Journal articles: 'Bin packing'

1

Gutin, Gregory, Tommy Jensen, and Anders Yeo. "Batched bin packing." Discrete Optimization 2, no. 1 (March 2005): 71–82. http://dx.doi.org/10.1016/j.disopt.2004.11.001.

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2

Epstein, Leah, and Elena Kleiman. "Selfish Bin Packing." Algorithmica 60, no. 2 (August 13, 2009): 368–94. http://dx.doi.org/10.1007/s00453-009-9348-6.

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3

Kuipers, Jeroen. "Bin packing games." Mathematical Methods of Operations Research 47, no. 3 (October 1998): 499–510. http://dx.doi.org/10.1007/bf01198407.

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4

Epstein, Leah. "On bin packing with clustering and bin packing with delays." Discrete Optimization 41 (August 2021): 100647. http://dx.doi.org/10.1016/j.disopt.2021.100647.

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5

Kartak, Vadim M., and Artem V. Ripatti. "Large proper gaps in bin packing and dual bin packing problems." Journal of Global Optimization 74, no. 3 (August 3, 2018): 467–76. http://dx.doi.org/10.1007/s10898-018-0696-0.

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6

Liu, Yang, and Thanh Vinh Vo. "Bin Packing Solution for Automated Packaging Application." Applied Mechanics and Materials 143-144 (December 2011): 279–83. http://dx.doi.org/10.4028/www.scientific.net/amm.143-144.279.

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This paper introduces the implementation of a new heuristic recursive algorithm for bin packing solution used in automated packaging application. The theoretical method proposed in this paper is successfully implemented on a real ABB robot arm with some important improvements such as added rotation flexibility and removing an added product from the structure. The computational results on a class of benchmark problems have shown that this algorithm not only finds shorter height than the known meta-heuristic ones, but also runs in shorter time. The average running time is very suitable for such kind of automated packaging application.

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7

Yang, Jianglong, Kaibo Liang, Huwei Liu, Man Shan, Li Zhou, Lingjie Kong, and Xiaolan Li. "Optimizing e-commerce warehousing through open dimension management in a three-dimensional bin packing system." PeerJ Computer Science 9 (October 9, 2023): e1613. http://dx.doi.org/10.7717/peerj-cs.1613.

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In the field of e-commerce warehousing, maximizing the utilization of packing bins is a fundamental goal for all major logistics enterprises. However, determining the appropriate size of packing bins poses a practical challenge for many logistics companies. Given the limited research on the open-size 3D bin packing problem as well as the high complexity and lengthy computation time of existing models, this study focuses on optimizing multiple-bin sizes within the e-commerce context. Building upon existing research, we propose a hybrid integer programming model, denoted as the three dimensional multiple option dimensional rectangular packing problem (3D-MODRPP), to address the multiple-bin size 3D bin packing problem. Additionally, we leverage well-established hardware and software technologies to propose a 3D bin packing system capable of accommodating multiple bin types with open dimensions. To reduce the complexity of the model and the number of constraints, we introduce a novel assumption method for 0–1 integer variables in the overlap and rotation constraints. By applying this approach, we significantly streamline the computational complexity associated with the model calculations. Furthermore, we refine the dataset by developing a customized version based on the classical Three-Dimensional One-Size Dependent Rectangular Packing Problem (3D-ODRPP) dataset, leading to improved outcomes. Through comprehensive analysis of the research results, our model exhibits remarkable advancements in addressing the strong heterogeneous bin packing problem, the weak heterogeneous bin packing problem, the actual bin packing problem, and the bin packing problem with multiple bin types and open sizes. Specifically, it significantly reduces model complexity and computation time and increases space utilization. The system designed in this study paves the way for practical applications based on the proposed model, providing researchers with broader research prospects and directions to expand the scope of investigation in the field of 3D bin packing. Consequently, this system contributes to solving complex 3D packing problems, reducing space waste, and enhancing transportation efficiency.

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Lin, Bingchen, Jiawei Li, Ruibin Bai, Rong Qu, Tianxiang Cui, and Huan Jin. "Identify Patterns in Online Bin Packing Problem: An Adaptive Pattern-Based Algorithm." Symmetry 14, no. 7 (June 23, 2022): 1301. http://dx.doi.org/10.3390/sym14071301.

