Abstract
In many industries solid materials are produced in sizes that are larger than needed by the users of the material. There are obvious economic advantages in doing this but the practice gives rise to a problem of determining how the material should be cut to obtain the required sizes. This cutting stock or trim problem is of considerable importance in deciding the final profitability of the manufacturing venture.
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References
APM Annual Report, 1972. APM Ltd, Melbourne.
Coverdale, I. & Wharton, F. An improved heuristic procedure for a non-linear cutting stock problem. Man. Sci. 23, 1976, 78–86.
Crone, J.M. NZFP Paper Trim System 1972. N.Z. Forest Products Ltd., Auckland, N.Z.
Eismann, K. The trim problem. Man. Sei. 3, 1957, 279–284.
Filmer, P.J. Duplex cutter deckle filling. Appita, 1970, 24, 189–196.
Gilmore, P.C. & Gomory, R.E. A linear programming approach to the cutting stock problem. Oper. Res. (USA), 9, 1961, 849–859.
Gilmore, P.C., Gomory, R. E. A linear programming approach to the cutting stock problem - part II. Oper. Res. (USA), 11, 1963, 77–82.
Haesslar, R.W. An application of heuristic programming to a non-linear cutting stock problem occurring in the paper industry. PhD Dissertation, 1968, Univ. of Mich.
Haesslar, R.W. A heuristic programming solution to a non-linear cutting stock problem. Man. Sci. 17, 1971, 8793–8802.
Haesslar, R.W. Controlling cutting pattern changes in one-dim ensional trim problems. Oper. Res. (USA), 23, 1975, 483–493.
Haesslar, R.W. A survey of one dimensional single stock size cutting stock problems and solution procedures, ORSA/Tims meeting, Chicago, 1975.
Hiron, A.M. Experiences with trim problem. Quart. Bull. of Brit. Fqp. and Board Industry Res. Ass., June, 1966.
Johnston, R.E., Bourke, S.B. The development of computer programs for reels deckle filling. Appita, 26, 1971, 444–448.
Johnston, R.E. Extensions to Haesslars heuristic for the trim problem. Centre Technique du Papier, 1979, Grenoble, France, C.R. No. 1366.
Johnston, R.E. Bounds for the one-dimensional cutting stock problem. Submitted for publication.
Kantorovitch, L.V. Mathematical methods of organising and planning production. Leningrad State University and reprinted, Man. Sci. 6, 1939, 366–422.
Metzger, R.W. Stock Slitting. Chap. 8 of Elementary Mathematical Programming, 1958, Wiley, N.Y.
Paull, A.E. & B Walter, J.R. The trim problem: an application of linear programming to the manufacture of Newsprint. Econometrica, 23, 1954, 336.
Pierce, J.F. Some Large scale production scheduling problems in the paper industry, 1964, Prentice-Hall, N.J.
Pierce, J.F. On the solution of integer cutting stock problems by combinatorial programming. Part I. 1967, IBM Cambridge Sci. Centre Report.
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© 1982 Springer Science+Business Media Dordrecht
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Johnston, R.E. (1982). A Direct Combinatorial Algorithm for Cutting Stock Problems. In: Anderssen, R.S., de Hoog, F.R. (eds) The Application of Mathematics in Industry. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7834-1_8
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DOI: https://doi.org/10.1007/978-94-011-7834-1_8
Publisher Name: Springer, Dordrecht
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