The ordered open-end bin-packing problem

Document Type

Article

Publication Date

9-1-2003

Abstract

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin's level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst-case analysis, pieces of size 1 play distinct roles and render the analysis more difficult with their presence. We give lower bounds for the performance ratio of any online algorithm for cases both with and without the 1-pieces, and in the case without the 1-pieces, identify an online algorithm whose worst-case performance ratio is less than 2 and an offline algorithm with good worst-case performance. In the average-case analysis, assuming that pieces are independently and uniformly drawn from [0, 1], we find the optimal asymptotic average ratio of the number of occupied bins over the number of pieces. We also introduce other online algorithms and conduct simulation study on the average-case performances of all the proposed algorithms.

Identifier

4344633213 (Scopus)

Publication Title

Operations Research

External Full Text Location

https://doi.org/10.1287/opre.51.5.759.16753

ISSN

0030364X

First Page

759

Last Page

770

Issue

5

Volume

51

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