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One-dimensional stock cutting: optimization of usable leftovers in consecutive orders

Author

Listed:
  • Luka Tomat

    (University of Ljubljana)

  • Mirko Gradišar

    (University of Ljubljana)

Abstract

This paper deals with usable leftovers (UL) in one-dimensional stock cutting in consecutive orders. UL are leftovers longer than a certain threshold and are returned to stock in order to be used in future orders. Shorter leftovers are treated as trim-loss. If UL are being used at a slower pace, than they are being generated for a longer period of time, excessive growth of UL in stock can appear. This is not acceptable due to higher costs of manipulations and warehousing. However, a certain amount of UL in stock is desirable because it contributes to greater variety of stock lengths, which in general results in lower trim-loss. The method solves the problem of how to calculate the near optimal amount of UL in stock and how to control the stock. The proposed method is tested by using a computer simulation in which UL from previous orders are used in the next ones instead of being randomly generated. The computational results indicate that trim-loss in consecutive orders is reduced, and excessive growth of UL in stock is prevented.

Suggested Citation

  • Luka Tomat & Mirko Gradišar, 2017. "One-dimensional stock cutting: optimization of usable leftovers in consecutive orders," 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. 25(2), pages 473-489, June.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-017-0466-y
    DOI: 10.1007/s10100-017-0466-y
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    References listed on IDEAS

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    1. Cui, Yaodong & Yang, Yuli, 2010. "A heuristic for the one-dimensional cutting stock problem with usable leftover," European Journal of Operational Research, Elsevier, vol. 204(2), pages 245-250, July.
    2. 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.
    3. Igor Kierkosz & Maciej Luczak, 2014. "A hybrid evolutionary algorithm for the two-dimensional packing problem," 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(4), pages 729-753, December.
    4. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki & Poldi, Kelly Cristina & Gonçalves Vianna, Andréa Carla, 2014. "The one-dimensional cutting stock problem with usable leftovers – A survey," European Journal of Operational Research, Elsevier, vol. 236(2), pages 395-402.
    5. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    6. Claudio Arbib & Fabrizio Marinelli & Fabrizio Rossi & Francesco Di Iorio, 2002. "Cutting and Reuse: An Application from Automobile Component Manufacturing," Operations Research, INFORMS, vol. 50(6), pages 923-934, December.
    7. Cherri, Adriana Cristina & Arenales, Marcos Nereu & Yanasse, Horacio Hideki, 2009. "The one-dimensional cutting stock problem with usable leftover - A heuristic approach," European Journal of Operational Research, Elsevier, vol. 196(3), pages 897-908, August.
    8. 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.
    9. Diegel, Adolf & Montocchio, Edouard & Walters, Edward & van Schalkwyk, Sias & Naidoo, Spurs, 1996. "Setup minimising conditions in the trim loss problem," European Journal of Operational Research, Elsevier, vol. 95(3), pages 631-640, December.
    10. Gradisar, Miro & Kljajic, Miroljub & Resinovic, Gortan & Jesenko, Joze, 1999. "A sequential heuristic procedure for one-dimensional cutting," European Journal of Operational Research, Elsevier, vol. 114(3), pages 557-568, May.
    11. 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.
    12. 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.
    13. Leão, Aline A.S. & Santos, Maristela O. & Hoto, Robinson & Arenales, Marcos N., 2011. "The constrained compartmentalized knapsack problem: mathematical models and solution methods," European Journal of Operational Research, Elsevier, vol. 212(3), pages 455-463, August.
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    1. Cherri, Adriana Cristina & Cherri, Luiz Henrique & Oliveira, Beatriz Brito & Oliveira, José Fernando & Carravilla, Maria Antónia, 2023. "A stochastic programming approach to the cutting stock problem with usable leftovers," European Journal of Operational Research, Elsevier, vol. 308(1), pages 38-53.
    2. 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.
    3. Santiago V. Ravelo & Cláudio N. Meneses & Maristela O. Santos, 2020. "Meta-heuristics for the one-dimensional cutting stock problem with usable leftover," Journal of Heuristics, Springer, vol. 26(4), pages 585-618, August.
    4. Douglas Nogueira Nascimento & Adriana Cristina Cherri & José Fernando Oliveira, 2022. "The two-dimensional cutting stock problem with usable leftovers: mathematical modelling and heuristic approaches," Operational Research, Springer, vol. 22(5), pages 5363-5403, November.
    5. 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.
    6. 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.
    7. 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.
    8. Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2017. "Editorial," 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. 25(3), pages 521-523, September.

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