Abstract
The integer round-up property of the linear cutting stock problem is investigated. An algorithm for verifying the sufficient conditions under which the problem has no integer round-up property is designed.
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REFERENCES
Dyckhoff, H., A Typology of Cutting and Packing Problems, Heidelberg: Springer, 1992.
Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NPCompleteness, San Francisco: Freeman, 1979. Translated under the title Vychislitel'nye mashiny i trudnoreshaemye zadachi, Moscow: Mir, 1982.
Mukhacheva, E.A. and Rubinshtein, G.Sh., Matematicheskoe programmirovanie (Mathematical Programming), Novosibirsk: Nauka, 1987.
Baum, S. and Trotter, L.E., Jr., Integer Rounding for Polymatroid and Branching Optimization Problems, SIAM J. Alg. Disc. Meth., 1981, no. 2(4), pp. 416–425.
Marcotte, O., The Cutting Stock Problem and Integer Rouding, Math.Program., 1985, no. 33/1, pp. 82–92.
Marcotte, O., An Instance of the Cutting Stock Problem for Which the Rounding Property does not hold, OR Lett., 1986, no. 4(5), pp. 239–243.
Diegel, A., Integer LP Solution for Large Trim Problems, University of Natal, South Africa, Working Paper, 1988.
Wascher, G. and Gau, T., Two Approaches to the Cutting Stock Problem, IFORS'93 Conf., Lisboa, 1993.
Nitsche, C., Scheithauer, G., and Terno, J., New Cases of the Cutting Stock Problem having MIRUP, Math. Meth. Oper. Res., 1998, vol. 48, pp. 105–115.
Scheithauer, G. and Terno, J., Improving the Formulation of the Cutting Stock Problem, Int. Sympos. Math. Program, Lausanne, 1997.
Mukhacheva, E.A., Belov, G.N., Kartak, V.M., and Mukhacheva, A.S., Linear One-Dimensional Cutting-Packing Problems: Numerical Experiments with Sequential Value Correction (SVC) and a Modified Branch-and-Bound Method (MBB), Pesquisa Oper., 2000, vol. 20, no. 2, pp. 153–168.
Shoenfield, J.E., Fast, Exact Solution of Open Bin Packing Problems without Linear Programming, Draft, US Army Space & Missile Defence Command, Huntsville, Alabama, 2002, (jonscho@hiwaay.net).
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Kartak, V.M. Sufficient Conditions for the Integer Round-Up Property to Be Violated for the Linear Cutting Stock Problem. Automation and Remote Control 65, 407–412 (2004). https://doi.org/10.1023/B:AURC.0000019372.73750.3b
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DOI: https://doi.org/10.1023/B:AURC.0000019372.73750.3b