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Bin packing is a typical optimization problem with many real-world application scenarios. In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into a bin immediately after its arrival. Inspired by duality in optimization, we proposed pattern-based adaptive heuristics for the online bin packing problem. The idea is to predict the distribution of items based on packed items, and to apply this information in packing future arrival items in order to handle uncertainty in online bin packing. A pattern in bin packing is a combination of items that can be packed into a single bin. Patterns selected according to past items are adopted and periodically updated in scheduling future items in the algorithm. Symmetry in patterns and the stability of patterns in the online bin packing problem are discussed. We have implemented the algorithm and compared it with the Best-Fit in a series of experiments with various distribution of items to show its effectiveness.

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9

Shah, Devavrat, and John N. Tsitsiklis. "Bin Packing with Queues." Journal of Applied Probability 45, no. 4 (December 2008): 922–39. http://dx.doi.org/10.1239/jap/1231340224.

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We study the best achievable performance (in terms of the average queue size and delay) in a stochastic and dynamic version of the bin-packing problem. Items arrive to a queue according to a Poisson process with rate 2ρ, where ρ ∈ (0, 1). The item sizes are independent and identically distributed (i.i.d.) with a uniform distribution in [0, 1]. At each time unit, a single unit-size bin is available and can receive any of the queued items, as long as their total size does not exceed 1. Coffman and Stolyar (1999) and Gamarnik (2004) have established that there exist packing policies under which the average queue size is finite for every ρ ∈ (0, 1). In this paper we study the precise scaling of the average queue size, as a function of ρ, with emphasis on the critical regime where ρ approaches 1. Standard results on the probabilistic (but static) bin-packing problem can be readily applied to produce policies under which the queue size scales as O(h2), where h = 1 / (1 - ρ), which raises the question of whether this is the best possible. We establish that the average queue size scales as Ω(hlogh), under any policy. Furthermore, we provide an easily implementable policy, which packs at most two items per bin. Under that policy, the average queue size scales as O(hlog3/2h), which is nearly optimal. On the other hand, if we impose the additional requirement that any two items packed together must have near-complementary sizes (in a sense to be made precise), we show that the average queue size must scale as Θ(h2).

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10

Shah, Devavrat, and John N. Tsitsiklis. "Bin Packing with Queues." Journal of Applied Probability 45, no. 04 (December 2008): 922–39. http://dx.doi.org/10.1017/s0021900200004885.

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We study the best achievable performance (in terms of the average queue size and delay) in a stochastic and dynamic version of the bin-packing problem. Items arrive to a queue according to a Poisson process with rate 2ρ, where ρ ∈ (0, 1). The item sizes are independent and identically distributed (i.i.d.) with a uniform distribution in [0, 1]. At each time unit, a single unit-size bin is available and can receive any of the queued items, as long as their total size does not exceed 1. Coffman and Stolyar (1999) and Gamarnik (2004) have established that there exist packing policies under which the average queue size is finite for every ρ ∈ (0, 1). In this paper we study the precise scaling of the average queue size, as a function of ρ, with emphasis on the critical regime where ρ approaches 1. Standard results on the probabilistic (but static) bin-packing problem can be readily applied to produce policies under which the queue size scales as O(h 2), where h = 1 / (1 - ρ), which raises the question of whether this is the best possible. We establish that the average queue size scales as Ω(hlogh), under any policy. Furthermore, we provide an easily implementable policy, which packs at most two items per bin. Under that policy, the average queue size scales as O(hlog3/2 h), which is nearly optimal. On the other hand, if we impose the additional requirement that any two items packed together must have near-complementary sizes (in a sense to be made precise), we show that the average queue size must scale as Θ(h 2).

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11

Kim, Jong-Kyou, H. Lee-Kwang, and Seung W. Yoo. "Fuzzy bin packing problem." Fuzzy Sets and Systems 120, no. 3 (June 2001): 429–34. http://dx.doi.org/10.1016/s0165-0114(99)00073-1.

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12

Dosa, Gyorgy. "Batched bin packing revisited." Journal of Scheduling 20, no. 2 (June 2, 2015): 199–209. http://dx.doi.org/10.1007/s10951-015-0431-3.

