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The summed start-up costs in a unit commitment problem


  • René Brandenberg

    () (Technische Universität München)

  • Matthias Huber

    () (Technische Universität München)

  • Matthias Silbernagl

    () (Technische Universität München)


Abstract We consider the sum of the incurred start-up costs of a single unit in a Unit Commitment problem. Our major result is a correspondence between the facets of its epigraph and some binary trees for concave start-up cost functions CU, which is bijective if CU is strictly concave. We derive an exponential $${\mathcal{H}}$$ H -representation of this epigraph, and provide an exact linear separation algorithm. These results significantly reduce the integrality gap of the Mixed Integer formulation of a Unit Commitment Problem compared to current literature.

Suggested Citation

  • René Brandenberg & Matthias Huber & Matthias Silbernagl, 2017. "The summed start-up costs in a unit commitment problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 203-238, March.
  • Handle: RePEc:spr:eurjco:v:5:y:2017:i:1:d:10.1007_s13675-016-0062-2
    DOI: 10.1007/s13675-016-0062-2

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    References listed on IDEAS

    1. Matthias Nowak & Werner Römisch, 2000. "Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty," Annals of Operations Research, Springer, vol. 100(1), pages 251-272, December.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    3. Jonas Egerer & Clemens Gerbaulet & Richard Ihlenburg & Friedrich Kunz & Benjamin Reinhard & Christian von Hirschhausen & Alexander Weber & Jens Weibezahn, 2014. "Electricity Sector Data for Policy-Relevant Modeling: Data Documentation and Applications to the German and European Electricity Markets," Data Documentation 72, DIW Berlin, German Institute for Economic Research.
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