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Stability of On-Line Bin Packing with Random Arrivals and Long-Run-Average Constraints

Published online by Cambridge University Press:  27 July 2009

Coastas Courcobetis  and
Richard Weber
Coastas Courcobetis
Affiliation:
AT&T Bell Laboratories Murray Hill, NJ 07974
Richard Weber
Affiliation:
Engineering DepartmentCambridge University, Cambridge CB3 9ET, England
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Abstract

Items of various types arrive at a bin-packing facility according to random processes and are to be combined with other readily available items of different types and packed into bins using one of a number of possible packings. One might think of a manufacturing context in which randomly arriving subassemblies are to be combined with subassemblies from an existing inventory to assemble a variety of finished products. Packing must be done on-line; that is, as each item arrives, it must be allocated to a bin whose configuration of packing is fixed. Moreover, it is required that the packing be managed in such a way that the readily available items are consumed at predescribed rates, corresponding perhaps to optimal rates for manufacturing these items. At any moment, some number of bins will be partially full. In practice, it is important that the packing be managed so that the expected number of partially full bins remains uniformly bounded in time. We present a necessary and sufficient condition for this goal to be realized and describe an algorithm to achieve it.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 4 , October 1990 , pp. 447 - 460
Copyright
Copyright © Cambridge University Press 1990

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References

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