The variable-width strip packing problem

• Published in: Central European journal of operations research Vol. 30; no. 4; pp. 1337 - 1351
• Main Authors: Bódis, Attila, Csirik, János
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Information management; Mathematical research; Operations research; Operations Research/Decision Theory; Packing for shipment; Packing problem; Scheduling; Strip; Hungary; Online algorithms; 68Q25; 68W40; Competitive ratio; 68W25; Strip packing; Variable widths
• ISSN: 1435-246X; 1613-9178
• DOI: 10.1007/s10100-021-00772-3

Here, we focus on a generalized version of the strip packing problem; namely we have several open-end strips with different widths, and we wish to pack rectangular items into these strips without overlapping such that we have to minimize either the makespan (i.e. the top of the topmost item), or the total area used. We investigate the online variant of the problem, where the items are arriving one-by-one, and we have to make irrevocable decisions on their packing. A similar framework was proposed by Ye and Mei (On-line scheduling of parallel jobs in heterogeneous multiple clusters. Frontiers in algorithmics and algorithmic aspects in information and management, Springer, Berlin, pp 139–148, 2012 . https://doi.org/10.1007/978-3-642-29700-7_13 ) for scheduling models, and they studied the absolute competitive ratio of their algorithm. Our contribution is to define a new objective function and several algorithms by combining so-called shelf algorithms with techniques taken from the areas of the variable-sized bin packing problem and scheduling. We analyzed the asymptotic competitive ratio of our algorithms.