IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i5p789-791.html
   My bibliography  Save this article

A Facet Generation Procedure for Solving 0/1 Integer Programs

Author

Listed:
  • Gyana Parija

    (IBM Corporation, Poughkeepsie, New York 12601)

  • Radu Gadidov

    (Emery Worldwide Airlines, Vandalia, Ohio 45377)

  • Wilbert Wilhelm

    (Texas A&M University, College Station, Texas 77843-3131)

Abstract

This paper presents the Facet Generation Procedure (FGP) for solving 0/1 integer programs. The FGP seeks to identify a hyperplane that represents a facet of an underlying polytope to cut off the fractional solution to the linear programming relaxation of the integer programming problem. A set of standard problems is used to provide insight into the computational characteristics of the procedure.

Suggested Citation

  • Gyana Parija & Radu Gadidov & Wilbert Wilhelm, 1999. "A Facet Generation Procedure for Solving 0/1 Integer Programs," Operations Research, INFORMS, vol. 47(5), pages 789-791, October.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:5:p:789-791
    DOI: 10.1287/opre.47.5.789
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.5.789
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.47.5.789?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. Egon Balas & Clarence H. Martin, 1980. "Pivot and Complement--A Heuristic for 0-1 Programming," Management Science, INFORMS, vol. 26(1), pages 86-96, January.
    2. Harlan Crowder & Ellis L. Johnson & Manfred Padberg, 1983. "Solving Large-Scale Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 31(5), pages 803-834, October.
    3. E. Andrew Boyd, 1994. "Fenchel Cutting Planes for Integer Programs," Operations Research, INFORMS, vol. 42(1), pages 53-64, February.
    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. Wilbert E. Wilhelm & Radu Gadidov, 2004. "A Branch-and-Cut Approach for a Generic Multiple-Product, Assembly-System Design Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 39-55, February.

    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. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    2. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    3. Mitchell, John E., 1997. "Fixing variables and generating classical cutting planes when using an interior point branch and cut method to solve integer programming problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 139-148, February.
    4. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    5. M T Ramos & J Sáez, 2005. "Solving capacitated facility location problems by Fenchel cutting planes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 297-306, March.
    6. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
    7. Wei-Kun Chen & Liang Chen & Mu-Ming Yang & Yu-Hong Dai, 2018. "Generalized coefficient strengthening cuts for mixed integer programming," Journal of Global Optimization, Springer, vol. 70(1), pages 289-306, January.
    8. He, Yan & Wu, Tao & Zhang, Canrong & Liang, Zhe, 2015. "An improved MIP heuristic for the intermodal hub location problem," Omega, Elsevier, vol. 57(PB), pages 203-211.
    9. Agarwal, Y.K. & Aneja, Y.P. & Jayaswal, Sachin, 2022. "Directed fixed charge multicommodity network design: A cutting plane approach using polar duality," European Journal of Operational Research, Elsevier, vol. 299(1), pages 118-136.
    10. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    11. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2011. "A new class of functions for measuring solution integrality in the Feasibility Pump approach," DIS Technical Reports 2011-08, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    12. Srinivasa, Anand V. & Wilhelm, Wilbert E., 1997. "A procedure for optimizing tactical response in oil spill clean up operations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 554-574, November.
    13. Liang Chen & Wei-Kun Chen & Mu-Ming Yang & Yu-Hong Dai, 2021. "An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron," Journal of Global Optimization, Springer, vol. 81(3), pages 659-689, November.
    14. Xiaoyi Gu & Santanu S. Dey & Jean-Philippe P. Richard, 2024. "Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 884-899, May.
    15. Pourbabai, B. & Ashayeri, J. & Van Wassenhove, L.N., 1992. "Strategic marketing, production, and distribution planning of an integrated manufacturing system," Other publications TiSEM 16c2bacb-2c2b-427e-b429-c, Tilburg University, School of Economics and Management.
    16. Altay, Nezih & Robinson Jr., Powell E. & Bretthauer, Kurt M., 2008. "Exact and heuristic solution approaches for the mixed integer setup knapsack problem," European Journal of Operational Research, Elsevier, vol. 190(3), pages 598-609, November.
    17. B. Dietrich & L. Escudero & A. Garín & G. Pérez, 1993. "O(n) Procedures for identifying maximal cliques and non-dominated extensions of consecutive minimal covers and alternates," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 139-160, December.
    18. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "New concave penalty functions for improving the Feasibility Pump," DIS Technical Reports 2010-10, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    19. Amitabh Basu & Pierre Bonami & Gérard Cornuéjols & François Margot, 2011. "Experiments with Two-Row Cuts from Degenerate Tableaux," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 578-590, November.

    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:47:y:1999:i:5:p:789-791. 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.