{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:24:57Z","timestamp":1759847097277,"version":"3.40.3"},"reference-count":24,"publisher":"Scientific and Business World","license":[{"start":{"date-parts":[[2014,3,10]],"date-time":"2014-03-10T00:00:00Z","timestamp":1394409600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Decision Sciences"],"published-print":{"date-parts":[[2014,3,10]]},"abstract":"<jats:p>The paper considers a packing optimization problem of different spheres and cuboids into a cuboid of the minimal height. Translations and continuous rotations of cuboids are allowed. In the paper, we offer a way of construction of special functions (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi mathvariant=\"normal\">\u03a6<\/mml:mi><\/mml:mrow><\/mml:math>-functions) describing how rotations can be dealt with. These functions permit us to construct the mathematical model of the problem as a classical mathematical programming problem. Basic characteristics of the mathematical model are investigated. When solving the problem, the characteristics allow us to apply a number of original and state-of-the-art efficient methods of local and global optimization. Numerical examples of packing from 20 to 300 geometric objects are given.<\/jats:p>","DOI":"10.1155\/2014\/571743","type":"journal-article","created":{"date-parts":[[2014,3,10]],"date-time":"2014-03-10T21:02:37Z","timestamp":1394485357000},"page":"1-19","source":"Crossref","is-referenced-by-count":10,"title":["Packing Different Cuboids with Rotations and Spheres into a Cuboid"],"prefix":"10.47654","volume":"2014","author":[{"given":"Y. G.","family":"Stoyan","sequence":"first","affiliation":[{"name":"Department of Mathematical Modeling and Optimal Design, Institute for Mechanical Engineering Problems, \n\t\t\t\t\tNational Academy of Sciences of Ukraine, 2\/10 Pozharsky Street, Kharkov 61046, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. 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