Cutting Stock Problems in the Paper and Sheet Metal Industries

  • G. S. R. MurthyEmail author
  • Katta G. Murty
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 212)


Paper, textiles, plastic film, metallic foil, and sheet-metal used for producing sheet-metal components for automobile and other industries are manufactured in rolls of large width (jumbo rolls) or rectangular sheets of large dimensions. The problems of cutting the available jumbo rolls into rolls of smaller widths, or master sheets of sheet-metal into components of specified dimensions as required by customers, with minimum trim waste, are known as cutting stock problems with 1 or 2 dimensions. In this chapter we discuss these cutting stock problems and efficient algorithms for solving them.

Supplementary material

273578_1_En_17_MOESM1_ESM.pdf (77 kb)
(pdf 77 KB)


  1. 1.
    Gilmore, P. C., & Gomory, R. E. (1961). A linear programming approach to the cutting stock problem. Operations Research, 9(6), 849–859.CrossRefGoogle Scholar
  2. 2.
    Gilmore, P. C., & Gomory, R. E. (1963). A linear programming approach to the cutting stock problem- part II. Operations Research, 11, 863–888.CrossRefGoogle Scholar
  3. 3.
    Haessler, R. W. (1988). A new generation of paper machine trim programs. TAPPI Journal, 71(August), 127–130.Google Scholar
  4. 4.
    Kantarovich, L. V. (1939). Mathematical methods for organizing and planning production (Leningrad State University). Managament Science, 6(4), 366–422.CrossRefGoogle Scholar
  5. 5.
    Kantarovich, L. V., & Zalgaller, V. A. (1951). Calculation of rational cutting of stock. Leningrad: Lenizdat.Google Scholar
  6. 6.
    Murty, K. G. (2010). Optimization for decision making: Linear and quadratic models. New York: Springer.CrossRefGoogle Scholar
  7. 7.
    Sweeney, P. E., & Haessler, R. W. (1991). Cutting stock problems and solution procedures. European Journal of Operational Research, 54(2), 141–150.
  8. 8.
    Vasek, C. (1980). Linear programming. New York: W.H. Freeman and Company.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.SQC & OR UnitIndian Statistical InstituteHyderabadIndia
  2. 2.Department of Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA

Personalised recommendations