Geodesic
Models of the Nonguillotine Sheet and Strip Rectangular Packing Problem
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 5-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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Mathematical models of the nonguillotine sheet and strip rectangular packing problem with rotation are suggested. The models have the form of the linear partially Boolean inequalities system and the linear partially Boolean programming problem. Several computing features of the Land and Doig method and the heuristic approaches for reducing general complexity of solving the problem are discussed.
Keywords: rectangular packing problem, 2BP, 2SP, exact method for solving strip rectangular packing problem, Land and Doig method. 
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A. A. Andrianova; T. M. Mukhtarova; V. R. Fazylov. Models of the Nonguillotine Sheet and Strip Rectangular Packing Problem. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 5-17. http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a0/

[1] Kantorovich L. V., Matematicheskie metody v organizatsii i planirovanii proizvodstva, Izd-vo LGU, L., 1939, 68 pp.

[2] Kantorovich L. V., Zalgaller V. A., Raschet ratsionalnogo raskroya promyshlennykh materialov, Leningr. gaz.-zhurn. izd-vo, L., 1951, 198 pp.

[3] Mukhacheva E. A., Ratsionalnyi raskroi promyshlennykh materialov. Primenenie v ASU, Mashinostroenie, M., 1984, 176 pp.

[4] Lodi A., Martello S., Monaci M., “Two-dimensional packing problems: A survey”, Eur. J. Oper. Res., 141:2 (2002), 241–252 | DOI | Zbl

[5] Rudnev A. S., “Veroyatnostnyi poisk s zapretami dlya zadachi upakovki krugov i pryamougolnikov v polosu”, Diskr. analiz i issled. operatsii, 16:4 (2009), 61–86 | Zbl

[6] Zhang D., Kang Y., Deng S., “A new heuristic recursive algorithm for the strip rectangular packing problem”, Comput. Oper. Res., 33:8 (2006), 2209–2217 | DOI | Zbl

[7] Starostin N. V., Silaev A. N., Sedykh I. O., “Mnogourovnevyi evolyutsionno-geneticheskii metod razmescheniya pryamougolnikov na ploskosti”, Vestn. Nizhegor. un-ta im. N. I. Lobachevskogo, 2009, no. 5, 163–168

[8] Chen M., Huang W., “A two-level search algorithm for 2D rectangular packing problem”, Comput. Ind. Eng., 53:1 (2007), 123–136 | DOI

[9] Kenmochi M., Imamichi T., Nonobe K., Yagiura M., Nagamochi H., “Exact algorithms for the two-dimensional strip packing problem with and without rotations”, Europ. J. Oper. Res., 198:1 (2009), 73–83 | DOI | Zbl

[10] Rudnev A. S., Algoritmy lokalnogo poiska dlya zadach dvumernoi upakovki, Avtoref. dis. \ldots kand. fiz.-matem. nauk, Novosibirsk, 2010, 19 pp.

[11] Bekrar A., Kacem I., Chu C., “A comparative study of exact algorithms for the two dimensional strip packing problem”, Int. J. Ind. Syst. Eng., 1:2 (2007), 151–170

[12] Land A. H., Doig A. G., “An automatic method of solving discrete programming problems”, Econometrica, 28:3 (1960), 497–520 | DOI | Zbl

[13] Lerner E. Yu., Fazylov V. R., “Funktsiya gilotinnogo razmescheniya”, Issled. po priklad. matem., 21, Unipress,, Kazan, 1999, 187–196

[14] Men A. S., “Zadacha kalendarnogo planirovaniya dlya predpriyatii edinichnogo i melkoseriinogo proizvodstva”, Kalendarnoe planirovanie, Progress, M., 1966, 222–226