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13

Coffman, Edward G., János Csirik, Lajos Rónyai, and Ambrus Zsbán. "Random-order bin packing." Discrete Applied Mathematics 156, no. 14 (July 2008): 2810–16. http://dx.doi.org/10.1016/j.dam.2007.11.004.

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14

Friesen, D. K., and M. A. Langston. "Variable Sized Bin Packing." SIAM Journal on Computing 15, no. 1 (February 1986): 222–30. http://dx.doi.org/10.1137/0215016.

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15

Epstein, Leah, David S. Johnson, and Asaf Levin. "Min-Sum Bin Packing." Journal of Combinatorial Optimization 36, no. 2 (May 23, 2018): 508–31. http://dx.doi.org/10.1007/s10878-018-0310-x.

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16

Baldi, Mauro Maria. "Generalized Bin Packing Problems." 4OR 12, no. 3 (December 28, 2013): 293–94. http://dx.doi.org/10.1007/s10288-013-0252-1.

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17

Fukunaga, A. S., and R. E. Korf. "Bin Completion Algorithms for Multicontainer Packing, Knapsack, and Covering Problems." Journal of Artificial Intelligence Research 28 (March 30, 2007): 393–429. http://dx.doi.org/10.1613/jair.2106.

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Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogood-based pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, min-cost covering, and bin packing. We show that our bin completion algorithms yield new, state-of-the-art results for the multiple knapsack, bin covering, and min-cost covering problems, outperforming previous algorithms by several orders of magnitude with respect to runtime on some classes of hard, random problem instances. For the bin packing problem, we demonstrate significant improvements compared to most previous results, but show that bin completion is not competitive with current state-of-the-art cutting-stock based approaches.

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18

Rhee, W. T. "Some inequalities for bin packing." Optimization 20, no. 3 (January 1989): 299–304. http://dx.doi.org/10.1080/02331938908843445.

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19

Rhee, W. T. "Inequalities for bin packing-III." Optimization 29, no. 4 (January 1994): 381–85. http://dx.doi.org/10.1080/02331939408843965.

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20

Baldi, Mauro Maria, Teodor Gabriel Crainic, Guido Perboli, and Roberto Tadei. "The generalized bin packing problem." Transportation Research Part E: Logistics and Transportation Review 48, no. 6 (November 2012): 1205–20. http://dx.doi.org/10.1016/j.tre.2012.06.005.

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21

Berndt, Sebastian, Klaus Jansen, and Kim-Manuel Klein. "Fully dynamic bin packing revisited." Mathematical Programming 179, no. 1-2 (September 1, 2018): 109–55. http://dx.doi.org/10.1007/s10107-018-1325-x.

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22

Epstein, Leah, and Meital Levy. "Dynamic multi-dimensional bin packing." Journal of Discrete Algorithms 8, no. 4 (December 2010): 356–72. http://dx.doi.org/10.1016/j.jda.2010.07.002.

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23

Mao, W. "Besk-k-Fit bin packing." Computing 50, no. 3 (September 1993): 265–70. http://dx.doi.org/10.1007/bf02243816.

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24

Rao, R. L., and S. S. Iyengar. "Bin-packing by simulated annealing." Computers & Mathematics with Applications 27, no. 5 (March 1994): 71–82. http://dx.doi.org/10.1016/0898-1221(94)90077-9.

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25

Epstein, Leah. "More on batched bin packing." Operations Research Letters 44, no. 2 (March 2016): 273–77. http://dx.doi.org/10.1016/j.orl.2016.02.006.

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26

BUJTÁS, CSILLA, GYÖRGY DÓSA, CSANÁD IMREH, JUDIT NAGY-GYÖRGY, and ZSOLT TUZA. "THE GRAPH-BIN PACKING PROBLEM." International Journal of Foundations of Computer Science 22, no. 08 (December 2011): 1971–93. http://dx.doi.org/10.1142/s012905411100915x.

