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Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models

Author

Listed:
  • Ellis L. Johnson

    (IBM Thomas J. Watson Research Center, Yorktown Heights, New York)

  • Michael M. Kostreva

    (GM Research Laboratories, Warren, Michigan)

  • Uwe H. Suhl

    (IBM Thomas J. Watson Research Center, Yorktown Heights, New York)

Abstract

We present methods that are useful in solving some large scale hierarchical planning models involving 0-1 variables. These 0-1 programming problems initially could not be solved with any standard techniques. We employed several approaches to take advantage of the hierarchical structure of variables (ordered by importance) and other structures present in the models. Critical, but not sufficient for success, was a strong linear programming formulation. We describe methods for strengthening the linear programs, as well as other techniques necessary for a commercial branch-and-bound code to be successful in solving these problems.

Suggested Citation

  • Ellis L. Johnson & Michael M. Kostreva & Uwe H. Suhl, 1985. "Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models," Operations Research, INFORMS, vol. 33(4), pages 803-819, August.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:4:p:803-819
    DOI: 10.1287/opre.33.4.803
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    Citations

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    Cited by:

    1. Kurt Spielberg, 2007. "IP over 40+ Years at IBM Scientific Centers and Marketing," Annals of Operations Research, Springer, vol. 149(1), pages 195-208, February.
    2. Bertsimas, Dimitris & Orlin, James B., 1953-., 1991. "A technique for speeding up the solution of the Lagrangean dual," Working papers 3278-91., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Xiangyong Li & Y. P. Aneja, 2012. "A Branch-and-Cut Approach for the Minimum-Energy Broadcasting Problem in Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 443-456, August.
    4. Bagloee, Saeed Asadi & Asadi, Mohsen, 2015. "Prioritizing road extension projects with interdependent benefits under time constraint," Transportation Research Part A: Policy and Practice, Elsevier, vol. 75(C), pages 196-216.
    5. Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
    6. W. Ogryczak & K. Zorychta, 1996. "Modular Optimizer for Mixed Integer Programming MOMIP Version 2.3," Working Papers wp96106, International Institute for Applied Systems Analysis.
    7. 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.
    8. Ellis Johnson, 2007. "My experiences as a student and researcher in OR during the 1960’s and 70’s," Annals of Operations Research, Springer, vol. 149(1), pages 121-135, February.
    9. R. Lougee-Heimer & W. Adams, 2005. "A Conditional Logic Approach for Strengthening Mixed 0-1 Linear Programs," Annals of Operations Research, Springer, vol. 139(1), pages 289-320, October.
    10. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
    11. L Virirakis, 1993. "The “Continuous Search Space Design Method†(CSSDM)," Environment and Planning B, , vol. 20(6), pages 617-643, December.
    12. W. Ogryczak & K. Zorychta, 1994. "Modular Optimizer for Mixed Integer Programming MOMIP Version 2.1," Working Papers wp94035, International Institute for Applied Systems Analysis.

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