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MIP models for two-dimensional non-guillotine cutting problems with usable leftovers

Author

Listed:
  • Ricardo Andrade

    (University of São Paulo, São Paulo, Brazil)

  • Ernesto G Birgin

    (University of São Paulo, São Paulo, Brazil)

  • Reinaldo Morabito

    (Federal University of São Carlos, São Carlos, Brazil)

  • Débora P Ronconi

    (University of São Paulo, São Paulo, Brazil)

Abstract

In this study we deal with the two-dimensional non-guillotine cutting problem of how to cut a set of larger rectangular objects to a set of smaller rectangular items in exactly a demanded number of pieces. We are concerned with the special case of the problem in which the non-used material of the cutting patterns (objects leftovers) may be used in the future, for example if it is large enough to fulfill future item demands. Therefore, the problem is seen as a two-dimensional non-guillotine cutting/packing problem with usable leftovers, also known in the literature as a two-dimensional residual bin-packing problem. We use multilevel mathematical programming models to represent the problem appropriately, which basically consists of cutting the ordered items using a set of objects of minimum cost, among all possible solutions of minimum cost, choosing one that maximizes the value of the usable leftovers, and, among them, selecting one that minimizes the number of usable leftovers. Because of special characteristics of these multilevel models, they can be reformulated as one-level mixed integer programming (MIP) models. Illustrative numerical examples are presented and analysed.

Suggested Citation

  • Ricardo Andrade & Ernesto G Birgin & Reinaldo Morabito & Débora P Ronconi, 2014. "MIP models for two-dimensional non-guillotine cutting problems with usable leftovers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(11), pages 1649-1663, November.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:11:p:1649-1663
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    Citations

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    Cited by:

    1. 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.
    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. Lorena Pradenas & Marco Fuentes & Víctor Parada, 2020. "Optimizing waste storage areas in health care centers," Annals of Operations Research, Springer, vol. 295(1), pages 503-516, December.
    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. Gonçalves, José Fernando & Wäscher, Gerhard, 2020. "A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects," European Journal of Operational Research, Elsevier, vol. 286(3), pages 867-882.

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