Type of Document Dissertation Author Ongkunaruk, Pornthipa Author's Email Address pongkuna@vt.edu URN etd-12152005-230125 Title Asymptotic Worst-Case Analyses for the Open Bin Packing Problem Degree PhD Department Industrial and Systems Engineering Advisory Committee

Advisor Name Title Chan, Lap Mui Ann Committee Chair Lin, Kyle Y. Committee Co-Chair Anderson-Cook, Christine M. Committee Member Bish, Ebru K. Committee Member Sarin, Subhash C. Committee Member Keywords

- Asymptotic Worst-Case Performance Ratio
- Off-Line Algorithms
- Bin Packing
Date of Defense 2005-10-07 Availability unrestricted AbstractThe open bin packing problem (OBPP) is a newvariant of the well-known bin packing problem. In the OBPP, items

are packed into bins so that the total content before the last item

in each bin is strictly less than the bin capacity. The objective is

to minimize the number of bins used. The applications of the OBPP

can be found in the subway station systems in Hong Kong and Taipei

and the scheduling in manufacturing industries. We show that the

OBPP is NP-hard and propose two heuristic algorithms instead of

solving the problem to optimality. We propose two offline algorithms

in which the information of the items is known in advance. First, we

consider the First Fit Decreasing (FFD) which is a good

approximation algorithm for the bin packing problem. We prove that

its asymptotic worst-case performance ratio is no more than 3/2.

We observe that its performance for the OBPP is worse than that of

the BPP. Consequently, we modify it by adding the algorithm that the

set of largest items is the set of last items in each bin. Then, we

propose the Modified First Fit Decreasing (MFFD) as an alternative

and prove that its asymptotic worst-case performance ratio is no

more than 91/80. We conduct empirical tests to show their

average-case performance. The results show that in general, the FFD

and MFFD algorithms use no more than 33% and 1% of the number

of bins than that of optimal packing, respectively. In addition, the

MFFD is asymptotically optimal when the sizes of items are (0,1)

uniformly distributed.

Files

Filename Size Approximate Download Time (Hours:Minutes:Seconds)

28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access final.pdf436.51 Kb 00:02:01 00:01:02 00:00:54 00:00:27 00:00:02

Browse All Available ETDs by
( Author |
Department )

If you have questions or technical problems, please Contact DLA.