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An effective heuristic based on column generation for the two-dimensional three-stage steel plate cutting problem

Author

Listed:
  • Jianyu Long

    (Dongguan University of Technology
    Chongqing University)

  • Zhong Zheng

    (Chongqing University)

  • Xiaoqiang Gao

    (Chongqing University)

  • Panos M. Pardalos

    (University of Florida)

  • Wanzhe Hu

    (Chongqing University
    University of Florida)

Abstract

In this study, we focus on the steel plate cutting problem (SPCP), where a set of rectangular order plates with specified demand are cut from large rectangular steel plates. The aim of solving SPCP is to minimize the number of steel plates used in the cutting process. According to the analysis of the cutting production line in steel mills, we regard the SPCP as a two-dimensional non-exact three-stage cutting stock problem (2D3SCSP) with two additional practical constraints. Since these two practical constraints limit the length between any two adjacent guillotine cuts in the first stage by a predetermined parameter and the number of guillotine cuts in the second stage by one, the existing solving methods proposed for 2D3SCSP cannot be used for SPCP directly. Four heuristics based on column generation (HCG) are proposed to solve SPCP. The performance of the four HCGs is analyzed through conducting a set of experiments, and an effective HCG with the ability of obtaining high-quality solutions within acceptable computational times is finally obtained.

Suggested Citation

  • Jianyu Long & Zhong Zheng & Xiaoqiang Gao & Panos M. Pardalos & Wanzhe Hu, 2020. "An effective heuristic based on column generation for the two-dimensional three-stage steel plate cutting problem," Annals of Operations Research, Springer, vol. 289(2), pages 291-311, June.
    • Handle: RePEc:spr:annopr:v:289:y:2020:i:2:d:10.1007_s10479-020-03604-w
    DOI: 10.1007/s10479-020-03604-w
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    1. Silva, Elsa & Alvelos, Filipe & Valério de Carvalho, J.M., 2010. "An integer programming model for two- and three-stage two-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 205(3), pages 699-708, September.
    2. François Vanderbeck, 2001. "A Nested Decomposition Approach to a Three-Stage, Two-Dimensional Cutting-Stock Problem," Management Science, INFORMS, vol. 47(6), pages 864-879, June.
    3. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. Bahadır Durak & Dilek Tuzun Aksu, 2017. "Dynamic programming and mixed integer programming based algorithms for the online glass cutting problem with defects and production targets," International Journal of Production Research, Taylor & Francis Journals, vol. 55(24), pages 7398-7411, December.
    5. Vitor Nesello & Maxence Delorme & Manuel Iori & Anand Subramanian, 2018. "Mathematical models and decomposition algorithms for makespan minimization in plastic rolls production," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(3), pages 326-339, March.
    6. Célia Paquay & Sabine Limbourg & Michaël Schyns & José Fernando Oliveira, 2018. "MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 56(4), pages 1581-1592, February.
    7. Nasr Al-Hinai & Chefi Triki, 2020. "A two-level evolutionary algorithm for solving the petrol station replenishment problem with periodicity constraints and service choice," Annals of Operations Research, Springer, vol. 286(1), pages 325-350, March.
    8. Cintra, G.F. & Miyazawa, F.K. & Wakabayashi, Y. & Xavier, E.C., 2008. "Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 61-85, November.
    9. Puchinger, Jakob & Raidl, Gunther R., 2007. "Models and algorithms for three-stage two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1304-1327, December.
    10. Puca Huachi Vaz Penna & Anand Subramanian & Luiz Satoru Ochi & Thibaut Vidal & Christian Prins, 2019. "A hybrid heuristic for a broad class of vehicle routing problems with heterogeneous fleet," Annals of Operations Research, Springer, vol. 273(1), pages 5-74, February.
    11. Yaodong Cui, 2013. "A new dynamic programming procedure for three-staged cutting patterns," Journal of Global Optimization, Springer, vol. 55(2), pages 349-357, February.
    12. M Mrad & I Meftahi & M Haouari, 2013. "A branch-and-price algorithm for the two-stage guillotine cutting stock problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(5), pages 629-637, May.
    13. Harald Dyckhoff, 1981. "A New Linear Programming Approach to the Cutting Stock Problem," Operations Research, INFORMS, vol. 29(6), pages 1092-1104, December.
    14. 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.
    15. Furini, Fabio & Malaguti, Enrico & Medina Durán, Rosa & Persiani, Alfredo & Toth, Paolo, 2012. "A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size," European Journal of Operational Research, Elsevier, vol. 218(1), pages 251-260.
    16. Goncalves, Jose Fernando, 2007. "A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1212-1229, December.
    17. Lodi, Andrea & Martello, Silvano & Monaci, Michele, 2002. "Two-dimensional packing problems: A survey," European Journal of Operational Research, Elsevier, vol. 141(2), pages 241-252, September.
    18. Lin Liu & Xinbao Liu & Jun Pei & Wenjuan Fan & Panos M. Pardalos, 2017. "A study on decision making of cutting stock with frustum of cone bars," Operational Research, Springer, vol. 17(1), pages 187-204, April.
    19. 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.
    20. Andrea Lodi & Silvano Martello & Daniele Vigo, 2004. "Models and Bounds for Two-Dimensional Level Packing Problems," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 363-379, September.
    21. P. C. Gilmore & R. E. Gomory, 1965. "Multistage Cutting Stock Problems of Two and More Dimensions," Operations Research, INFORMS, vol. 13(1), pages 94-120, February.
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