee an approximation ratio better than 1.76 under the online model considered.

Mathematics Subject Classification. 68W25, 68Q17, 90B05, 90C27.

Key words: Online approximation algorithm, asymptotic worst case ratio, bin covering problem, bin packing problem, longest item, uniform sized bins.

© EDP Sciences 2006

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