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New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems

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  • Ortmann, Frank G.
  • Ntene, Nthabiseng
  • van Vuuren, Jan H.

Abstract

We consider two types of orthogonal, oriented, rectangular, two-dimensional packing problems. The first is the strip packing problem, for which four new and improved level-packing algorithms are presented. Two of these algorithms guarantee a packing that may be disentangled by guillotine cuts. These are combined with a two-stage heuristic designed to find a solution to the variable-sized bin packing problem, where the aim is to pack all items into bins so as to minimise the packing area. This heuristic packs the levels of a solution to the strip packing problem into large bins and then attempts to repack the items in those bins into smaller bins in order to reduce wasted space. The results of the algorithms are compared to those of seven level-packing heuristics from the literature by means of a large number of strip-packing benchmark instances. It is found that the new algorithms are an improvement over known level-packing heuristics for the strip packing problem. The advancements made by the new and improved algorithms are limited in terms of utilised space when applied to the variable-sized bin packing problem. However, they do provide results faster than many existing algorithms.

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  • Ortmann, Frank G. & Ntene, Nthabiseng & van Vuuren, Jan H., 2010. "New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems," European Journal of Operational Research, Elsevier, vol. 203(2), pages 306-315, June.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:2:p:306-315
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    Cited by:

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    2. Andreas Bortfeldt & Sabine Jungmann, 2012. "A tree search algorithm for solving the multi-dimensional strip packing problem with guillotine cutting constraint," Annals of Operations Research, Springer, vol. 196(1), pages 53-71, July.
    3. de Queiroz, Thiago A. & Miyazawa, Flávio K., 2013. "Two-dimensional strip packing problem with load balancing, load bearing and multi-drop constraints," International Journal of Production Economics, Elsevier, vol. 145(2), pages 511-530.
    4. Castro, Pedro M. & Oliveira, José F., 2011. "Scheduling inspired models for two-dimensional packing problems," European Journal of Operational Research, Elsevier, vol. 215(1), pages 45-56, November.
    5. Gašper Žerovnik & Janez Žerovnik, 2011. "Constructive heuristics for the canister filling problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(3), pages 371-389, September.
    6. Polyakovskiy, Sergey & M’Hallah, Rym, 2022. "A lookahead matheuristic for the unweighed variable-sized two-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 104-117.
    7. Hong, Shaohui & Zhang, Defu & Lau, Hoong Chuin & Zeng, XiangXiang & Si, Yain-Whar, 2014. "A hybrid heuristic algorithm for the 2D variable-sized bin packing problem," European Journal of Operational Research, Elsevier, vol. 238(1), pages 95-103.
    8. Leung, Stephen C.H. & Zhang, Defu & Sim, Kwang Mong, 2011. "A two-stage intelligent search algorithm for the two-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 57-69, November.
    9. Shaojie Tang & Jing Yuan & Zhao Zhang & Ding-zhu Du, 2017. "iGreen: green scheduling for peak demand minimization," Journal of Global Optimization, Springer, vol. 69(1), pages 45-67, September.
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    Bin packing Strip packing;

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