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We deal with a very general problem: a given graph G is to be "packed" into a host graph H, and we are asked about some natural optimization questions concerning this packing. The problem has never been investigated before in this general form. The input of the problem is a simple graph G = (V, E) with lower and upper bounds on its edges and weights on its vertices. The vertices correspond to items which have to be packed into the vertices (bins) of a host graph, such that each host vertex can accommodate at most L weight in total, and if two items are adjacent in G, then the distance of their host vertices in H must be between the lower and upper bounds of the edge joining the two items. Special cases are bin packing with conflicts, chromatic number, and many more. We give some general structure statements, treat some special cases, and investigate the performance guarantee of polynomial-time algorithms both in the offline and online setting.

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27

Epstein, Leah, Csanád Imreh, and Asaf Levin. "Class constrained bin packing revisited." Theoretical Computer Science 411, no. 34-36 (July 2010): 3073–89. http://dx.doi.org/10.1016/j.tcs.2010.04.037.

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28

Azar, Boyar, Favrholdt, Larsen, Nielsen, and Epstein. "Fair versus Unrestricted Bin Packing." Algorithmica 34, no. 2 (October 2002): 181–96. http://dx.doi.org/10.1007/s00453-002-0965-6.

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29

Epstein, Leah. "Bin Packing with Rejection Revisited." Algorithmica 56, no. 4 (April 8, 2008): 505–28. http://dx.doi.org/10.1007/s00453-008-9188-9.

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30

Boyar, Joan, Shahin Kamali, Kim S. Larsen, and Alejandro López-Ortiz. "Online Bin Packing with Advice." Algorithmica 74, no. 1 (November 7, 2014): 507–27. http://dx.doi.org/10.1007/s00453-014-9955-8.

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31

Rhee, Wansoo T. "Inequalities for Bin Packing—II." Mathematics of Operations Research 18, no. 3 (August 1993): 685–93. http://dx.doi.org/10.1287/moor.18.3.685.

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32

Epstein, Leah, and Asaf Levin. "On Bin Packing with Conflicts." SIAM Journal on Optimization 19, no. 3 (January 2008): 1270–98. http://dx.doi.org/10.1137/060666329.

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33

Liu, Mozhengfu, and Xueyan Tang. "Dynamic Bin Packing with Predictions." Proceedings of the ACM on Measurement and Analysis of Computing Systems 6, no. 3 (December 2022): 1–24. http://dx.doi.org/10.1145/3570605.

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The MinUsageTime Dynamic Bin Packing (DBP) problem aims to minimize the accumulated bin usage time for packing a sequence of items into bins. It is often used to model job dispatching for optimizing the busy time of servers, where the items and bins match the jobs and servers respectively. It is known that the competitiveness of MinUsageTime DBP has tight bounds of Θ(√łog μ ) and Θ(μ) in the clairvoyant and non-clairvoyant settings respectively, where μ is the max/min duration ratio of all items. In practice, the information about the items' durations (i.e., job lengths) obtained via predictions is usually prone to errors. In this paper, we study the MinUsageTime DBP problem with predictions of the items' durations. We find that an existing O(√łog μ )-competitive clairvoyant algorithm, if using predicted durations rather than real durations for packing, does not provide any bounded performance guarantee when the predictions are adversarially bad. We develop a new online algorithm with a competitive ratio of minØ(ε^2 √łog(ε^2 μ) ), O(μ) (where ε is the maximum multiplicative error of prediction among all items), achieving O(√łog μ) consistency (competitiveness under perfect predictions where ε = 1) and O(μ) robustness (competitiveness under terrible predictions), both of which are asymptotically optimal.

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34

Kinnerseley, Nancy G., and Michael A. Langston. "Online variable-sized bin packing." Discrete Applied Mathematics 22, no. 2 (1988): 143–48. http://dx.doi.org/10.1016/0166-218x(88)90089-3.

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35

Wang, Zhenbo, and Kameng Nip. "Bin packing under linear constraints." Journal of Combinatorial Optimization 34, no. 4 (May 25, 2017): 1198–209. http://dx.doi.org/10.1007/s10878-017-0140-2.

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36

Bilò, Vittorio, Francesco Cellinese, Giovanna Melideo, and Gianpiero Monaco. "Selfish colorful bin packing games." Journal of Combinatorial Optimization 40, no. 3 (June 11, 2020): 610–35. http://dx.doi.org/10.1007/s10878-020-00599-9.

