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A Dynamic Stochastic Stock-Cutting Problem

Author

Listed:
  • Elena V. Krichagina

    (Institute of Control Sciences, Moscow, Russia)

  • Rodrigo Rubio

    (McKinsey and Company, Mexico City)

  • Michael I. Taksar

    (State University of New York, Stony Brook, New York)

  • Lawrence M. Wein

    (Massachusetts Institute of Technology, Boston, Massachusetts)

Abstract

We consider a stock cutting problem for a paper plant that produces sheets of various sizes for a finished goods inventory that services random customer demand. The controller decides when to shut down and restart the paper machine and how to cut completed paper rolls into sheets of paper. The objective is to minimize long-run expected average costs related to paper waste (from inefficient cutting), shutdowns, backordering, and holding finished goods inventory. A two-step procedure (linear programming in the first step and Brownian control in the second step) is developed that leads to an effective, but suboptimal, solution. The linear program greatly restricts the number of cutting configurations that can be employed in the Brownian analysis, and hence the proposed policy is easy to implement, and the resulting production process is considerably simplified. In an illustrative numerical example using representative data from an industrial facility, the proposed policy outperforms several policies that use a larger number of cutting configurations. Finally, we discuss some alternative production settings where this two-step procedure may be applicable.

Suggested Citation

  • Elena V. Krichagina & Rodrigo Rubio & Michael I. Taksar & Lawrence M. Wein, 1998. "A Dynamic Stochastic Stock-Cutting Problem," Operations Research, INFORMS, vol. 46(5), pages 690-701, October.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:5:p:690-701
    DOI: 10.1287/opre.46.5.690
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    References listed on IDEAS

    as
    1. Elena V. Krichagina & Sheldon X. C. Lou & Michael I. Taksar, 1994. "Double Band Policy for Stochastic Manufacturing Systems in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 560-596, August.
    2. Costas Courcoubetis & Uriel G. Rothblum, 1991. "On Optimal Packing of Randomly Arriving Objects," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 176-194, February.
    3. Bruce L. Miller, 1974. "Dispatching from Depot Repair in a Recoverable Item Inventory System: On the Optimality of a Heuristic Rule," Management Science, INFORMS, vol. 21(3), pages 316-325, November.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Daniel Adelman & George L. Nemhauser, 1999. "Price-Directed Control of Remnant Inventory Systems," Operations Research, INFORMS, vol. 47(6), pages 889-898, December.
    6. 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.

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