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An effective solution for a real cutting stock problem in manufacturing plastic rolls

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  • Ramiro Varela
  • Camino Vela
  • Jorge Puente
  • María Sierra
  • Inés González-Rodríguez

Abstract

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Ramiro Varela & Camino Vela & Jorge Puente & María Sierra & Inés González-Rodríguez, 2009. "An effective solution for a real cutting stock problem in manufacturing plastic rolls," Annals of Operations Research, Springer, vol. 166(1), pages 125-146, February.
  • Handle: RePEc:spr:annopr:v:166:y:2009:i:1:p:125-146:10.1007/s10479-008-0407-1
    DOI: 10.1007/s10479-008-0407-1
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. Gleb Belov & Guntram Scheithauer, 2007. "Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 27-35, February.
    3. Suliman, Saad M. A., 2001. "Pattern generating procedure for the cutting stock problem," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 293-301, December.
    4. Song, X. & Chu, C.B. & Nie, Y.Y. & Bennell, J.A., 2006. "An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1870-1889, December.
    5. François Vanderbeck, 2000. "Exact Algorithm for Minimising the Number of Setups in the One-Dimensional Cutting Stock Problem," Operations Research, INFORMS, vol. 48(6), pages 915-926, December.
    6. Robert W. Haessler, 1975. "Controlling Cutting Pattern Changes in One-Dimensional Trim Problems," Operations Research, INFORMS, vol. 23(3), pages 483-493, June.
    7. Chen, Chuen-Lung S. & Hart, Stephen M. & Tham, Wai Mui, 1996. "A simulated annealing heuristic for the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 93(3), pages 522-535, September.
    8. Umetani, Shunji & Yagiura, Mutsunori & Ibaraki, Toshihide, 2003. "One-dimensional cutting stock problem to minimize the number of different patterns," European Journal of Operational Research, Elsevier, vol. 146(2), pages 388-402, April.
    9. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    10. Haessler, Robert W. & Sweeney, Paul E., 1991. "Cutting stock problems and solution procedures," European Journal of Operational Research, Elsevier, vol. 54(2), pages 141-150, September.
    11. Goulimis, Constantine, 1990. "Optimal solutions for the cutting stock problem," European Journal of Operational Research, Elsevier, vol. 44(2), pages 197-208, January.
    12. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
    13. Vahrenkamp, Richard, 1996. "Random search in the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 95(1), pages 191-200, November.
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