Bin packing and covering with longest items at the bottom: online version

Manyem, Prabhu

doi:10.21914/anziamj.v43i0.470

Cited by 9 publications

(16 citation statements)

References 5 publications

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“…In the online bin packing problem with LIB (Larger Item in the Bottom) constraints [4,[9][10][11], the subsequence of items which are packed into one bin, a j 1 , a j 2 , . .…”

Section: Alg(i ) Opt(i )mentioning

confidence: 99%

“…In particular, it was shown by Manyem [9,10] that a natural variant of Next Fit (NF) (see Johnson [6]), cannot achieve a finite competitive ratio. This variant uses a single active bin and closes it to open a new active bin if the new item is either larger than the last item packed in the active bin, or if assigning it to the active bin would cause its contents to exceed a total size of 1.…”

Section: Previous Workmentioning

confidence: 99%

“…A natural algorithm for the problem, which is in fact a variation of the well-known algorithm FF [7,13] for classic bin packing, and is called FF as well, was studied in [9][10][11] and is defined as follows.…”

Section: First Fitmentioning

confidence: 99%

“…In the case of packing with LIB constraints, this is not necessarily the case. In particular, due to the unsatisfactory behavior of NF for packing with LIB constraints [9,10], and similarly to [11], we consider the variant which applies FF to each class.…”

Section: Other Algorithmsmentioning

confidence: 99%

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On online bin packing with LIB constraints

Epstein

2009

Naval Research Logistics

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In many applications of packing, the location of small items below large items, inside the packed boxes, is forbidden. We consider a variant of the classic online one-dimensional bin packing, in which items allocated to each bin are packed there in the order of arrival, satisfying the condition above. This variant is called online bin packing problem with LIB (larger item in the bottom) constraints. We give an improved analysis of First Fit showing that its competitive ratio is at most 5 2 = 2.5, and design a lower bound of 2 on the competitive ratio of any online algorithm. In addition, we study the competitive ratio of First Fit as a function of an upper bound(where d is a positive integer) on the item sizes. Our upper bound on the competitive ratio of First Fit tends to 2 as d grows, whereas the lower bound of two holds for any value of d. Finally, we consider several natural and well known algorithms, namely, Best Fit, Worst Fit, Almost Worst Fit, and Harmonic, and show that none of them has a finite competitive ratio for the problem.

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“…In the online bin packing problem with LIB (Larger Item in the Bottom) constraints [4,[9][10][11], the subsequence of items which are packed into one bin, a j 1 , a j 2 , . .…”

Section: Alg(i ) Opt(i )mentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Section: First Fitmentioning

confidence: 99%

Section: Other Algorithmsmentioning

confidence: 99%

See 2 more Smart Citations

On online bin packing with LIB constraints

Epstein

2009

Naval Research Logistics

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“…Step 9 Assign One Product to the Last Pallet if Pallet Cube < 120 % I OutPut -Output Number of Pallet Required and Pallet Loading Sequence i 7 4 1. Assign Full Pallets The first step assigns any products order that has cartons quantity greater than or equal to 100% pallet utilization to a new pallet.…”

mentioning

confidence: 99%

A heuristic algorithm for carton to pallet loading problem

Lel

Creighton

Nahavandi

INDIN '05. 2005 3rd IEEE International Conference on Industrial Informatics, 2005.

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This paper presents an algorithm used to solve a carton to pallet packing problem in a drink manufacturing firm. The aim was to determine the cartons loading sequence and the number pallets required, prior to dispatch by truck. The algorithm consists of a series of nine parts to solve this industrial application problem. The pallet loading solution relatively computationally efficient and reduces the number pallets required, compared to other 'trail and error' or manual spreadsheet calculation methods.

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Colorful Bin Packing

Dósa

Epstein

2014

Algorithm Theory – SWAT 2014

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We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s i ∈ [0, 1] and a color c i ∈ C, where C is a set of colors (that is not necessarily known in advance). The total size of items packed into a bin cannot exceed its size, thus an item i can always be packed into a new bin, but an item cannot be packed into a non-empty bin if the previous item packed into that bin has the same color, or if the occupied space in it is larger than 1 − s i . This problem generalizes standard online bin packing and online black and white bin packing (where |C| = 2). We prove that colorful bin packing is harder than black and white bin packing in the sense that an online algorithm for zero size items that packs the input into the smallest possible number of bins cannot exist for |C| ≥ 3, while it is known that such an algorithm exists for |C| = 2. We show that natural generalizations of classic algorithms for bin packing fail to work for the case |C| ≥ 3, and moreover, algorithms that perform well for black and white bin packing do not perform well either, already for the case |C| = 3. Our main results are a new algorithm for colorful bin packing that we design and analyze, whose absolute competitive ratio is 4, and a new lower bound of 2 on the asymptotic competitive ratio of any algorithm, that is valid even for black and white bin packing.

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Bin packing and covering with longest items at the bottom: online version

Cited by 9 publications

References 5 publications

On online bin packing with LIB constraints

On online bin packing with LIB constraints

A heuristic algorithm for carton to pallet loading problem

Colorful Bin Packing

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