Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Cutting stock problems

  • Robert W. Haessler
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_203

INTRODUCTION

Solid materials such as aluminum, steel, glass, wood, leather, paper and plastic film are generally produced in larger sizes than required by the customers for these materials. As a result, the producers or primary converters must determine how to cut the production units of these materials to obtain the sizes required by their customers. This is known as a cutting stock problem. It can occur in one, two or three dimensions depending on the material. The production units may be identical, may consist of a few different sizes, or may be unique. They may be of consistent quality throughout or may contain defects. The production units may be regular (rectangular) or irregular. The ordered sizes may be regular or irregular. They may all have the same quality requirements or some may have different requirements. They may have identical or different timing requirements which impact inventory.

Some examples follow:
  • cutting rolls of paper from production reels of the same diameter.

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References

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    Gilmore, P. C. and Gomory, R. E. (1961). “A Linear Programming Approach to the Cutting Stock Problem,” Operations Research, 9, 848–859.Google Scholar
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    Gilmore, P. C. and Gomory, R. E. (1963). “A Linear Programming Approach to the Cutting Stock Problem, Part II,” Operations Research, 11, 863–888.Google Scholar
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    Gilmore, P. C. and Gomory, R. E. (1965). “Multistage Cutting Stock Problems of Two and More Dimensions,” Operations Research, 13, 94–120.Google Scholar
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    Gilmore, P. C. and Gomory, R. E. (1966). “The Theory and Computation of Knapsack Functions,” Operations Research, 14, 1045–1074.Google Scholar
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    Pierce, J. F. (1964). Some Large Scale Production Problems in the Paper Industry, Prentice-Hall, Inc. Englewood Cliffs, New Jersey.Google Scholar
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    Sweeney, P. E. and Paternoster, E. R. (1991). “Cutting and Packing Problems: An Updated Literature Review,” working paper No. 654, University of Michigan, School of Business. Google Scholar
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    Wang, P. Y. (1983). “Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems,” Operations Research, 31, 573–586.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Robert W. Haessler
    • 1
  1. 1.University of MichiganAnn ArborUSA