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Reformulation and Decomposition of Integer Programs

In: 50 Years of Integer Programming 1958-2008

Author

Listed:
  • François Vanderbeck

    (Institut de Mathématiques de Bordeaux (IMB) and INRIA, Université de Bordeaux)

  • Laurence A. Wolsey

    (Université Catholique de Louvain, Center for Operations Research and Econometrics)

Abstract

We examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover reformulations based on decomposition, such as Lagrangean relaxation, the Dantzig-Wolfe reformulation and the resulting column generation and branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.

Suggested Citation

  • François Vanderbeck & Laurence A. Wolsey, 2010. "Reformulation and Decomposition of Integer Programs," Springer Books, in: Michael Jünger & Thomas M. Liebling & Denis Naddef & George L. Nemhauser & William R. Pulleyblank & (ed.), 50 Years of Integer Programming 1958-2008, chapter 0, pages 431-502, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-68279-0_13
    DOI: 10.1007/978-3-540-68279-0_13
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    Citations

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    Cited by:

    1. Katrin Halbig & Adrian Göß & Dieter Weninger, 2025. "Exploiting user-supplied Decompositions inside Heuristics," Journal of Heuristics, Springer, vol. 31(4), pages 1-38, December.
    2. Barış Yıldız & Natashia Boland & Martin Savelsbergh, 2022. "Decomposition Branching for Mixed Integer Programming," Operations Research, INFORMS, vol. 70(3), pages 1854-1872, May.
    3. Jens Vinther Clausen & Richard Lusby & Stefan Ropke, 2022. "Consistency Cuts for Dantzig-Wolfe Reformulations," Operations Research, INFORMS, vol. 70(5), pages 2883-2905, September.
    4. Prunet, Thibault & Absi, Nabil & Cattaruzza, Diego, 2025. "The storage location assignment and picker routing problem: A generic branch-cut-and-price algorithm," European Journal of Operational Research, Elsevier, vol. 327(3), pages 857-874.
    5. Maenhout, Broos & Šůcha, Přemysl & Valdmanova, Viktorie & Tkadlec, Ondřej & Rozlivkova, Jana Thao, 2026. "A bilevel approach to integrated surgeon scheduling and surgery planning solved via branch-and-price," Omega, Elsevier, vol. 138(C).

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