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37

Bódis, Attila, and János Balogh. "Bin packing problem with scenarios." Central European Journal of Operations Research 27, no. 2 (August 21, 2018): 377–95. http://dx.doi.org/10.1007/s10100-018-0574-3.

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38

Liu, Mozhengfu, and Xueyan Tang. "Dynamic Bin Packing with Predictions." ACM SIGMETRICS Performance Evaluation Review 51, no. 1 (June 26, 2023): 57–58. http://dx.doi.org/10.1145/3606376.3593538.

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The MinUsageTime Dynamic Bin Packing (DBP) problem aims to minimize the accumulated bin usage time for packing a sequence of items into bins. It is often used to model job dispatching for optimizing the busy time of servers, where the items and bins match the jobs and servers respectively. It is known that the competitiveness of MinUsageTime DBP has tight bounds of Θ(√, log μ) and Θ(μ) in the clairvoyant and non-clairvoyant settings respectively, where μ is the max/min duration ratio of all items. In practice, the information about items' durations (i.e., job lengths) obtained via predictions is usually prone to errors. In this paper, we study the MinUsageTime DBP problem with predictions of items' durations. We find that an existing O(√ log μ)-competitive clairvoyant algorithm, if using predicted durations rather than real durations for packing, does not provide any bounded performance guarantee when the predictions are adversarially bad. We develop a new online algorithm with a competitive ratio of {O(∈2 √ log(∈2 μ)}, O(μ) (where ε is the maximum multiplicative error of prediction among all items), achieving O(√ log μ) consistency (competitiveness under perfect predictions where ∈ = 1) and O(μ) robustness (competitiveness under terrible predictions), both of which are asymptotically optimal.

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39

Gai, Ling, Weiwei Zhang, and Zhao Zhang. "Selfish bin packing with punishment." Theoretical Computer Science 982 (January 2024): 114276. http://dx.doi.org/10.1016/j.tcs.2023.114276.

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40

Angelopoulos, Spyros, Shahin Kamali, and Kimia Shadkami. "Online Bin Packing with Predictions." Journal of Artificial Intelligence Research 78 (December 20, 2023): 1111–41. http://dx.doi.org/10.1613/jair.1.14820.

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Bin packing is a classic optimization problem with a wide range of applications, from load balancing to supply chain management. In this work, we study the online variant of the problem, in which a sequence of items of various sizes must be placed into a minimum number of bins of uniform capacity. The online algorithm is enhanced with a potentially erroneous prediction concerning the frequency of item sizes in the sequence. We design and analyze online algorithms with efficient tradeoffs between the consistency, which is the competitive ratio assuming no prediction error, and the robustness, which is the competitive ratio under adversarial error. Moreover, we demonstrate that the performance of our algorithm degrades near-optimally as a function of the prediction error. This is the first theoretical and experimental study of online bin packing under competitive analysis in the realistic setting of learnable predictions. Previous work addressed only extreme cases with respect to the prediction error and relied on overly powerful and error-free oracles.

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41

Chekanin, Vladislav A., and Alexander V. Chekanin. "Multilevel Linked Data Structure for the Multidimensional Orthogonal Packing Problem." Applied Mechanics and Materials 598 (July 2014): 387–91. http://dx.doi.org/10.4028/www.scientific.net/amm.598.387.

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The actual NP-completed orthogonal bin packing problem is considered in the article. In practice a solution of a large number of different practical problems, including problems in logistics and scheduling comes down to the bin packing problem. A decision of an any packing problem is represented as a placement string which contains a sequence of objects selected to pack. The article proposes a new multilevel linked data structure that improves the effectiveness of decoding of the placement string and as a consequence, increases the speed of packing generation. The new data structure is applicable for all multidimensional orthogonal bin packing problems.

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42

Wu, Yong, Wenkai Li, Mark Goh, and Robert de Souza. "Three-dimensional bin packing problem with variable bin height." European Journal of Operational Research 202, no. 2 (April 2010): 347–55. http://dx.doi.org/10.1016/j.ejor.2009.05.040.

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43

Li, Chung-Lun, and Zhi-Long Chen. "Bin-packing problem with concave costs of bin utilization." Naval Research Logistics 53, no. 4 (June 2006): 298–308. http://dx.doi.org/10.1002/nav.20142.

