IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v46y1998i5p690-701.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.46.5.690
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.46.5.690?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
    ---><---

    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.
    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. 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.

    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. Mahar, Stephen & Bretthauer, Kurt M. & Venkataramanan, M.A., 2009. "The value of virtual pooling in dual sales channel supply chains," European Journal of Operational Research, Elsevier, vol. 192(2), pages 561-575, January.
    2. Daniel Adelman & George L. Nemhauser, 1999. "Price-Directed Control of Remnant Inventory Systems," Operations Research, INFORMS, vol. 47(6), pages 889-898, December.
    3. Peter L. Jackson & John A. Muckstadt, 1989. "Risk pooling in a two‐period, two‐echelon inventory stocking and allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 1-26, February.
    4. Melda Ormeci & J. G. Dai & John Vande Vate, 2008. "Impulse Control of Brownian Motion: The Constrained Average Cost Case," Operations Research, INFORMS, vol. 56(3), pages 618-629, June.
    5. Guide, V. Daniel R. & Srivastava, Rajesh, 1997. "Repairable inventory theory: Models and applications," European Journal of Operational Research, Elsevier, vol. 102(1), pages 1-20, October.
    6. Topan, E. & Eruguz, A.S. & Ma, W. & van der Heijden, M.C. & Dekker, R., 2020. "A review of operational spare parts service logistics in service control towers," European Journal of Operational Research, Elsevier, vol. 282(2), pages 401-414.
    7. Paul Zipkin, 1991. "Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 397-412, June.
    8. Rezaei Somarin, Aghil & Chen, Songlin & Asian, Sobhan & Wang, David Z.W., 2017. "A heuristic stock allocation rule for repairable service parts," International Journal of Production Economics, Elsevier, vol. 184(C), pages 131-140.

    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:inm:oropre:v:46:y:1998:i:5:p:690-701. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.