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A Method of Decomposition for Integer Programs

Author

Listed:
  • Dennis J. Sweeney

    (University of Cincinnati, Cincinnati, Ohio)

  • Richard A. Murphy

    (University of Cincinnati, Cincinnati, Ohio)

Abstract

A method of decomposing integer programs with block angular structure is presented. It is based on the notion of searching for the optimal solution to an integer program among the near-optimal solutions to its Lagrangian relaxation. An optimality theorem is obtained and a generic decomposition algorithm is presented. An application of this approach is discussed and some computational results are reported.

Suggested Citation

  • Dennis J. Sweeney & Richard A. Murphy, 1979. "A Method of Decomposition for Integer Programs," Operations Research, INFORMS, vol. 27(6), pages 1128-1141, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1128-1141
    DOI: 10.1287/opre.27.6.1128
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    Cited by:

    1. Albrecht, Martin & Stadtler, Hartmut, 2015. "Coordinating decentralized linear programs by exchange of primal information," European Journal of Operational Research, Elsevier, vol. 247(3), pages 788-796.
    2. Torbjörn Larsson & Michael Patriksson, 2006. "Global Optimality Conditions for Discrete and Nonconvex Optimization---With Applications to Lagrangian Heuristics and Column Generation," Operations Research, INFORMS, vol. 54(3), pages 436-453, June.
    3. Sonmez, Ayse Durukan & Lim, Gino J., 2012. "A decomposition approach for facility location and relocation problem with uncertain number of future facilities," European Journal of Operational Research, Elsevier, vol. 218(2), pages 327-338.
    4. Rönnberg, Elina & Larsson, Torbjörn, 2014. "All-integer column generation for set partitioning: Basic principles and extensions," European Journal of Operational Research, Elsevier, vol. 233(3), pages 529-538.
    5. Syam Menon & Linus Schrage, 2002. "Order Allocation for Stock Cutting in the Paper Industry," Operations Research, INFORMS, vol. 50(2), pages 324-332, April.

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