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Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges

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  • Kallrath, Julia
  • Rebennack, Steffen
  • Kallrath, Josef
  • Kusche, Rüdiger

Abstract

We discuss cutting stock problems (CSPs) from the perspective of the paper industry and the financial impact they make. Exact solution approaches and heuristics have been used for decades to support cutting stock decisions in that industry. We have developed polylithic solution techniques integrated in our ERP system to solve a variety of cutting stock problems occurring in real world problems. Among them is the simultaneous minimization of the number of rolls and the number of patterns while not allowing any overproduction. For two cases, CSPs minimizing underproduction and CSPs with master rolls of different widths and availability, we have developed new column generation approaches. The methods are numerically tested using real world data instances. An assembly of current solved and unsolved standard and non-standard CSPs at the forefront of research are put in perspective.

Suggested Citation

  • Kallrath, Julia & Rebennack, Steffen & Kallrath, Josef & Kusche, Rüdiger, 2014. "Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges," European Journal of Operational Research, Elsevier, vol. 238(1), pages 374-389.
    • Handle: RePEc:eee:ejores:v:238:y:2014:i:1:p:374-389
    DOI: 10.1016/j.ejor.2014.03.027
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    1. 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.
    2. Harjunkoski, Iiro & Westerlund, Tapio & Porn, Ray & Skrifvars, Hans, 1998. "Different transformations for solving non-convex trim-loss problems by MINLP," European Journal of Operational Research, Elsevier, vol. 105(3), pages 594-603, March.
    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. Douglas Alem & Pedro Munari & Marcos Arenales & Paulo Ferreira, 2010. "On the cutting stock problem under stochastic demand," Annals of Operations Research, Springer, vol. 179(1), pages 169-186, September.
    5. Hatem Ben Amor & José Valério de Carvalho, 2005. "Cutting Stock Problems," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 131-161, Springer.
    6. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    7. Cui, Yaodong & Zhao, Zhigang, 2013. "Heuristic for the rectangular two-dimensional single stock size cutting stock problem with two-staged patterns," European Journal of Operational Research, Elsevier, vol. 231(2), pages 288-298.
    8. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    9. 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.
    10. Sônia Poltroniere & Kelly Poldi & Franklina Toledo & Marcos Arenales, 2008. "A coupling cutting stock-lot sizing problem in the paper industry," Annals of Operations Research, Springer, vol. 157(1), pages 91-104, January.
    11. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    12. 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.
    13. Johnston, Robert E. & Sadinlija, Enes, 2004. "A new model for complete solutions to one-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 153(1), pages 176-183, February.
    14. Gramani, Maria Cristina N. & Franca, Paulo M., 2006. "The combined cutting stock and lot-sizing problem in industrial processes," European Journal of Operational Research, Elsevier, vol. 174(1), pages 509-521, October.
    15. 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.
    16. 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.
    17. Scheithauer, Guntram & Terno, Johannes, 1995. "The modified integer round-up property of the one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 562-571, August.
    18. Holthaus, Oliver, 2002. "Decomposition approaches for solving the integer one-dimensional cutting stock problem with different types of standard lengths," European Journal of Operational Research, Elsevier, vol. 141(2), pages 295-312, September.
    19. Trkman, Peter & Gradisar, Miro, 2007. "One-dimensional cutting stock optimization in consecutive time periods," European Journal of Operational Research, Elsevier, vol. 179(2), pages 291-301, June.
    20. Robert W. Haessler, 1971. "A Heuristic Programming Solution to a Nonlinear Cutting Stock Problem," Management Science, INFORMS, vol. 17(12), pages 793-802, August.
    21. Arbib, Claudio & Marinelli, Fabrizio, 2005. "Integrating process optimization and inventory planning in cutting-stock with skiving option: An optimization model and its application," European Journal of Operational Research, Elsevier, vol. 163(3), pages 617-630, June.
    22. Yanasse, Horacio Hideki & Pinto Lamosa, Maria Jose, 2007. "An integrated cutting stock and sequencing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1353-1370, December.
    23. Alves, Claudio & Valerio de Carvalho, J.M., 2007. "Accelerating column generation for variable sized bin-packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1333-1352, December.
    24. 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.
    25. Reinertsen, Harald & Vossen, Thomas W.M., 2010. "The one-dimensional cutting stock problem with due dates," European Journal of Operational Research, Elsevier, vol. 201(3), pages 701-711, March.
    26. Robert W. Haessler & F. Brian Talbot, 1983. "A 0-1 Model for Solving the Corrugator Trim Problem," Management Science, INFORMS, vol. 29(2), pages 200-209, February.
    27. Beraldi, P. & Bruni, M.E. & Conforti, D., 2009. "The stochastic trim-loss problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 42-49, August.
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    Cited by:

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    2. Ronghua Meng & Yunqing Rao & Qiang Luo, 2020. "Modeling and solving for bi-objective cutting parallel machine scheduling problem," Annals of Operations Research, Springer, vol. 285(1), pages 223-245, February.
    3. Wuttke, David A. & Heese, H. Sebastian, 2018. "Two-dimensional cutting stock problem with sequence dependent setup times," European Journal of Operational Research, Elsevier, vol. 265(1), pages 303-315.
    4. Hu, Xiaoxuan & Zhu, Waiming & Ma, Huawei & An, Bo & Zhi, Yanling & Wu, Yi, 2021. "Orientational variable-length strip covering problem: A branch-and-price-based algorithm," European Journal of Operational Research, Elsevier, vol. 289(1), pages 254-269.
    5. Martinovic, J. & Scheithauer, G. & Valério de Carvalho, J.M., 2018. "A comparative study of the arcflow model and the one-cut model for one-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 458-471.
    6. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
    7. Florian Jaehn & Raisa Juopperi, 2019. "A Description of Supply Chain Planning Problems in the Paper Industry with Literature Review," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-39, February.
    8. Cui, Yaodong & Zhong, Cheng & Yao, Yi, 2015. "Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 243(2), pages 540-546.
    9. Alyne Toscano & Socorro Rangel & Horacio Hideki Yanasse, 2017. "A heuristic approach to minimize the number of saw cycles in small-scale furniture factories," Annals of Operations Research, Springer, vol. 258(2), pages 719-746, November.

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