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Cross Decomposition Applied to Integer Programming Problems: Duality Gaps and Convexification in Parts

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  • Kaj Holmberg

    (Linköping Institute of Technology, Linköping, Sweden)

Abstract

We study the lower bounds on the optimal objective function value of linear pure integer programming problems obtainable by the convexification in parts that results from using Benders' or cross decomposition, and the best lower bounds obtainable by the convexification resulting from Lagrangian relaxation together with subgradient optimization or Dantzig-Wolfe decomposition. A comparison shows that generalized Benders' and generalized cross decomposition yield the best of these bounds, while ordinary Benders' decomposition yields bounds that are sometimes better and sometimes worse than those of Lagrangian relaxation. However, cross decomposition can be used to automatically get the best of the two bounds. The conclusion of this paper is that cross decomposition can be useful for getting good lower bounds for pure integer programming problems, bounds that can be made better than those of the frequently used Lagrangian relaxation.

Suggested Citation

  • Kaj Holmberg, 1994. "Cross Decomposition Applied to Integer Programming Problems: Duality Gaps and Convexification in Parts," Operations Research, INFORMS, vol. 42(4), pages 657-668, August.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:4:p:657-668
    DOI: 10.1287/opre.42.4.657
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    Cited by:

    1. Santiago Cerisola & Álvaro Baíllo & José M. Fernández-López & Andrés Ramos & Ralf Gollmer, 2009. "Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods," Operations Research, INFORMS, vol. 57(1), pages 32-46, February.
    2. Holmberg, Kaj, 1997. "Mean value cross decomposition applied to integer programming problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 124-138, February.
    3. Yuceer, Umit, 1997. "A multi-product loading problem: a model and solution method," European Journal of Operational Research, Elsevier, vol. 101(3), pages 519-531, September.

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