Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins

The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive a...
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Autor*in:	Kaiyuan Liu [verfasserIn] Hongyu Zhang [verfasserIn] Chong Wang [verfasserIn] Hui Li [verfasserIn] Yongquan Chen [verfasserIn] Qiong Chen [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	robust optimization two-dimensional strip-packing problem variable-sized bins column generation contiguous relaxation one-dimensional bin-packing problem

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 11(2023), 23, p 4781
Übergeordnetes Werk:	volume:11 ; year:2023 ; number:23, p 4781

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/math11234781

Katalog-ID:	DOAJ099960362

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callnumber-first	Q - Science
author	Kaiyuan Liu
spellingShingle	Kaiyuan Liu misc QA1-939 misc robust optimization misc two-dimensional strip-packing problem misc variable-sized bins misc column generation misc contiguous relaxation misc one-dimensional bin-packing problem misc Mathematics Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins
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topic_title	QA1-939 Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins robust optimization two-dimensional strip-packing problem variable-sized bins column generation contiguous relaxation one-dimensional bin-packing problem
topic	misc QA1-939 misc robust optimization misc two-dimensional strip-packing problem misc variable-sized bins misc column generation misc contiguous relaxation misc one-dimensional bin-packing problem misc Mathematics
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title	Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins
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title_sort	robust optimization for the two-dimensional strip-packing problem with variable-sized bins
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title_auth	Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins
abstract	The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions.
abstractGer	The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions.
abstract_unstemmed	The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions.
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title_short	Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins
url	https://doi.org/10.3390/math11234781 https://doaj.org/article/6e1cee26c185409387eb7d0bbbe772f8 https://www.mdpi.com/2227-7390/11/23/4781 https://doaj.org/toc/2227-7390
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Robust Optimization for the Two-Dimensional Strip-Packing Problem with Variable-Sized Bins

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