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The one-dimensional cutting stock problem with due dates

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  • Reinertsen, Harald
  • Vossen, Thomas W.M.

Abstract

The one-dimensional cutting stock problem is the problem of cutting stock material into shorter lengths, in order to meet demand for these shorter lengths while minimizing waste. In industrial cutting operations, it may also be necessary to fill the orders for these shorter lengths before a given due date. We propose new optimization models and solution procedures which solve the cutting stock problem when orders have due dates. We evaluate our approach using data from a large manufacturer of reinforcement steel and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock lengths and cutting different types of material on the same machine. In addition, we evaluate operational performance in terms of resulting waste and tardiness of orders using our model in a rolling horizon framework.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:201:y:2010:i:3:p:701-711
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    3. 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.
    4. Kennedy A. G. Araújo & Tibérius O. Bonates & Bruno A. Prata & Anselmo R. Pitombeira-Neto, 2021. "Heterogeneous prestressed precast beams multiperiod production planning problem: modeling and solution methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 660-693, October.
    5. Pascoal, Marta M.B. & Sedeño-Noda, Antonio, 2012. "Enumerating K best paths in length order in DAGs," European Journal of Operational Research, Elsevier, vol. 221(2), pages 308-316.
    6. 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.
    7. Arbib, Claudio & Felici, Giovanni & Servilio, Mara, 2019. "Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs," Omega, Elsevier, vol. 84(C), pages 18-30.
    8. 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.
    9. 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.
    10. Arbib, Claudio & Marinelli, Fabrizio & Pezzella, Ferdinando, 2012. "An LP-based tabu search for batch scheduling in a cutting process with finite buffers," International Journal of Production Economics, Elsevier, vol. 136(2), pages 287-296.
    11. 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.
    12. Arbib, Claudio & Marinelli, Fabrizio, 2017. "Maximum lateness minimization in one-dimensional bin packing," Omega, Elsevier, vol. 68(C), pages 76-84.
    13. Arbib, Claudio & Marinelli, Fabrizio & Pizzuti, Andrea, 2021. "Number of bins and maximum lateness minimization in two-dimensional bin packing," European Journal of Operational Research, Elsevier, vol. 291(1), pages 101-113.
    14. Bennell, Julia A. & Soon Lee, Lai & Potts, Chris N., 2013. "A genetic algorithm for two-dimensional bin packing with due dates," International Journal of Production Economics, Elsevier, vol. 145(2), pages 547-560.
    15. 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.
    16. Polyakovskiy, Sergey & M’Hallah, Rym, 2018. "A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 819-839.
    17. Nikolaus Furian & Siegfried Vössner, 2014. "A hybrid algorithm for constrained order packing," 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. 22(1), pages 157-186, March.
    18. Keehoon Kwon & Doyeong Kim & Sunkuk Kim, 2021. "Cutting Waste Minimization of Rebar for Sustainable Structural Work: A Systematic Literature Review," Sustainability, MDPI, vol. 13(11), pages 1-21, May.
    19. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).

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