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44

Courcobetis, Coastas, and Richard Weber. "Stability of On-Line Bin Packing with Random Arrivals and Long-Run-Average Constraints." Probability in the Engineering and Informational Sciences 4, no. 4 (October 1990): 447–60. http://dx.doi.org/10.1017/s0269964800001753.

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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.

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45

Peeters, Marc, and Zeger Degraeve. "Branch-and-price algorithms for the dual bin packing and maximum cardinality bin packing problem." European Journal of Operational Research 170, no. 2 (April 2006): 416–39. http://dx.doi.org/10.1016/j.ejor.2004.06.034.

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46

Wei, Lijun, Wee-Chong Oon, Wenbin Zhu, and Andrew Lim. "A goal-driven approach to the 2D bin packing and variable-sized bin packing problems." European Journal of Operational Research 224, no. 1 (January 2013): 110–21. http://dx.doi.org/10.1016/j.ejor.2012.08.005.

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47

Chekanin, Alexander V., and Vladislav A. Chekanin. "Improved Packing Representation Model for the Orthogonal Packing Problem." Applied Mechanics and Materials 390 (August 2013): 591–95. http://dx.doi.org/10.4028/www.scientific.net/amm.390.591.

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The multidimensional NP-hard orthogonal bin packing problem is considered in the article. Usually the problem is solved using heuristic algorithms of discrete optimization which optimize a selection sequence of objects to be packed in containers. The quality and speed of getting the resulting packing for a given sequence of placing objects is determined by the used packing representation model. In the article presented a new packing representation model for constructing the orthogonal packing. The proposed model of potential containers describes all residual free spaces of containers in packing. The developed model is investigated on well-known standard benchmarks of three-dimensional orthogonal bin packing problem. The model can be used in development of applied software for the optimal allocation of orthogonal resources.

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48

Jansen, Klaus, and Kim-Manuel Klein. "About the Structure of the Integer Cone and Its Application to Bin Packing." Mathematics of Operations Research 45, no. 4 (November 2020): 1498–511. http://dx.doi.org/10.1287/moor.2019.1040.

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We consider the bin packing problem with d different item sizes and revisit the structure theorem given by Goemans and Rothvoß about solutions of the integer cone. We present new techniques on how solutions can be modified and give a new structure theorem that relies on the set of vertices of the underlying integer polytope. As a result of our new structure theorem, we obtain an algorithm for the bin packing problem with running time [Formula: see text], where V is the set of vertices of the integer knapsack polytope, and [Formula: see text] is the encoding length of the bin packing instance. The algorithm is fixed-parameter tractable, parameterized by the number of vertices of the integer knapsack polytope [Formula: see text]. This shows that the bin packing problem can be solved efficiently when the underlying integer knapsack polytope has an easy structure (i.e., has a small number of vertices). Furthermore, we show that the presented bounds of the structure theorem are asymptotically tight. We give a construction of bin packing instances using new structural insights and classical number theoretical theorems which yield the desired lower bound.

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49

Qiao, Gaoyang. "A variable neighborhood search framework combining improved simulated annealing search to solve the one-dimensional crating problem." Applied and Computational Engineering 4, no. 1 (June 14, 2023): 364–69. http://dx.doi.org/10.54254/2755-2721/4/20230489.

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The N-P problem, similar to bin packing, has a great impact on us in real life. Similar to the classical combinatorial problem, with the expansion of the problem size, usually there is no way to solve it by enumeration. The common solution is to solve by heuristic methods, in addition to the improved local search method by forbidden search or simulated annealing to solve. However, due to the multivariate nature of the bin packing problem, it is difficult to solve most of the bin packing problems by the above single method. In this paper, a variable neighborhood search combined with an improved local search is used to solve the one-dimensional bin packing problem. The method in this paper is generalizable and can easily improve the existing method to suit new problems, and the results are acceptable.

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50

Camacho, Guillermo Alberto, David Alvarez, and Daniel Cuellar. "Heuristic Approach For The Multiple Bin-Size Bin Packing Problem." IEEE Latin America Transactions 16, no. 2 (February 2018): 620–26. http://dx.doi.org/10.1109/tla.2018.8327421.

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Journal articles on the topic 'Bin packing'

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