IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v50y2002i2p324-332.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.50.2.324.427
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.50.2.324.427?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. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    2. Pamela H. Vance & Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser, 1997. "Airline Crew Scheduling: A New Formulation and Decomposition Algorithm," Operations Research, INFORMS, vol. 45(2), pages 188-200, April.
    3. Martin Savelsbergh, 1997. "A Branch-and-Price Algorithm for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 45(6), pages 831-841, December.
    4. Dennis J. Sweeney & Richard A. Murphy, 1979. "A Method of Decomposition for Integer Programs," Operations Research, INFORMS, vol. 27(6), pages 1128-1141, December.
    5. 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.
    6. P. C. Gilmore & R. E. Gomory, 1963. "A Linear Programming Approach to the Cutting Stock Problem---Part II," Operations Research, INFORMS, vol. 11(6), pages 863-888, December.
    7. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    8. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    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. 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.

    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. Marc Peeters & Zeger Degraeve, 2004. "The Co-Printing Problem: A Packing Problem with a Color Constraint," Operations Research, INFORMS, vol. 52(4), pages 623-638, August.
    2. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    3. Valerio de Carvalho, J. M., 2002. "LP models for bin packing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 253-273, September.
    4. Muter, İbrahim & Sezer, Zeynep, 2018. "Algorithms for the one-dimensional two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 20-32.
    5. Zeger Degraeve & Marc Peeters, 2003. "Optimal Integer Solutions to Industrial Cutting-Stock Problems: Part 2, Benchmark Results," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 58-81, February.
    6. Park, Jongyoon & Han, Jinil & Lee, Kyungsik, 2024. "Integer optimization models and algorithms for the multi-period non-shareable resource allocation problem," European Journal of Operational Research, Elsevier, vol. 317(1), pages 43-59.
    7. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    8. Letchford, Adam N. & Amaral, Andre, 2001. "Analysis of upper bounds for the Pallet Loading Problem," European Journal of Operational Research, Elsevier, vol. 132(3), pages 582-593, August.
    9. 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.
    10. Amy Cohn & Michael Magazine & George Polak, 2009. "Rank‐Cluster‐and‐Prune: An algorithm for generating clusters in complex set partitioning problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 215-225, April.
    11. Richard Freling & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2003. "A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem," Operations Research, INFORMS, vol. 51(6), pages 922-939, December.
    12. Cizman, Anton & Cernetic, Janko, 2004. "Improving competitiveness in veneers production by a simple-to-use DSS," European Journal of Operational Research, Elsevier, vol. 156(1), pages 241-260, July.
    13. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.
    14. 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.
    15. Timo Gschwind & Stefan Irnich, 2014. "Dual Inequalities for Stabilized Column Generation Revisited," Working Papers 1407, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 23 Jul 2014.
    16. Morabito, Reinaldo & Belluzzo, Luciano, 2007. "Optimising the cutting of wood fibre plates in the hardboard industry," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1405-1420, December.
    17. 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.
    18. Toth, Paolo, 2000. "Optimization engineering techniques for the exact solution of NP-hard combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 125(2), pages 222-238, September.
    19. Adejuyigbe O. Fajemisin & Steven D. Prestwich & Laura Climent, 2023. "Cutting uncertain stock and vehicle routing in a sustainability forestry harvesting problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 139-164, April.
    20. 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.

    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:50:y:2002:i:2:p:324-332. 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.