IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v238y2016i1d10.1007_s10479-015-2103-2.html
   My bibliography  Save this article

Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem

Author

Listed:
  • Kelly Cristina Poldi

    (Universidade Estadual de Campinas-UNICAMP)

  • Silvio Alexandre Araujo

    (Universidade Estadual Paulista-UNESP)

Abstract

The multiperiod cutting stock problem arises in the production planning and programming of many industries that have the cutting process as an important stage. Ordered items are required in different periods of a finite planning horizon. It is possible to bring forward or not the production of items. Unused inventory in a certain period becomes available for the next period, all together with new inventory which may come to be acquired in the market. Based on mixed integer optimization models from the literature, extensions are proposed to deal with the multiperiod case and a residual heuristic is used. Computational experiments showed that effective gains can be obtained when comparing multiperiod models with the lot for lot solution, which is typically used in practice. Most of the instances are solved satisfactorily with a high performance optimization package and the heuristic method is used for solving the hard instances.

Suggested Citation

  • Kelly Cristina Poldi & Silvio Alexandre Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2103-2
    DOI: 10.1007/s10479-015-2103-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2103-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-015-2103-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. E Silva & F Alvelos & J M Valério de Carvalho, 2014. "Integrating two-dimensional cutting stock and lot-sizing problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(1), pages 108-123, January.
    2. Valerio de Carvalho, J. M., 2002. "LP models for bin packing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 253-273, September.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    4. 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.
    5. 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.
    6. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    7. 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.
    8. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    9. SOUSA, Jorge P. & WOLSEY, Laurence A., 1992. "A time indexed formulation of non-preemptive single machine scheduling problems," LIDAM Reprints CORE 984, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Gau, T. & Wascher, G., 1995. "CUTGEN1: A problem generator for the standard one-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 84(3), pages 572-579, August.
    11. 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.
    12. 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.
    13. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    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. 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.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Amanda O. C. Ayres & Betania S. C. Campello & Washington A. Oliveira & Carla T. L. S. Ghidini, 2021. "A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1047-1076, December.
    2. Anselmo Ramalho Pitombeira-Neto & Bruno de Athayde Prata, 2020. "A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 178-192, April.
    3. Pedro Rochavetz Lara Andrade & Silvio Alexandre Araujo & Adriana Cristina Cherri & Felipe Kesrouani Lemos, 2023. "The cutting stock problem applied to the hardening process in an automotive spring factory," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 637-664, June.
    4. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    5. Silva, Eduardo M. & Melega, Gislaine M. & Akartunalı, Kerem & de Araujo, Silvio A., 2023. "Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 304(2), pages 443-460.
    6. Martin Grunewald & Thomas Volling & Christoph Müller & Thomas S. Spengler, 2018. "Multi-item single-source ordering with detailed consideration of transportation capacities," Journal of Business Economics, Springer, vol. 88(7), pages 971-1007, September.
    7. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.
    8. D. N. Nascimento & S. A. Araujo & A. C. Cherri, 2022. "Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers," Annals of Operations Research, Springer, vol. 316(2), pages 785-803, September.
    9. Gislaine Mara Melega & Silvio Alexandre de Araujo & Reinaldo Morabito, 2020. "Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems," Annals of Operations Research, Springer, vol. 295(2), pages 695-736, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kelly Poldi & Silvio Araujo, 2016. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem," Annals of Operations Research, Springer, vol. 238(1), pages 497-520, March.
    2. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    3. Oliveira, Washington A. & Fiorotto, Diego J. & Song, Xiang & Jones, Dylan F., 2021. "An extended goal programming model for the multiobjective integrated lot-sizing and cutting stock problem," European Journal of Operational Research, Elsevier, vol. 295(3), pages 996-1007.
    4. 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.
    5. 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.
    6. Gislaine Mara Melega & Silvio Alexandre de Araujo & Reinaldo Morabito, 2020. "Mathematical model and solution approaches for integrated lot-sizing, scheduling and cutting stock problems," Annals of Operations Research, Springer, vol. 295(2), pages 695-736, December.
    7. Amanda O. C. Ayres & Betania S. C. Campello & Washington A. Oliveira & Carla T. L. S. Ghidini, 2021. "A Bi-Integrated Model for coupling lot-sizing and cutting-stock problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 1047-1076, December.
    8. Silva, Eduardo M. & Melega, Gislaine M. & Akartunalı, Kerem & de Araujo, Silvio A., 2023. "Formulations and theoretical analysis of the one-dimensional multi-period cutting stock problem with setup cost," European Journal of Operational Research, Elsevier, vol. 304(2), pages 443-460.
    9. Tao Wu & Kerem Akartunal? & Raf Jans & Zhe Liang, 2017. "Progressive Selection Method for the Coupled Lot-Sizing and Cutting-Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 523-543, August.
    10. Hajizadeh, Iman & Lee, Chi-Guhn, 2007. "Alternative configurations for cutting machines in a tube cutting mill," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1385-1396, December.
    11. 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.
    12. 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.
    13. 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.
    14. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    15. W. D. D. Madhavee & N. Saldin & U. C. Vaidyarathna & C. J. Jayawardene, 2018. "A Practical Application of the Generalized Cutting Stock Algorithm," Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group, vol. 4(3), pages 15-21, 03-2018.
    16. Sierra-Paradinas, María & Soto-Sánchez, Óscar & Alonso-Ayuso, Antonio & Martín-Campo, F. Javier & Gallego, Micael, 2021. "An exact model for a slitting problem in the steel industry," European Journal of Operational Research, Elsevier, vol. 295(1), pages 336-347.
    17. Mateus Martin & Horacio Hideki Yanasse & Luiz Leduíno Salles-Neto, 2022. "Pattern-based ILP models for the one-dimensional cutting stock problem with setup cost," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 557-582, August.
    18. 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.
    19. 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.
    20. de Gelder, E.R. & Wagelmans, A.P.M., 2007. "The two-dimensional cutting stock problem within the roller blind production process," Econometric Institute Research Papers EI 2007-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2103-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.