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Order Allocation for Stock Cutting in the Paper Industry

Author

Listed:
  • Syam Menon

    (College of Business Administration, Oklahoma State University, Stillwater, Oklahoma 74078)

  • Linus Schrage

    (Graduate School of Business, University of Chicago, Chicago, Illinois 60637)

Abstract

A common problem encountered in paper-production facilities is that of allocating customer orders to machines so as to minimize the total cost of production. It can be formulated as a dual-angular integer program, with identical machines inducing symmetry. While the potential advantages of decomposing large mathematical programs into smaller subproblems have long been recognized, the solution of decomposable integer programs remains extremely difficult. Symmetry intensifies the difficulty. This paper develops an approach, based on the construction of tight subproblem bounds, to solve decomposable dual-angular integer programs and successfully applies it to solve the problem from the paper industry. This method is of particular interest as it significantly reduces the impact of symmetry.

Suggested Citation

  • Syam Menon & Linus Schrage, 2002. "Order Allocation for Stock Cutting in the Paper Industry," Operations Research, INFORMS, vol. 50(2), pages 324-332, April.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:2:p:324-332
    DOI: 10.1287/opre.50.2.324.427
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Florian Jaehn & Raisa Juopperi, 2019. "A Description of Supply Chain Planning Problems in the Paper Industry with Literature Review," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-39, February.
    4. Sônia Poltroniere & Kelly Poldi & Franklina Toledo & Marcos Arenales, 2008. "A coupling cutting stock-lot sizing problem in the paper industry," Annals of Operations Research, Springer, vol. 157(1), pages 91-104, January.
    5. Dowsland, Kathryn A. & Soubeiga, Eric & Burke, Edmund, 2007. "A simulated annealing based hyperheuristic for determining shipper sizes for storage and transportation," European Journal of Operational Research, Elsevier, vol. 179(3), pages 759-774, June.
    6. 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.
    7. Hakim Akeb & Mhand Hifi, 2010. "A hybrid beam search looking-ahead algorithm for the circular packing problem," Journal of Combinatorial Optimization, Springer, vol. 20(2), pages 101-130, August.

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