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Cutting stock problems and solution procedures. (English) Zbl 0736.90062

Summary: This paper discusses some of the basic formulation issues and solution procedures for solving one- and two-dimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern.

MSC:

90C27 Combinatorial optimization
90B30 Production models
90C05 Linear programming
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming

References:

[1] Beasley, J. E., Algorithms for unconstrained two-dimensional guillotine cutting, Journal of the Operational Research Society, 36, 297-306 (1985) · Zbl 0589.90040
[2] Beasley, J. E., An exact two-dimensional non-guillotine cutting tree search procedure, Operations Research, 33, 49-64 (1985) · Zbl 0569.90038
[3] Beged Dov, A. G., Some computational aspects of the \(M\) paper mills and \(P\) printers paper trim problem, Journal of Business Administration, 1, 15-34 (1970)
[4] Christofides, N.; Whitlock, C., An algoritham for two-dimensional cutting problems, Operational Research, 2530-2544 (1977)
[5] Dyckhoff, H., A typology of cutting an packing problems, European Journal of Operational Research, 44, 145-159 (1990) · Zbl 0684.90076
[6] Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting stock problem, Operations Research, 9, 848-859 (1961) · Zbl 0096.35501
[7] Gilmore, P. C.; Gomory, R. E., A linear programming approach to the cutting stock problem, Part II, Operations Research, 11, 863-888 (1963) · Zbl 0124.36307
[8] Gilmore, P. C.; Gomory, R. E., Multistage cutting stock problems of two and more dimensions, Operations Research, 13, 94-120 (1965) · Zbl 0128.39601
[9] Gilmore, P. C.; Gomory, R. E., The theory and computation of knapsack functions, Operations Research, 14, 1045-1074 (1966) · Zbl 0173.21502
[10] Hadjiconstantinou, E.; Christofides, N., An optimal algorithm for general, orthogonal, 2-D cutting problems, (Technical Report MS-91/2 (1991), Imperial College: Imperial College London) · Zbl 0959.90060
[11] Haessler, R. W., A heuristic programming solution to a nonlinear cutting stock problem, Management Science, 17, 793-802 (1971) · Zbl 0219.90021
[12] Haessler, R. W., A note on computational modifications to the Gilmore-Gomory cutting stock algorithm, Operations Research, 28, 1001-1005 (1980) · Zbl 0441.90066
[13] Haessler, R. W., A new generation of paper machine trim programs, TAPPI Journal, 71, 127-130 (1988), (August)
[14] Haessler, R. W.; Talbot, F. B., A 0-1 model for solving the corrugator trim problem, Management Science, 29, 200-209 (1983), (December)
[15] Kantorovich, L. V., Mathematical methods of organizing and planning production, Management Science, 6, 366-422 (1960), reprinted in · Zbl 0995.90532
[16] Pierce, J. F., Some Large Scale Production Problems in the Paper Industry (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, NY
[17] Rinnooy Kan, A. H.G.; De Wit, J. R.; Wijmenga, R. T., Nonorthogonal two-dimensional cutting patterns, Management Science, 33, 670-684 (1987) · Zbl 0629.90044
[18] Sweeney, P. E.; Paternoster, E. R., Cutting and packing problems: An updated literature review, (Working Paper No. 654 (1991), University of Michigan: University of Michigan School of Business)
[19] Sweeney, P. E.; Haessler, R. W., One-dimensional cutting stock decisions for rolls with multiple quality grades, European Journal of Operational Research, 44, 224-231 (1990) · Zbl 0684.90077
[20] Vasko, F. J., A computational improvement to Wang’s two-dimensional cutting stock algorithm, Computers and Industrial Engineering, 16, 109-115 (1989)
[21] Viswanathan, K. V.; Bagchi, A., An exact best-first search procedure for the constrained rectangular guillotine knapsack problem, (Proceedings of the American Association for Artificial Intelligence (1988)), 145-149
[22] Wang, P. Y., Two algorithms for constrained two-dimensional cutting stock problems, Operations Research, 31, 573-586 (1983) · Zbl 0517.90093
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